Indian Institute of Astrophysics

Indian Institute of Astrophysics (Autonomous Institute under Dept. of Science & Technology, Government of India)

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IIA Repository (Digital)

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IIA Technical Report Series

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Development of a microthermal seeing measurement device for evaluating the optical characteristics of an astronomical site

Complete list of authors

K. Dhananjay

Key words

atmospheric eects, site testing, standards, turbulence

Description of les appended for archival

1) GUI-Program in LabVIEW-2010 for data acquisition and logging 2) Schematic layout + PCB layout + Gerber les of MSMD -> 3 types of les for each of these, using Dip Trace (Free-ware)

Development of a microthermal seeing measurement device for evaluating the optical characteristics of an astronomical site K. Dhananjay Indian Institute of Astrophysics, 2nd Block, Koramangala, Bengaluru - 560 034

Abstract An economical microthermal seeing measurement device has been developed in-house, that measures the amount of translucency (that is caused due to the temperature gradients) present in the strata of the atmospheric layers. The temperature structure function ‘DT (r, h)’ and the air temperature ‘Tair (h)’ of the site under test are being measured by this instrument. While a pressure sensor located adjacent to this instrument measures the average barometric pressure ‘P(h)’. From these measured data, the temperature structure co-efficient ‘CT2 (r, h)’ and the refractive index structure constant ‘CN2 (h)’ for the microthermal seeing layer can be calculated. Also, the statistical analysis on coherence length ‘ro(loc) ’ and its corresponding values of atmospheric seeing ‘ε(loc) ’ for the microthermal seeing slab are computed, plotted and the data are logged in real time. This measurement is essential for evaluating the optical characteristics of an astronomical site and also for deciding the height of the telescope mount. The theory, description and test results of the instrument are comprehensively presented in the report. Keywords: effects, site testing, standards, turbulence

1

Background

tion (AWS), by Bhatt et al. (2000), (iii) optical aberrance to atmospheric opacity (air glow variations and aircraft lights), monitored by all sky survey camera, by Prabhu (2000), (iv) airborne aerosols and its properties, measured using Multi-Filter Rotating Shadow-band Radiometer (MFRSR), by Neeharika et al. (2010), (v) properties of the scattered light, measured using LIght Detection And Ranging (LIDAR), by Schwemmer et al. (2006), (vi) optical extinction and sky brightness, measured using small aperture telescope, fitted with filters, by Penn et al. (2004) and Nawar et al. (1997) and (vii) sub-millimetre (220 GHz) atmospheric transparency, measured using tipping radiometer by Ananthasubramanian et al. (2002). The Indian Astronomical Observatory (IAO), located on Mt. Saraswati, Hanle, is equipped with all these instruments, except (v) and (vi).

1.2

Seeing parameters of the atmosphere

Measurement and evaluation of the refractive index (RI) structure constant/atmospheric turbulence strength ‘CN2 ’, coherence length/Fried parameter ‘ro ’ and atmospheric seeing ‘ε f whm ’, measured using: (i) Multi Aperture Scintillation Sensor (MASS) by Els et al. (2008), (ii) Differential Image Motion Monitor (DIMM) by Sarazin & Roddier (1990), (iii) SLOpe Detection And Ranging (SLODAR) by Wilson et al. (2008), (iv) SCIntillation Detection And Ranging (SCIDAR) by Avila et al. (2004) and Egner & Masciadri (2007), (v) SHAdow BAnd Ranger (SHABAR) by Moore et al. (2006) and Guus Sliepen et al. (2010), (vi) microthermal seeing measurements by Barletti et al. (1977), Vernin & Munoz (1992), K. Dhananjay (2013) (vii) Scintillometer by Norman Chonacky & Robert Deuel (1988) and Nieveen et al. (1998), (viii) SOnic Detection And Ranging (SODAR) by Murthy et al. (1996) and Kelly et al. (2007), etc.

Based on few customary observations such as: domain, altitude, topography, number of days of clear skies round the year (occurrence of cirrus and contrails) for long term observations, man-made (dust/smoke) pollution and light pollution in Na and Hg bands [Nawar et al. (1997)], etc., astronomers short-list few probable sites. By measuring and evaluating the following pa- 2 Introduction rameters linked to the sites, we need to select the best one for setting up an observatory. The microthermal seeing measurement device (MSMD) is an instrument that measures the vertical (as a function of height) temperature gradients (where sensors 1.1 Meteorological parameters are placed) present either in the surface layer (SL) or (i) Ground deformations and seismic data, measured in the boundary layer (BL) of the atmosphere, that are using a seismometer, by Jade Sridevi et al. (2004), responsible for the RI (optical characteristics) changes (ii) diurnal and nocturnal weather conditions (temper- of air in those layers. Unlike DIMM or any other ature, surface wind speed and direction, relative hu- device which measures the seeing parameters for the midity, precipitation, rain, snow, sleet, dew and fog integrated layers, the MSMD measures it for the local formed by the condensation of water vapour in the at- layers of the free atmosphere (FA). Also, the analysis mosphere), measured using the automatic weather sta- performed using MSMD serves as a tool to determine

Development of Microthermal Seeing Measurement Device

the optimal height for the telescope mount, so as to minimize the optical turbulence effects. Conventionally MSMD and DIMM are used conjunctionally for two reasons: (i) During the normal pointing condition of the DIMM, it measures the CN2 (h), ro and ε f whm parameters for the FA only, whereas, the MSMD measures these parameters only for the local layers, so it acts as an auxiliary instrument for DIMM. (ii) During the distorted pointing condition of the DIMM [although DIMM is developed to overcome the erratic motions (during pointing) of the Image Motion Monitor (IMM) caused by wind and or ground vibrations and or object tracking] measurements, DIMM suffers from measuring the actual dynamic image distortion, because, the differential technique used in DIMM cancels the common errors (erratic motions) on image frames, so MSMD acts as a substitute for DIMM under this condition. The simultaneous and continuous measurements done by DIMM and MSMD give us the sampling profiles of the vertical distribution of CN2 (h) and the statistical analysis of ro and ε f whm . It is interesting to correlate the amplitude and phase variations of ε f whm profiles as analysed by these two instruments with time as a common function. The DIMM is an instrument that consists of a medium sized reflecting telescope, whose light entering pupil has a diaphragm, which in turn creates two sub-pupils (apertures) separated by a distance, inside the telescope. One of the sub-pupils (apertures) has an optical wedge, so that on the focal plane, two distinct images of the observed point source (star) are formed. An intensified CCD fitted with the telescope, records the image frames formed on the focal plane, every 20 ms interval, with an exposure time of 10 ms. With the algorithms and image processing techniques, the centre of interest (CoI) of each of the two star images is determined for each frame. These CoIs vary randomly as a consequence of atmospheric turbulence. From the set of 400 frames, the variance of the differential image positions is calculated and related to the atmospheric seeing using the standard theory of optical turbulence by Roddier (1981). Previous publications suggest that the contribution of optical turbulence to the atmospheric seeing gradually decreases with the height when precise temperature probes (TPs) are placed over the tower/mast in the SL ranging from 0 m to 50 m [Marks et al. (1996), Pant et al. (1999), Ehgamberdiev et al. (2000), Martin et al. (2000) and Sanchez et al. (2003)]. On the other hand, TPs flown through balloon-borne radiosonde in the local BL ranging from 50 m to 20 km reports the contribution of optical turbulence to the atmospheric seeing gradually increases with the height [Barletti et al. (1977), Vernin & Munoz-Tunon (1992) and Azouit & Vernin (2005)]. Therefore, it is essential to find the optimal height for the telescope mount in the SL, so as to minimize the difficulties involved in raising the height as well as optical turbulence effects. Taking these two criteria into consideration, the MSMD was developed in-house. The report discusses a summarised theory in § 3, detailed descriptions in § 4 and Lab test results and discussions in § 5, that are associated with the MSMD.

3

Page no.2

Theory

We know that the presence of temperature, pressure and humidity in air changes its RI, which causes translucency of air for a given wavelength of light. Gladstone, J. H. and Dale, T. P. (1864) theory discusses these effects and its optical effect on the interferometry in detail. Fig (1) summarises this effect. . ∆λ

is due to the presence of temperature, pressure, humidity, etc. in the air

λ air

Index of Refraction of air

λ vaccum

n=

∆λ

λ vaccum λ air

Figure 1: RI of air

3.1

Atmospheric turbulence

The fundamental physics of the atmospheric turbulence is derived from the renowned Reynolds number formula, which defines the properties of the fluid flow mechanics [Patel et al. (1985)] : ℜ=

ρf V L V L QL = = µ υ υA

(1)

where ρ f (kg/m3 ) is the density of the fluid/gas, V (m/s) is the mean fluid/wind velocity, L (m) is the length of travel of the fluid, µ (N-s-m2 ) is the dynamic viscosity of the fluid, υ (m2 /s) is the kinematic viscosity of the fluid/gas, Q (m3 /s) is the volumetric flow rate of fluid/gas and A (m2 ) is the pipe cross-sectional area. To understand the concept, let us substitute data: υ ≈ 1.5 ∗ 10−5 (m2 /s), V = 1 (m/s) and L = 15 (m) into equation (1), we get ℜ = 106 and therefore the physical properties of the atmosphere, is almost always turbulent and unstable.

3.2

Optical turbulence of air

The denser cool air masses present in the SLs, while sinking, comes in contact with the heated earth surface (due to solar irradiance) and transforms into less denser hot air masses and starts diffusing and rising above the earth surface. On the other hand, the dispersed, less denser, hot air masses present in the BL, while rising, comes in contact with the cool

K. Dhananjay, Indian Institute of Astrophysics


cumulus clouds and gets transformed into denser cool air masses and starts condensing and sinking below the surface of the clouds. Also, since, the transformed air masses in the BL, cannot escape beyond the Ozone Layer, the intensity of the optical turbulence strength of the BL is more than that of the SLs. The wind present in the atmosphere spontaneously stirs up these two air masses causing buoyancy of air or differential density (mass and heat) and momentum among them and this gives rise to a vertical temperature gradient (natural convection) or optical turbulence profiles in the atmosphere. The intensity of optical turbulence reduces with height from the ground in the SLs, whereas, it reduces with depth from the clouds in the BL. The experiment discussed in the report establishes the findings of this natural phenomenon at the SLs.

Page no.3

image scintillation, etc. which are generally described using the Fried’s ro parameter and ε f whm . Astronomers have traditionally measured such cumulative effects along the line of sight through ε f whm for long exposure images taken through a medium sized telescope. Tatarski (1961 & 1993) has described the correlation between the amplitude and phase variations of temperature fluctuations and the ε f whm . The Kolmogorov (1941 & 1991) theory of energy spectrum discusses the atmospheric turbulence effect at an outer scale length, 2

−5

which is given by: E(kw , ε) = [A ∗ ε 3 kw 3 ], where A is a constant, ε (J-s−1 -m3 ) is the rate of energy dissipation per unit volume and kw is the wave number. For simple illustration, the effect of atmospheric turbulence on wave-front distortion is summarised in Fig (2).

The fundamental physics of the optical turbulence of air is derived from the well known dimensionless parameter known as Richardson’s number Ri, which defines the atmospheric instability based on the principles of fluid flow mechanics. These concepts are comprehensively explained in the Kelvin-Helmholtz billows. The atmospheric stability is classified on the basis of Ri value [John (2010)]. dθe Rd Po c pd g dz here, θe = T Ri = dU 2 θe ( dz ) P

(2)

where g is the gravitational acceleration (9.8 ms−2 ), θe (K) is the equivalent potential temperature derived from Poisson’s equation, U (m/s) is the modulus of horizontal wind velocity, z (m) is the height, T (K) is the air temperature at pressure P, Po is one atmospheric pressure (1013.25 hPa), P(hPa) is the pressure of air mass at a given height, Rd is the specific Figure 2: Portrayal of seeing concept gas constant for dry air (287.04 J-kg−1 -K−1 ) and c pd is the specific heat of dry air at constant pressure (1005.7 J-kg−1 -K−1 ). To understand the concept, let us substitute data linked to Hanle site (Alt.=4500 m): 3.3 Formulae involved in designing MSMD T = 278.15 K; P = 650.25 hPa; g1 = 3.39 m-s−2 and c pd 2 = 1018.05 J-kg−1 -K−1 values in equation (2), we The dispersion of differential temperature between a get θe = 315.2 K; also, if dθe = 0.5 K, dz = 3 m and dU pair of TPs is 2 the temperature structure co-efficient − 2 2 = 0.5 (m/s), then Ri = 0.06453. Therefore, the optical CT (r, h) (K -m 3 ), introduced by Tatarski (1961) as: properties of the atmosphere is almost always unstable DT (r, h) and turbulent for the condition Ri ≤ 0.25. CT2 (r, h) = (3) 2 r3 The diversity in physical properties of the strucwhere r (m) is the separation between pair a of TPs and ture of the atmosphere deposits turbulent layers in the h (m) is the height of a separate microthermal seeing atmosphere. The large scale variation distribution of layer. The above equation is valid only for an inertial the eddies in the atmosphere, deposits energies at range of l r L, (where, ‘l’ and ‘L’ are the inner and distinctive ranges of the atmospheric layers, to induce outer scale lengths of the atmosphere as defined in turbulence ranging from large scales to be broken up Kolmogorov-Obuchov law). into smaller scales, as the energy dissipates. The turbulent energies present in the terrestrial atmosphere The well known temperature structure function DT (r, h) causes substantial inhomogeneities on the RI, which (K2 ) is derived by Fried (1965) as: results in asymmetrical distortion of the optical wavefront. These distortions are often classified as: image DT (r, h) = h[T (P1 ) − T (P2 )]2 i (4) displacement, image motion, speckle image, image oscillation, image smearing, image blurring, image tilting, where the angle brackets denote the ensemble average 1 http://www.physicsclassroom.com/class/circles/u6l3e.cfm 2 http://www.engineeringtoolbox.com/dry-air-properties-d_973.html

and P1 and P2 are the positions of the TPs. [Note: let us introduce differential temperature dT (r, h) (o C or K)



Page no.4

here ε(ideal) (radian) is the mean seeing of the optical turbulence free (ideal) condition and D (m) is the The RI inhomogeneities due to the optical turbulence telescope diameter. intensity is derived by combining and simplifying the Lorenz-Lorentz equation and the ideal gas equation, It is known that the relative size of the distorted image due to the relative quantity of the diffraction-limitation which is given by Vernin & Munoz-Tunon (1992): and the seeing limitation, depends on the relative size 2 P(h) CT2 (r, h) (5) of the telescope diameter D and the coherence length CN2 (h) = 80 ∗ 10−6 2 Tair (h) ro respectively. On comparing equations (7) & (8), we find that the seeing limited image is affected by a factor − 23 2 where, CN (h) (m ) is the mean RI structure constant, of D r , which can reach a value as high as 80 times, o P(h) (hPa) is the mean barometric pressure, Tair (h) (K) for example, for r = 0.1 m and D = 8 m. o −6 is the air temperature and 80 ∗ 10 is a constant derived by Gladstone formulae. The sum of coherence lengths of n local microther= T(P1 ) - T(P2 )].

Along a vertical path, the Fried parameter ro is: − 3 Z ∞ 5 1 CN2 (h)dh ro = 0.423 kw2 cos (z) 0

(6)

here kw = 2π λ is the wave number and cos (z) is the zenith viewing angle and cos (360) = 1(∵ TPs views in 360 o angle).

mal seeing slabs (10 slabs in this experiment) gives a value similar to the one as measured by DIMM ‘ro(DIMM) (hmin , FA)’ or any other seeing measurement device, which is also the coherence length of the astronomical site (as measured by the MSMD) given by [Echevarria et al. (1998)]: ro(MSMD)(tot) (hmin , FA) =

− 3 5 − 53 (h , h ) r ∑ o(loc)i 1 2 n

(10)

i=1

Simplifying equation (6) and comparing it with equation (5), we get the vertical contribution to ro between h1 here, hmin = 3 m is the height of the first/lowest microthermal seeing layer and FA = ∞ is the total height and h2 is: of the integrated layers of the whole atmosphere. 3 Z h2 −5 −2 2 ro(loc) (h1 , h2 ) = 16.7 λ ∗ 100 CN (h)dh h1 (7) − 3 The corresponding seeing value is: Z h2 5 = 66.8 ∗ 1012 ∗ 100 CN2 (h)dh n 3 h1 5 5 3 ε(MSMD)(tot) (hmin , FA) = ∑ ε(loc)i (h1 , h2 ) (11) where, ro(loc) (cm) is the mean coherence length or i=1 Fried parameter of the local microthermal seeing slab, h1 (m) is the height of the lower microthermal seeing By correlating the seeing values of the individual slabs layer, h2 (m) is the height of the higher microthermal of the SLs with the total seeing value of the FA, we can seeing layer, λ = 500 nm and 100 is a m ⇒ cm conver- estimate the feasible seeing improvement achieved (resion factor (note: here, ro corresponds to the diameter fer § 5.3) by raising the height of the telescope mount of the telescope for a diffraction limited image under in the SL as well as the contribution of BL using the un-obscured atmospheric condition, while it corre- equation: sponds to the coherence length for a seeing limited 5 5 3 image under obscured atmospheric condition). ε (h1 , h2 ) = [ε 3 (hmin , FA) − ε 3 (h1 , h2 )] 5 (12) (rel)

(DIMM)

(loc)

The corresponding contribution to seeing is: ε(loc) (h1 , h2 ) =

0.98 ∗ λ ∗ 206265 10.106985 = ro(loc) (h1 , h2 ) ro(loc) (h1 , h2 )

(8)

here, ε(loc) (arcsec) is the mean seeing parameter of the local microthermal seeing slab and 206265 is a radian ⇒ arcsec conversion factor. To understand the concept, let us assume ro(loc) = 20 cm (for an ideal astronomical site), then for various (extremes of UV and red bands) values of λ = (100, 380, 500 and 710) nm, we get: ε(loc) (arcsec) = (0.101, 0.384, 0.505 and 0.718) arcsec, respectively. We know that for un-obscured (diffraction limited) images, the Rayleigh criterion for Airy disk of an equivalent width εD , is defined by Vernin & Munoz-Tunon (1992): 1.22 λ (9) ε(ideal) = D

5 3 (hmin , FA) or We can use either ε(DIMM) ε(MSMD)(tot) (hmin , FA) for calculating the relative seeing values of equation (11), but, the later is used for calculating the results shown in Table 2. Also, this equation is valid, if the height of the DIMM mount is hmin (or else, we need to re-define this equation), refer Fig (4)].

4 4.1

Description of the MSMD Review of precise sensors

For very fine wires or thin films made of certain pure transition metals (Pt, Ni, W, Cu, etc.), the resistance changes proportionately for a given change in its temperature. When such a wire or thin film is wound around



a former or insulator with lead terminals, it is often referred to as a resistance temperature detector (RTD). The quality factors essential for building a precise TP for this scientific application is: (i) response time and time constant, (ii) sensitivity, (iii) accuracy or resolution, (iv) stability (sensor’s ability to maintain a consistent output for an applied constant input signal) and linearity, maintained over full measuring range, (v) repeatability (inherent precision of the sensor to repeat the same output, under repeated identical conditions) and (vi) environmental degradation and incessant measurements. To quantify temperatures at the milli to micro degree Celsius level, the RTD element of the TP should have [refer Table (A1) & (A2) and Fig (A1)]: (a) smaller thermal inertia (TI) ‘I’ which implies quicker response time, (b) smaller wire diameter offers larger resistance, which implies smaller wire length, so, the response is quicker and (c) larger temperature coefficient of resistance (TCR) α implies greater temperature resolution. Based on the consolidated evaluation [although, Ni responds quickest due to highest α value, its linearity is poorest, refer sub-fig (A) & (B) of Fig (A1), so, W or wolfram wire is clearly the best] of these parameters, the precision of RTD elements for this application, in the descending order is: W, Ni, Pt, Cu, Al, Au and Ag. Astronomers, in the past, had used distinctive TPs, such as: (a) Hartley & Smith (1981), had optimally, used a coil of 20 µm diameter Pt wire of 1.8 m long, wound around a plastic former of 3 cm diameter as TP, (b) Pant et al. (1999), had ideally, used coil of 25 µm diameter Ni wire, having resistance of 250 Ω as TP, (c) Gur’yanov et al. (1992), had economically, used a pair of TPs with coils of 7 µm and 10 µm diameters W wires wound around 1 cm and 2 cm formers respectively; also, Azouit & Vernin (2005), had economically used 5 µm diameter wolfram wire of 60 mm long (resistivity: 220 Ω at 20 o C) as TP and (d) Short et al. (2003) and Jorgensen et al. (2009) group had used the sturdy, fast response thermistors as TP, but at the cost of linearity [thermistors are negative temperature coefficient based sensors, see sub-fig (F) of Fig (A1)]. By taking recourse to an original approach, a TP is developed using Cu-100 RTD, which is more economical than the RTDs used in the past, but of comparable accuracy. Although, Cu-RTD is a poor candidate in the above order, the linearity of Cu-RTD among all RTD elements in the above list is superior [α value is almost a constant for the range −50 o C to 150 o C, refer sub-fig (C) of Fig (A1)] among all RTD elements [refer Fig. (A1)]. Also, the testing standards [International Electrotechnical Commission (IEC), International Temperature Standards (ITS) and American Society for Testing and Material (ASTM)] certified pure Cu wire (MWS, Hitachi, Electrisola and HUBER-SUHNER brands) up-to 24 µm is readily and economically available in the local markets. The precision of the Cu-RTD can be further improved proportionately by decreasing its diameter (refer Table A2). The following reasons prompted us to chose Cu-RTD for this project: (i) since, the astronomical sites located in the Himalayan

Page no.5

plateau, record negative temperatures, for maximum days through the year and Cu maintains the best linearity over negative temperatures, (ii) although, W-RTD is cheaper and preferable than Cu-RTD, the purity of the former available in the local markets is ambiguous, as they are not certified by the testing standards, (iii) the test results in the laboratory on Platinum thin-film (Pt) 1000 or 100 RTDs have shown poor response time due to their shielding with inorganic fillers such as Al2 O3 or MgO, (iv) frequent replacement of TPs, as they are prone to get damaged by thunderstorm winds, hail stones, birds pecking, etc., because they are used in un-shielded form. Hence, economy as well as availability of the RTD element in the local markets is an important factor. Electrisola3 branded, Cu wire of 0.0251 mm diameter having nominal resistance of 34.6 Ω /m at 20 o C is chosen as RTD element to make TP. This wire of ≈ 3.195 m length is used as Cu-100 RTD TP, whose nominal resistance is ≈ 100 Ω at 0 o C and ≈ 110.55 Ω at ≈ 20 o C [see Fig (3)]. This TP can sample the temperature micro-fluctuations up to ± 85.36 µK (refer Table 2).

Figure 3: Existing and to be modified configuration of Cu-100 RTD TP

The existing configuration of the TP is prone to get damaged by rain. Also, it is impossible to a make uniform and precise resistance value for all the ’n’ of TPs, as the sensor’s wire length can’t be fixed exactly to 3.2 m. To overcome these shortcomings, a 10 cm long, cylindrical solid hylam core of ≈ 15 mm diameter is fastened to a circular hylam sheet (for sun-shade) of 15 cm diameter as shown in Fig (4). This figure also shows the configuration of Ni-100 RTD TP, whose purity is 99.5%, the nominal resistance is 166 Ω /m at 20 o C, the wire diameter is 0.0251 mm and the wire length is 65.66 cm at 20 o C (60.24 cm at 0 o C). Ni-100 RTD TP yields greater response time and higher resolution than the Cu-100 RTD TP. Unlike, the Cu-100 RTD wire, the Ni-100 RTD wire is not enamel coated, so, it cannot be wound like a coil, but can be overlaid as a straight wire on a longer flat core and also, it cannot be used during raining. To make the MSMD made of Cu-100 RTD TP to function during raining, we need to apply Fevibond/Fevicol adhesive to seal all the holes/openings and exposed contacts that are present on the sensors, connectors, etc. 3 http://www.elektrisola.com/enamelled-wire/technical-data-by-size/iec-60-317.html



Circular hylam sheet with at−least 15 cm this is for Sun−shade

Circular hylam sheet with at−least 15 cmφ this is for Sun−shade

φ

Suitable screw for fastening circular plate with hylam core

Suitable screw for fastening circular plate with hylam core

A small grove is to be cut on the core for bending and routing the Ni−wire

Cylindrical solid hylam core with core φ range 5 − 20 mm and length range 5 − 10 cm

25 µ

φ

Ni−wire has been flatly bent and routed from one side of the core to the other side

Cu−wire of 3.195 m long o

is wound on a core to make it 109 Ω at 20 C

25 µ φ Ni−wire of 65.66 cm long o is layed on a core to make it 109 Ω at 20 C Rectangular flat hylam core with core width range 1 − 2 cm and height range 70 − 75 cm Since Cu−wire is enamel coated (insulated)

Since Ni−wire is not enamel coated it should be flatly over−layed on the core

one turn of the coil can be superposed over others without resistance shorting/shunting

Cu−Sensor wire soldered to rail−mate connector

2−pin rail−mate connector−Male

Ni−Sensor wire soldered to rail−mate connector

2−pin rail−mate connector−Male

2−pin rail−mate connector−Female

2−pin rail−mate connector−Female

Page no.6

We now have the finite numerical values of CN2 (h) with finite limits, so, a simple summation approach for calculating the numerical integration is done for performing statistical analysis on ro(loc) (h1 , h2 ) and ε(loc) (h1 , h2 ) in real time. We know the splitting of one definite integral into two definite integrals as: Rhh12 CN2 (h)dh = Rh∆1h1 CN2 (h)dh + R∆h2h1 CN2 (h)dh; using this we have four actual microthermal seeing slabs [(i) to (iv)] and six extrapolated slabs as follows [here, dh = 3 m, refer Fig (3)]: R 2 (h)dh = R 4.5 C2 (h)dh + R 6 C2 (h)dh = [C2 (3) +C2 (6)] ∗ 3 (i) (3m, 6m) slab B 36 CN N N N 2 3 4.5 N R 2 (h)dh = R 7.5 C2 (h)dh + R 9 C2 (h)dh = [C2 (6) +C2 (9)] ∗ 3 (ii) (6m, 9m) slab B 69 CN N N N 2 6 7.5 N

Lead wires to connect to DB−9 connector

Lead wires to connect to DB−9 connector

R 2 (h)dh = R 10.5 C2 (h)dh + R 12 C2 (h)dh = [C2 (9) +C2 (12)] ∗ 3 (iii) (9m, 12m) slab B 912 CN N N N 2 10.5 N 9 R 15 2 R 13.5 2 R 15 2 (h)dh = [C2 (12) +C2 (15)] ∗ 3 CN (iv) (12m, 15m) slab B 12 CN (h)dh = 12 CN (h)dh + 13.5 N N 2

Figure 4: To be modified configuration of Cu-100 RTD and Ni-100 RTD TPs

R 2 (h)dh = R 6 C2 (h)dh + R 9 C2 (h)dh = [C2 (3) ∗ 3 +C2 (6) ∗ 3 +C2 (9) ∗ 3 ] (v) (3m, 9m) slab B 39 CN N N N 2 2 3 N 6 N R 2 (h)dh = R 6 C2 (h)dh + R 9 C2 (h)dh + R 12 C2 (h)dh = [C2 (3) ∗ 3 +C2 (6) ∗ 3 +C2 (9) ∗ (vi) (3m, 12m) slab B 312 CN N N N 9 N 2 3 N 6 N

2 (12) ∗ 3 ] 3 +CN 2 R 2 (h)dh = R 6 C2 (h)dh + R 9 C2 (h)dh + R 12 C2 (h)dh + R 15 C2 (h)dh = [C2 (3) ∗ 3 + (vii) (3m, 15m) slab B 315 CN N 9 N 2 3 N 12 N 6 N

2 (6) ∗ 3 +C2 (9) ∗ 3 +C2 (12) ∗ 3 +C2 (15) ∗ 3 ] CN N N N 2 R 2 (h)dh = R 9 C2 (h)dh + R 12 C2 (h)dh = [C2 (6) ∗ 3 +C2 (9) ∗ 3 +C2 (12) ∗ 3 ] (viii) (6m, 12m) slab B 612 CN N N N 9 N 2 2 6 N

4.2 Theory of operation

R 2 (h)dh = R 9 C2 (h)dh + R 12 C2 (h)dh + R 15 C2 (h)dh = [C2 (6) ∗ 3 + C2 (9) ∗ 3 + (ix) (6m, 15m) slab B 615 CN N N 9 N 2 12 N 6 N

2

2

3

The physical arrangement of MSMD, SDIMM and CS- CN (12) ∗ 3 +CN (15) ∗R2 ] R 12 2 R 15 2 3 3 15 2 2 2 2 AWS, used to characterise the site, is shown in a (x) (9m, 15m) slab B 9 CN (h)dh = 9 CN (h)dh + 12 CN (h)dh = [CN (9) ∗ 2 +CN (12) ∗ 3 +CN (15) ∗ 2 ] Refer Table (2) for results. schematic diagram Fig (5) (position of the tower is where the proposed telescope mount is). The MSMD 4.3 Components of MSMD Block diagram of the MSMD is shown in Fig (6) and the schematic circuit diagram is shown in Fig (8). Blocks of MSMD are : (i) Differential temperature measuring circuit, (ii) Air temperature measuring circuit and (iii) Instrumentation amplifier (IA) and filter and (iv) Data logging. One channel of Differential temperature measuring circuit Sallen−Key active Wheatstone bridge

low pass filter Instrumentation Amplifier Gain = 400

F_h = 100 Hz Calib. Pot 10 Ω

Figure 5: Schematic diagram showing the physical arrangement of instruments can be used to determine different quantities given in equations (3) to (12) by the following procedure: A pair of TPs separated by r=1 m [note: assuming (a) l r L, (b) the proposed telescope diameter] and a temperature sensor (TS) (AD584JH) are installed on each of the five microthermal seeing layers, at heights h = 3 m, 6 m, 9 m, 12 m and 15 m above ground. The dispersion of differential temperature micro-fluctuations dT (r, h) measured by these TPs, on each separate layer are applied to equation (5) for computing DT (r, h) and then to equation (3) for computing CT2 (r, h) [here, CT2 (r, h) = DT (r, h), ∵ r = 1 m]. Separate layer’s Tair (h) are measured by separate TSs and a barometric pressure sensor (model ‘CS100’) installed on a custom configured Campbell Scientific (CS)’s AWS, at an height of ≈ 3 m above ground measures the average P(h) for these layers. These measured data are substituted in equation (4) to compute CN2 (h) values for sampling the vertical distribution of the turbulence strength in real time.

Calib. Pot 10 Ω

One channel of Air temperature measuring circuit

STA−300 Screw terminal panel

KPCI−3102 DAQ

LabVIEW program for data logging

Instrumentation Amplifier Gain = 10

Figure 6: Schematic block diagram of MSMD


Page no.7

GND

GND

GND

GND

A

C

B

D


Figure 7: Schematic diagram of MSMD-PCB (all components are shown for reference only)


Page no.8

GND

GND

GND

GND

A

C

B

D


Figure 8: Schematic diagram of actual existing PCB



Figure 9: Components assembly layout of actual existing PCB


Page no.9


Figure 10: Top layout (scaled PCB fabrication version) of actual existing PCB


Page no.10


Figure 11: Bottom layout (scaled PCB fabrication version) of actual existing PCB


Page no.11


Sl. no

Bill of required components list for the Existing Board of MSMD Note: Below list is for just One channel of MSMD, for N-channels, buy N times Component reference no. Component specification

Page no.12

Qty.

1

Toshiba AC-DC Adapter:

DC-15V-5A; Model: PA3301U-1ACA

2

C3, C4, C5, C6, C7, C9, C10, C11, C12, C14, C15, C17, C18, C20, C21, C22, C23, C24

0.1 micro-farad, 20V, +/-20 tolerance, numeric code- 18 nos. 104; tantalum capacitors

3

C1, C2, C8, C13, C16, C19

220 micro-farad, 20V, +/-20 tolerance; electrolytic capacitors;

4

J1, J2, J3, J4, J5, J7, J8, J9, 2 pin burg-sticks J10 Jumper/Shunt-plug

10 nos. 2 nos.

5

J6

1 no.

6

R3, R8, R11, R14, R19, R23 10k, Square Trim-pot, 0.5 W, +/-10%, 100ppm/K, part no.3296W-1, Top Adjust

6 nos.

7

R4, R5, R12, R13

10E, Square Trim-pot, 0.5 W, +/-10%, 100ppm/K, part no.3296W-1, Top Adjust

4 nos.

8

R9, R10, R15, R16, R22


5 nos.

9

R21


1 no.

10 R1, R2

120E, MFR, 0.25W, +/-1%, 100 ppm/K

2 nos.

11 R6, R7

11k, MFR, 0.25W, +/-1%, 100 ppm/K

2 nos.

12 R17, R18

1M, MFR, 0.25W, +/-1%, 100 ppm/K

2 nos.

13 R20

950E, MFR, 0.25W, +/-1%, 100 ppm/K

1 no.

14 U1, U7

5V regulator, part no.LM7805CT

2 nos.

15 U2, U6

Ins. Amp, part no. AD624AD

2 nos.

16 U3

Quad Op-amp, part no.LM224N

1 no.

17 U4

+12V regulator, part no.MC78L12ABP

1 no.

18 U5

-12V regulator, part no.MC79L12ABP

1 no.

19 U?

Temperature Transducer, part no.AD590JH

1 no.

20 J?

D-Sub, Solder bucket, 9 Pos Plug, Part no. DE09P064TXLF

1 no.

D-Sub, R/A, 9Pos Socket; Part no. 10090099S094LLF

Figure 12: Components list of actual existing PCB


2 nos.

6 nos.


4.3.1

Differential temperature measurement

Page no.13

offset adjustments that are to be set to 0V , for precise measurements. If this adjustment is not done, then very often, the output voltage of the differential temperature drifts and reaches the saturation level. Hence, for each AD624AD, these two off-set adjustments are to be compulsorily ensured.

A pair (placed 1 m apart) of resistance matched TPs are connected in a balanced, Wheatstone bridge circuit, as shown in Fig (6), such that it produces a differential voltage Vdi f f .temp. proportionately, as a function of temperature micro-fluctuations. The so developed voltage is a result of the resistance disparity of either or both Active filter: A Sallen-Key topology based, second TPs, while encountering the instantaneous temperature order low pass filter (LPF), having unity gain, was micro-fluctuations, as compared to the other. used for filtering the signals above cut-off frequency fH . Assuming the wind velocity reaching a maximum o of 100 m/s, the temperature fluctuations was fixed to Using equation (A2), the resistance of TP (at 27 C) f ≈ is: R(T P) = 100 [1 + 0.00393 (27 − 0)] = 110.55 Ω, there- H 100 Hz. The op-amp OP27 was used to design the fore, the TCR of the TP is 0.393 Ω/K and that of Cu is LPF, whose circuit diagram is shown in Fig. (8). Using 0.00393 Ω/K. We need to calculate all the parameters the well known transfer functions, we can design the of MSMD, with reference to the temperature at 0 o C or values of the resistors and capacitors as follows: 5V ], 273.15 K condition. A current of 22.73 mA[ (120+100)Ω ωH2 Vout (s) (13) = H(s) = 2 flows through each branches of the bridge, consistωH Vin (s) [s + ( Q0 )s + ωH2 ] ing of ≈ 100 Ω (TP) and 120 Ω [refer Fig (6)]. Therefore, the amount of voltage change per o C or K is: here, s = j ω simplifying H and ωH = 2π f H , on q 22.73 mA∗0.393 Ω/K = 8.933 mV /K, which is the temperC1 1 1 √ ature co-efficient of voltage (TCV) of the MSMD. A gain this, we get ωH = [ R C1C2 ]; Q0 = [ 2 C2 ]; Q0 = 1 ]; R = [ (2Q ω1 H C ) ];C1 = 4Q20C2 ;C2 = [ (2RQ1 ω ) ]. For, of AG = 400, is used, therefore, the acquired signal’s [ 2ζ 0 2 0 0 V(di f f .temp.) differential temperature is: dT (r, h) (K) = (400 ∗8.933 mV /K) . fH = 100 Hz; ζ = 1; Q0 = 0.707; R = R1 = R2 ;C1 = 2C2 and The resolution of a 16 bit DAQ is 0.305 mV, so, the tem- C1 = 0.1 µf, we get R1 ≈ 11 kΩ. 0.305 mV perature resolution of the TP = 3.57316V /K = 85.36 µK [Table (1)]. ‘dT (r, h)’ is acquired at a sampling rate of 10 kS/s, then every 10 samples are ensemble averaged to get a packet of 1 kS/s, then these packets are squared to compute ‘DT (r, h)’ in equation (4). These data are logged at 1 kS/s and 1 S/s for short and long duration observations respectively.

A 1V (p-p) sinusoidal wave is applied to LPF i/p,

Note: Suppose, Ni-100 RTD is used in place of above described Cu-100 RTD as TP, then the resistance of Ni-100 RTD TP is: R(T P) = 100 [1+0.00641 (27− 0)] = 117.307 Ω, the TCR of the TP is 0.641 Ω/K and that of Ni is 0.00641 Ω/K. The amount of voltage change per o C or K for Ni-100 RTD TP is: 22.73 mA ∗ 0.641 Ω/K = 14.57 mV /K, which is its TCV. A gain of AG = 200, can be used, therefore, the acquired signal’s differenV(di f f .temp.) tial temperature would be: dT (r, h) (K) = (200 ∗14.57 mV /K) . The temperature resolution of a Ni-100 RTD TP is: 0.305 mV 2.913V /K = 104.7 µK. Figure 13: LPF response 4.3.2

IA and filter

IA is a combination of a pair of buffer amplifiers and a differential amplifier (DA), that prevents the loading of the transducer resistance over the input resistors of the op-amp or vice-versa. Unlike, DA, the IA rejects the power line frequencies (50 Hz), its second harmonics and electro-magnetic-interfering signals that are common to the inputs. A precise integrated circuit (IC) AD624AD was selected as IA, whose differential i/p resistance is 109 Ω, i/p capacitance is 10 pF, common mode rejection ration (CMRR) is 130 dB, slew √ rate is Hz and 5 V/µs, noise voltage (at 1 kHz) R.T.I. is 4 nV/ √ voltage referred to input (RTI) is 75 nV/ Hz. The input and output nulling in AD624AD are the two crucial

whose Bode plot is shown in Fig (13) and the curve decays at a roll-off rate of 12 dB per octave or 40 dB per decade in the stop band region. A buffer amplifier is used as an impedance matching between the preceding electronics and the lengthy cables leading to DAQ system. 4.3.3

Air temperature measurement

A semiconductor based TS AD590JH, is used to log the air temperature Tair (h) (K), whose nominal current varies proportionately as a function of sensed temperature change, which is the temperature co-efficient of current (TCI) of the AD590JH and is 1 µA/K. A 1 kΩ



Page no.14

is applied across this as a potential divider, to convert TCI to TCV and is 1 mV/K (Table 2). A gain of AG = 10 is used to pass the low level signals through the lengthy cables. The air temperature is calculated using: (h) Tair (h) K = (10V∗1airmV /K) and this value is substituted in equation (5) for real time computation. Also, Tair (h) o C = [Tair (h) K - 273.15] is computed to plot and analyse the temperature fluctuations as referred below.

RTD (as shown in Fig 15) in the Lab. The temporal responses of these two sensors are shown in Fig 16. For greater accuracy of equation (b), Callendar-van Dusen has defeined equations which is used as IEC751 standard. Howerver, by using a rational polynomial function, the temperature versus resistance data of Pt-100 RTD is fit using following equation, with a maximum error factor of ≈ ±0.015o C, for the range -200 to +850 o C (refer Fig 69-71): Rre f {C1 +Rre f [C2 +Rre f (C3 +C4 ∗Rre f )]} − − > (c) Since the semiconductor based TS AD590JH is Tx = C0 + 1+Rre f [C5 +Rre f (C6 +C7 ∗Rre f )] sturdy, it is currently being used to log air temperature here the co-efficients are: C0 =-245.19; C1 =2.5293; Tair (h) (K). However, for better accuracy, a Cu-100 RTD C2 =-0.066046; C3 =4.0422E-3; C4 =-2.0697E-6; C5 =TP put in a bridge can be used, as shown in Fig (14). 0.025422; C6 =1.6883E-3; C7 =-1.3601E-6 (refer Pt-100-RTD calibration details-Page-1&2 at Appendix). The output voltage of the bridge is : If similar equations and co-efficients are derived for Cu and Ni RTDs (refer Ni-RTD calibration details-Page-2 R2 x at Appendix), using MATLAB sub-routines, we can − Vo = Vi ∗ (R R+R (R1 +R2 ) x) 3 improve the accuracy of these two TPs too. By simplifying and re-arranging the above equation, We can use commercially available Pt-100 RTD TP we can calculate the un-known resistance ‘Rx ’ of the as a standard reference temperature thermometer for TP as: all our Lab testing purposes by incorporating the equa3 )+(Vo ∗R1 ∗R3 )+(Vo ∗R2 ∗R3 ) tions (a) & (c) in a LabVIEW program. A simple exper− − − − > (a) Rx = (Vi ∗R2(V∗Ri ∗R 1 )−(Vo ∗R1 )−(Vo ∗R2 ) iment was planned, but, could not be performed is: a V Clinical thermometer (reference source), a AD590JH, a here, R1 = R2 = R3 = 120Ω, Vi = 5 V and Vo = (airtemp) 10 Pt-100 RTD and a Cu-100 RTD, all with long lead wires where, AG = 10. were to be put in a refrigerator, without switching on the From this ‘Rx ’, we can now calculate the un-known refrigerator, the temperature measured by all these sensors were to be recorded. Then, after switching on the Air temperature ‘Tx ’ as follows: refrigerator, the fall in temperature were to be recorded continuously till the freezing point of water was reached Rx = Rre f ∗ [1 + α(Tx − Tre f )] [Note: a schematic diagram incorporating Cu-100 RTD o here, Rre f = 100Ω, Tre f = 0 C and α = 0.00393 Ω/K TP is shown in Fig (17). Also, for testing MSMD in Lab, (for Cu) and 0.00641 Ω/K (for Ni), these are the values another schematic diagram is shown in Fig (22)]. used for testing. Air temperature measuring circuit for one channel

To calculate the unknown ‘Rx’ value in Air temperature circuit, simplify the bridge circuit as follows : Vo = Vi * { [Rx / (R3 + Rx)] − [R2 / (R1 + R2)] } On simplifying and re−arranging the above equation, we get :

Note: manufacturers of RTDs state that a notable increase in α values occurs from 99.0% to 99.999% pure transition metals. So, based on purity, the range of α values for Cu is 0.00393-0.00427 Ω/K; for Pt, it is 0.00385-0.003925 Ω/K, for W, it is 0.0044030.0045 Ω/K and for Ni, it is 0.00618-0.00672 Ω/K.

Rx = [ (Vi * R2 * R3) + (Vo * R1 * R3) + (Vo * R2 * R3)] / [ (Vi * R1) − (Vo * R1) − (Vo * R2) ] here, R1 = R2 = R3 = 120 Ω (0.1%, 0.5Watt), Vi = 5V and Vo = V_(airtemp)/10; where gain Ag = 10 From the above calculated ‘Rx’ value, we can now compute the un−known Air temperature ‘Tx’ using the TCR formula as: Rx = R_(ref) * [1 + α (Tx − T_(ref)]

V_(airtemp)

here, R_(ref) = 100Ω , T_(ref) = 0 oC and

α

= 0.00393 (for Cu)

Tx = [Rx − R_(ref)] / [α * R_(ref)] here, the ‘Tx’ is a linear fit value with an average error of +/−0.12 oC for the range 0 o C to 100 o C If a quadratic fit is derived for ‘Tx’, using Callendar−Van Dusen’s (IEC−751 & ITS−90 Std), then the average error would be +/−0.03 oC for the range −100o C to 600o C

Also, if a rational polynomial function is derived for ‘Tx’, then the average error would be +/−0.0015o C for the range −200o C to 850o C

TL−074−M/AM/BM/I/AI/BI

Instrumentation amplifier gain Ag = 1 + [ 2 * (R / Rg) ] For Air temperature circuit, Ag = 10, Gain Adj.Pot = 50k Ω and

Wheat−stone bridge

R = R4 = R5 = R6 = R7 = R8 = R9 = 56kΩ

Instrumentation amplifier

For Differential temperature circuit, Ag = 400, Gain Adj.Pot = 50k Ω and R = R3 = R4 = R5 = R6 = R7 = R8 = 56kΩ

Buffer amplifier

Sallen−Key Butterworth Low Pass Filter Cut−off frequency f_H = 100Hz

Low pass filter V_(diff.temp)

f_H = 1 / [2 *

π* R *

(C_t * C3)]

here, R = R9 = R10 = 11k Ω and C1 = C2 = C3 = 100nF; here, C_t = 2 * C3 and C1 & C2 together is C_t

Re-arranging the above linear equation, we get a linear fit for Air temperature ‘Tx ’: Tx =

(Rx −Rre f ) α∗Rre f

Current flowing through Cu−100 Ω RTD (TP) in each branch of the bridge is: Ix = 5V / (120 Ω + 100Ω ) = 22.73mA TCV = Ix *

α Cu−100= 22.73mA * 0.393 Ω = 8.933 mV /

o

C

The un−known differential temperature ‘d_T(r, h)’ = V_(diff.temp) / (400 * 8.933); here, Ag = 400 here, the sampling rate of ‘d_T(r, h) is 10kS/s and every 10 samples of 10kS/s are collected for ensemble averaging sake, so that the data packets of 1kS/s are finally collected, logged and then squared to compute equation (3)

Differential temperature measuring circuit for one channel

− − − − − − − − > (b)

Equation (b) measures ‘Tx ’ values with a maximum tolerance (error) range of: (a) ±1.2o C for -100 to 0o C and ±0.1o C for 0 to 100o C for Cu-100 RTD TP [apply Rx values from Table-A4 of appendix into euqation (b)], which is the most linear RTD; (b) ±19.5o C for -100 to 0o C and ±12.5o C for 0 to 100o C for Ni-100 RTD TP [apply Rx values from Table-A6 of appendix into euqation (b)] and ±3.22o C for -100 to 0o C and ±0.38o C for 0 to 100o C for Pt-100 RTD TP [apply Rx values from Table-A8 of appendix into euqation (b)]. A LabVIEW program was written for equations (a) & (b) for testing and comparing the behaviours of a commercially available Platinum thin-film (Pt)-100 RTD and a Cu-100

Figure 14: Improved version of MSMD

Figure 15: Pt-100 and Cu-100 tested in Lab



Figure 16: Temporal response of Pt-100 versus Cu-100 in Lab


Page no.15

Page no.16

B GND

GND

GND

GND

A

B

A

C

C

D

D


Figure 17: Schematic diagram of TP used for Air temperature measurement PCB



Page no.17

Figure 18: Components assembly layout of TP used for air temperature measurement PCB



Page no.18

Figure 19: Top layout (scaled PCB fabrication version) of TP used for air temperature measurement PCB



Page no.19

Figure 20: Bottom layout (scaled PCB fabrication version) of TP used for air temperature measurement PCB



Sl. no

Bill of required components list for TP as Air-Temp-sensor Board of MSMD Note: Below list is for just One channel of MSMD, for N-channels, buy N times Component reference no. Component specification

Page no.20

Qty.

1



2

C3, C4, C5, C6, C7, C9, C11, C12, C14, C15, C17, C18


3

C1, C2, C8, C10, C13, C16


6 nos.

4

J1


1 no.

5

R1, R2, R5, R14, R15, R16, R19, R20, R21, R33, R34, R35

56k, MFR, 0.25W, +/-1%, 100 ppm/K

12 nos.

6

R6, R24

20k, Square Trimpot, 0.5 W, +/-10%, 100ppm/K, part 2 nos. no.3296W-1, Top Adjust

7

R7, R8, R11, R22, R23, R29, 10E, Square Trimpot, 0.5 W, +/-10%, 100ppm/K, R30 part no.3296W-1, Top Adjust

7 nos.

8

R12, R13, R27, R28, R32

1E, Square Trimpot, 0.5 W, +/-10%, 100ppm/K, part no.3296W-1, Top Adjust

5 nos.

9

R3, R4, R17, R18, R31

120E, MFR, 0.25W, +/-1%, 100 ppm/K

5 no.

10 R9, R10

11k, MFR, 0.25W, +/-1%, 100 ppm/K

2 nos.

11 R25, R26

1M, MFR, 0.25W, +/-1%, 100 ppm/K

2 nos.

12 U1, U6

5V regulator, part no.LM7805CT,

2 nos.

13 U2, U5

Quad Opamp, part no.TL074-AI/BI/AM/BM OR LM224N

2 nos.

14 U3


1 no.

15 U4

-12V regulator, part no.MC79L12ABP,

1 no.

16 U?


1 no.

17 J?

D-Sub, Solder bucket, 9 Pos Plug, Part no. DE09P064TXLF;

1 no.

Figure 21: Components list of TP used for Air temperature measurement PCB


2 nos.

Page no.21

B GND

GND

GND

GND

A

B

A

C

C

D

D


Figure 22: Schematic diagram of testing board PCB



Figure 23: Components assembly layout of testing board PCB


Page no.22


Figure 24: Top layout (scaled PCB fabrication version) of testing board PCB


Page no.23


Figure 25: Bottom layout (scaled PCB fabrication version) of testing board PCB


Page no.24


Sl. no

Bill of required components list for Testing Board of MSMD Note: Below list is for just One channel of MSMD, for N-channels, buy N times Component reference no. Component specification

Page no.25

Qty.

1



2

C3, C4, C5, C6, C7, C9, C11, C12, C14, C15, C17, C18


3

C1, C2, C8, C10, C13, C16


6 nos.

4

J1


1 no.

5

R1, R2, R5, R14, R15, R16, R17, R18, R19, R31, R32, R33

56k, MFR, 0.25W, +/-1%, 100 ppm/K

12 nos.

6

R6, R23

20k, Square Trimpot, 0.5 W, +/-10%, 100ppm/K, part 2 nos. no.3296W-1, Top Adjust

7

R7, R8, R11, R20, R21, R22, 10E, Square Trimpot, 0.5 W, +/-10%, 100ppm/K, R29, R30 part no.3296W-1, Top Adjust

8 nos.

8

R12, R13, R27, R28


4 nos.

9

R3, R4

120E, MFR, 0.25W, +/-1%, 100 ppm/K

2 nos.

10 R22

950E, MFR, 0.25W, +/-1%, 100 ppm/K

1 no.

11 R24


1 no.

12 R9, R10

11k, MFR, 0.25W, +/-1%, 100 ppm/K

2 nos.

13 R25, R26

1M, MFR, 0.25W, +/-1%, 100 ppm/K

2 nos.

14 U1, U6

5V regulator, part no.LM7805CT,

2 nos.

15 U2, U5

Quad Opamp, part no.TL074-AI/BI/AM/BM OR LM224N

2 nos.

16 U3


1 no.

17 U4

-12V regulator, part no.MC79L12ABP,

1 no.

18 U?


1 no.

19 J?

D-Sub, Solder bucket, 9 Pos Plug, Part no. DE09P064TXLF;

1 no.

Figure 26: Components list of testing board PCB


2 nos.


4.3.4

Page no.26

Data logging

An NI-ENET-9205 DAQ having an integrated NI-ENET9163 4 device is used to acquire the results presented in the report, whose salient features are: 16 bits resolution, 250 kS/s aggregate sampling rate (4 µs analog to digital conversion time), 32 single-ended or 16 differential analog inputs, ± 200 mV, ± 1 V, ± 5 V, and ± 10 V programmable input ranges, Ethernet cable length up to 100 m, supports Visual C++ , LabVIEW, MATLAB, etc. We set the voltage range of the DAQ at ± 10 V, so, the digitization step size or the resolution of the DAQ V = 0.305 mV. NI-DAQmx 8.9.5 is the driver system is 20 216 software, supplied along with this device, which is compatible with LabVIEW 2009 or older versions (Note: DAQmx 8.9.5 does not support advanced featurs of Figure 28: Flowchart depicting the measurement of LabVIEW 2010). Vdi f f , DT (r, h), CN2 (h), ro (h1 , h2 ) and ε f whm (h1 , h2 ), for disLabVIEW’s salient feature is: amateur programmer crete microthermal seeing layers and slabs can easily write complicated programs in less time. A LabVIEW program is written for plotting and logging five layer’s V(di f f .temp.) , dT (r, h),CT2 (r, h), Tair (h) and CN2 (h) data and ten slab’s ro(loc) (h1 , h2 ) and ε(loc) (h1 , h2 ) data in real time. Observer/user has to edit few mandatory data (Pressure, sampling rate and data averaging rate) and few optional data (sky status, wind-speed, etc.) in the GUI, before executing the program. Each of the logged data sample is preambled with milli-seconds level timestamp. All computers acquiring data from the instruments shown in Fig (5) are connected to a GPS configured network switch for a common timing source. Associated data from all the instruments (on a common time scale), can be compared and analysed for amplitude and phase responses of optical turbulence profiles. The time scale lengths, the sampling rate and the temperature difference are all typical of the atmospheric turbulence.

based RTDs, set-up the required expensive testing facilities to define the parameters, complying to the standards, such as: (a) DIN IEC-751 by International Electro-technical Commission, (b) ASTM-1137 by American Society for Testing and Material, (c) ANSI DIN 43762:1986 by American National Standards Institute, (d) ITS-90 and BS-1904 by International Temperature Standards, etc. However, this project has adopted a simple, inexpensive, experimental approach for calibrating the TPs and TSs (AD584JHs). Since, the very accurate, crystalline rubber hydrocarbon (HY-CAL) shielded, 1000 Ω Pt RTD-TP (model:43347 RTD) 5 used in the CS-AWS is expensive and for other practical difficulties, it was not used as a reference TS for calibrating the TPs and TSs used in MSMD. However, a good quality, K-type thermocouple based clinical thermometer (TM), with an extended cable for probe, was used as a reference TM (RTM), whose resolution was in steps of 100 m o C. By making use of the simplified ideal gas formula, it was verified that the RTM was more accurate than the mercury TM and alcohol TM, available in the laboratory, accordingly, it was used to calibrate the TPs and TSs.

Calibration of TPs and TSs in compliance with the ITS 90 standards is very expensive, so a simple, inexpensive and scientific approach was followed. A good quality clinical thermometer (K-type thermocouFigure 27: Flowchart depicting the measurement of ple) with an extended cable for probe was used as a Tair (h) (K), at discrete microthermal seeing layer reference thermometer (RTM) to calibrate the sensors. The simplified Claussius-Clapeyron’s equation6 was used to calculate the actual local location’s boiling point temperature (BPT) and melting point temperature 4.4 Calibration of MSMD (MPT) of water, so as to calculate the average (for BPT On the basis of physical characteristics, performance, and MPT) error factor measured by RTM with respect testing requirement, resistance versus temperature to the theoretical actual value, which was found to be relationship, tolerances, etc., the manufacturers of Pt 4 http://sine.ni.com/ds/app/doc/p/id/ds-190/lang/en

5 http://s.campbellsci.com/documents/us/manuals/rtd.pdf 6 http://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation



Page no.27

≈ ± 0.44 o C.

its error factor consideration). After this calibration, all the sensors were allowed to measure for long duration, 4Hvap 1 P1 1 − (14) a drift factor of ≈ ± 0.3 o C, was recorded by individual ln = P2 R T1 T2 sensors, which is its inherent property that cannot be where, P1 (mm of Hg) is 1 atm. pressure = corrected. 760 mm of Hg, P2 (mm of Hg) is the given pressure, 4Hvap (J/mol) is the enthalpy of vaporization of Similarly, to calibrate the TP, each one of it was an element (for water = 40650J/mol), T1 (K) is the BPT connected to individual bridge circuits [refer Fig (17)] to of an element at a given pressure, T2 (K) is the BPT of measure the un-calibrated ambient temperature. The an element at 1 atm. (for water it is 373.15 K) and R is RTM and all the TPs were dropped into the pit with the procedure as outlined above. The wire length of the the gas constant = 8.314 J-mol−1 K−1 . individual TPs was trimmed, such that all measured the The GPS installed close to the laboratory mea- same temperature as that of the RTM then a drift factor o sured the location’s altitude as 2970 ft, above mean of ≈ ± 0.04 C, was noted. To minimize this drift factor, we need to redefine the TCR equation (A2), similar to sea level, while its corresponding barometric pressure, the Callendar-Van Dusen equation. obtained from the nearby meteorological department at the time of experiment, was 26.79 inches of Hg = 680.47 mm of Hg (for better accuracy, the pressure Finally, the sensing portion of each of the TS was should be measured at the place of this experiment). dipped into ice-bath and boiling water respectively, to Now, assuming the theoretical BPT = T2 = 373.15 K, corroborate the temperatures measured by each one of we get the physical BPT of water for the location = T1 them was the same as that of the RTM. This procedure = 96.82o C by using equation (14). Similarly, for the could not be adopted to TPs owing to its configuration theoretical MPT = T2 = 273.15 K, we get the physical and fragility. The MSMD, under testing, calibration, simulation stages and operation at three sites is shown MPT of water for the location = T1 = -1.71o C. in Fig (30). The RTM, mercury TM and alcohol TM were all dipped into the boiling water (distilled) and allowed the readings of the TMs to get stagnated, the measured BPT of each of the TMs was noted. Similarly, all the referred TMs were placed in a ice-bath (distilled), crushed the ice blocks and allow it to melt, the value of MPT measured by each of the TMs was noted (see Table 1). It was noted that RTM measured reliably, with a minimal and uniform errors for BPT and MPT, it also, measured close to the theoretical calculations. The average error factor of 0.44 o C was noted and adjusted, while calibrating the TPs and TSs. A stable tempera

Table 1: Experiment to select RTM for calibrating TPs and TSs Type of measurement

BPT (o C)

Error (o C)

MPT (o C)

Error (o C)

Theoretical

96.82

-

-1.71

-

K-type TM

97.3

0.48

-1.32

0.39

Mercury TM

92.5

4.32

0

-1.71

Alcohol TM

89

7.82

0

-1.71

Figure 30: Test conducted on a tower at terrace floor of IIA

ture environment was created by placing a thermocol (polystyrene) box into a corrugated fibreboard box, they together constituted one layer, over which, up-to five such layers were stacked and sealed to form an enclosure, with a small aperture for guiding the lead wires of all sensors. All the five TSs (AD590JH) and the RTM were placed into the so built enclosure and dropped it into a 20 feet deep experimental pit and sealed the pit opening, this was done to ensure the identical testing conditions and a stable environment. All the sensors were enabled and their readings were allowed to stabilize, individual sensor’s associated potentiometers were tuned such that all the TSs measured the same temperature as that of the RTM (with K. Dhananjay, Indian Institute of Astrophysics


Figure 29: Screen-shots showing the GUI program acquiring the test results


Page no.28


4.5 Electronic noise of MSMD

Table 2: Technical specifications of the MSMD

The procedures described in the technical literatures of the Texas Instrument Inc. has been adopted to calculate the theoretical intrinsic noise generated by the circuit elements, which was corroborated with the test results in the laboratory. Similar calculations were done in the past by Short et al. (2003) and Jorgensen et al. (2009), which is described as below: The voltage noise vn_v is defined as: q vn_v = (v2n f + v2nBB )

Page no.29

Parameter Measuring temperature range

-55o C to 125o C

0.393 Ω/ K

1 µA/K

TCV/Sensitivity of the sensor

8.933 mV /K

10 mV / o C

Gain used Temperature resolution Time constant of the sensor

400

10

± 85.36 µK

± 0.5 o C

-

0.04 watt − sec/ o C

Bandwidth of MSMD

100 Hz

-

Sampling rate

10 kS/s

10 kS/s

± 10V

± 10V

ADC steps Digitization step size

here, vn f (Vrms ) is related to 1f voltage noise component and vnBB is the broadband (radio frequency) noise voltage

AD590JH TS

23 K to 933 K

TCR/TCI (at 27 o C)

ADC voltage levels

(15)

Cu-100 RTD TP

RMS digitization noise

q v2 d

RMS electronic noise Equivalent temperature noise

216 = 65536

65536

20V 65536 = 0.305 mV

0.305 mV

0.305 √ mV = 1.191 µV 16

1.191 µV

2.53 mVrms

368 µVrms

0.95 mK

36.8 µ o C

The current noise vn_i is defined as: terrace floor of IIA, for mounting the same on to a (16) 9 m tower (housing the lightning arrestor). Since, no organised pre-arrangement was made for hoisting and here, in (Arms ) is the current noise density and Req (Ω) is fixing the sensor arms smoothly onto the tower, all the the equivalent resistance of the MSMD TPs got damaged. A new set of sensors were replaced to conduct the test, so, the test results presented below The thermal (resistor) noise vn_r is defined as: is by the uncalibrated sensors. The long span of cables q running from tower top to its base acts like an antenna (17) to pick up the electromagnetic interference as noise. vn_r = (4kB T Req 4 f ) Also, the impedance mismatch occurs while interfacing here, kB is the Boltzmann’s constant = 1.38 × 10−23 J/K, these cables with the DAQ, which results in added T and is the absolute temperature (K) of the resistor noise. The inherent quantization noise of DAQ too adds and 4f (Hz) is the band width of the MSMD up. All these noises are embedded on the temporally varying data signals. So, a smoothing (averaging) of We can calculate the total rms noise RTI, using: 36 data points is uniformly applied to all the temporally varying bulky data signals [Tair (h), Vdi f f (r, h), dT (r, h), q 2 2 (18) CT (r, h), CN (h), ro(loc) (h1 , h2 ) and ε(loc) (h1 , h2 )] plotted vn_in = (v2n_v + v2n_i + v2n_r ) in graphs (Figs 31-44). Table (3 & 4) summarises the results of these graphs. vn_i = in Req

The data sheets of the used components were referred for the values of the above parameters and distinctively calculated the vn_in for differential and air temperature measuring units as: vn_in (di f f .temp.) = q (14.76e − 9)2 + (1.4e − 6)2 + (0.253e − 6)2 + (12.58e − 6)2 = 12.66 µVrms

vn_in (airtemp.) = q (17.54e − 9)2 + (3.64e − 6)2 + (0.506e − 6)2 = 3.68 µVrms

For quick reference in Tables 3 & 4, the respective equation numbers are shown for calculating the respective values. In Table (4), the values shown in the last column (Avg. of all) is the final results obtained from this experiment, which is the aggregate average of the mean values of five days and five nights observations. From the final results, we can infer that the seeing values gradually improves from 3 m layer (1.54 00 ) to 15 m layer 1.04 (00 ).

We can now calculate the total rms noise voltage The microthermal array (MTA) placed over a telereferred to output (RTO), using: scopic mast (up-to 30 m) and on hot air balloon (from 30 m to 100 m) at the site of Observatorio Astronomico vn_out = vn_in ∗ Noise_Gain (19) Nacional, by the Echevarria et al. (1998) found that the local seeing values measured using MTA becomes vn_out (di f f .temp.) = 12.66 µ Vrms ∗ 200 = 2.53 mVrms 00 vn_out (airtemp.) = 3.68 µ Vrms ∗ 100 = 368 µVrms All calcu- zero at an height of 100 m from ground. This is the ideal height for the location of the telescope mount lated values are summarised in Table (1). in the surface layers, but, is an impractical task. The broader perspective of microthermal seeing measure5 Test results and discussions ment experiment is to find this ideal height linked to every site. The optical turbulence contributed by the All five channel sensors, those were calibrated as FA in the BL starts approximately from 10 km and per the procedure outlined above were carried to the extends upto the boundary line of Ozone layer (around K. Dhananjay, Indian Institute of Astrophysics


Page no.30

25-30 km). Based on the theory discussed in § 3, this ice) and Mw = 0.018015 kg/mol, is the molar mass of pattern is conventional to all sites. water vapour. The refractivity of moist air n prop as defined by Ciddor The distribution of CN2 (h) datasets for the separate (1996) in compliance with the International Bureau of and collated five layers, along with the distribution of Weights and Measures (BIPM) is: ro(loc) (h1 , h2 ) and ε(loc) (h1 , h2 ) datasets for the collated ρa (naxs − 1) ρw (nws − 1) ten slabs, fit with log-normal curve is shown as his+ (21) (n prop − 1) = ρaxs ρws togram plots in Figs 45-52. In histogram plots, we can note that the data-sets rises sharply and falls with where, ρa is the actual density of dry air, naxs is the an elongated tail, which is log-normal (orange curve) refractivity of dry air, ρaxs is the reference density of dry distribution pattern. The mean, median and standard air at NTP conditions [15o C, 101.325 kPa, xw = 0 (as deviation results in Tables 3 & 4 describes the data distribution of these histogram plots. Note: Fig A3 of found from equn.18)], ρw is the actual density of pure water vapour, nws is the refractivity of pure water vapour Appendix shows the abnormal and unclean data. and ρws is the reference density of pure water vapour at o The measurements done using MSMD are the ba- NTP conditions [20 C, 1333 Pa, xw = 1 (as found from sic requirements for every site evaluation, because, the equn.20)]. If a new equation is derived by correlating equations site’s in-situ parameters such as dT (r, h), Tair (h) and (20) & (21) with equation (5), then, we can significantly P(h) are correlated to site’s altitude and are the funcimprove the accuracy and precision of seeing measuretions of equation (5). It is to be noted that the relaments. tive humidity (RH) factor is not a function in equation (5), because of the assumption of its significance is only for coastal areas and is negligible for higher altitudes. However, the Bengt Elden (1966), while, advancing his research findings on the Barrell & Sears formula (1939) for refraction and dispersion of air for the visible spectrum, has derived equations to demonstrate that the absolute refractivity of air and dispersion formula depends not just on temperature and pressure, but, also, on the contents of carbon dioxide (CO2 ) and water vapour (humidity). Under Normal Temperature and Pressure (NTP) conditions, he demonstrated that since, the refractivity of CO2 is about 50 % higher than that of air, while, that of water vapour (H2 O) is about 15 % lower than that of air, so, the contributions of these two parameters to the RI changes in the atmospheric air can not be neglected. Subsequently, several physicists derived several equations improving the accuracy and uncertainties of Bengt Elden’s equations. The Birch & Downs (1988) equation is often used, but, the Ciddor (1996) equation has been adopted by the International Association of Geodesy (IAG) as the standard equation for calculating the index of refraction of air and is believed to provide more accurate results under the more extreme temperature and humidity conditions of interest for geodetic surveying. The density of moist air ρ as derived by Ciddor (1996) is: Mw Pr ∗Ma (1 − xw ) 1 − (20) ρ= Z ∗R∗T Ma where, Pr (Pa) is the the total pressure of air, Ma = 10−3 [28.9635+12.011∗10−6 (xc −400)] kg/mol, is the molar mass of dry air containing xc ppm of CO2 , Z is the compressibility of the moist air, R = 8.31451 J-mol −1 K −1 , is the gas constant, T (K) is the air temperature, xw = f ∗h∗svp Pr , is the molar fraction of water vapour in moist air (Note: partial pressure of water vapour Prw = h*svp) , f = α + β ∗ Pr +γ ∗ t 2 , is the enhancement factor of water vapour in air, t = T-273.15, h is the fractional humidity (between 0 and 1), svp = exp(AT 2 +BT+C+ D T) is the saturation vapour pressure of water vapour in air at temperature T, over liquid water (if the vapour is over K. Dhananjay, Indian Institute of Astrophysics


Figure 31: Temporal evolution of Tair (h) for long duration observation


Page no.31


Figure 32: Temporal evolution of Tair (h) for short duration observation


Page no.32


Figure 33: Temporal evolution of Vdi f f (r, h) for long duration observation


Page no.33


Figure 34: Temporal evolution of Vdi f f (r, h) for short duration observation


Page no.34


Figure 35: Temporal evolution of dT (r, h) for long duration observation


Page no.35


Figure 36: Temporal evolution of dT (r, h) for short duration observation


Page no.36


Figure 37: Temporal evolution of CT2 (r, h) for long duration observation


Page no.37


Figure 38: Temporal evolution of CT2 (r, h) for short duration observation


Page no.38


Figure 39: Temporal evolution of CN2 (h) for long duration observation


Page no.39


Figure 40: Temporal evolution of CN2 (h) for short duration observation


Page no.40


Figure 41: Temporal evolution of ro(loc) (h1 , h2 ) for long duration observation


Page no.41


Figure 42: Temporal evolution of ro(loc) (h1 , h2 ) for short duration observation


Page no.42


Figure 43: Temporal evolution of ε(loc) (h1 , h2 ) for long duration observation


Page no.43


Figure 44: Temporal evolution of ε(loc) (h1 , h2 ) for short duration observation


Page no.44


Page no.45

Table 3: Seeing results obtained from the terrace floor of IIA (part-I) Observation date Parameter

15-16/Oct/2013

16-17/Oct/2013

17-18/10/2013

18-19/Oct/2013

19-20/Oct/2013

Mean

Med.

Std.Dev.

Mean

Med.

Std.Dev.

Mean

Med.

Std.Dev.

Mean

Med.

Std.Dev.

Mean

Med.

850

-

-

850

-

-

850

-

-

850

-

-

850

-

-

Vdi f f (1m, 3m) (o C)

0.00899

0.00885

0.00332

0.00884

0.00889

0.00247

-0.00164

-0.0019

0.00291

0.00556

-8.523E-4 0.01108

0.01088

0.00665

0.01285

Vdi f f (1m, 6m)

-0.00448 -0.0069

0.00773 -0.00253 6.926E-4 0.01048

-0.00246

-0.00157

0.00648

-0.00303

-0.00248

0.00434

0.01219

0.00597

0.01026

Vdi f f (1m, 9m)

0.00624

0.00629

0.00271

0.00635

0.00633

0.00207 -2.05155E-4 -3.026E-4 0.00213 -5.67908E-4 -4.355E-4 0.00264

-0.00649

-0.00156

0.0104

Vdi f f (1m, 12m)

0.00903

0.00955

0.00339

0.00822

0.0083

0.00234

0.00264 -6.85948E-4 0.00125

0.00549

P(h) (hPa) (assumed value)

0.00255

0.00329

6.401E-4 0.00377 8.92398E-4 7.025E-4 0.00247 -4.76091E-4 1.794E-6 0.00256

Vdi f f (1m, 15m)

-0.0083 -0.00878 0.00366 -0.00843 -0.00867 0.00266

0.00125

dT (1m, 3m) (o C)

1.00608

dT (1m, 6m)

0.9903

0.37129

0.98936

0.00619

0.003

0.00277

Std.Dev.

0.9957

0.27665

-0.18364

-0.2125

0.32566

0.62288

-0.09541

1.24027

1.21787

0.7442

1.43846

-0.50099 -0.7722

0.86517 -0.28317 0.07754

1.17295

-0.27537

-0.1757

0.72539

-0.33941

-0.2777

0.48618

1.36494

0.6682

1.14861

dT (1m, 9m)

0.69828

0.7045

0.30362

0.71065

0.7085

0.23196

-0.02297

-0.03388

0.23809

-0.06357

-0.04876

0.29606

-0.72671

-0.174

1.1641

dT (1m, 12m)

1.01142

1.069

0.37966

0.92011

0.9287

0.26249

0.2853

0.3685

0.69326

0.33612

0.3103

0.29609

-0.07679

0.1396

0.61456

dT (1m, 15m)

-0.92963 -0.9828

0.40925 -0.94364

-0.971

0.29788

0.14044

0.07166

0.4222

0.0999

0.07864

0.277

-0.0533

2 2 (1m, 3m) (K 2 − m− 3 ) CT

1.15

0.98

0.81

1.06

0.99

0.5

0.14

0.07

0.21

1.93

0.17

2.87

3.55

2.008E-4 0.28676 1.34

2 (1m, 6m) CT

1.0

0.67

1.32

1.46

0.74

1.59

0.6

0.09

1.1

0.35

0.1

0.76

3.18

0.47

3.4

2 (1m, 9m) CT

0.58

0.5

0.5

0.56

0.5

0.44

0.06

0.01

0.12

0.09

0.01

0.23

1.88

0.04

3.59

2 (1m, 12m) CT

1.17

1.15

0.57

0.92

0.87

0.38

0.56

0.16

1.54

0.2

0.1

0.42

0.38

0.15

0.48

2 (1m, 15m) CT 2 2 (3m) (m− 3 ) CN

1.03

0.97

0.58

0.98

0.95

0.37

0.2

0.01

0.92

0.09

0.01

0.24

0.09

0.01

0.21

6.21E-13 5.41E-13 4.17E-13 5.94E-13 5.63E-13 2.68E-13

3.03E-14

1.4E-14

4.33E-14

1.12E-12

9.64E-14 1.66E-12

2.2E-12

7.36E-13 2.14E-12

2 (6m) CN

5.46E-13 3.74E-13 6.96E-13 8.3E-13 4.16E-13 8.97E-13

4.26E-14

2.06E-14 5.72E-14

2.01E-13

5.85E-14 4.27E-13

1.99E-12

2.63E-13 2.14E-12

2 (9m) CN

3.15E-13 2.77E-13 2.71E-13 3.18E-13 2.87E-13 2.41E-13

4.01E-14

1.79E-14 5.84E-14

5.18E-14

7.81E-15

1.3E-13

7.27E-13

1.9E-14 1.37E-12

2 (12m) CN

6.41E-13 6.38E-13 3.06E-13 5.19E-13 4.93E-13 2.03E-13

1.69E-13

1.42E-13 1.24E-13

1.16E-13

5.84E-14 2.33E-13

2.37E-13

8.78E-14 2.98E-13

2 (15m) CN

5.56E-13 5.32E-13 3.04E-13 5.49E-13 5.33E-13 2.01E-13

8.5E-14

5.97E-14 8.67E-14

6.74E-15 1.26E-13

3.44

4.88E-14

6.1E-15

1.32E-13

5.04E-14

ro(loc) (3m, 6m) (00 )

6.96

5.91

4.21

6.17

5.74

2.43

33.27

21.7

62.77

29.34

18.78

63.7

12.26

6.32

ro(loc) (3m, 9m)

4.826

4.46

1.6

4.46

4.42

1.71

22.34

16.7

25.23

18.46

14.18

23.9

8.22

4.59

8.7

ro(loc) (3m, 12m)

3.55

3.43

0.84

3.41

3.5

0.95

13.59

11.88

10.17

12.62

11.92

10.83

7.0

4.0

6.89

ro(loc) (3m, 15m)

2.85

2.72

0.65

2.76

2.77

0.61

11.11

9.62

8.21

10.7

10.48

8.42

6.29

3.75

6.03

ro(loc) (6m, 9m)

9.2

8.4

10.91

8.07

7.8

4.06

59.78

30.77

125.4

50.1

27.68

96.15

16.77

11.57

26.1

ro(loc) (6m, 12m)

4.76

4.72

1.14

4.63

4.79

1.16

19.62

15.8

17.42

21.25

19.39

18.08

11.66

9.08

11.71

ro(loc) (6m, 15m)

3.44

3.32

0.83

3.39

3.4

0.6

14.65

11.77

12.52

16.4

15.22

12.01

9.74

7.56

9.11

ro(loc) (9m, 12m)

6.79

6.5

2.1

7.15

7.15

0.76

32.37

24.01

40.69

37.30

28.35

49.57

33.46

19.88

65.95

ro(loc) (9m, 15m)

4.3

4.01

1.6

4.39

4.38

0.6

20.6

15.78

20.75

23.73

18.95

22.46

20.53

13.03

29.7

ro(loc) (12m, 15m)

7.39

5.72

15.73

6.45

6.18

3.18

32.88

24.16

46.88

41.23

30.17

60.52

39.25

21.43

80.09

ε(loc) (3m, 6m) (00 )

1.69

1.71

0.61

1.89

1.76

0.72

0.76

0.47

0.73

1.42

0.54

1.54

3.1

1.6

2.59

ε(loc) (3m, 9m)

2.35

2.27

0.88

2.67

2.29

1.14

1.09

0.61

1.1

1.6

0.71

1.65

4.17

2.2

3.53

ε(loc) (3m, 12m)

3.02

2.95

0.83

3.24

2.88

1.05

1.41

0.85

1.27

1.78

0.85

1.67

4.52

2.53

3.82

ε(loc) (3m, 15m)

3.72

3.71

0.86

3.86

3.65

0.96

1.69

1.05

1.54

1.91

0.96

1.73

4.65

2.69

3.85

ε(loc) (6m, 9m)

1.37

1.2

0.67

1.61

1.3

0.83

0.67

0.33

0.73

0.55

0.37

0.57

2.31

0.87

2.14

ε(loc) (6m, 12m)

2.24

2.14

0.61

2.35

2.11

0.71

1.05

0.64

0.99

0.79

0.52

0.69

2.77

1.11

2.6

ε(loc) (6m, 15m)

3.06

3.05

0.65

3.09

2.98

0.63

1.37

0.86

1.34

0.97

0.66

0.83

2.95

1.34

2.65

ε(loc) (9m, 12m)

1.55

1.56

0.27

1.43

1.41

0.2

0.63

0.42

0.74

0.46

0.36

0.39

1.16

0.51

1.32

ε(loc) (9m, 15m)

2.5

2.52

0.54

2.34

2.3

0.34

1.02

0.64

1.18

0.69

0.53

0.59

1.44

0.78

1.4

ε(loc) (12m, 15m)

1.73

1.77

0.52

1.65

1.64

0.33

0.7

0.42

0.85

0.44

0.34

0.4

0.64

0.47

0.5

ε(MSMD)(tot) (3m, ∞) (00 ) B(equn. 11)

9.544

9.418

2.628

9.918

9.184

2.928

4.283

2.604

4.26

4.573

2.413

4.376

11.882

6.159

10.338

ε(MSMD)(tot) (6m, ∞)

6.24

6.156

1.625

6.243

5.898

1.584

2.731

1.673

2.898

1.957

1.386

1.735

5.881

2.589

5.512


3.78

3.825

0.879

3.545

3.498

0.57

1.538

0.967

1.81

1.04

0.804

0.901

2.153

1.155

2.177


1.73

1.77

0.52

1.65

1.64

0.33

0.7

0.42

0.85

0.44

0.34

0.4

0.64

0.47

0.5

ε(rel) (3m, 6m) (00 ) B(equn. 12)

9.221

9.086

2.487

9.538

8.829

2.755

4.137

2.512

4.124

4.171

2.292

3.898

11.106

5.76

9.708

ε(rel) (3m, 9m)

8.979

8.881

2.365

9.235

8.629

2.547

4.015

2.462

3.987

4.078

2.219

3.837

10.59

5.469

9.266

ε(rel) (3m, 12m)

8.676

8.577

2.389

8.965

8.362

2.597

3.866

2.354

3.91

3.977

2.149

3.826

10.396

5.278

9.109

ε(rel) (3m, 15m)

8.298

8.166

2.375

8.627

7.944

2.645

3.712

2.243

3.772

3.899

2.087

3.79

10.32

5.177

9.092

ε(rel) (6m, 9m)

9.317

9.235

2.463

9.628

8.97

2.708

4.165

2.554

4.124

4.492

2.349

4.288

11.411

6.017

9.882

ε(rel) (6m, 12m)

9.024

8.932

2.487

9.368

8.701

2.759

4.031

2.45

4.031

4.425

2.299

4.254

11.241

5.944

9.704

ε(rel) (6m, 15m)

8.657

8.527

2.471

9.04

8.312

2.79

3.886

2.349

3.877

4.363

2.242

4.21

11.169

5.864

9.683

ε(rel) (9m, 12m)

9.265

9.133

2.592

9.68

8.94

2.908

4.177

2.529

4.12

4.513

2.352

4.329

11.734

6.1

10.136

ε(rel) (9m, 15m)

8.916

8.776

2.514

9.372

8.625

2.879

4.043

2.45

3.952

4.455

2.295

4.282

11.67

6.04

10.115

ε(rel) (12m, 15m)

9.208

9.066

2.521

9.616

8.869

2.882

4.156

2.529

4.084

4.517

2.357

4.327

11.828

6.108

10.299


19.9


Page no.46

Table 4: Seeing results obtained from the terrace floor of IIA (part-II) Observation date

16/Oct/2013

Parameter

17/Oct/2013

Avg.of all

Mean

Med.

Std.Dev.

Mean

Med.

Std.Dev.

850

-

-

850

-

-

Vdi f f (1m, 3m) (V )

0.00903

0.00906

Vdi f f (1m, 6m)

-0.00445 -0.00697 0.00656

Vdi f f (1m, 9m)

0.00686

0.00692

0.00226

-0.00117

-0.00113 0.00215

0.001574 0.002302

Vdi f f (1m, 12m)

0.0079

0.00791

0.00198

0.00467

0.00461

0.00185

0.004955 0.005383 0.003411

Vdi f f (1m, 15m)

-0.00787 -0.00775 0.00209

-0.00301

-0.003

0.00196

-0.003706 -0.003837 0.002739

dT (1m, 3m) (o C)

1.01063

1.014

0.25363

0.10834

0.1067

0.21225

0.6816

0.5064

0.5883

dT (1m, 6m)

-0.49776

-0.7803

0.73399

0.17929

0.1733

0.21793

-0.05035

-0.15527

0.6295

dT (1m, 9m)

0.7677

0.7747

0.25304

-0.13089

-0.127

0.24089

0.0859

0.166

0.3897

dT (1m, 12m)

0.88428

0.8859

0.22163

0.52251

0.5155

0.20762

0.5547

0.6025

0.3822

dT (1m, 15m)

-0.88062

-0.8678

0.23405

-0.33643

-0.3361

0.20762

-0.4148

-0.4296

0.305

1.09

1.03

0.52

0.06

0.03

0.08

1.28

0.66

1.2

2 (1m, 6m) CT

0.79

0.66

0.69

0.07

0.04

0.1

1.06

0.4

1.28

2 (1m, 9m) CT

0.65

0.6

0.39

0.06

0.03

0.09

0.55

0.24

0.77

2 (1m, 12m) CT

0.83

0.78

0.4

0.28

0.24

0.21

0.62

0.49

0.57

2 (1m, 15m) CT 2 2 (3m) (m− 3 ) CN

0.83

0.75

0.43

0.13

0.09

0.14

0.48

0.4

0.41

6.02E-13 5.69E-13 2.86E-13

2 (6m) CN 2 (9m) CN

P(h) (hPa) (assumed value)

2 (1m, 3m) (K 2 − m CT

− 32

)

0.00227 9.67803E-4 9.536E-4 0.0016

0.00155

0.0019 0.00195

7.89E-14

4.15E-14 1.15E-13

4.39E-13 3.71E-13 3.85E-13

3.4E-13

3.66E-13 3.35E-13 2.2E-13

3.21E-14

2 (12m) CN

4.641E-13 4.38E-13 2.21E-13

2 (15m) CN

4.57E-13 4.14E-13 2.34E-13

Mean

Med.

Std.Dev.

0.0061

0.0045

0.00605

-0.000451 -0.000752 0.00683 0.00348

7.49E-13

3.66E-13 7.04E-13

5.14E-14 6.2E-13

6.27-13

2.22E-13 7.46E-13

7.17E-15 6.83E-14

2.64E-13

1.36E-13 3.37E-13

3.12E-13

9.45E-14 8.42E-13

3.51E-13

2.79E-13 3.18E-13

1.08E-13

6.34E-15 6.33E-13

2.65E-13

2.23E-13 2.45E-13

ro(loc) (3m, 6m) (00 )

7.22

5.76

3.24

80.06

43.75

195.98

13.73

15.42

50.32

ro(loc) (3m, 9m)

4.82

4.44

1.4

38.38

26.77

45.47

14.5

10.79

11.15

ro(loc) (3m, 12m)

3.65

3.53

0.69

15.79

14.12

8.53

8.52

7.48

5.56

ro(loc) (3m, 15m)

3.02

2.87

0.51

11.14

9.8

5.89

6.84

6.0

4.33

ro(loc) (6m, 9m)

8.4

7.97

3.11

72.38

39.39

242.54

32.1

19.08

72.61

ro(loc) (6m, 12m)

4.89

4.87

0.85

18.2

15.99

11.07

12.14

10.66

8.78

ro(loc) (6m, 15m)

3.67

3.6

0.48

12.17

10.52

7.06

9.07

7.91

6.09

ro(loc) (9m, 12m)

7.18

7.11

0.85

22.54

18.78

18.54

20.97

15.97

25.49

ro(loc) (9m, 15m)

4.66

4.63

0.74

13.81

11.38

10.46

13.15

10.31

12.33

ro(loc) (12m, 15m)

7.43

6.85

2.56

22.37

16.06

65.37

22.43

15.8

39.19

ε(loc) (3m, 6m) (00 )

1.6

1.75

0.47

0.29

0.23

0.21

1.54

1.15

0.98

ε(loc) (3m, 9m)

2.26

2.28

0.6

0.46

0.38

0.32

2.09

1.53

1.32

ε(loc) (3m, 12m)

2.86

2.86

0.53

0.81

0.72

0.4

2.52

1.95

1.37

ε(loc) (3m, 15m)

3.43

3.52

0.53

1.13

1.03

0.52

2.91

2.37

1.43

ε(loc) (6m, 9m)

1.36

1.27

0.47

0.31

0.26

0.22

1.17

0.8

0.8

ε(loc) (6m, 12m)

2.13

2.08

0.39

0.71

0.63

0.35

1.72

1.32

0.91

ε(loc) (6m, 15m)

2.8

2.81

0.35

1.04

0.97

0.48

2.18

1.81

0.99

ε(loc) (9m, 12m)

1.43

1.42

0.16

0.59

0.54

0.27

1.04

0.89

0.48

ε(loc) (9m, 15m)

2.22

2.19

0.36

0.95

0.89

0.43

1.59

1.41

0.69

ε(loc) (12m, 15m)

1.49

1.48

0.41

0.66

0.63

0.31

1.04

0.96

0.47

ε(MSMD)(tot) (3m, ∞) (00 ) B(equn. 11)

8.861

8.909

1.744

2.912

2.651

1.435

7.353

5.86

3.91


5.72

5.642

1.071

2.16

2.0

1.029

4.382

3.61

2.173


3.36

3.326

0.624

1.439

1.348

0.66

2.39

2.132

1.069


1.49

1.48

0.41

0.66

0.63

0.31

1.04

0.96

0.47

ε(rel) (3m, 6m) (00 ) B(equn. 12)

8.551

8.55

1.624

2.875

2.624

1.4

7.022

5.624

3.671

ε(rel) (3m, 9m)

8.304

8.346

1.56

2.831

2.588

1.363

6.797

5.477

3.512

ε(rel) (3m, 12m)

8.028

8.079

1.596

2.7

2.466

1.33

6.586

5.279

3.486

ε(rel) (3m, 15m)

7.718

7.718

1.596

2.535

2.307

1.27

6.367

5.044

3.453

ε(rel) (6m, 9m)

8.625

8.7

1.624

2.87

2.618

1.397

7.145

5.732

3.741

ε(rel) (6m, 12m)

8.358

8.427

1.656

2.742

2.503

1.351

6.954

5.562

3.7

ε(rel) (6m, 15m)

8.057

8.104

1.671

2.586

2.341

1.291

6.755

5.349

3.667

ε(rel) (9m, 12m)

8.605

8.657

1.724

2.788

2.537

1.381

7.183

5.707

3.839

ε(rel) (9m, 15m)

8.321

8.383

1.667

2.633

2.384

1.316

7.004

5.527

3.778

ε(rel) (12m, 15m)

8.586

8.638

1.649

2.762

2.503

1.367

7.183

5.686

3.841



Figure 45: CT2 (r, h) Log-normal fit histograms for long duration observation


Page no.47


Figure 46: CT2 (r, h) Log-normal fit histograms for short duration observation


Page no.48


0 .0 5

-1 3

9 .0 x 1 0

1 .8 x 1 0

2 .7 x 1 0

2

C

0 .0 5

2 .5 2 .0 1 .5 1 .0 5 .0

x 1 0 5 x 1 0 5 x 1 0 5 x 1 0 4 x 1 0 0 .0

2 .0 1 .5 1 .0 5 .0

x 1 0 5 x 1 0 5 x 1 0 4 x 1 0 0 .0

9 .0 x 1 0

-1 3

1 .8 x 1 0

-1 2

-1 2

2 .7 x 1 0

3 .6 x 1 0

0 .0

9 .0 x 1 0

-1 3

1 .8 x 1 0

-1 2

)

4 .5 x 1 0

-1 2

2

C

3 .6 x 1 0

(1 2 m N

-1 2

-1 2

(9 m N

2 .7 x 1 0

5 .4 x 1 0

-1 2

-1 2

)

-1 2

3 .6 x 1 0

0 .0

-1 2

5 x 1 4 x 1 3 x 1 2 x 1 1 x 1

1 .6 1 .2 8 .0 4 .0

1 7 -1 8 O c t. 2 0 1 3

2

C

2 .0 x 1 0

(1 5 m N

-1 3

2

C 5

0

N

5

0

-1 3

4 .0 x 1 0

5

0

)

(1 2 m

6 .0 x 1 0

-1 3

)

5

0 0

5

0 0 .0 6

-1 3

2 .0 x 1 0

2

C

0 .0

-1 3

4 .0 x 1 0

x 1 0 6 x 1 0 5 x 1 0 5 x 1 0 0 .0 2 .0 x 1 0

6 .0 x 1 0

(9 m N

-1 3

8 .0 x 1 0

-1 3

)

-1 3

-1 3

4 .0 x 1 0

-1 3

6 .0 x 1 0

C

2

5

0 .0

9 .0 x 1 0

-1 3

-1 2

1 .8 x 1 0

-1 2

2 .7 x 1 0

x 1 0 5 x 1 0 5 x 1 0 4 x 1 0 0 .0

C

0 .0

9 .0 x 1 0

-1 3

-1 2

1 .8 x 1 0 2

a l fit H is to g r a m

2 N

)

-1 2

4 .5 x 1 0

(3 m

2 .7 x 1 0

-2 /3

(h ) (m N

(6 m N

3 .6 x 1 0

D a ta c o u n t

5

-1 2

)

-1 2

3 .6 x 1 0

-1 2

1 .2 x 1 0

6

8 .0 x 1 0

5

4 .0 x 1 0 0 .0

5

0 .0 1 .6 1 .2 8 .0 4 .0

2

C

2 .0 x 1 0

-1 3

(6 m N

4 .0 x 1 0

)

-1 3

6 .0 x 1 0

-1 3

8 .0 x 1 0

-1 3

6 .0 x 1 0

-1 3

8 .0 x 1 0

-1 3

6

x 1 0 6 x 1 0 5 x 1 0 5 x 1 0 0 .0

2

C 0 .0

2 .0 x 1 0

-1 3

N

4 .0 x 1 0

)

2

C

(3 m

-2 /3

(h ) (m N

)

-1 3

)

1 5 -1 6 O c t. 2 0 1 3

5

1 .5 x 1 0

C

2

C

2

C

2

N

1 .0 x 1 0

5

N N

C

2

C

2

(3 m

)

(6 m

)

(9 m

)

(1 2 m N N

(1 5 m

D a ta c o u n t

D a ta c o u n t

-1 2

)


5

x 1 0 5 x 1 0 5 x 1 0 5 x 1 0 0 .0

6

1 .4 x 1 0

6

1 .2 x 1 0

6

1 .0 x 1 0

6

L o g -n o r m

1 .6 x 1 0


1 7 -1 8 O c t. 2 0 1 3

5

2 .0 x 1 0

5 .0 x 1 0

(1 5 m N

D a ta c o u n t

x 1 0 5 x 1 0 5 x 1 0 4 x 1 0 4 x 1 0 0 .0

L o g -n o r m 5

L o g -n o r m 8 .0 6 .0 4 .0 2 .0

D a ta c o u n t

2 .0 1 .6 1 .2 8 .0 4 .0

2

C

C

2 .5 x 1 0

1 5 -1 6 O c t. 2 0 1 3

D a ta c o u n t

x 1 0 5 x 1 0 5 x 1 0 4 x 1 0 0 .0

2 .0 1 .5 1 .0 5 .0


5

2 .0 1 .5 1 .0 5 .0

D a ta c o u n t

D a ta c o u n t

D a ta c o u n t

D a ta c o u n t

D a ta c o u n t

D a ta c o u n t

L o g -n o r m

Page no.49

)

8 .0 x 1 0

5

6 .0 x 1 0

5

)

4

0 .0

4 .0 x 1 0

5

2 .0 x 1 0

5

C

2

C

2

C

2

C

2

C

2

N N N

(3 m

)

(6 m

)

(9 m

)

(1 2 m N N

(1 5 m

) )

0 .0 0 .0

2 .0 x 1 0

C N

2

-1 2

(h ) (m

4 .0 x 1 0 -2 /3

-1 2

0 .0

2 .0 x 1 0

-1 3

)

4 .0 x 1 0

C N

2

-1 3

(h ) (m

6 .0 x 1 0 -2 /3

)

Figure 47: CN2 (h) Log-normal fit histograms for long duration observation


-1 3

8 .0 x 1 0

-1 3


L 7

x

1

0

5

5

x

1

0

5

D a ta c o u n t D a ta c o u n t D a ta c o u n t D a ta c o u n t D a ta c o u n t

6

x

0

5

0

5

1

4

x 3

1 x

o

r m

a

l

f i t

H

i s

t o

g

r a

2

0

N

1

0

5

6

x

1

0

5

5

x

1

0

5

4

x

1

0

5

D a ta c o u n t

x

3

x

0

0

1

x

0

. 0

1

0

m

)

O

c

t .

2

0

1

3

6

. 0

x

1

- 1

0

1

x

1

0

4

x

1

0

1

. 2

x

1

- 1

0

0

1

. 8

x

1

- 1

0

0

2

. 4

x

1

- 1

0

0

3

. 0

x

1

0

- 1

0

3

x

1

0

2

x

1

0

1

x

1

0

5

5

5

2

C 5

( 1 N

5

2

5

0 0 5

6

x

1

0

5

x

1

0

4

x

1

0

3

x

1

0

2

x

1

0

1

x

1

0

4

x

1

0

5

3

x

1

0

5 5

. 0 1

. 0

x

1

- 1

0

2

2

. 0

x

1

- 1

0

2

3

. 0

x

1

- 1

0

2

4

. 0

x

1

- 1

0

2

5

. 0

x

1

- 1

0

2

5 5

2

C 5

( 9 N

5

m

)

5

0 0

2

x

1

0

1

x

1

0

. 0 3

. 0

x

- 1

1

0

3

6

. 0

x

1

- 1

0

3

2

C

9

( 6 N

. 0

m

x

1

- 1

0

3

1

. 2

x

1

- 1

0

2

1

. 5

x

1

- 1

0

2

)

5

0 0

. 0 9

. 0

x

1

- 1

0

3

1

. 8

x

1

- 1

0

x

1

0

4

x

1

0

3

x

1

0

2

. 7

x

1

- 1

0

2

3

. 6

x

1

- 1

0

2

4

. 5

x

1

- 1

0

2

2

x

1

0

1

x

1

0

5

2

C 5 5

- n

( 3 N

m

)

5

0 0

g

2

5

5

. 0 3

. 0

x

1

o

r m

a

l

f i t

- 1

0

H

3

i s

C

2

C

6

. 0

x

2

C

2

C

2

C

2

t o

N N N

5

1

x

o

)

7

m

0

5

1

2

L

1

5

5

1

1

- 1

0

3

N N

g

9

2

C

7

m

( 1

5

1 x

- n

C

0

x 1

g

5

1

2

o

Page no.50

r a

( 3

m

)

( 6

m

)

( 9

m

( 1

2

m

)

( 1

5

m

)

. 0

( h N

x

1

)

- 1

0

3

1

m

1

( m

- 2

. 2

- 2

( m

7

/ 3

x

1

- 1

0

2

1

. 5

x

1

0

- 1

. 0

x

2

1

. 8

x

1

0

- 1

2

O

)

c

t .

2

0

1

3

)

5

0

0 0

. 0 5

. 0

x

1

0

- 1

1

1

. 0

x

C

1

0 N

2

- 1

( h

0

1

)

. 5 / 3

x

1

0

- 1

0

2

1

0

- 1

0

2

. 5

x

)

Figure 48: CN2 (h) Log-normal fit histograms for short duration observation


1

0

- 1

0


Figure 49: ro(loc) (h1 , h2 ) Log-normal fit histograms for long duration observation


Page no.51


Figure 50: ro(loc) (h1 , h2 ) Log-normal fit histograms for short duration observation


Page no.52


Figure 51: ε(loc) (h1 , h2 ) Log-normal fit histograms for long duration observation


Page no.53


Figure 52: ε(loc) (h1 , h2 ) Log-normal fit histograms for short duration observation


Page no.54


Page no.55

5.1 Coherence length ratio (CLR)

Table 5: CLR, SD and SIR results

The percentage contributions of local SLs (3 to 15 m) to the total atmospheric optical turbulence can be estimated using a factor known as CLR, given by [Martin et al. (2000)]: −5

CLR(%) =

3 (hmin , hmax ) ro(loc)

− 53

(22)

ro(tot) (hmin , FA) here, ro(loc) (hmin , hmax ) (cm) and ro(tot) (hmin , FA) (cm) are the mean coherence lengths as measured by MSMD. The calculated values of CLR are tabulated in Table (5). The contribution of 3 to 15 m layers is 11.1 %.

Parameter (Y:2013)

15-16/10 16/10 16-17/10 17/10 17-18/10 18-19/10 19-20/10 Avg.of all

CLR (%)B(equn.22)

5.2

5.25

13.22

13.86

28.10

5.07

6.99

SD (%)B(equn.23)

3.15

3.18

8.16

8.56

17.96

3.07

4.25

11.1 6.9

SIRSL (6 m)(%)B(equn.24)

11.06

12.5

11.83

33.4

23.89

11.46

4.86

15.57

SIRSL (9 m)

21.22

25.94

26.14

45.71

50.5

22.97

9.89

28.91

SIRSL (12 m)

36.83

39.95

41.07

58.56

69.57

39.36

27.58

44.7

SIRBL (6 m)(%)B(equn.25)

2.51

2.77

2.71

6.52

4.63

2.55

1.18

3.27

SIRBL (9 m)

4.22

4.84

5.0

7.69

7.11

4.41

2.25

5.07

SIRBL (12 m)

6.05

6.3

6.55

8.45

7.86

6.19

5.01

6.63

SIRtot (6 m)(%)B(equn.26)

22.5

24.25

23.66

39.91

34.43

23.1

16.41

26.32

SIRtot (9 m)

42.63

46.06

45.91

58.88

64.12

44.11

34.49

48.03

SIRtot (12 m)

64.11

65.91

66.27

75.46

82.67

65.69

58.96

68.44

Sensor transition metal physics

5.2 Seeing degradation (SD)

To estimate the percentage contributions of seeing lim- .1 TI ‘I’ ited images in context with the diffraction limited images as discussed in § 3, we have a factor known as SD as It is the physical property of the transition metal, that offers impedance to the temperature change (the reintroduced by Martin et al. (2000): sponse time). In other words, it is a measure of the ther3 (23) mal mass and thermal wave velocity which controls the SD(%) = [1 − (1 −CLR) 5 ] surface of the transition metal and is defined as [MarThe calculated values of SD are tabulated in Table (5). ciak et al. (1996)]: √ The percentage contribution of the diffraction limited (no (27) I = κt ∗ ρd ∗ c optical turbulence) images to distort the quality of the image is 6.9 %, whereas, that of the seeing limited im- here, κt is the thermal conductivity (TC), ρd is the denages, it is 93.1 %. sity (D) of the transition metal and c is the specific heat capacity (SHC) of an transition metal [for units and calculated values of I, refer Table (A1)]. 5.3 Seeing improvement ratio (SIR) To estimate the percentage decrease in optical turbu.2 TCR ‘α’ lence over height, a factor known as SIR with respect to SL, BL and FA is introduced as: It is the amount of change in resistance of the transition metal, for a given change in temperature, which is 3 5 ε(loc) (hi , hmax ) defined in the National Bureau of Standards Handbook SIRSL (hi )(%) = 1 − 3 (24) 100 (Copper Wire Tables) as: 5 ε(loc) (hmin , hmax ) R = Rre f [1 + α (T − Tre f )] (28) − 53 ε(rel) (hi , hmax ) SIRBL (hi )(%) = 1 − 3 −5 (hmin , hmax ) ε(rel) 3 5 ε(tot) (hi , hFA ) SIR(tot) (hi )(%) = 1 − 3 5 ε(tot) (hmin , hFA )

here, R (Ω) is the sensor wire’s resistance at tempera(25) ture T (oC), Rre f ≈ 100Ω is the sensor wire’s resistance at Tre f ≈ 0 oC, which is the reference temperature at which the α constant for the transition metal is defined. The TCR values (at ≈ 20 oC) of various sensor transition (26) metals are shown in Table (A1).

here, hmin =3 m hi =6 m, 9 m & 12 m; hmax =15 m and .3 The time taken for heat conduction ‘th ’ FA=∞. To conduct heat, through a cylindrical transition metal, The data from Tables 3 & 4 are referred to calcuthe expression is:7 late the SIR values in Table (5). SIR values help us to choose a optimal height for the telescope mount. Qh κt Ac (Thot − Tcold ) = (29) th d Acknowledgements

here, Qh (W=J/s) is the rate of heat flow, κt is the thermal conductivity, Ac (m2 ) is the cross-sectional area, This report is dedicated to all students of IIA. Correct- Thot (oC) is the temperature at hot junction, Tcold (oC) is ing the report by Prof. Das, B.P., is thankfully acknowl- the temperature at cold junction and d (m) is the diamedged. eter. From this, we can note that the time is directly proportional to the diameter of the wire. [Appendix]

7 http://www.engineersedge.com/heat_transfer/conduction_cylidrical_coor.htm



Page no.56

Figure 53: Fig (A1): Comparison of RTDs: Cu-RTD is most linear and Ni-RTD is fastest responsive among all RTDs



.4 The time constant ‘τ’ and response time ‘t’ The time constant τ and the response time ‘t’ of the TS can also be defined using linear differential equation for thermal response by invoking the law of conservation of energy as (Weeks et al. 1988): dTs 1 [Ta + ∆U(t)] − Ts = 0 dt τ

Page no.57

the sensor transition metal and time constant ‘τ’ can be related by the equation 8 :

τ=f

dw1.5 ρg ∗V

(36)

(30)

here, Ts (oC) is the sensor temperature, t (s) is the time, τ (watt-sec/ o C), Ta (oC) is the ambient temperature, ∆ is the delta increase in temperature due to the step input of heat flux, U(t) is the unit step function of heat wave

here, f is a dimensionless proportionality constant, dw (m) is the diameter of the wire, ρg (kg − m−3 ) is the density of gas/fluid and V (m/s) is the velocity of gas/fluid. To understand the concept, let us assume f = 1, ρg of air at sea level = 1.29 kg-m−3 and V = 5 m/s, c (31) then for various diameters of the sensor transition τ= h0 S0 metal, the values of τ can be calculated as shown in here, c is the specific heat capacity of the transition Table (A2). metal, h0 is the convection heat transfer coefficient and S0 (m2 ) is the surface area of the sensor. The sensor’s frequency response equation (7) can be rewritten using the Laplace transform as: Ts (ω) 1 = ∆ (1 + iω τ)

RTD

(32)

here, ω = 2π f and the equation (8) follows the pattern of a first order LPF, that is the response drops at a rate of 20 dB per decade at 3 dB cut-off, the equation (8) can therefore be re-written as ω3dB =

1 h0 S0 = τ c

(33)

here ω3dB is the 3 dB point of the sensor’s response to U(t) The convective heat transfer relation is given by κ = h0 S0 (Ts − Tc )

Thermal cond. ‘κt ’ Density ‘ρd ’ Specific heat cap. ‘c’

TCR ‘α’

(W-m−1 -K−1 )

(kg-m−3 )

(J-kg−1 -K−1 )

Nickel (Ni)

99.0

8.906 × 103

445.9

19827.94

0.0064136

Tungsten (W)

180.0

19.35 × 103

134.4

21635.97

0.0045203

Copper (Cu)

386.0

8.954 × 103

380.0

36240.48

0.00393

Aluminium (Al)

220.0

2.707 × 103

896.0

23099.87

0.0039003

Platinum (Pt)

71.6

21.46 × 103

130.0

14133.28

0.00385

Silver (Ag)

418.0

10.51 × 103

230.0

31787.28

0.0038460

Gold (Au)

318.0

18.9 × 103

130.0

27952.21

0.0034392

Table-A1: Electrical properties of transition metals

(34)

here, κ (W ) is the rate of heat loss and Tc (oC) is the convection temperature, comparing and simplifying the equations (9) & (10), we can write as 1 κ ω3dB = = τ c (Ts − Tc )

TI ‘I’

−1 (J-m−2 -K−1 -s 2 ) (Ω-o C−1 )

(symbol)

dw

d 1.5 τ = f ρwV g

(µm) (watt − sec/ o C)

(35)

50

54.81

40

39.22

30

25.48

25

19.38

With the aid of a square wave generator (or optically 20 13.87 chopped laser beam), a heat pulse (air jet) is generated 15 9 and modulated sinusoidally with the sensor’s frequency 10 4.9 response. The velocity of the air jet, changes the width 5 1.73 of the pulse and its corresponding sensor’s response is 1 0.16 analysed through the spectrum analyser in the laboratory. The response time t is the time taken by sensor to reach 99.99 % of the amplitude of the heat pulse U(t) Table-A2: Wire diameter vs time constant of RTD and is ≈ 4.6τ. Also, the time constant τ is the time taken transition metals by sensor to reach 63.2% of the amplitude of the heat pulse U(t) and is ≈ τ (refer Figure 15 of Appendix A). We did not have adequate facilities in the laboratory for this experiment, hence could not perform it.

.5 Significance of sensor diameter On the basis of well known Stokes law and within the framework of a semi-empirical theory, the diameter of

8 http://www.ariindustries.com/rtds/rtd_information.php3



Page no.58

Figure 54: Fig (A2): Measurement of time constant ‘τ’ and response time ‘t’ of a sensor Table-A3: Electrical properties of transition metals

Refer:http://www.goodfellow.com/catalogue/ ____________________________________________________________________ Material TCR “α” (Ω/K) Resistivity (µΩ/K) ____________________________________________________________________ o Aluminum (Al) 0.0045 @ (0-100) C 2.67 @ 20 oC Antimony (Sb) 0.0051 @ (0-100) oC 40.1 @ 20 oC Arsenic (As) 33.3 @ 20 oC Beryllium (Be) 0.0090 @ (0-100) oC 3.3 @ 20 oC o Bismuth (Bi) 0.0046 @ (0-100) C 117 @ 20 oC Boron (B) 1.8E+12 @ 27 oC Cadmium (Cd) 0.0043 @ (0-100) oC 7.3 @ 20 oC Calcium (Ca) 0.00457 @ (0-100) oC 3.7 @ 20 oC Carbon (C) 1375 @ 0 oC o Cerium (Ce) 0.0087 @ (0-100) C 85.4 @ 20 oC Cesium (Cs) 0.0044 @ (0-100) oC 20 @ 20 oC o Chromium (Cr) 0.00214 @ (0-100) C 13.2 @ 20 oC o Cobalt (Co) 0.0066 @ (0-100) C 6.34 @ 20 oC Copper (Cu) 0.0043 @ (0-100) oC 1.69 @ 20 oC Dysprosium (Dy) 0.0012 @ (0-100) oC 91 @ 20 oC o Erbium (Er) 0.00201 @ (0-100) C 86 @ 20 oC o Europium (Eu) 0.0048 @ (0-100) C 90.0 @ 25 oC Gadolinium (Gd) 0.00176 @ (0-100) oC 134 @ 20 oC Gallium (Ga) 0.004 @ (0-100) oC 15.5 @ 20 oC Germanium (Ge) 46E+06 @ 22 oC o Gold (Au) 0.0040 @ (0-100) C 2.20 @ 20 oC Hafnium (Hf) 0.0044 @ (0-100) oC 32.2 @ 20 oC Holmium (Ho) 0.00171 @ (0-100) oC 94 @ 20 oC o Indium (In) 0.0052 @ (0-100) C 8.8 @ 20 oC o Iridium (Ir) 0.0045 @ (0-100) C 5.1 @ 20 oC Iron (Fe) 0.0065 @ (0-100) oC 10.1 @ 20 oC Lanthanum (La) 0.00218 @ (0-100) oC 57 @ 20 oC o Lead (Pb) 0.0042 @ (0-100) C 20.6 @ 20 oC o Lithium (Li) 0.00435 @ (0-100) C 9.29 @ 20 oC Lutetium (Lu) 0.0024 @ (0-100) oC 68 @ 20 oC Magnesium (Mg) 0.00425 @ (0-100) oC 4.2 @ 20 oC Manganese (Mn) 160 @ 20 oC o Mercury (Hg) 0.001 @ (0-100) C 95.9 @ 20 oC Molybdenum (Mo) 0.00435 @ (0-100) oC 5.7 @ 20 oC Neodymium (Nd) 0.00164 @ (0-100) oC 64 @ 20 oC o Nickel (Ni) 0.0068 @ (0-100) C 6.9 @ 20 oC o Niobium (Nb) 0.0026 @ (0-100) C 16 @ 20 oC Osmium (Os) 0.0041 @ (0-100) oC 8.8 @ 20 oC Palladium (Pd) 0.0042 @ (0-100) oC 10.8 @ 20 oC o Platinum (Pt) 0.00392 @ (0-100) C 10.58 @ 20 oC o Potassium (K) 0.0057 @ (0-100) C 6.8 @ 20 oC Praseodymium (Pr) 0.00171 @ (0-100) oC 68 @ 20 oC o Rhenium (Re) 0.0045 @ (0-100) C 18.7 @ 20 oC o Rhodium (Rh) 0.0044 @ (0-100) C 4.7 @ 20 oC Rubidium (Rb) 0.0048 @ (0-100) oC 12.1 @ 20 oC Samarium (Sm) 0.00148 @ (0-100) oC 92 @ 20 oC o Scandium (Sc) 0.00282 @ (0-100) C 66 @ 20 oC Selenium (Se) 12 @ 20 oC Silicon (Si) 23E+1O @ 20 oC Silver (Ag) 0.0041 @ (0-100) oC 1.63 @ 20 oC o Sodium (Na) 0.0055 @ (0-100) C 4.9 @ 27 oC o Tantalum (Ta) 0.0035 @ (0-100) C 13.5 @ 20 oC Tellurium (Te) 1.6E+5 @0 oC Terbium (Tb) 116 @ 20 oC o Thallium (Tl) 0.0052 @ (0-100) C 16.6 @ 20 oC o Thorium (Th) 0.0040 @ (0-100) C 14.0 @ 20 oC Thulium (Tm) 0.00195 @ (0-100) oC 90 @ 20 oC Tin (Sn) 0.0046 @ (0-100) oC 12.6 @ 20 oC o Titanium (Ti) 0.0038 @ (0-100) C 54 @ 20 oC o Tungsten (W) 0.0048 @ (0-100) C 5.4 @ 20 oC Uranium (U) 0.0034 @ (0-100) oC 27 @ 20 oC Vanadium (V) 0.0039 @ (0-100) oC 19.6 @ 20 oC o Ytterbium (Yb) 0.0013 @ (0-100) C 28 @ 20 oC o Yttrium (Y) 0.00271 @ (0-100) C 53 @ 20 oC Zinc (Zn) 0.0042 @ (0-100) oC 5.96 @ 20 oC Zirconium (Zr) 0.0044 @ (0-100) oC 44 @ 20 oC



Page no.59

[Appendix]

Technical Information Data Bulletin T E M P E R A T U R E & P R O C E S S I N S T R U M E N T S I N C

Copper 100 Ohms (Cu100) α 0.00427 Temperature vs Resistance Table Resistance @ 0°C Temperature Range: -140 to 500°F -100 to 260°C

Temp -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Temp 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

0 56.757 61.166 65.558 69.932 74.289 78.629 82.903 87.177 91.451 95.726 100.000 0 100.000 104.274 108.549 112.823 117.097 121.372 125.646 129.920 134.194 138.469 142.743 147.017 151.292 155.566 159.840 164.114 168.425 172.736 177.048 181.361 185.675 189.990 194.305 198.621 202.938 207.256 211.574

-1

-2

-3

-4

-5

-6

-7

-8

-9

60.726 65.120 69.496 73.854 78.195 82.475 86.750 91.024 95.298 99.573 1 100.427 104.702 108.976 113.250 117.525 121.799 126.073 130.348 134.622 138.896 143.170 147.445 151.719 155.993 160.268 164.546 168.856 173.167 177.480 181.793 186.106 190.421 194.736 199.053 203.370 207.687

60.286 64.681 69.059 73.419 77.762 82.048 86.322 90.597 94.871 99.145 2 100.855 105.129 109.403 113.678 117.952 122.226 126.501 130.775 135.049 139.324 143.598 147.872 152.146 156.421 160.695 164.977 169.287 173.599 177.911 182.224 186.538 190.853 195.168 199.484 203.801 208.119

59.845 64.242 68.622 72.984 77.329 81.621 85.895 90.169 94.443 98.718 3 101.282 105.557 109.831 114.105 118.379 122.654 126.928 131.202 135.477 139.751 144.025 148.300 152.574 156.848 161.122 165.408 169.718 174.030 178.342 182.655 186.969 191.284 195.600 199.916 204.233 208.551

59.405 63.803 68.185 72.549 76.895 81.193 85.467 89.742 94.016 98.290 4 101.710 105.984 110.258 114.533 118.807 123.081 127.356 131.630 135.904 140.178 144.453 148.727 153.001 157.276 161.550 165.839 170.149 174.461 178.773 183.087 187.401 191.716 196.031 200.348 204.665 208.983

58.964 63.364 67.747 72.113 76.461 80.766 85.040 89.314 93.589 97.863 5 102.137 106.411 110.686 114.960 119.234 123.509 127.783 132.057 136.332 140.606 144.880 149.154 153.429 157.703 161.977 166.270 170.581 174.892 179.205 183.518 187.832 192.147 196.463 200.779 205.097 209.415

58.523 62.925 67.310 71.677 76.027 80.338 84.613 88.887 93.161 97.435 6 102.565 106.839 111.113 115.387 119.662 123.936 128.210 132.485 136.759 141.033 145.308 149.582 153.856 158.130 162.405 166.701 171.012 175.323 179.636 183.949 188.264 192.579 196.894 201.211 205.528 209.847

58.082 62.486 66.872 71.241 75.593 79.911 84.185 88.459 92.734 97.008 7 102.992 107.266 111.541 115.815 120.089 124.364 128.638 132.912 137.186 141.461 145.735 150.009 154.284 158.558 162.832 167.132 171.443 175.755 180.067 184.381 188.695 193.010 197.326 201.643 205.960 210.278

57.640 62.046 66.434 70.805 75.158 79.483 83.758 88.032 92.306 96.581 8 103.419 107.694 111.968 116.242 120.517 124.791 129.065 133.340 137.614 141.888 146.162 150.437 154.711 158.985 163.260 167.563 171.874 176.186 180.499 184.812 189.127 193.442 197.758 202.074 206.392 210.710

57.199 61.606 65.996 70.369 74.724 79.056 83.330 87.605 91.879 96.153 9 103.847 108.121 112.395 116.670 120.944 125.218 129.493 133.767 138.041 142.316 146.590 150.864 155.138 159.413 163.687 167.994 172.305 176.617 180.930 185.244 189.558 193.873 198.189 202.506 206.824 211.142

PTC-8010 Precision Universal Thermocouple and RTD Temperature Calibrator Features • Measure or Simulate RTD Types: Pt 385 (100, 200, 500, 1000 ohms) Pt 392, JIS, Ni 120, CU10, • Measure or Simulate Ten (10) T/C types plus YSI 400 Thermistors • Read and source modes • NEMA 4 rated case, rugged design • RTD simulation works with all pulsed (smart) transmitters • New ClearBrite High Graphic Display • 3 Key Martel Menu System • Store up to nine (9) setpoints for each output function • RS232 interface Temperature & Process Instruments Inc. Visit us on the web at www.tnp-instruments.com 1767 Central Avenue * Suite 112 * Yonkers * NY * USA * 10710 * Phone: (800) 555-1212 Fax: (866) 292-1456

Table-A4: Resistance v/s temperature table for Cu-10Ω RTD



Page no.60

[Appendix]

The limits of electrical resistance are derived from the calculations made in IEC standard 317-0-1 Annex C.1 “Method for the calculation of linear resistance” for copper wire. Nom. AWG Diameter [mm] 0.0098 58 0.0101 0.0109 57 0.0113 0.0120 0.0125 56 0.0130 55.5 0.0135 55 0.0140 0.0145 54.5 0.0155 54 0.0160 0.0165 53.5 0.0170 0.0175 53 0.0180 0.0185 52.5 0.0190 0.0195 52 0.0200 0.0210 51.5 0.0215 0.0220 51 0.0230 50.5 0.0240 0.0245 50 0.0250 0.0260 49.5 0.0270 0.0275 49 0.0280 0.0290 48.5 0.0300 0.0310 48 0.0320 0.0330 47.5 0.0340 0.0350 47 0.0360 0.0370 46.5 0.0380 0.0381 46.1 0.0390 46.0 0.0400 0.0410 45.5 0.0420

Min

Nominal

Max

[Ω/m] 204.0 192.0 164.9 153.4 136.0 125.4 115.9 107.5 99.94 93.17 81.53 76.52 71.95 67.78 63.96 60.46 57.23 54.26 51.51 48.97 44.42 42.38 40.47 37.03 34.01 32.63 31.34 28.98 26.87 25.90 24.99 23.29 21.76 20.38 19.13 18.05 17.00 16.04 15.16 14.36 13.61 13.54 12.92 12.28 11.69 11.14

[Ω/m] 226.6 213.4 183.2 170.5 151.1 139.3 128.8 119.4 111.0 103.5 90.59 85.02 79.94 75.31 71.07 67.18 63.59 60.29 57.24 54.41 49.35 47.08 44.97 41.14 37.79 36.26 34.82 32.20 29.86 28.78 27.76 25.88 24.18 22.65 21.25 19.99 18.83 17.77 16.79 15.90 15.07 14.99 14.31 13.60 12.95 12.34

[Ω/m] 249.3 234.7 201.5 187.5 166.3 153.2 141.7 131.4 122.1 113.9 99.65 93.52 87.94 82.84 78.18 73.89 69.95 66.32 62.96 59.85 54.29 51.79 49.47 45.26 41.56 39.89 38.31 35.42 32.84 31.66 30.54 28.47 26.60 24.91 23.38 21.92 20.65 19.49 18.42 17.44 16.53 16.45 15.70 14.92 14.20 13.54

September 2009

Nom. AWG Diameter [mm] 0.0430 0.0437 0.0440 45 0.0450 0.0460 0.0470 44.5 0.0480 0.0490 0.0500 44 0.0520 43.5 0.0530 0.0550 43 0.0560 0.0580 0.0600 42.5 0.0620 0.0630 42 0.0650 41.5 0.0670 0.0680 0.0700 41 0.0710 0.0740 0.0750 40.5 0.0780 40 0.0800 0.0830 39.5 0.0850 0.0880 39 0.0900 0.0930 38.5 0.0950 0.1000 0.101 38.0 0.106 37.5 0.110 0.112 0.113 37 0.115 0.118 36.5 0.120 0.125 0.126 36 0.130 0.132 0.134 35.5

Min

Nominal

Max

[Ω/m] 10.63 10.29 10.15 9.705 9.360 8.966 8.596 8.249 7.922 7.325 7.051 6.547 6.316 5.952 5.562 5.209 5.045 4.667 4.404 4.281 4.050 3.941 3.640 3.547 3.289 3.133 2.918 2.787 2.606 2.495 2.342 2.247 2.034 1.995 1.816 1.690 1.632 1.604 1.550 1.474 1.426 1.317 1.297 1.220 1.184 1.150

[Ω/m] 11.77 11.40 11.24 10.75 10.29 9.853 9.447 9.065 8.706 8.049 7.748 7.195 6.940 6.470 6.046 5.662 5.484 5.151 4.848 4.707 4.442 4.318 3.975 3.869 3.577 3.401 3.159 3.012 2.811 2.687 2.516 2.412 2.176 2.134 1.937 1.799 1.735 1.705 1.646 1.563 1.511 1.393 1.371 1.288 1.249 1.212

[Ω/m] 12.91 12.50 12.33 11.79 11.21 10.74 10.30 9.881 9.489 8.774 8.446 7.843 7.565 6.988 6.529 6.115 5.922 5.711 5.359 5.196 4.890 4.747 4.355 4.235 3.903 3.703 3.430 3.265 3.038 2.900 2.710 2.594 2.333 2.286 2.069 1.917 1.848 1.814 1.750 1.660 1.604 1.475 1.451 1.361 1.319 1.279

1

Table-A5: Resistance v/s wire diameter table for Cu


www.elektrisola.com

Cu Copper

Electrical Resistance


Page no.61

[Appendix]

Technical Information Data Bulletin T E M P E R A T U R E & P R O C E S S I N S T R U M E N T S

Nickel 100 Ohms α 0.00618 Temperature vs Resistance Table Resistance @ 0°C Temperature Range: -76 to 356°F -60 to 180°C

Temp -60 -50 -40 -30 -20 -10 0 Temp 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 69.520 74.255 79.131 84.146 89.296 94.582 100.000 0 100.000 105.552 111.236 117.056 123.011 129.105 135.340 141.721 148.251 154.936 161.781 168.792 175.978 183.345 190.902 198.658 206.622 214.806 223.221

-1

-2

-3

-4

-5

-6

-7

-8

-9

73.775 78.637 83.638 88.775 94.047 99.452 1 100.549 106.114 111.812 117.645 123.614 129.722 135.972 142.367 148.912 155.613 162.474 169.503 176.706 184.092 191.668 199.444 207.431 215.637

73.297 78.145 83.132 88.256 93.514 98.906 2 101.100 106.678 112.390 118.236 124.219 130.341 136.605 143.015 149.575 156.292 163.169 170.215 177.436 184.841 192.437 200.233 208.241 216.470

72.820 77.654 82.627 87.737 92.982 98.361 3 101.651 107.243 112.968 118.828 124.825 130.961 137.239 143.664 150.240 156.972 163.866 170.929 178.168 185.591 193.207 201.025 209.054 217.306

72.344 77.164 82.124 87.220 92.451 97.817 4 102.205 107.809 113.548 119.421 125.432 131.582 137.875 144.315 150.906 157.654 164.565 171.645 178.902 186.344 193.980 201.818 209.869 218.144

71.870 76.676 81.621 86.704 91.922 97.274 5 102.759 108.377 114.129 120.016 126.041 132.205 138.512 144.967 151.574 158.338 165.265 172.363 179.638 187.099 194.754 202.613 210.686 218.984

71.397 76.189 81.121 86.190 91.394 96.733 6 103.315 108.946 114.712 120.613 126.651 132.829 139.151 145.621 152.243 159.023 165.967 173.082 180.376 187.855 195.531 203.411 211.506 219.826

70.926 75.703 80.621 85.677 90.868 96.193 7 103.872 109.517 115.296 121.210 127.262 133.455 139.791 146.276 152.914 159.710 166.671 173.803 181.115 188.614 196.309 204.210 212.327 220.671

70.456 75.219 80.123 85.165 90.343 95.655 8 104.431 110.089 115.881 121.809 127.875 134.082 140.433 146.933 153.586 160.398 167.376 174.526 181.856 189.375 197.090 205.012 213.151 221.519

69.987 74.736 79.627 84.655 89.819 95.117 9 104.990 110.662 116.468 122.409 128.489 134.710 141.076 147.591 154.260 161.089 168.083 175.251 182.600 190.137 197.873 205.816 213.978 222.368

PTC-8010 Precision Universal Thermocouple and RTD Temperature Calibrator Features • Measure or Simulate RTD Types: Pt 385 (100, 200, 500, 1000 ohms) Pt 392, JIS, Ni 120, CU10, • Measure or Simulate Ten (10) T/C types plus YSI 400 Thermistors • Read and source modes • NEMA 4 rated case, rugged design • RTD simulation works with all pulsed (smart) transmitters • New ClearBrite High Graphic Display • 3 Key Martel Menu System • Store up to nine (9) setpoints for each output function • RS232 interface

I N C Temperature & Process Instruments Inc. Visit us on the web at www.tnp-instruments.com 1767 Central Avenue * Suite 112 * Yonkers * NY * USA * 10710 * Phone: (914) 673-0333 Fax: (866) 292-1456

Table-A6: Resistance v/s temperature table Ni-100Ω RTD



Page no.62

[Appendix]

The limits of electrical resistance are derived from the calculations made in IEC standard 317-0-1 Annex C.1 “Method for the calculation of linear resistance” for copper wire and are restricted by a factor of 2. Nom. AWG Diameter [mm] 0.0098 58 0.0101 0.0109 57 0.0113 0.0120 0.0125 56 0.0130 55.5 0.0135 55 0.0140 0.0145 54.5 0.0155 54 0.0160 0.0165 53.5 0.0170 0.0175 53 0.0180 0.0185 52.5 0.0190 0.0195 52 0.0200 0.0210 51.5 0.0215 0.0220 51 0.0230 50.5 0.0240 0.0245 50 0.0250 0.0260 49.5 0.0270 0.0275 49 0.0280 0.0290 48.5 0.0300 0.0310 48 0.0320 0.0330 47.5 0.0340 0.0350 47 0.0360 0.0370 46.5 0.0380 0.0381 46.1 0.0390 46.0 0.0400 0.0410 45.5 0.0420

Min

Nominal

Max

[Ω/m] 1086 1022 878 817 724 667 617 572 532 496 434 407 383 361 340 322 305 289 274 261 236 226 215 197 181 174 166.8 154.3 143.0 137.9 133.0 124.0 115.9 108.5 101.8 95.9 90.3 85.3 80.6 76.3 72.3 71.9 68.7 65.3 62.1 59.2

[Ω/m] 1143 1076 924 860 762 702 649 602 560 522 457 429 403 380 358 339 321 304 289 274 249 237 227 207 191 183 176 162.4 150.6 145.1 140.0 130.5 122.0 114.2 107.2 100.8 94.9 89.6 84.7 80.2 76.0 75.6 72.2 68.6 65.3 62.2

[Ω/m] 1200 1130 970 903 800 738 682 632 588 548 480 450 423 399 376 356 337 319 303 288 261 249 238 218 200 192 184 170.5 158.1 152.4 147.0 137.0 128.1 119.9 112.5 105.7 99.6 93.9 88.8 84.1 79.7 79.3 75.7 71.9 68.5 65.2

November 2011

Nom. AWG Diameter [mm] 0.0430 0.0437 0.0440 45 0.0450 0.0460 0.0470 44.5 0.0480 0.0490 0.0500 44 0.0520 43.5 0.0530 0.0550 43 0.0560 0.0580 0.0600 42.5 0.0620 0.0630 42 0.0650 41.5 0.0670 0.0680 0.0700 41 0.0710 0.0740 0.0750 40.5 0.0780 40 0.0800 0.0830 39.5 0.0850 0.0880 39 0.0900 0.0930 38.5 0.0950 0.1000 0.101 38.0 0.106 37.5 0.110 0.112 0.113 37 0.115 0.118 36.5 0.120 0.125 0.126 36 0.130 0.132 0.134 35.5

Min

Nominal

Max

[Ω/m] 56.5 54.7 53.9 51.6 49.4 47.5 45.5 43.7 41.9 38.8 37.3 34.7 33.4 31.2 29.3 27.4 26.5 24.8 23.3 22.7 21.4 20.8 19.2 18.7 17.3 16.47 15.32 14.62 13.66 13.07 12.25 11.75 10.62 10.41 9.46 8.80 8.49 8.34 8.06 7.66 7.41 6.83 6.73 6.32 6.14 5.96

[Ω/m] 59.4 57.5 56.7 54.2 51.9 49.7 47.6 45.7 43.9 40.6 39.1 36.3 35.0 32.6 30.5 28.6 27.7 26.0 24.5 23.7 22.4 21.8 20.0 19.5 18.0 17.15 15.93 15.19 14.17 13.55 12.69 12.16 10.98 10.76 9.77 9.07 8.75 8.60 8.30 7.88 7.62 7.02 6.91 6.49 6.30 6.11

[Ω/m] 62.2 60.3 59.4 56.8 54.4 51.9 49.8 47.8 45.9 42.4 40.8 37.9 36.6 34.1 31.7 29.7 28.8 27.4 25.7 25.0 23.5 22.9 21.0 20.4 18.9 17.9 16.61 15.83 14.75 14.09 13.18 12.62 11.37 11.14 10.10 9.37 9.03 8.87 8.56 8.13 7.85 7.23 7.12 6.68 6.48 6.28

1

Table-A7: Resistance v/s wire diameter table for Ni


www.elektrisola.com

Ni Pure Nickel

Electrical Resistance


Page no.63

[Appendix]

RTD Temperature vs. Resistance Table For European Curve, Alpha = 0.00385, ITS-90

1° Celsius Increments

°C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. -200 18.52 -140 43.88 0.42 -80 199 18.96 0.44 139 44.29 0.41 79 198 19.39 0.43 138 44.71 0.42 78 197 19.82 0.43 137 45.12 0.41 77 196 20.25 0.43 136 45.53 0.41 76 195 20.68 0.43 135 45.95 0.42 75 194 21.11 0.43 134 46.35 0.40 74 193 21.54 0.43 133 46.76 0.41 73 192 21.97 0.43 132 47.18 0.42 72 191 22.40 0.43 131 47.59 0.41 71 190 22.83 0.43 130 48.00 0.41 70 189 23.26 0.43 129 48.41 0.41 69 188 23.69 0.43 128 48.82 0.41 68 187 24.12 0.43 127 49.23 0.41 67 186 24.55 0.43 126 49.64 0.41 66 185 24.97 0.42 125 50.06 0.42 65 184 25.39 0.42 124 50.47 0.41 64 183 25.82 0.43 123 50.88 0.41 63 182 26.25 0.43 122 51.29 0.41 62 181 26.67 0.42 121 51.70 0.41 61 180 27.10 0.43 120 52.11 0.41 60 179 27.52 0.42 119 52.52 0.41 59 178 27.95 0.43 118 52.92 0.40 58 177 28.37 0.42 117 53.33 0.41 57 176 28.80 0.43 116 53.74 0.41 56 175 29.22 0.42 115 54.15 0.41 55 174 29.65 0.43 114 54.56 0.41 54 173 30.07 0.42 113 54.97 0.41 53 172 30.49 0.42 112 55.38 0.41 52 171 30.92 0.43 111 55.78 0.40 51 170 31.34 0.42 110 56.19 0.41 50 169 31.76 0.42 109 56.60 0.41 49 168 32.18 0.42 108 57.00 0.40 48 167 32.61 0.43 107 57.41 0.41 47 166 33.03 0.42 106 57.82 0.41 46 165 33.45 0.42 105 58.22 0.40 45 164 33.86 0.41 104 58.63 0.41 44 163 34.28 0.42 103 59.04 0.41 43 162 34.70 0.42 102 59.44 0.40 42 161 35.12 0.42 101 59.85 0.41 41 160 35.54 0.42 100 60.26 0.41 40 159 35.96 0.42 99 60.67 0.41 39 158 36.38 0.42 98 61.07 0.40 38 157 36.80 0.42 97 61.48 0.41 37 156 37.22 0.42 96 61.87 0.41 36 155 37.63 0.41 95 62.29 0.42 35 154 38.05 0.42 94 62.69 0.40 34 153 38.47 0.42 93 63.10 0.41 33 152 38.89 0.42 92 63.50 0.40 32 151 39.31 0.42 91 63.91 0.41 31 150 39.72 0.41 90 64.30 0.39 30 149 40.14 0.42 89 64.70 0.40 29 148 40.56 0.42 88 65.11 0.41 28 147 40.97 0.41 87 65.51 0.40 27 146 41.39 0.42 86 65.91 0.40 26 145 41.80 0.41 85 66.31 0.40 25 144 42.22 0.42 84 66.72 0.41 24 143 42.64 0.42 83 67.12 0.40 23 142 43.05 0.41 82 67.52 0.40 22 141 43.46 0.41 81 67.92 0.40 21

68.33 0.41 -20 92.16 0.39 ± 0 100.00 0.39 +60 123.24 0.38 68.73 0.40 19 92.55 0.39 + 1 100.39 0.39 61 123.62 0.38 69.13 0.40 18 92.95 0.40 2 100.78 0.39 62 124.01 0.39 69.53 0.40 17 93.34 0.39 3 101.17 0.39 63 124.39 0.38 69.93 0.40 16 93.73 0.39 4 101.56 0.39 64 124.77 0.38 70.33 0.40 15 94.12 0.39 5 101.95 0.39 65 125.17 0.40 70.73 0.40 14 94.52 0.40 6 102.34 0.39 66 125.55 0.38 71.13 0.40 13 94.91 0.39 7 102.73 0.39 67 125.93 0.38 71.53 0.40 12 95.30 0.39 8 103.12 0.39 68 126.32 0.39 71.93 0.40 11 95.69 0.39 9 103.51 0.39 69 126.70 0.38 72.33 0.40 10 96.09 0.40 10 103.90 0.39 70 127.08 0.38 72.73 0.40 9 96.48 0.39 11 104.29 0.39 71 127.46 0.38 73.13 0.40 8 96.87 0.39 12 104.68 0.39 72 127.85 0.39 73.53 0.40 7 97.26 0.39 13 105.07 0.39 73 128.23 0.38 73.93 0.40 6 97.65 0.39 14 105.46 0.39 74 128.61 0.38 74.33 0.40 5 98.04 0.39 15 105.85 0.39 75 128.99 0.38 74.73 0.40 4 98.44 0.40 16 106.24 0.39 76 129.38 0.39 75.13 0.40 3 98.83 0.39 17 106.63 0.39 77 129.76 0.38 75.53 0.40 2 99.22 0.39 18 107.02 0.39 78 130.14 0.38 75.93 0.40 1 99.61 0.39 19 107.40 0.38 79 130.52 0.38 76.33 0.40 20 107.79 0.39 80 130.90 0.38 76.73 0.40 21 108.18 0.39 81 131.28 0.38 77.13 0.40 22 108.57 0.39 82 131.67 0.39 77.52 0.39 23 108.96 0.39 83 132.05 0.38 77.92 0.40 24 109.35 0.39 84 132.43 0.38 78.32 0.40 25 109.73 0.38 85 132.81 0.38 78.72 0.40 26 110.12 0.39 86 133.19 0.38 79.11 0.39 27 110.51 0.39 87 133.57 0.38 79.51 0.40 28 110.90 0.39 88 133.95 0.38 79.91 0.40 29 111.28 0.38 89 134.33 0.38 80.31 0.40 30 111.67 0.39 90 134.71 0.38 80.70 0.39 31 112.06 0.39 91 135.09 0.38 81.10 0.40 32 112.45 0.39 92 135.47 0.38 81.50 0.40 33 112.83 0.38 93 135.85 0.38 81.89 0.39 34 113.22 0.39 94 136.23 0.38 82.29 0.40 35 113.61 0.39 95 136.61 0.38 82.69 0.40 36 113.99 0.38 96 136.99 0.38 83.08 0.39 37 114.38 0.39 97 137.37 0.38 83.48 0.40 38 114.77 0.39 98 137.75 0.38 83.88 0.40 39 115.15 0.38 99 138.13 0.38 84.27 0.39 40 115.54 0.39 100 138.51 0.38 84.67 0.40 41 115.93 0.39 101 138.89 0.38 85.06 0.39 42 116.31 0.38 102 139.27 0.38 85.46 0.40 43 116.70 0.39 103 139.65 0.38 85.85 0.39 44 117.08 0.38 104 140.03 0.38 86.25 0.40 45 117.47 0.39 105 140.39 0.36 86.64 0.39 46 117.85 0.38 106 140.77 0.38 87.04 0.40 47 118.24 0.39 107 141.15 0.38 87.43 0.39 48 118.62 0.38 108 141.53 0.38 87.83 0.40 49 119.01 0.39 109 141.91 0.38 88.22 0.39 50 119.40 0.39 110 142.29 0.38 88.62 0.40 51 119.78 0.38 111 142.66 0.37 89.01 0.39 52 120.16 0.38 112 143.04 0.38 89.40 0.39 53 120.55 0.39 113 143.42 0.38 89.80 0.40 54 120.93 0.38 114 143.80 0.38 90.19 0.39 55 121.32 0.39 115 144.18 0.38 90.59 0.40 56 121.70 0.38 116 144.56 0.38 90.98 0.39 57 122.09 0.39 117 144.94 0.38 91.37 0.39 58 122.47 0.38 118 145.32 0.38 91.77 0.40 59 122.86 0.39 119 145.69 0.37 (DIN 43 760)

Note: At 100°C, resistance is 138.50 ohms.

Z-232

Table-A8-Page-1: Pt-100Ω RTD

Resistance v/s temperature table


Z


Page no.64

[Appendix]



°C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. +120 146.07 0.38 +180 168.48 0.37 +240 190.47 0.36 +300 212.05 0.36 +360 233.21 0.35 +420 253.96 0.34 121 146.45 0.38 181 168.85 0.37 241 190.83 0.36 301 212.40 0.35 361 233.56 0.35 421 254.30 0.34 122 146.82 0.37 182 169.22 0.37 242 191.20 0.37 302 212.76 0.36 362 233.91 0.35 422 254.65 0.35 123 147.20 0.38 183 169.59 0.37 243 191.56 0.36 303 213.12 0.36 363 234.26 0.35 423 254.99 0.34 124 147.58 0.38 184 169.96 0.37 244 191.92 0.36 304 213.47 0.35 364 234.60 0.36 424 255.33 0.34 125 147.95 0.37 185 170.33 0.37 245 192.28 0.36 305 213.83 0.36 365 234.95 0.35 425 255.67 0.34 126 148.33 0.38 186 170.69 0.36 246 192.66 0.38 306 214.19 0.36 366 235.30 0.35 426 256.01 0.34 127 148.71 0.38 187 171.06 0.37 247 193.02 0.36 307 214.55 0.36 367 235.65 0.35 427 256.35 0.34 128 149.08 0.37 188 171.43 0.37 248 193.38 0.36 308 214.90 0.35 368 236.00 0.35 428 256.70 0.35 129 149.46 0.38 189 171.80 0.37 249 193.74 0.36 309 215.26 0.36 369 236.35 0.35 429 257.04 0.34 130 149.83 0.37 190 172.17 0.37 250 194.10 0.36 310 215.61 0.35 370 236.70 0.35 430 257.38 0.34 131 150.21 0.38 191 172.54 0.37 251 194.47 0.37 311 215.97 0.36 371 237.05 0.35 431 257.72 0.34 132 150.58 0.37 192 172.91 0.37 252 194.83 0.36 312 216.32 0.35 372 237.40 0.35 432 258.06 0.34 133 150.96 0.38 193 173.27 0.36 253 195.19 0.36 313 216.68 0.36 373 237.75 0.35 433 258.40 0.34 134 151.34 0.38 194 173.64 0.37 254 195.55 0.36 314 217.03 0.35 374 238.09 0.34 434 258.74 0.34 135 151.71 0.37 195 174.01 0.37 255 195.90 0.35 315 217.39 0.36 375 238.44 0.35 435 259.08 0.34 136 152.09 0.38 196 174.39 0.38 256 196.26 0.36 316 217.73 0.34 376 238.79 0.35 436 259.42 0.34 137 152.46 0.37 197 174.75 0.36 257 196.62 0.36 317 218.08 0.35 377 239.14 0.35 437 259.76 0.34 138 152.84 0.38 198 175.12 0.37 258 196.98 0.36 318 218.44 0.36 378 239.48 0.34 438 260.10 0.34 139 153.21 0.37 199 175.49 0.37 259 197.35 0.37 319 218.79 0.35 379 239.83 0.35 439 260.44 0.34 140 153.58 0.37 200 175.86 0.37 260 197.71 0.36 320 219.15 0.36 380 240.18 0.35 440 260.78 0.34 141 153.95 0.37 201 176.23 0.37 261 198.07 0.36 321 219.50 0.35 381 240.52 0.34 441 261.12 0.34 142 154.32 0.37 202 176.59 0.36 262 198.43 0.36 322 219.85 0.35 382 240.87 0.35 442 261.46 0.34 143 154.71 0.39 203 176.96 0.37 263 198.79 0.36 323 220.21 0.36 383 241.22 0.35 443 261.80 0.34 144 155.08 0.37 204 177.33 0.37 264 199.15 0.36 324 220.56 0.35 384 241.56 0.34 444 262.14 0.34 145 155.46 0.38 205 177.70 0.37 265 199.51 0.36 325 220.91 0.35 385 241.91 0.35 445 262.48 0.34 146 155.83 0.37 206 178.06 0.36 266 199.87 0.36 326 221.27 0.36 386 242.25 0.34 446 262.83 0.35 147 156.21 0.38 207 178.43 0.37 267 200.23 0.36 327 221.62 0.35 387 242.60 0.35 447 263.17 0.34 148 156.58 0.37 208 178.80 0.37 268 200.59 0.36 328 221.97 0.35 388 242.95 0.35 448 263.50 0.33 149 156.96 0.38 209 179.16 0.36 269 200.95 0.36 329 222.32 0.35 389 243.29 0.34 449 263.84 0.34 150 157.33 0.37 210 179.53 0.37 270 201.31 0.36 330 222.68 0.36 390 243.64 0.35 450 264.18 0.34 151 157.71 0.38 211 179.90 0.37 271 201.67 0.36 331 223.03 0.35 391 243.98 0.34 451 264.52 0.34 152 158.08 0.37 212 180.26 0.36 272 202.03 0.36 332 223.38 0.35 392 244.33 0.35 452 264.86 0.34 153 158.45 0.37 213 180.63 0.37 273 202.38 0.35 333 223.73 0.35 393 244.67 0.34 453 265.20 0.34 154 158.83 0.38 214 180.99 0.36 274 202.74 0.36 334 224.09 0.36 394 245.02 0.35 454 265.54 0.34 155 159.20 0.37 215 181.36 0.37 275 203.10 0.36 335 224.45 0.36 395 245.36 0.34 455 265.87 0.33 156 159.56 0.36 216 181.73 0.37 276 203.46 0.36 336 224.80 0.35 396 245.71 0.35 456 266.21 0.34 157 159.94 0.38 217 182.09 0.36 277 203.82 0.36 337 225.15 0.35 397 246.05 0.34 457 266.55 0.34 158 160.31 0.37 218 182.46 0.37 278 204.18 0.36 338 225.50 0.35 398 246.40 0.35 458 266.89 0.34 159 160.68 0.37 219 182.82 0.36 279 204.54 0.36 339 225.85 0.35 399 246.74 0.34 459 267.22 0.33 160 161.05 0.37 220 183.19 0.37 280 204.90 0.36 340 226.21 0.36 400 247.09 0.35 460 267.56 0.34 161 161.43 0.38 221 183.55 0.36 281 205.25 0.35 341 226.56 0.35 401 247.43 0.34 461 267.90 0.34 162 161.80 0.37 222 183.92 0.37 282 205.61 0.36 342 226.91 0.35 402 247.78 0.35 462 268.24 0.34 163 162.17 0.37 223 184.28 0.36 283 205.97 0.36 343 227.26 0.35 403 248.12 0.34 463 268.57 0.33 164 162.54 0.37 224 184.65 0.37 284 206.33 0.36 344 227.61 0.35 404 248.46 0.34 464 268.91 0.34 165 162.91 0.37 225 185.01 0.36 285 206.70 0.37 345 227.96 0.35 405 248.81 0.35 465 269.25 0.34 166 163.28 0.37 226 185.38 0.37 286 207.05 0.35 346 228.31 0.35 406 249.15 0.34 466 269.58 0.33 167 163.66 0.38 227 185.74 0.36 287 207.41 0.36 347 228.66 0.35 407 249.50 0.35 467 269.92 0.34 168 164.03 0.37 228 186.11 0.37 288 207.77 0.36 348 229.01 0.35 408 249.84 0.34 468 270.26 0.34 169 164.40 0.37 229 186.47 0.36 289 208.13 0.36 349 229.36 0.35 409 250.18 0.34 469 270.59 0.33 170 164.77 0.37 230 186.84 0.37 290 208.48 0.35 350 229.72 0.34 410 250.53 0.35 470 270.93 0.34 171 165.14 0.37 231 187.20 0.36 291 208.84 0.36 351 230.07 0.35 411 250.89 0.34 471 271.27 0.34 172 165.51 0.37 232 187.56 0.36 292 209.20 0.36 352 230.42 0.35 412 251.21 0.34 472 271.60 0.33 173 165.88 0.37 233 187.93 0.37 293 209.55 0.35 353 230.77 0.35 413 251.55 0.34 473 271.94 0.34 174 166.25 0.37 234 188.29 0.36 294 209.91 0.36 354 231.12 0.35 414 251.90 0.35 474 272.27 0.33 175 166.62 0.37 235 188.65 0.36 295 210.27 0.36 355 231.47 0.35 415 252.24 0.34 475 272.61 0.34 176 167.00 0.38 236 189.02 0.37 296 210.62 0.35 356 231.81 0.36 416 252.59 0.35 476 272.95 0.34 177 167.37 0.37 237 189.38 0.36 297 210.98 0.36 357 232.16 0.35 417 252.94 0.35 477 273.28 0.33 178 167.74 0.37 238 189.74 0.36 298 211.34 0.36 358 232.51 0.35 418 253.28 0.34 478 273.62 0.34 179 168.11 0.37 239 190.11 0.37 299 211.69 0.35 359 232.86 0.35 419 253.62 0.34 479 273.95 0.33 Note: At 100°C, resistance is 138.50 ohms.

Table-A8-Page-2: Pt-100Ω

Z-233



(DIN 43 760)


Page no.65

[Appendix]



°C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. °C Ohms Diff. +480 274.29 0.34 +542 294.87 0.33 +604 315.00 0.32 +666 334.68 0.32 +728 353.91 0.30 +790 372.71 0.30 481 274.62 0.33 543 295.20 0.33 605 315.32 0.32 667 334.99 0.31 729 354.22 0.31 791 373.01 0.30 482 274.96 0.34 544 295.53 0.33 606 315.64 0.32 668 335.31 0.32 730 354.53 0.31 792 373.31 0.30 483 275.29 0.33 545 295.85 0.32 607 315.96 0.32 669 335.62 0.31 731 354.83 0.30 793 373.61 0.30 484 275.63 0.34 546 296.18 0.33 608 316.28 0.32 670 335.93 0.31 732 355.14 0.31 794 373.91 0.30 485 275.96 0.33 547 296.51 0.33 609 316.60 0.32 671 336.25 0.32 733 355.44 0.30 795 374.21 0.30 486 276.31 0.34 548 296.84 0.33 610 316.92 0.32 672 336.56 0.31 734 355.75 0.31 796 374.51 0.30 487 276.64 0.33 549 297.16 0.32 611 317.24 0.32 673 336.87 0.31 735 356.06 0.31 797 374.80 0.29 488 276.97 0.33 550 297.49 0.33 612 317.56 0.32 674 337.18 0.31 736 356.37 0.31 798 375.10 0.30 489 277.31 0.34 551 297.82 0.33 613 317.88 0.32 675 337.50 0.32 737 356.68 0.31 799 375.40 0.30 490 277.64 0.33 552 298.14 0.32 614 318.20 0.32 676 337.81 0.31 738 356.98 0.30 800 375.70 0.30 491 277.98 0.34 553 298.47 0.33 615 318.52 0.32 677 338.12 0.31 739 357.29 0.31 801 376.00 0.30 492 278.31 0.33 554 298.80 0.33 616 318.85 0.33 678 338.43 0.31 740 357.59 0.30 802 376.29 0.29 493 278.64 0.33 555 299.12 0.32 617 319.17 0.32 679 338.75 0.32 741 357.90 0.31 803 376.59 0.30 494 278.98 0.34 556 299.45 0.33 618 319.49 0.32 680 339.06 0.31 742 358.20 0.30 804 376.89 0.30 495 279.31 0.33 557 299.78 0.33 619 319.81 0.32 681 339.37 0.31 743 358.51 0.31 805 377.19 0.30 496 279.64 0.33 558 300.10 0.32 620 320.12 0.31 682 339.68 0.31 744 358.81 0.30 806 377.49 0.30 497 279.98 0.34 559 300.43 0.33 621 320.44 0.32 683 339.99 0.31 745 359.12 0.31 807 377.79 0.30 498 280.31 0.33 560 300.75 0.32 622 320.76 0.32 684 340.30 0.31 746 359.42 0.30 808 378.09 0.30 499 280.64 0.33 561 301.08 0.33 623 321.08 0.32 685 340.62 0.32 747 359.72 0.30 809 378.39 0.30 500 280.98 0.34 562 301.41 0.33 624 321.40 0.32 686 340.94 0.32 748 360.03 0.31 810 378.68 0.29 501 281.31 0.33 563 301.73 0.32 625 321.72 0.32 687 341.25 0.31 749 360.33 0.30 811 378.98 0.30 502 281.64 0.33 564 302.06 0.33 626 322.03 0.31 688 341.55 0.30 750 360.64 0.31 812 379.28 0.30 503 281.97 0.33 565 302.38 0.32 627 322.34 0.31 689 341.87 0.32 751 360.94 0.30 813 379.57 0.29 504 282.31 0.34 566 302.71 0.33 628 322.66 0.32 690 342.18 0.31 752 361.24 0.30 814 379.87 0.30 505 282.64 0.33 567 303.03 0.32 629 322.98 0.32 691 342.49 0.31 753 361.55 0.31 815 380.17 0.30 506 282.97 0.33 568 303.36 0.33 630 323.30 0.32 692 342.80 0.31 754 361.85 0.30 816 380.46 0.29 507 283.30 0.33 569 303.68 0.32 631 323.61 0.31 693 343.11 0.31 755 362.15 0.30 817 380.76 0.30 508 283.63 0.33 570 304.01 0.33 632 323.93 0.32 694 343.42 0.31 756 362.46 0.31 818 381.05 0.29 509 283.97 0.34 571 304.33 0.32 633 324.25 0.32 695 343.73 0.31 757 362.76 0.30 819 381.35 0.30 510 284.30 0.33 572 304.66 0.33 634 324.57 0.32 696 344.04 0.31 758 363.06 0.30 820 381.65 0.30 511 284.63 0.33 573 304.98 0.32 635 324.88 0.31 697 344.35 0.31 759 363.36 0.30 821 381.94 0.29 512 284.96 0.33 574 305.30 0.32 636 325.21 0.33 698 344.66 0.31 760 363.67 0.31 822 382.24 0.30 513 285.29 0.33 575 305.63 0.33 637 325.53 0.32 699 344.97 0.31 761 363.97 0.30 823 382.53 0.29 514 285.62 0.33 576 305.95 0.32 638 325.85 0.32 700 345.28 0.31 762 364.27 0.30 824 382.83 0.30 515 285.95 0.33 577 306.28 0.33 639 326.16 0.31 701 345.59 0.31 763 364.57 0.30 825 383.12 0.29 516 286.30 0.35 578 306.60 0.32 640 326.48 0.32 702 345.90 0.31 764 364.88 0.31 826 383.42 0.30 517 286.63 0.33 579 306.92 0.32 641 326.79 0.31 703 346.21 0.31 765 365.18 0.30 827 383.71 0.29 518 286.96 0.33 580 307.25 0.33 642 327.11 0.32 704 346.52 0.31 766 365.49 0.31 828 384.01 0.30 519 287.29 0.33 581 307.57 0.32 643 327.43 0.32 705 346.83 0.31 767 365.79 0.30 829 384.30 0.29 520 287.62 0.33 582 307.89 0.32 644 327.74 0.31 706 347.15 0.32 768 366.09 0.30 830 384.60 0.30 521 287.95 0.33 583 308.22 0.33 645 328.06 0.32 707 347.46 0.31 769 366.40 0.31 831 384.89 0.29 522 288.28 0.33 584 308.54 0.32 646 328.38 0.32 708 347.76 0.30 770 366.70 0.30 832 385.18 0.29 523 288.61 0.33 585 308.86 0.32 647 328.69 0.31 709 348.07 0.31 771 367.00 0.30 833 385.48 0.30 524 288.94 0.33 586 309.19 0.33 648 329.01 0.32 710 348.38 0.31 772 367.30 0.30 834 385.77 0.29 525 289.27 0.33 587 309.51 0.32 649 329.32 0.31 711 348.69 0.31 773 367.60 0.30 835 386.07 0.30 526 289.60 0.33 588 309.83 0.32 650 329.64 0.32 712 349.00 0.31 774 367.90 0.30 836 386.37 0.30 527 289.93 0.33 589 310.15 0.32 651 329.95 0.31 713 349.31 0.31 775 368.20 0.30 837 386.66 0.29 528 290.26 0.33 590 310.48 0.33 652 330.27 0.32 714 349.61 0.30 776 368.50 0.30 838 386.96 0.30 529 290.59 0.33 591 310.80 0.32 653 330.58 0.31 715 349.92 0.31 777 368.81 0.31 839 387.25 0.29 530 290.92 0.33 592 311.12 0.32 654 330.90 0.32 716 350.23 0.31 778 369.11 0.30 840 387.55 0.30 531 291.25 0.33 593 311.45 0.33 655 331.21 0.31 717 350.54 0.31 779 369.41 0.30 841 387.84 0.29 532 291.58 0.33 594 311.78 0.33 656 331.53 0.32 718 350.85 0.31 780 369.71 0.30 842 388.13 0.29 533 291.90 0.32 595 312.10 0.32 657 331.84 0.31 719 351.15 0.30 781 370.01 0.30 843 388.42 0.29 534 292.23 0.33 596 312.43 0.33 658 332.16 0.32 720 351.46 0.31 782 370.31 0.30 844 388.72 0.30 535 292.56 0.33 597 312.75 0.32 659 332.47 0.31 721 351.77 0.31 783 370.61 0.30 845 389.01 0.29 536 292.90 0.34 598 313.07 0.32 660 332.79 0.32 722 352.07 0.30 784 370.91 0.30 846 389.31 0.30 537 293.23 0.33 599 313.39 0.32 661 333.10 0.31 723 352.38 0.31 785 371.21 0.30 847 389.61 0.30 538 293.56 0.33 600 313.71 0.32 662 333.41 0.31 724 352.69 0.31 786 371.52 0.31 848 389.90 0.29 539 293.89 0.33 601 314.04 0.33 663 333.73 0.32 725 352.99 0.30 787 371.82 0.30 849 390.19 0.29 540 294.21 0.32 602 314.36 0.32 664 334.04 0.31 726 353.30 0.31 788 372.12 0.30 850 390.48 0.29 541 294.54 0.33 603 314.68 0.32 665 334.36 0.32 727 353.61 0.31 789 372.41 0.29 Note: At 100°C, resistance is 138.50 ohms.

Table-A8-Page-3: Pt-100Ω

Z-234



(DIN 43 760)

Z


Page no.66

[Appendix]

Ultrafine Precious Metal Wire Ultrafine precious metal wire is used in a wide range of industrial applications, where specific requirements for wire at very small diameters (0.025 mm to 0.01mm) with tightly controlled material properties are essential. Applications include resistance thermometry and combustible gas detection. Specifications can be tailor-made to suit individual customer requirements, and can include characteristics such as temperature coefficient of resistance (alpha value), actual resistance and tensile requirements. Johnson Matthey work to the highest quality standards and have BS EN ISO 9001, BS EN ISO 14001 and UKAS accreditation, ensuring a high level of control in our processes and consistent product quality. 1) Platinum wire for Resistance Thermometry (Alpha platinum Wire) The measurement of temperature by means of the resistance thermometer is based on the fact that a change in the temperature of a conductor produces a measurable change in resistance. The magnitude of this change per unit increase in temperature depends on the temperature coefficient of resistance of the conductor (the alpha value). Commonly required wires for Resistance Thermometry available as below:

Alpha Value >= 0.003925

Comments Very pure platinum wire for high precision PRTD’s (standards). Typical wire diameter = 0.07 mm.

0.003850

For the Pt100 detector. This alpha value is the industry standard for the majority of sensors outside the USA and Japan (as per IEC Publication 751, 1983). Typical wire diameter is 0.018 mm.

0.003916

Alpha value requirement that is common in the USA and Japan, where it is the accepted standard (as per JIS C1604, 1981 and US standard curve).

0.003900

Alpha value originally specified for the British Aircraft Industry (as per BS 2G 148).

Typical diameters and capabilities for combustible gas detection as below:

Nominal Diameter

For the production of wire wound platinum resistance thermometers (PRTs), the consistent supply of high quality, specific alpha value platinum wires at diameters of around 0.018 mm is essential. Wires are available with alpha values from 0.003800 to 0.003925, with a tolerance on alpha value as tight as ±3ppm. Johnson Matthey tightly controls the wire diameter (resistance measured, with typical tolerances of ±3%). Through batch selection and careful doping, tailor-made ingots can be produced to specific customer requirements. Once batch selections are complete, dedicated material can be held in stock for customer requirements.

Measured Resistance (Tolerance)

0.025 mm

220 ohms/m (± 3%)

0.015 mm

600 ohms/m (± 5%)

0.0125 mm

865 ohms/m (± 5%)

0.010 mm

Platinum is a conductor of high melting point and exceptional chemical inertness, combined with extremely stable electrical properties. This combination of properties makes it the best available material for resistance thermometer elements.

2) Platinum Wire for Combustible Gas Detection (Sensors)

1347 ohms/m (± 5%)

The data, text, graphics and links contained in these pages are provided for information purposes only. Johnson Matthey plc does not warrant the accuracy, or completeness of data, text, links, and other items contained on this datasheet.

Combustible gas sensors are based on an established catalytic bead technology. They are supplied in pairs, a detector and compensator; the detector element consists of a catalytic bead supported on a very fine diameter platinum wire. In the presence of combustible gas, a catalytic oxidation reaction occurs, producing heat and changing the resistance of the wire. This produces a signal from the bridge circuit proportional to the concentration of gas.

If you require more information on Johnson Matthey Noble Metals products please contact our technical support team. Europe Johnson Matthey, Noble Metals, Orchard Road, Royston, Hertfordshire, SG8 5HE UK Tel: +44 (0) 1763 253000 Fax: +44 (0) 1763 253313 E-mail: [email protected]

North America Johnson Matthey, Noble Metals, 1401 King Road Pennsylvania 19380- 1497 USA Tel: (1) 610 648 8000 Fax: (1) 610 648 8105 E-mail: [email protected]

Asia Johnson Matthey Hong Kong Ltd Suite 2101, CMG Asia Tower, The Gateway, 15 Canton Road, Tsimshatsui, Kowloon, Hong Kong Tel: (852) 2738 0380 Fax: (852) 2736 2345 E-mail: [email protected]

www.noble.matthey.com

Table-A9: Resistance v/s wire diameter details for Pt (note: resistance values shown above are wrong)



Page no.67

[Appendix]

RTD Calibration Convert RTD resistance to temperature using rational polynomial equations

Relating resistance to temperature The resistance of an RTD changes almost linearly with temperature. Often, widely available tables are used for converting temperature to resistance and vice versa. (In fact, we include tables you can use for the two most commonly used RTD temperature coefficients. See the Excel file below.) Conversion of resistance to temperature via an equation offers more flexibility than using a look-up table or chart. The available tabulated values may be curve-fitted to simple equations for the temperature ranges of interest. The following graph shows the temperature dependence of RTD resistance for a typical RTD:

RTDs are characterized by their temperature coefficient, α, defined as the average fractional change in resistance per degree Centigrade over a temperature interval of 0°C to 100°C. That is, α = (R100 – R0)/R0/100°C Because the resistance is roughly proportional to absolute temperature, the temperature coefficient α is approximately given by, α = (373°K-273°K)/273°K/100°C = 1/273°K = 0.0037 Depending on the particular alloy of platinum that is used the temperature coefficient may vary a bit from this value, and different standards organizations have settled on different temperature coefficients. The most common values are α = 0.00385 for the European standard and α = 0.003916 for the less used US Industrial Standard. When using RTDs, you need to compute temperature from the measured RTD resistance. Depending on the temperature range and accuracy you need, you may use a simple linear fit, quadratic or cubic equations, or a rational polynomial function. We'll discuss each in turn.

Using a linear fit As an example of a simple equation you might use, for the case of measurements between 0°C and 100°C, you could use a linear approximation as, T = (R/R0 – 1) / α

where R0 = 100, and α = 0.00385

This equation fits a line through the points at 0°C and 100°C (and so has zero error at those temperatures), and has a maximum error in the middle of the range of 0.38°C. The average error over the interval can be minimized by shifting the equation a little, as, T = (R/R0 – 1)/α - 0.19 to provide a maximum error over the interval of ±0.19°C. In fact, if you are using the RTD over a

http://www.mosaic-industries.com/embedded-syst...

Pt-100-RTD calibration details-Page-1


1 of 3


Page no.68

[Appendix] small temperature range and want good accuracy there you can calibrate by measuring the resistance at the temperature of interest and adding or subtracting a small offset to the computed temperature to force it to equal the calibration temperature.

Using a quadratic fit A quadratic fit provides a much greater accuracy. A quadratic fit over the range of 0°C to 200°C provides an rms error over the range of only 0.014°C, and a maximum error of only 0.036°C. The equation for a European standard 100Ω RTD is, T = -244.83 + 2.3419 R + .0010664 R2 You would generally reformulate the above equation to minimize the number of computations as, T = -244.83 + R ( 2.3419 + .0010664 R )

Using a cubic fit If you need to measure temperature over a much wider range you can use a cubic fit. A cubic fit over the range of -100°C to +600°C provides an rms error of only 0.038°C over the entire range, and 0.026°C in the range of 0°C to 400°C. The equation is, T = -247.29 + 2.3992 R + .00063962 R2 + 1.0241E-6 R3 or, using fewer computations, T = -247.29 + R ( 2.3992 + R (.00063962 + 1.0241E-6 R))

Using a rational polynomial function If you need to fit the RTD response over a greater range and with greater accuracy than the cubic fit is capable, you can fit RTD data to higher order polynomials. However, rather than using a simple polynomial you should use a rational polynomial function, that is, the ratio of two polynomials. In general, for the same number of determined parameters and arithmetical operations, rational polynomial functions fit continuous functions more smoothly (that is, with better interpolation) and more accurately than do simple polynomials.

1)

Fitting the RTD data over its full range (-200 to +850°C) produces the following formula for computing temperature from RTD resistance,

with the following coefficients, co

c1

c2

c3

c4

c5

c6

c7

-245.19 2.5293 -0.066046 4.0422E-3 -2.0697E-6 -0.025422 1.6883E-3 -1.3601E-6

Using the rational polynomial function results in an average absolute error of only 0.015°C over the full temperature range.

Accuracy of the various approximations Average absolute errors for the above approximations to the temperature vs resistance RTD curve are summarized in the following table. Equation

Temperature range Average error

Linear

0 → +100°C

Linear

-200 → +850°C

± 0.12°C

Quadratic

0 → +200°C

Quadratic

-200 → +850°C

± 3.2°C

Cubic

-100 → +600°C

±0.03°C

Cubic

-200 → +850°C

± 0.31°C

Rational poly

-200 → +850°C

± 0.015°C

± 25°C ± 0.11°C

In each case, for their temperature range of applicability, these errors are less than the tolerance of




2 of 3


Page no.69

[Appendix] an off-the-shelf RTD. If you need greater accuracy, you may calibrate the RTD at one or two fixed temperatures, but in that case you will need an independent, accurate temperature measurement at the time of calibration. The errors of the various calibrations, linear, quadratic, cubic, and rational polynomial function, are shown in the following figure.

The periodic fine jitter in the curve results from rounding errors on the numbers in the resistance vs temperature tables.

Excel spreadsheet for RTD resistance/temperature computations Here is a link to an Excel spreadsheet containing the computations for the above error graph, as well as resistance vs temperature values for both American and European RTDs. Excel spreadsheet for RTD temperature resistance computations

See also → RTD Calibration

Notes: 1)

See

rational polynomial function.

This page is about: RTD Measurement, RTD Temperature Curve, Calibrating RTDs, RTD Calibration – RTD (resistance temperature device) resistance may be calibrated to temperature using linear, quadratic, cubic or rational polynomial approximations or curve fits. Convert RTD resistance to temperature using a simple polynomial equation. RTD curve, RTD table, RTD resistance vs temperature, convert RTD resistance to temperature, RTD resistance vs temperature graph, RTD temperature coefficient, RTD tolerance




3 of 3


Page no.70

[Appendix]

Resistance Temperature Detectors (RTDs)

Resistance Temperature Detectors operate through the principle of electrical resistance changes in pure metal elements. Platinum is the most widely specified RTD element type although nickel, copper, and Balco (nickel-iron) alloys are also used. Platinum is popular due to its wide temperature range, accuracy, stability, as well as the degree of standardization among manufacturers. RTDs are characterized by a linear positive change in resistance with respect to temperature. They exhibit the most linear signal with respect to temperature of any electronic sensing device. There are two common constructions for RTD elements. Wire-wound devices are manufactured by winding a small diameter of wire into a coil on a suitable winding bobbin. A number of methods have been used to protect the wire element from shock and vibration. One common technique is to use a ceramic bobbin with a glass or epoxy seal over the coil and welded connections. An alternative to the wire-wound RTD is the thin-film element. It consists of a very thin layer of the base metal, which is deposited onto a ceramic substrate and then laser trimmed to the desired resistance value. Thin-film elements can attain higher resistances with less metal and, thus tend to be less costly than the equivalent wire-wound element. Most RTD elements are too fragile to be used in their raw form. They’re typically connected to extension lead wires and housed in a protective sheath. The housing immobilizes the element while protecting it from mechanical strain and environmental conditions. MS specializes in packaging thin-film RTD sensors in a

Temperature Sensor Products precisionsensors.meas-spec.com

wide variety of surface, air, and immersion housings that can operate from -100°C to +600°C. The table below compares some of the different types of base metals that are used in the construction of RTD elements. Element Material

Temperature Range

Benefits

a (%/˚C)

Platinum Thin-film

-200˚C to 800˚C

Best range Best stability Good linearity

0.375 to 0.385

Nickel Thin-film

-100˚C to 260˚C

Low cost Best sensitivity

0.618

Balco

-100˚C to 204˚C

Low cost High sensitivity

0.518 to 0.527

Std. Probes & Assemblies

Because of their linearity, stability and accuracy over a wide temperature range, RTDs (resistance temperature detectors) have been the gold standard of temperature measurement devices for many years. Compared to thermocouples and thermistors, RTDs have also been known as the most expensive sensing elements. But recent advances in thin-film technology have produced RTD elements that now offer the design engineer a product that can be competitively priced in OEM quantities.

Note: a is normally used to distinguish between RvT curves of the same element or those of different material.

RTD Terminology

RTDs are generally characterized by their base resistance at 0°C. Typical base resistance values available for platinum thin-film RTDs include 100Ω, 500Ω and 1000Ω. For other element types, typical base values include 120Ω for nickel, and 1000Ω and 2000Ω for Balco. The resistance versus temperature relationship for a platinum thin-film RTD follows the following equation over its operating temperature range: t(ITS-90) (°C) Equation 0°C Rt = R0[ 1 + At + Bt2] Where: Rt = resistance at temperature t R0 = base resistance at 0°C A, B and C are constants of the equation t = temperature in accordance with ITS90

RTD Sensors & Assemblies

Introduction:

The most popular thin-film RTD is manufactured using platinum and has an a of 0.385%/°C and is specified per DIN EN 60751. The A, B and C constants for this material are as follows: A = 3.9083 x 10-3 B = -5.775 x 10-7 C = -4.183 x 10-12

1028 Graphite Road, St. Marys, PA 15857 Ph: 814.834.1541 Fax: 814.834.1556

Ni-RTD calibration details-Page-1


8-7-13 www.meas-spec.com

67


Page no.71

[Appendix]

Resistance Temperature Detectors (RTDs) Different constants are available for other grades of platinum. Please contact the factory for information on these other platinum grades. The corresponding equation for one style of a thin-film nickel elements with an a of 0.618%/°C is Rt = R0[1 + At + Bt2 + Ct3 +Dt4 + Et5 + Ft6] Where: A = 5.485 x 10-3 C = 0 E = 0

B = 6.65 x 10-6 D = 2.805 x 10-11 F = -2 x 10-17

For Balco, individual manufacturers have developed proprietary curves for their elements based on actual measurements at defined points along the resistance versus temperature curve. A number of methods are used to define the curve outside those points. Please contact the factory to obtain information on the types of curves available as well as resistance versus temperature information. Temperature Coefficient of Resistance (a) The temperature coefficient of resistance, a, for RTDs is normally defined as the average resistance change per °C over the range 0˚C to 100°C divided by R at 0°C. The temperature coefficient is expressed in ohms/ ohms/°C or more typically %/°C. Note that this definition differs from the definition of a for an NTC thermistor. The a for an NTC thermistor will vary widely over its temperature range, from as high as 8%/°C to less than 2%/°C. The a for an RTD does not have nearly as large a change over its temperature range. For a standard platinum thin-film RTD, the a is 0.385%/°C while other grades of platinum have a values of 0.3911%/°C and 0.3926%/°C. a for other common RTD elements include: Thin-film Nickel = 0.618%/°c Balco = 0.518 to 0.527%/°C In one sense a defines the sensitivity of the RTD element as it defines the average temperature change of a 1Ω RTD. However, a is normally used to distinguish between resistance/temperature curves of the same element or those of different materials.

68 Temperature Sensor Products precisionsensors.meas-spec.com

RTDs and self-heating

An RTD is a passive device and requires a measuring current to produce a useful signal. Because of I2R heating, this current can raise the temperature of the RTD sensing element above that of the ambient temperature unless the extra heat can be dissipated. The amount of self-heat that will be generated is dependent upon the measuring current as well as the ability of the sensor assembly to dissipate that heat. The ability of the sensor to dissipate heat is defined by its dissipation factor, d, which has units of mW/°C. The definition for d is the amount of power that it takes to the raise the body temperature of the sensing element 1°C. The ability of the sensor to dissipate power is a function of the size and construction of the sensing element as well as the materials that surround it in the assembly and the environment that the sensor is used in. The higher the a, the less amount of self-heating that will occur. The amount of self-heating is more for higher resistance elements used in constant current circuits, as well as in constructions where the sensing element cannot shed heat to its outside environment. Also, self-heating is more in air than in a liquid and in still air rather than moving air.

Effects of leadwire resistance

Because the RTD is a resistive device, any resistance elsewhere in the circuit will cause errors in the readings for the sensor. The most common source of additional resistance is in the leadwires attached to the sensor, especially with assemblies that have long extension leads of heavy AWG# wire. The amount of error introduced into the system will depend upon the length and AWG# of the wire as well as the base resistance value of the RTD. Leadwire error can be significant, especially with long runs of small diameter leads or low resistance elements. Fortunately, the use of a 3-wire or 4-wire system will reduce errors to negligible levels in most applications. The need for a 3-wire or 4-wire system will be dependent upon the resistance value of the sensing element, the length and AWG of the leadwires as well as the amount of accuracy required. Please contact the factory to discuss your specific application.






Page no.72

[Appendix]

Resistance Temperature Detectors (RTDs) Features: • • • • • • • •

Excellent long-term stability Platinum and nickel elements -60°C to 250°C operation for Nickel -200°C to 600°C operation for Platinum Values from 100Ω to 1,000Ω Small size, fast response time Resistant to vibration and thermal shock Available in standard DIN class accuracies

Description:

Resistance temperature detectors (RTDs) are characterized by a linear change in resistance with respect to temperature. RTDs exhibit the most linear signal with respect to temperature of any sensing device. RTDs are specified primarily where accuracy and stability are critical to the application. RTDs operate through the principal of electrical resistance changes in pure metal elements. MS offers elements manufactured with platinum, the most common element, as well as nickel. The RTD element consists of a thin film of platinum or nickel which is deposited onto a ceramic substrate and laser trimmed to the desired resistance. Thin-film elements attain higher resistances with less metal and, thus, tend to be less costly then the equivalent wire-wound element.

Resistance Temperature Detectors

Drawing of a Nickel RTD R@0˚C (Ω)

DIN Class

RP102T22

Platinum

100

A, B

RP502T22

Platinum

500

A, B

RP103T22

Platinum

1,000

A, B

RN102T25

Nickel

100

1/2 DIN, DIN 43760

RN502T25

Nickel

500

1/2 DIN, DIN 43760

RN103T25

Nickel

1,000

1/2 DIN, DIN 43760

Basic P/N

RTD Type

Width in mm

Length in mm

Drawing of a Platinum RTD

Tolerance Class

Examples: RP102T22-A................. Platinum RTD, 100Ω@0˚C, thin-film element, 2mm x 2mm, DIN Class A RN502T25-5D.............. Nickel RTD, 500Ω@0˚C, thin-film element, 2mm x 5mm, 1/2 DIN Temperature Sensor Products precisionsensors.meas-spec.com





69

Other Advanced Thermal Products

RTD Type

MS Part Number

RTD Sensors & Assemblies

Ordering Information


Page no.73

[Appendix]

Resistance Temperature Detectors (RTD’s) Resistance tolerance and temperature accuracy Accuracy classes for platinum RTDs are defined by IEC 751 and are typically listed as either DIN Class A or DIN Class B. The following table shows the accuracies associated with the two class of elements. Temperature accuracies according to IEC751 and DIN EN 60751

-200

Class A Limit ±0.55˚C

Class B Limit ±1.3˚C

-100

±0.35˚C

±0.8˚C

0

±0.15˚C

±0.3˚C

100

±0.35˚C

±0.8˚C

200

±0.55˚C

±1.3˚C

300

±0.75˚C

±1.8˚C

400

±0.95˚C

±2.3˚C

500

±1.15˚C

±2.8˚C

600

±1.35˚C

±3.3˚C

350

±1.45˚C

±3.6˚C

Temperature (˚C)

These tolerances can be specified in another way in the following formulas: Class A : Δt = ±(0.15°C + 0.002 | t | ) Class B : Δt = ±(0.3°C + 0.005 | t | ) Note : | t | is absolute value of temperature in °C For thin-film nickel RTDs, they are typically broken up into three classes of temperature accuracies as defined by DIN 43760. These classes are as follows: Class

± Temperature accuracy in ˚C t < 0˚C

t > 0˚C

1/2 DIN

0.2 + 0.014 [T]

0.2 + 0.0035 [T]

DIN 43760

0.4 + 0.028 [T]

0.4 + 0.007 [T]

2 x DIN

0.8 + 0.028 [T]

0.8 + 0.007 [T]

No specific standard exists for defining temperature accuracies for Balco RTDs. However a typical interchangeability would be ±1°C at 0°C for Balco.

The following table lists Rt/R0 for the three most common types of RTDs used by MS. To obtain the value at any temperature multiply the Rt/R0 value at that temperature by the base resistance of the part, R0. For example for a platinum RTD with a R0 = 1000Ω, the nominal resistance value for the part at 230°C would be 1.868 x 1000 = 1868Ω. Temp (˚C)

Rt/R0 Platinum

Nickel

Balco

-50

0.803

0.743

0.810

-40

0.843

0.791

-30

0.882

-20

Temp (˚C)

Rt/R0 Platinum

Nickel

Balco

110

1.423

1.688

1.514

0.845

120

1.461

1.760

1.567

0.841

0.882

130

1.498

1.833

1.622

0.922

0.893

0.920

140

1.536

1.909

1.677

-10

0.961

0.945

0.960

150

1.573

1.986

0

1.000

1.000

1.000

160

1.611

2.066

10

1.039

1.055

1.041

170

1.648

2.148

20

1.078

1.112

1.084

180

1.685

2.231

30

1.117

1.171

1.127

190

1.722

2.318

40

1.155

1.230

1.172

200

1.759

2.407

50

1.194

1.291

1.218

210

1.795

2.498

60

1.232

1.353

1.264

220

1.832

2.592

70

1.271

1.417

1.312

230

1.868

2.689

80

1.309

1.482

1.361

240

1.905

2.789

90

1.347

1.549

1.411

250

1.941

2.892

100

1.385

1.618

1.462

260

1.977

2.998

70 Temperature Sensor Products precisionsensors.meas-spec.com






[Appendix]

Fig A3: Histograms showing bad data-Page-1


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[Appendix]



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[Appendix]



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[Appendix]



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