IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 5, OCTOBER 2002
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Slow-Wave Structures-Based Method of Measurements Yu. N. Pchelnikov and David S. Nyce
Abstract—A novel electromagnetic measurement method is described from the physical point of view. Based on the application of slow-wave structures, this method combines the advantages of relatively high and relatively low frequency bands. Concentration of an electromagnetic field, caused by wave deceleration, leads to a significant increase in sensitivity. The main parameters and characteristics of the sensitive elements, built as sections of slow-wave structures, are considered in this paper. It is shown that the electric and magnetic fields split in the transverse direction in sensors based on coupled slow-wave structures. This leads to an additional increase in sensitivity. Some examples of practical slow-wave structure-based measurement methods are also presented.
Along with their advantages (high sensitivity, high resolution, and small dimensions), RF and microwave sensors have some serious drawbacks. Among these are: complexity and high cost of the microwave measuring circuits, restricted volume inside the waveguide, radiation and electromagnetic losses in conductors, and resonance frequency dependence on the ambient temperature.
Index Terms—Attenuation, deceleration, resonant frequency, RF measurements, slow-wave structures.
Replacing a standard transmission line with a slow-wave structure (SWS) makes it possible to achieve the high sensitivity of RF and microwave methods while operating at a relatively low frequency, thus eliminating the disadvantages mentioned above. Decelerating (slowing) an electromagnetic wave by a factor of -times results in an -times decrease of the SWS resonant length. Therefore, it follows that the same sensitivity can be achieved at an -times lower frequency, or the same sensitivity can be achieved by an SE with -times less length. Some physical attributes of SWS-based sensitive elements are analyzed and presented in this paper to illustrate the advantages and possible applications of using this type of sensitive element for the purpose of making physical measurements.
I. INTRODUCTION
T
HE development and realization of RF and microwave measurement techniques have shown advantages in using electromagnetic waves for monitoring various parameters of industrial processes. Methods for monitoring of liquid and freeflowing materials, measurements of sheet metal thickness, and of inner and outer diameters of metallic and dielectric materials, etc., have been created and patented [1]. In most of the measurement methods listed in [1], a section of a transmission line was used as a sensitive element (SE). A phase delay in the SE, or its resonance frequency, can be used to indicate the measured parameter of the material or process being monitored. A change in the electrical parameters of a material placed in an electromagnetic field leads to electromagnetic wave reflection, or to changes in the electromagnetic wave velocity and attenuation. The measured changes in the parameters of the electromagnetic wave are proportional to the electrically active length of the electrodynamic SE. The higher the electromagnetic wave frequency and the longer the electrically active length, the larger the sensitivity will be. As a rule, the sensitivity of the SE is approximately proportional to the relationship between the volume of the monitored material, , and the measuring volume , the latter being inversely proportional to or , where is the operating or resonance frequency. From this, it follows that the sensitivity is proportional to the second or third power of the frequency, the degree depending on the SE design. This relationship provides the basis for a wide range of measurement applications using RF and microwave technology. Manuscript received May 29, 2001; revised July 1, 2002. Y. N. Pchelnikov is with the Sensors Division, MTS Systems Corporation, Cary, NC 27513 USA (e-mail:
[email protected]). D. S. Nyce is with the Sensors Division, MTS Systems Corporation, Cary, NC 27513 USA (e-mail:
[email protected]). Digital Object Identifier 10.1109/TIM.2002.806011
II. SLOW-WAVE STRUCTURE APPLICATION
A. SWS-Based SE In general, the SWS is a transmission line in which one or more specially shaped conductors (impedance conductors) are used to decelerate an electromagnetic wave. An impedance conductor of this type comprises a series of conducting elements that are periodic along the direction of propagation of the wave and separated by a gap. Their shape can be in the form of a helix (Fig. 1), a meander line (Fig. 2), a radial spiral, or any configuration that increases the length of the path to be taken by the electromagnetic wave. An additional (nonimpedance) conductor, called a screen conductor, can be used with the impedance conductor, this one having a simple configuration (a cylinder, a tape, or a rod). The deceleration of an electromagnetic wave in the SWS is caused mostly by the increase in the length of the path traveled by a wave along the conductors forming the SWS. Slow-wave structures were originally developed for use with an electron beam. Therefore, in the previous microwave literature [2], [3], many important features of slow waves have not been fully considered. Detailed consideration of these features has permitted the creation of new methods and devices for the measurement of several physical parameters, e.g., surface resistance [4], liquid level [5], [6], etc.
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Fig. 1. Helical SWS.
Fig. 3. Two-wire helix; arrows show directions of the currents for anti-phase mode wave.
B. Main Properties of an The amplitudes of electric and magnetic fields , electromagnetic wave that has been slowed down are proportional to the “wave factor” (1)
Fig. 2.
Meander line; arrows show directions of the currents in the conductors.
The impedance and screen conductors are usually aligned with their wide sides against each other, or in the case of axially symmetric systems, installed axially. The main geometrical parameters that define the SWS are the period of the layout or perimeter , of the transversal conductors, and width where is the impedance conductor radius. In many cases, the distance between the impedance and screen conductors is also essential. In a one-wire helix, the period coincides with its pitch; and in a multiwire helix, for example, the two-wire helix shown in Fig. 3, the period is equal to the distance between the axes of adjacent coils. In the case of a meander-line, the period is twice the distance between the proximate axes of the transversal conductors. The SWS-based SE is a section of the SWS, in which one or both ends are connected to a measuring circuit. When formed from thin conductors on a dielectric base, the SWS-based SE is simple to produce and uses only a small amount of metal. When the conductor pattern is deposited on a dielectric substrate, it is more stable with temperature than a solid metal SE would be. Functioning at relatively low frequency results in small electromagnetic losses in the conductors and the surrounding media, and a very small amount of radiation due to heating. The SWS-based sensitive elements can differ by configuration and number of conductors, by the direction of the slowed wave propagation (axial, radial), or by the configuration of their cross section, etc. This allows the creation of sensors for measuring plane, cylindrical, and other shapes of areas or volumes, optimizing the design for a given problem.
where is a time, is an angular frequency, is a coordinate in the direction of wave propagation, and is a wave constant in which the real part is defined by phase velocity , as (2) The velocity of electromagnetic wave propagation in any , where and transmission line is equal to are the specific distributed inductance per unit length and the specific distributed capacitance per unit length, depending on the configuration of the conductors and the distance between them. Coiling one or both conductors of a two-conductor transmission line increases the inductance and adds additional capacitance. This leads to deceleration of the propagated wave, defined as the ratio of light velocity in a vacuum to phase in the SWS velocity (3) are the permittivity and the permeability of the where , vacuum. In a simple two-conductor transmission line, it is obvious that a decrease in spacing between the conductors will cause an increase in capacitance . Because the currents in the conductors are in opposite directions, there will also be a decrease in inductance , thus allowing the wave velocity to remain the same (equal to the velocity of light). In the SWS, however, the and differs because the influence of conductor spacing on currents in adjacent conductors flow in the same direction. This means that it is possible to change the wave velocity by changing the distance between conductors of the SWS. As a result, deceleration and attenuation of a surface electromagnetic wave de-
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pend not only on the parameters of the surrounding medium, but also on the distance from the conductors to the metal surface and the distance between the conductors of the SWS. This can be used to obtain information on the displacement, deformation, and thickness of different objects, on the gaps between a sensor and a measured surface and on the electrical parameters of different materials. Deceleration of an electromagnetic wave, followed by an in, increases the characteristic crease in specific inductance wave impedance . Using the formula for wave impedance and (3), one can write (4) It is seen from (4) that, in the case of a constant value of specific capacitance , the wave impedance is proportional to deceleration . This means that the impedance can vary over a wide range, thereby producing sensitive elements having wave impedances from a few ohms to thousands of ohms. It is important to note that an increase in wave impedance leads to an increase in electromagnetic losses in an adjacent medium and a decrease in losses caused by currents induced in SE conductors. This also leads to an increase in the sensitivity of measurements that can be made using the dependence of the attenuation of a slowed wave upon a monitored parameter, e.g., the measurement of humidity, low conductivity, etc. III. IMPORTANT CHARACTERISTICS As explained above, the sensitivity of a transmission line can be increased by forming the impedance conductor in the shape of an SWS. This increase in sensitivity is similar to that achieved with a simple transmission line through increasing the resonant or operating frequency. In addition, there are other important advantages of using the SWS-based SE, some of which are described below. A. Energy Concentration Slowing of the electromagnetic wave leads to concentration of the electromagnetic field near the impedance conductors, thus eliminating the radiation of energy. This makes it possible to work with open volumes, mounting the SE either inside or outside of the measured volume. In a flat impedance conductor, electric and magnetic field distribution near the surface is exponential (Fig. 4), the field intensity being approximately propor, where is the coordinate perpendicular to tional to the surface of the impedance conductor. As a result, 86% of the –thick, energy is concentrated in a layer approximately where is the electromagnetic wave length in vacuum. The field distribution is more complex in an axially symmetric structure, but always having a “surface” character where the thick. ness of the energy concentration area is proportional to This makes it possible to have two ways by which to vary the range of volume to be measured: either by changing the deceleration while maintaining the same frequency or by changing the frequency while maintaining the same deceleration. Alternatively, a simultaneous change in both frequency and deceleration enables the transverse structure of the field to remain
Fig. 4. Distribution of electric E and magnetic H fields of a slowed wave near a plane impedance conductor.
unchanged. Consequently, this enables one to carry out similar measurements on objects of different sizes. For example, one can measure the thickness of a resistive coating on a dielectric or a semiconductor substrate or the thickness of a radio-absorbing coating on an aircraft or warship [7]. B. Splitting the Electric and Magnetic Fields Slowed waves in the SWS, unlike fast waves in waveguides, are hybrid waves, comprising fields with electric ( ) and magnetic ( ) polarization. In many practical cases, a slowed wave can be represented as the sum of - and -waves, the transverse components of which are expressed in terms of the derivative of the longitudinal component of the electric or magnetic fields with respect to the transverse coordinate [8]. However, these waves only exist together in the SWS and have the same velocity as eachother. The distribution of electric and magnetic fields of - and -waves in the cross section of the SWS can differ due to the difference in polarization. For example, a longitudinally conducting screen can shield an -wave. An -wave can be shielded by a transversally conducting screen. As it follows, from Maxwell’s equations, the energy of an electric field stored in an -wave exceeds the energy of the magnetic field by times. The energy of a magnetic field stored in more than an -wave exceeds the energy of the electric field by more times. This means that the electrical parameters of the than medium or the object being monitored (the conductivity, the permittivity, and the permeability) have different effects on the -wave and -wave, thus manifesting their characteristic type of anisotropy [9]. C. Space Harmonics A slow wave is shaped by a periodic sequence of conductive elements and has a composite field representing an infinite amount of space harmonics [3]. However, in the case of the SWS-based SE, the length of the SWS segments is usually selected to be about one-fourth or one-half of the length of the slow wave . The period is selected to be much smaller than the SWS segment length , i.e., satisfying the condition in which . This the phase progression of one period is much less than allows the replacement of a periodic sequence of conductive elements by a continuous conductor with an anisotropic conduc-
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Fig. 5. Interdigital comb; arrows show directions of the currents in the fingers and in the bases.
Fig. 6. Coupled arithmetic spirals (i.e., one clockwise, the other counter clockwise).
tivity. This impedance approximation takes into account only the harmonics that contain most of the energy of the wave. As a rule, it is the zeroth harmonic for which the dependence on coordinate is defined by the wave factor (1). In some cases, it could be the total of the plus and minus first harmonics, which have phase velocities in opposite directions. These harmonics represent a standing wave with a space period of the SWS being considered. By representing this standing wave as a periodic function, it can be approximated using cosines or sines, depending on the component of the field to be considered (5) where is the distance between centers of the neighboring transverse conductors, equal to a half period in a meander-line or to a period in the case of a bifilar helix. There is another dependence on coordinate that leads to another distribution in the transverse direction. The field components of 1, 1 harmonics are concentrated in a much thinner layer in comparison to the zeroth harmonic. Taking into account , one can see that in the application being considered, that the dependence of the amplitudes of the 1, 1 harmonics on coordinate does not depend on frequency and is propor. This means that the area of energy contional to . centration is approximately equal to The field distribution depends not only on the configuration and period of the SWS, but also on the type of the wave excited in the SWS. For example, an anti-phase wave in a bifilar helix (Fig. 3) is basically represented by the 1, 1 harmonics, while an in-phase wave of the same structure is represented by the zeroth space harmonic. In a meander line, due to the alternation of the current direction in the transverse conductors (Fig. 2), components of the -wave are represented by a total of the 1, 1 harmonics and are proportional to the right part of (5), while components of the -wave are represented by the zeroth harmonic and are proportional to the right part of (1). An opposite combination can be seen in an interdigital comb (Fig. 5). Here, due to the opposite voltage potentials between neighboring fingers, the -wave components are represented by 1, 1 harmonics, while components of the -wave are represented by the zeroth harmonic (direction of the current in neighboring fingers is the same). Due to a substantial decrease in the phase velocities of the 1, 1 harmonics in comparison to the phase velocity of the zeroth harmonic, the fields of the - or -waves (or both),
Fig. 7. Coupled meanders, shifted longitudinally with respect to one another at half period.
represented by 1, 1 harmonics, can be concentrated near an impedance conductor’s surface without decreasing the phase velocity of the zeroth space harmonic. This allows the use of a relatively low frequency for measuring the conductivity of semiconductors, and makes possible the noncontact measurement of a resistive coating with resistance exceeding 0.5 M per square [10]. IV. COUPLED SWS-BASED SE The electromagnetic wave in the SWS can be slowed by other means, in addition to increasing the length of the conductors. In a coupled SWS formed by two impedance conductors rotated 180 (mirror images of one another), such as oppositely directed radial spirals (Fig. 6), or meander lines shifted in the longitudinal direction (Fig. 7), the deceleration of the anti-phase wave can exceed the deceleration of the slowed wave in one impedance conductor by many times. When the distance between impedance conductors is much less than their period , of a coupled SWS for anti-phase exthe specific inductance citation exceeds the inductance of one conductor by four times. is approximately equal to the caThe specific capacitance pacitance between the two plates, i.e., it is inversely proportional to the distance , and can be very large. This approximate analysis shows that the specific parameters of one plane impedance conductor with a zeroth space harmonic are given by the expressions (6)
PCHELNIKOV AND NYCE: SLOW-WAVE STRUCTURES-BASED METHOD OF MEASUREMENTS
Fig. 9. Fig. 8. Distribution of electric and magnetic fields in a resonant SE based on coupled arithmetic spirals.
(7) is the where is the width of the impedance conductor, and geometric deceleration, which is equal to the ratio of the length of the conducting elements forming the impedance conductor to the length in the direction of wave propagation. If a second conductor of the SWS is a metal plate placed in parallel to the impedance conductor at a small distance , the inductance decreases and capacitance increases approximately by the same factor, i.e. (8) (9) The characteristic wave impedance
in this case is (10)
Taking into account that the inductance of a coupled SWS increases fourfold in comparison to a free conductor’s inductance, as mentioned above, one can obtain the following from (3), (8)–(10) (11) (12) These expressions show that the deceleration of an electromagnetic wave in the coupled SWS can be many times more than the geometric deceleration. It is important that the increase in deceleration due to the decrease in distance is not accompanied by a very large decrease in the characteristic wave impedance . Coupled SWS-based sensitive elements have another important advantage. When the anti-phase wave is excited, the -wave is concentrated between the impedance conductors and the -wave is concentrated outside of the conductors (Fig.8). Remembering that the electrical energy is concentrated mainly in the -wave and the magnetic energy is concentrated mainly in the -wave, we see the possibility of splitting the electrical and magnetic fields. Such splitting increases the sensitivity when making a gap measurement, or measuring a resistive coating, etc. When the in-phase wave is excited in a coupled SWS, the electric field is outside of the impedance conductors, while the
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Precision gap sensor developed by MTS systems corporation.
magnetic field intensity has a maximum value between the conductors. The specific capacitance in this case is the same as for a one-impedance conductor, while the specific inductance is the same as for an impedance conductor with a metal plate at half the distance of that between impedance conductors. Both the impedance and capacitance are much less than for an anti-phase wave. It follows that the deceleration of in-phase waves is less than the geometric deceleration . If both modes (in-phase and anti-phase) are excited in a coupled SWS at the same frequency simultaneously, two different parameters of the monitored material can be measured. For example, the thickness of a dielectric coating on a metal surface can be measured without making contact with the coating. V. PRACTICAL APPLICATION The characteristics of the SWS-based method of measurements presented above allow the creation of sensors for monitoring different industrial processes, and measuring practically all physical parameters, including electromagnetic parameters of materials, linear and angular displacement, position, vibration, pressure, thickness, etc. The SWS-based sensors can be used at power generation stations, on vehicles, at chemical plants, in scientific research, in agriculture, and in medicine. The advantage of making measurements using the SWS was demonstrated by the fabrication of a sensor to measure the thickness of a thin metallization layer [11], and by developing a new method for monitoring liquid level [5]. Splitting of - and -waves in a coupled SWS, for example, -wave shielding, allows noncontact detection of the distance to a metal target. Developed by MTS Systems Corporation, a precision sensor with the SWS-based SE, shown in Fig. 9, can measure the distance to a metal target with accuracy of 1 micron in the 5 mm range. This sensor is not sensitive to dielectric materials, and is stable with temperature and electromagnetic radiation. It was also shown that sensors based on a coupled SWS could be used for monitoring corrosion in pipelines [12]. One of the most promising applications can be semiconductor material monitoring. From the analysis of the interaction between a slowed electromagnetic wave and a semi-conducting film [4], the measurement of a relatively small resistivity requires using an -type slowed wave while a large resistivity can be measured using an -type wave. This interaction is ildependence upon the lustrated by the relative frequency surface resistivity , measured in an -type wave (curve 1 in Fig. 10) and in an -type wave (curve 2 in Fig. 10). Here, is
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Fig. 10. Relative resonance frequency f =f versus surface resistance measured in H -wave field (curve 1) and E -wave field (curve 2) accordingly. Curve 3 shows a calculated dependence.
the resonance frequency of the SE, and is the resonance frequency in the absence of the monitored film. In the first case, the measured film was placed in parallel to the SE, based on coupled arithmetic spirals (Fig. 6). The anti-phase excitation of coupled spirals ensures a mainly magnetic field in the measured MHz). films and a relatively low resonance frequency ( In the second case, a meander line (Fig. 2) was used to ensure a mainly -type field in the measured films. The small conductivity of films in this case could not influence an -type wave. Curve 3 in Fig. 10 shows the calculated dependence of the relative frequency. In general, SWS-based sensors are not sensitive to external signals, to radiation, to high electromagnetic fields, or to aggressive media. In spite of such valuable characteristics, they have a very simple design and technology required for production. Slight variations in the construction allow one to create transducers with a very wide range of different possibilities and applications. VI. CONCLUSION Generalizing, it should be noted that the features of the slow-wave structure-based sensitive element (SWS-based SE) described herein enable them to be used for measurements of practically all physical parameters. Using the advantages of systems with distributed constants, the SWS operates at a relatively low frequency, which is more convenient for primary conversion of the information signal, but at a sufficiently large frequency to provide high accuracy and high speed of response. Splitting of the electrical and magnetic fields leads to a large increase in sensitivity and allows the development of new measuring technologies. The low electromagnetic losses inherent with these devices also help to increase their accuracy and sensitivity. REFERENCES [1] E. Nyfors and P. Vainikainen, Industrial sors. Norwood, MA: Artech House, 1989.
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[2] J. R. Pierce, Traveling-Wave Tubes. Princeton, NJ: D. Van Nostrand, 1950. [3] D. A. Watkins, Topics on Electromagnetic Theory. New York: Wiley, 1958. [4] Y. N. Pchelnikov and D. S. Nyce, “Analysis of the interaction between a surface wave and conducting coating,” Proc. 13th Int. Conf. Vacuum Web Coating, pp. 91–101, 1999. , “Electromagnetic method of liquid level monitoring,” U.S. Patent [5] 6 293 142 B1. [6] D. S. Nyce and Y. N. Pchelnikov, “Application of slow-wave structures for liquid level monitoring,” J. Commun. Technol. Electron., pp. S115–S119, 2000. [7] Y. N. Pchelnikov and A. A. Elizarov, “Radio wave methods of monitoring the electromagnetic parameters of radioabsorbent materials,” Meas. Tech., vol. 37, no. 12, pp. 1336–1340, 1994. [8] L. N. Loshakov and Y. N. Pchelnikov, Theory and Calculation of Amplification of the Traveling Wave Tube (in Russian). Moscow, USSR: Sov. Radio, 1964. [9] Y. N. Pchelnikov, “Anisotropy of a semiconductor film in the field of a slow wave,” J. Comm. Technol. Electron., vol. 39, no. 10, pp. 66–69, 1994. [10] , “Novel possibilities of secure papers manufacturing,” Proc. 11th Int. Conf. Vacuum Web Coating, pp. 83–91, 1997. [11] Y. N. Pchelnikov, A. V. Fadeev, and V. V. Annenkov, “Opportunities of liktash thin film measurement method in comparison with existing hardware,” Proc. 7th Int. Conf. Vacuum Web Coating, pp. 26–42, 1993. [12] Y. N. Pchelnikov and A. S. Sovlukov, “Radio-frequency nondestructive methods for metal pipeline surfaces defects monitoring,” Paper Summaries of ASNT Sum Fall Conf. Quality Testing Show, pp. 239–241, 1996.
Yu. N. Pchelnikov was born in Leningrad, Russia, in 1928. He received the M. S. degree from Moscow High Technical School (after Bauman; now Moscow Engineering University), Moscow, Russia, in 1952. He received the Ph.D. and the Doctor of Science degrees in radio electronics in 1958 and 1971, respectively. He joined tbe radio electronics defense industry, where he participated in the creation of the new traveling-wave tubes and the development of their theory. In 1973, he earned the title of Professor. Between 1971 and 1991, he was a Head of the Microwave and Quantum Electronics Department, Moscow Institute of Electronics and Mathematics, Moscow, where he remained until 1996. The last years of his scientific interests were concentrated on the unconventional application of slow-wave structures (for defense and industrial purposes). He created new radiators for physiotherapy and new measurement methods and devises based on slow-wave structures’ applications. He also developed noncontact sensors for measuring thin metal layer thickness and detection of cracks on metal surface. Since 1996, he was been with MTS Systems Corporation as a Research Scientist, participating in the creation of new measurement technology based on slow-wave structure application. He has approximately 200 certified inventions, including four U.S. patents. He has published two books, and approximately 200 articles and papers. He has also mentored 35 Ph.D. dissertations.
David S. Nyce studied electronics engineering at Temple University, Philadelphia, PA, and Lehigh University, Bethlehem, PA, and business at Temple University and Concordia College, receiving the BSEE and MBA degrees. He has worked on sensor development with six different corporations, including Honeywell and MTS systems corporation. His work as an Electronics, Mechanical, and Chemical Engineer has included the design of sensors and systems for measuring pressure, flow, temperature, position, acceleration, and gas analysis. In addition to sensors, he has designed analog, digital, and microcomputer circuitry and software. He was Vice President of Neutronics, Inc., in Exton, PA, and is currently Director of Technology with the Sensors Group of MTS Systems Corporation, headquartered in Eden Prairie, MN.
