2152

PROPOSED HIGH-ACCURACY SUPERCONDUCTING P O W E R METER FOR MILLIMETER WAVES *

R. L. Kautz, D. G. McDonald, D. K. Walker, and D. Williams National Institute of Standards and Technology

Boulder, Colorado 80303

Abstract The accuracy of conventional microwave power meters is limited by the fact that some of the power dissipated in the meter is not sensed by the bolometric detector. In a proposed power meter, superconducting materials are used to virtually eliminate this source of error. Our goal is to measure a power of lOmW at frequencies in the WR-22 band (33 to 50 GHz) with an accuracy of 0.02%.

Introduction

The accurate measurement of microwave power is presently based on bolometric devices in which the power dissipated in a resistive element is sensed by measuring its temperature rise.' In principle, absolute microwave power can be evaluated by equat- ing it to the dc power required to produce the same tempera- ture rise in the resistive element. In practice, however, this basic equation must be modified to account for systematic errors, the largest of which results from microwave losses in the structure that supports the resistive element. For typical power meters,' the mount efficiency is about 95%, and 5% of the power is ab- sorbed in the mount instead of the intended microwave load. To determine the mount efficiency, it is necessary to perform a separate calorimetry experiment in which the microwave dissi- pation in the entire bolometer is compared to dc heating.2 When calibrated in this way, conventional bolometers allow microwave power to be measured with an accuracy typically between 0.2 and 0.5%.'*'

In this paper, we propose a design for a power meter in which superconducting materials are used to virtually eliminate microwavelosses in the bolometer mount. Our goal is to measure power with an accuracy of 0.02% without a separate determina- tion of mount efficiency. Attaining this goal depends in part on achieving a mount efficiency greater that 99.98% but requires in addition that all other sources of error be reduced below 0.02%. While our goal is ambitious, we describe in this paper a design which appears to meet all necessary criteria and present exper- imental verification of several crucial design assumptions.

Prototype Bolometer

The work described here centers on the prototype bolome- ter illustrated in Fig. 1, which is designed for the WR-22 mi- crowave band extending from 33 to 50GHz. The backbone of the device is a section of superconducting niobium waveguide which provides a low-loss support for the bolometer's resistive element. A copper flange at one end of the waveguide connects the bolometer to the source of microwave power and also makes contact with a heat sink at 4 K. The resistive element is a wedge of nichrome-coated sapphire attached to the opposite end of the waveguide. Because the bolometer is to be operated in a vac- uum, the only thermal contact between this microwave load and the waveguide occurs at the point of attachment, and heat gen- erated in the load must flow through the length of waveguide before being absorbed by the 4 K heat sink.

Microwave power is detected in this device by sensing the heat flow through the waveguide. Two sections of the waveguide are clad with copper and define approximate isothermal regions. The temperatures TI and Tz of these regions are monitored by germanium thermometers. Two other sections of the waveguide

* Contribution of the U. S. Government, not subject to copy- right. Manuscript received August 24, 1992.

are unclad and define thermal weak links across which a tem- perature difference will appear in the presence of heat flow. The longer of these weak links, assumed to have a thermal conduc- tance G, defines the sensitivity of the bolometer to microwave power. That is, the heat flow corresponding to a power P gives rise to a temperature difference between the two thermometers according to

The dc substitution resistor RI allows the bolometer to be cal- ibrated through the replacement of microwave power with a known dc power dissipated in the resistor.

Fabrication of the bolometer begins with the niobium waveguide, which is cut by electric discharge machining from a block of high-purity niobium having a nominal residual resis- tance ratio of nearly 300. Copper cladding is then electroplated onto the exterior of the waveguide and machined to form the isothermal sections and a pad for mounting the flange. Finally, the interior walls of the waveguide are mechanically polished to help reduce microwave losses.

The cryogenic environment required for operation of the bolometer is provided by the cryostat shown in Fig. 2. The arrangement shown here provides a good thermal connection between the bolometer flange and the 4 K cold plate and a good microwave connection between the bolometer flange and the room-temperature environment. The key element of the de- sign is a thermal ground consisting of a copper column, roughly 2.5 cm square in cross section, with a rectangular waveguide cut through it by electric discharge machining. The copper column

WR-22 FLANGE (COPPER, 4 K )

ISOTHERMAL

MICROWAVE LOAD 1 (NICHROME ON SAPPHIRE)

N GERMANIUM e THERMOMETER

L H E A T E R dcSUBSTITUTION / / RESISTOR RESISTOR

I- I

Figure 1. Prototype bolometer shown in cross section from the top and side. Hatching indicates either electroformed or OFHC copper.

insures that the bolometer flange is at a temperature near that of the cold plate while allowing direct microwave access to the bolometer. The microwave link to room temperature is com- pleted by a section of thin-wall stainless-steel waveguide that minimizes the heat leak between the 300 K and 4 K environ- ments. This waveguide section makes thermal contact with the 77 K shield, allowing a large fraction of the heat leak to be ab- sorbed by the liquid-nitrogen reservoir. The power that reaches the 4 K thermal ground by conduction through the stainless waveguide is estimated to be 35mW. An additional 7mW of power associated with thermal radiation from the 300 K environ- ment is intercepted by an infrared absorber located in the ther- mal ground. In the absence of this infrared block, the bolometer temperature is elevated significantly. The vacuum envelope of the cryostat is completed by a 25pm thick film of Mylar sand- wiched between microwave flanges at the 300 K port.

Having described the prototype bolometer, we now ask whether it is capable of measuring microwave power with an accuracy of 0.02%. In this regard, we can identify five areas of concern: calibration of the microwave path between 4 and 300 K, temperature resolution of the thermometry, dc substi- tution errors, reflection coefficient of the bolometer, and mount efficiency. With the exception of calibrating the microwave path, each potential source of error will be considered in detail. While calibration of the path between 4 and 300K is essential to the final utility of the bolometer and problematic because the path is interrupted by the vacuum seal and infrared block, a careful study of calibration methods has yet to be made. In the fol- lowing, we thus focus on the sources of error intrinsic to the bolometer.

Temperature Resolution

As indicated by Eq. (l), the sensitivity of the bolometer is determined by the conductance G of the thermal weak link, a smaller G yielding a larger temperature difference for a given input power. Because the temperature of the niobium must re- main well below its supercdnducting transition temperature, the largest temperature difference that can be used in the bolome- ter is roughly 1 K. Assuming that G is chosen to p d d this tem- perature difference for the power to be measured, we find that temperature must be known with an uncertainty of less than 200pK if the power is to be measured with an accuracy 0.02%.

Given that microwave power calibrations are usually per- formed near lOmW, an appropriate thermal conductance for

VACUUM JACKET (300 K)

77 K SHIELD /- PLATE

VACUUM SEAL (MYLAR)

WR-22 FLANGE

METER

\ STAINLESS WAVEGUIDE

Figure 2. Cross section of the cryostat showing how the bolome- ter makes thermal contact with the 4 K cold plate and is linked by waveguide to the room-temperature environment.

our bolometer is roughly G for the device shown in Fig. (l),

W/K. T

with an uncertainty of less than at 10 mW.

simply by monitoring Ti. that the flange temperature minutes. This observation led us to inc that is separated from the flange by a the shown in Fig. 1 and allows the tem

be stable within 50 pK over lo

dc Substitution Error

2154

Reflection Coefficient

Some fraction of the power incident on any bolometer is re- flected back toward the source rather than absorbed in the load. While the reflected power can in principle be measured and ac- counted for in a calibration, this correction must be made with an accuracy commensurate with the entire experiment. For ex- ample, if 1% of the incident power is reflected and the calibration is to be performed with an overall accuracy of 0.02%, then the reflected power must itself be measured to within 2%. Thus, power measurement i s greatly simplified and potentially more accurate if the reflection coefficient of the bolometer is small.

In designing a load for the prototype bolometer, we adopted an empirical approach to obtaining a low reflection coefficient. The basic design, used previously in cryogenic applications,' consists of a thin sapphire wedge coated with a nichrome film. A sapphire substrate is advantageous hccause its relatively high thermal conductivity gives the load a short thermal response time, Nichrome is also suited to the application because films with a relatively high sheet resistance are easily deposited and because its resistance is relatively insensitive to temperat~re.~ This temperature insensitivity allows the load to be tested at room temperature with the assurance that its reflection coeffi- cient will be nearly the same at 4 K.

In order to select an appropriate load, we fabricated and tested a variety of sapphire wedges coated with nichrome. The wedges were all 0.25" thick and 2.8" wide at the base (to match the waveguide height) but varied in length from 13 to 38". The nichrome films, with a nominal composition of 80% Ni and 20% Cr by weight, were deposited in thicknesses rang- ing from 6 to 19nm to yield sheet resistances between 120 and 40 fl/U. For testing, each load was mounted in WR-22 waveguide as shown in Fig. 1, with its surface parallel to the electric field and the tip positioned near a corner of the waveguide. (Some- what higher reflection coefficients were obtained with the tip centered in the waveguide.)

The results of tests made at room temperature using an au- tomatic network analyzer are shown in Fig. 3, where we plot the ratio of reflected to incident power as a function of frequency over the WR-22 band. Results are shown for two sheet resis- tances at each of three wedge lengths. As Fig. 3 indicates, the reflected power decreases dramatically as the length of the load increases from 13 to 38". At a length of 38mm, the power reflected by the load is less than 0.01% of the incident power (roughly the resolution limit of our measurement) over the en- tire WR-22 band, regardless of whether the sheet resistance is 53 or 86 fl/o. Thus, for measuring power at an accuracy of 0.02%, the power reflected from these loads is negligible. The fact that a suitably low reflection coefficient is obtained for values of sheet resistance differing by a factor of 1.6 implies that the change in film resistivity with cooling to 4K, typically a few percent, will not appreciably affect the reflected power.

Mount Efficiency

Finally, we turn to the error resulting from loss in the super- conducting waveguide that serves as a mount for the microwave load of the bolometer. In the prototype, this error is associ- ated with the section of waveguide between the bolometer flange and the thermometer TI where dissipation does not result in a heat flow sensed by the thermometer. If the mount efficiency is to be greater than 99.98%, then the loss in this 3cm section of niobium waveguide must be less than 0.02% of the incident power, and the attenuation of the waveguide must be less than 3 x dB/m.

Can an attenuation of less than 3 x loT2 dB/m be achieved in WR-22 waveguide? To answer this question, we have ex- amined waveguide losses in both theory and experiment. Ex- perimentally, at tenuation was measured at 4.2 K by calorimetry for both a superconducting lead-plated waveguide and a normal gold-plated waveguide. These experiments were performed on

2.5 cm fixed shorts fabricated by plating lead or gold on a rect- angular mandrel, electroforming the copper body of the short over the plated surface, then removing the mandrel and attach- ing a flange. With shorts made in this way, the interior plating is continuous between the wall of the waveguide and the shorted end. The loss in each fixed short was measured using an ar- rangement similar to that shown in Fig. 2 with the bolometer replaced by the fixed short. In this case, the short was supported separately and positioned with a gap of about 0.03 mm between its flange and the thermal ground. With this vacuum gap to thermally isolate the short from the microwave feed line and a weak thermal link between the short and the 4K cold plate provided by its support structure, microwave dissipation in the short could be sensed by monitoring its temperature. Calibra- tion ww provided by a dc substitution resistor attached to the short.

Theoretical values for the attenuation were calculated from the formula'

appropriate to the TElo mode in a rectangular waveguide with a height-to-width ratio of 112. In this equation, R, is the surface resistance of the conductor, b is the height of the waveguide, pl is the impedance of free space, f is the microwave frequency, and fc is the guide cutoff frequency (fc = 26.35GHz for WR- 22 waveguide). Equation (2) thus allows the attenuation of a waveguide to be evaluated provided the surface resistance of the conductor is known.

For gold at 4.2K the mean free path of the conduction electrons is much larger than the classical penetration depth at 40GHz and the surface resistance must be calculated using

(3)

13mm. 40RlO i n

23 mm, 40 OIL!

-30

-40

-50

-- 35 40 45 50

FREQUENCY (G H Z)

Figure 3. Ratio of reflected to incident power as a function of frequency measured at room temperature for various nichrome on sapphire loads in WR-22 waveguide. Each curve is labeled by the length of the sapphire wedge and the sheet resistance of the nichrome film.

for the extreme anomalous limit, where po is the permeability of free space, a is the conductivity, and k is the mean free path. Because the ratio u/e is nearly independent of conductivity and assumes a value of roughly 10'' S/mZ for gold,' Eq. (3) allows the surface resistance to be evaluated even though the conduc- tivity of our gold plating is not known.

For superconducting lead and niobium, calculation of the surface resistance is more problematic. The calculations pre- sented here are based on the Mattis-Bardeen expression for the complex conductivity.* In this formulation, the surface resis- tance at a given temperature and frequency depends on three material parameters: the energy gap parameter A(0) at OK, the transition temperature T,, and the normal-state conduc- tivity a,. While values for A(0) and T, are well known for lead (A(0) = 1.37meV and T, = 7.2K) and niobium (A(0) = 1.53meV and T, = 9.2K), the normal-state conductivity is de- pendent on material preparation. To obtain realistic estimates for the surface resistance, we determine a, by adjusting it to pro- duce agreement between our calculation and measured values of the surface resistance. Based on experimental values of R, at 4.2K and 10GHz tabulated by Halbritter: 34pQ for lead and 24pQ for niobium, we obtain the normal state conductivities Q,, = 9 x 10" S/m and U, = 4 x 10" S/m for lead and niobium. Thus, the surface resistances calculated here are, in a sense, ex- trapolated from values of R, measured at lower frequencies.

Results for the attenuation in WR-22 waveguide derived from both theory and experiment are plotted as a function of frequency in Fig. 4. Comparing the theory curves for Au, Pb, and Nb with the attenuation required for a 99.98% mount ef- ficiency (indicated by a dashed line), we find that the losses predicted for gold are an order of magnitude too high to be ne- glected, while those predicted for lead and niobium are almost an order of magnitude lower than required. Thus, while the ad- vantage of superconductivity is not nearly as large here as at lower temperatures and frequencies, it is sufficient to make the proposed power meter a real possibility.

lolr--l h

E a \ U v

z 0

100

10-1

10-2

FREQUENCY (GHz)

Figure 4. Attenuation as a function of frequency for WR-22 waveguide at 4.2 K. Experimental and theoretical results are shown for lead and gold plated waveguides and theory alone is shown for niobium. A dashed line indicates the level of atten- uation required for a 99.98% mount efficiency in the prototype bolometer.

The attenuation measured gold-plated waveguides CO

for lead are significantly lo experimental data show rap not understood. These variati of resonances in the vacuum gap th the fixed short from the thermal is correct, then our measur with waveguide propagatio artificially high. Taking th however, we still find that that required for a 99.98% of the WR-22 band.

Conclusion

The prototype bolomete nearly ideal power meter by of the incident power. As we this bolometer reflects no mo Assuming that the losses i lead, the power absorbed less that 0.02% over a s i p the dc substitution error can the proposed bolometer offe

magnitude.

Acknowledgments

and J. E. Sauvageau for c the course of this work with lead electroplating.

92MP00017.