A 330 GHz, 19 mm i.d.,. 4.5 m long brass circular waveguide was tapped and tested. ... rectangular shape at a pitch of at least 2.5 grooves per Î» along the waveguide length .... and up taper transitions to the 330 GHz transmission line diameter.
IRMMW-THz2011 Houston, TX
330 GHz Helically Corrugated Waveguide Paul P. Woskova, Emilio A. Nannia, Michael A. Shapiroa, Sudheer K. Jawlaa, Jason S. Hummelta, Richard J. Temkina and Alexander B. Barnesb a Plasma Science and Fusion Center, MIT, Cambridge, MA USA b Department of Chemistry and Francis Bitter Magnet Laboratory, MIT Abstract—Corrugated waveguide made with a tap can significantly lower fabrication costs. A 330 GHz, 19 mm i.d., 4.5 m long brass circular waveguide was tapped and tested. Transmission measurements were compared with models that take into account the shape of the corrugation.
groove narrower than the wall between. The depth of the cutting thread wore down about 10% over the course of fabrication.
I. INTRODUCTION AND BACKGROUND
YNAMIC nuclear polarization (DNP) experiments require transmission of multiwatt cw millimeter/ submillimeter-wave power over several meters distance between the gyrotron and DNP magnets which must be sufficiently far apart to avoid mutual field interference . The most efficient waveguide propagation mode is the HE11 mode in metal waveguide with diameter > 2λ and having internal circumferential corrugations with a depth of 1/4λ for Figure 1. Photos of the 330 GHz tap and waveguide cross sections. Chips from cutting are present on the second tap rectangular shape at a pitch of at least 2.5 grooves per λ along tooth from left. the waveguide length [2, 3]. Machining individual corrugations becomes increasingly difficult as the corrugation III. MODELING dimensions shrink with frequency. Tapping a single helical We have derived an analytic formula for the exponential groove is more cost effective for making long HE11 waveguide runs. We report modeling and testing of a 4. 5 m long attenuation coefficient of a corrugated metallic waveguide 330 GHz transmission line that was constructed from fifteen with ideal rectangular grooves. The result was obtained by 19 mm i.d. 30 cm long brass tubing sections tapped with an 80 integrating the field equations of Doane  over the groove surfaces to obtain the ohmic loss: grooves per inch (3.15/mm) tap. Polarization rotation by a helically grooved waveguide becomes less of an issue at higher frequencies because of the 1 − t + d + t cos 2 ( kd ) + 1 sin( kd ) cos( kd ) inverse frequency cubed scaling. The rotation angle in radians 2 Rs 2.4 p p p kp can be estimated by : = + 1 α 2 2 3 2Z o k a (1 − t p ) sin 2 ( kd ) 3
2.405 LP ψ ≅ ka λ a where P is the groove pitch (period dependent on λ), L is the waveguide length, a is the internal waveguide radius, k the wavenumber and λ the wavelength. For our waveguide parameters the total rotation is estimated as 0.1° at 330 GHz, which is not sufficient to cause a problem for DNP experiments. II. FABRICATION Brass was chosen as the waveguide material due to its hardness for fine machining and good conductivity. The tap thread before and after machining and the resulting corrugations where examined under magnification as shown in Figure 1. The corrugations mirror the shape of the cutting thread looking approximately trapezoidal and with the cut
where t, d, p are the corrugation wall thickness, depth, and period, Rs surface resistance, and Zo the impedance filling the waveguide. As shown in Figure 2 for brass (conductivity 1.56 x 107 mhos/m), narrowing the groove width or decreasing the depth increases the transmission losses with the most marked effect on the lower frequency side of the transmission bandwidth. The deviation of the groove shape from rectangular was also found to have a similar effect on transmission losses. Expanding the groove shape in a Fourier series and adjusting the groove depth to be deeper as guided by the weight of the first Fourier term can be used to compensate the transmission losses for non-rectangular shape. The depth correction factor as determined by this approach is listed in Table 1 for various corrugation shapes. HFSS computer modeling for our waveguide groove shape (Figure 1) and assuming ideal brass
IRMMW-THz2011 Houston, TX 0.10
Corrugation Parameters Period = 0.3175 mm
thickness 0.5p, depth 1/8λ thickness 0.3p, depth 1/8λ thickness 0.5p, depth 1/4λ thickness 0.3p, depth 1/4λ
0.04 0.02 0 100
600 500 400 300 Frequency (GHz) Figure 2. HE11 calculated waveguide transmission loss (lines), measurements (□ radiometer, ∇ vector network analyzer), and model (⊕ HFSS) for ideal brass conductivity and a=9.5 mm. 200
conductivity is consistent with the analytical model. The HFSS calculated attenuation (Figure 2, lower point) corresponds to a thicker wall rectangular groove as expected.
Figure 3. VNA setup for 330 GHz waveguide transmission line loss measurements. resulting losses of about 2 - 3% for the complete 4.5 m straight waveguide length are acceptable for the intended application. Consequently using a tap to save fabrication costs of corrugated waveguide does not cause the quality of the waveguide to suffer, with deeper groove depth compensating for non-ideal rectangular shape. Reconstructed/Measured Intensity @ 10 cm 0
Table 1. Corrugation Shape Depth Correction Shape Correction Factor (d/drect) Rectangular ( t/p=0.5) 1.00 Trapezoidal (flat top 0.3p) 1.07 Sinusoidal 1.27 Triangular 1.57
0.5 -15 0 -20 -0.5 -25
IV. MEASUREMENTS Two methods were used to measure transmission losses near 250 GHz. In the first method a heterodyne radiometer and liquid nitrogen cooled blackbody (Eccosorb) were used to measure insertion losses to thermal noise over the band 248 ± 4 GHz as previously described . In the second method a vector network analyzer (Agilent E8363B with millimeterwave VNA extender V03VNA2-T/R) was swept over the 240 – 260 GHz range, averaging the influence of standing waves. The HE11 mode for testing was obtained from the rectangular WR-5 radiometer waveguide and the WR-3 VNA waveguide by rectangular to circular, smooth to corrugated, and up taper transitions to the 330 GHz transmission line diameter. From WR-5 the transitions used were the same ones for both methods. The VNA setup for transmission line losses is shown in Figure 3 with the VNA extender head and up tapers in the lower left of the photo. Spatial scans of the resulting beam at 10/20/30 cm distances from the waveguide aperture and using a phase retrieval reconstruction code showed an HE11 mode purity of 94.5 ± 1%, see Figure 4. The measured insertion losses were 0.047 ± 0.01 and 0.0259 ± 0.015 dB/m for the radiometer and VNA, respectively and are plotted in Figure 2. The measurements are somewhat higher than the analysis, but can be explained by conductivity that is less than the assumed idea value. The
-1 -30 -1.5
0 0.5 X-axis [cm]
Figure 4. Measured and phase reconstructed beam profile used for the measurements 10 cm from the aperture. This research was supported by NIH / NIBIB Grants R01EB004866 and R01-EB001965. REFERENCES 
P. Woskov, V. Bajaj, M. Hornstein, R. Temkin, R. Griffin, “Corrugated waveguide and directional coupler for CW 250-GHz gyrotron DNP Experiments”, IEEE Trans. on Microwave Theory and Tech., vol. 53, 2005, pp. 1863-1869. J. L. Doane, “Propagation and Mode Coupling in Corrugated and Smooth-Walled Circular Waveguides”, in Infrared and Millimeter Waves, vol. 13, chap. 5, K. J. Button Ed., New York: Academic Press, 1985, pp. 123-170. C.. Dragone, “Attenuation and Radiation Characteristics of the HE11 Mode”, IEEE Trans. on Microwave Theory and Tech., vol. MTT-28, 1980, pp. 704-710.