To: file waveguidecalorimeters1.wpd

From: Jon Hagen

Date: 9-25-2006

Subject: Waveguide calorimetry for transmitter power measurement

Summary

Measuring the heat produced by waveguide loss is a way to make accurate and stable RF power measurements in our high-power transmitters. Waveguide calorimeters can be calibrated initially using dummy load calorimetry. Some waveguide calorimeter designs can also be calibrated from fundamental principles, providing a cross check against dummy load calorimetry.

1. Introduction

It would seem that monitoring the power of a megawatt transmitter is simple: just tap off a known tiny fraction of the power in the output waveguide and measure it with an accurate off- the-shelf microwave power sensor. This is easier said than done, however, and neither our 430 MHz transmitter nor our S-band transmitter has a power monitor accurate to more than about 1dB (25%). The problem lies in the calibration of the directional couplers and any attenuators that follow them. The total attenuation, i.e., coupling coefficient plus attenuators, must be very high in order to present, say, 100mW to the power meter. For the S-band transmitter, the attenuation needed to produce 100mW from 1MW is 70 dB, a factor of 10 7. If we want to measure the power with an accuracy of 2%, the attenuation factor must be known to 2 parts in 109. In order to calibrate the power monitors, both transmitters have dummy loads equipped with instrumentation to measure the coolant flow rate and the temperature rise. Dummy load calorimetry can provide a calibration for the RF power sensor that monitors total power. However, it does not provide a calibration for the other RF power sensors, e.g., output power monitors for the individual klystrons, unless those power sensors, together with their directional couplers, are temporarily placed in line at the input to the dummy load, a procedure which is hardly practical.

The dummy load calorimeters on both transmitters should be improved1 and restored to operating condition to serve as calibration standards for the total power monitors, which can be the standard sampled RF power meters2, or waveguide calorimeters as discussed below.

The disadvantage of sampled RF power monitors is that, rather than sensing an effect caused by the total signal, they monitor only a fraction, and that fraction must be stable to, say, two parts in 109. Even after accurate calibration using dummy load calorimetry, it is difficult to guarantee that the coupling is not altered by dimensional changes in the coupler caused by temperature fluctuations and mechanical stresses.

2. Waveguide Calorimeters

When operating at 1MW, the aluminum WR430 S-band waveguide dissipates heat at a rate of 783 watts per foot, a value directly proportional to the product of the power and the resistivity of the waveguide walls. If the resistivity of the walls is known to 2% accuracy, the heat dissipation per foot is known to 2% accuracy, so power determination via calorimetric measurement of the heat dissipation can be considered a secondary standard. The heat is extracted from the outside of the waveguide walls by cooling jackets on the broad top and bottom walls of each waveguide section. The top and bottom jackets are connected in series, so that each waveguide section has one input and one output for the coolant flow.

The coolant flows from one waveguide section to the next, as shown in the above figure. Note that, if the cooled waveguide sections are identical, the heat added to the water flowing through any section will be equal to the heat dissipated3 in that section, as long as the sections are wrapped with thermal insulation so that no heat is exchanged with the ambient air. The power dissipated in the waveguide section is given by

Dissipation|WATTS = 146.3 x flow|gpm x T|Fahrenheit degrees .

The power flowing through the waveguide section is proportional to the dissipation as follows:

Pwaveguide = (2 ) x (Dissipation) x (length|meters)

where the constant depends on the size and material of the waveguide and the frequency. Note that is just the real part of the propagation constant of the wave in the guide; the amplitude decreases as e- x and the power decreases as e-2 x. Appendices 1 and 2 calculate for the S-band and 430MHz waveguides, both of which operate in the fundamental TE10 mode of the rectangular guides.

2.1 Absolute Flow Calorimeter

The figure above shows a straightforward setup to measure the heat produced by a waveguide section. The temperature difference between coolant inlet and outlet is measured and the flow rate is either measured or set by a positive-displacement pump ("metering pump"). The accuracy is probably limited by the accuracy in measuring T. If thermocouple or thermopile (several thermocouples in series) is not accurate enough over the range of temperatures encountered, platinum resistance thermometers often are used to monitor the separate input and output temperatures and their readings are then subtracted.

2.2 Series Substitution Calorimeter

The substitution calorimeter shown above, uses an electric (dc or low-frequency ac) heater in series with the waveguide cooling circuit. The power to the heater is adjusted until the heater and the waveguide produce equal values of T. With this method there is no need for a flow meter or flow regulator. The power to the heater would be regulated with a feedback circuit to automatically maintain equal values of T. The heater power is then equal to the RF power. This circuit requires either two thermopiles or three absolute temperature sensors.

2.3 Parallel Substitution Calorimeter

In this substitution method, only a single T is sensed and, since it is made zero by adjusting the heater, a single thermopile will suffice over a wide range of temperatures. The 'catch' in this method is that the coolant flow must be split in half (or by a known and stable value close to 1/2). Some experimentation could show whether this can be done sufficiently well with "Y" fittings in the fluid lines or whether it might require something as elaborate as a motor-driven fluid "commutator valve" or a dual metering pump. Pulsed flow would be acceptable, as the pulsing could be fast with respect to the long thermal time constants. This method is particularly appealing, in that no actual measurements need be made of either flow rate or temperature difference(s). Another intriguing feature of this design is that, if the heater is designed to have the same heat capacity as the waveguide section, the response time could be quite fast since both units would equilibrate at the same rate, even if that rate is slow.

2.4 Balanced Series Substitution Calorimeter

The configuration shown above puts the heater back in series with the waveguide cooler, so there is no need for a coolant flow divider. Nor is a flow meter required. With only the RF on, T is measured. Then the RF is turned on and the heater is turned on and adjusted to produce the same T. The advantage is that the actual value of T is not important. But note that when the RF is turned off, the waveguide must be thermally isolated at its flanges so that there will be no net heat loss from it. Such isolation would be difficult to provide. Moreover, because an 'off' and then an 'on' must be done, this is not a steady-state measurement, and the environment may change between the "off" and the "on."

5. Dry Waveguide Calorimeter

The calorimeter shown below was described by Brady4, who also pointed out the difficulties in

"making high-power measurements by using reduced-signal sampling devices in which a low- power meter is used." The high power he intended to monitor was a mere kilowatt. Brady's

calorimeter uses a section of waveguide, uncooled, except at the end where water-cooled

blocks maintain a constant temperature. The waveguide section is wrapped with insulation in order that all the dissipated heat must travel by conduction to the water-cooled blocks. A sensor (or sensors) measures T, the temperature difference between the middle of the section and one of the blocks.

In principle, the power dissipation of the section can be absolutely determined from T, but this requires knowledge of the electrical resistivity, and thermal resistivity of the material and a theoretical calculation of the temperature distribution throughout the guide. Brady made the simplifying assumption that the guide is equivalent to a one-dimensional bar. In fact the dissipation is constant over the side walls of the guide, but varies over the broad walls, reaching a maximum at the center. The figures below show the relative dissipation per unit wall area for both the WR430 (S-band) and the WR2100 (430MHz) waveguides.

Nevertheless, the assumption that the guide is a one-dimensional rod will be correct if the walls of the waveguide are thickened in proportion to the head dissipation, or at least approximately, as shown below.

Assuming one-dimensional heat flow, a straightforward heat flow analysis shows that the temperature drop between the middle and either end of the device will be given by

where Pd is the power dissipated per unit length, l is half the length of the section, K is the thermal conductivity of the wall material, and A is the cross-sectional wall area.

This results in quite practical numbers: For the S-band, running at 1MW through a 10-inch waveguide section (l=5 in.) made of copper, with an average wall thickness of .102", T should be 50 centigrade degrees. For the 430MHz system with 150kW (avg.) running through a 21" long section (l= 10.5") with an average wall thickness of .063", T should be 10 centigrade degrees.

Brady built his dry calorimeter by clamping heat sink blocks around an ordinary waveguide. It would be difficult to ensure that the thermal contact is uniform and that it will not change. This problem could be solved by machining the whole thing from a single piece of metal. ( Note that this consideration can also apply to water-cooled waveguide sections, depending on the way the water jackets are made.

Of course, this device, like the others, would best be calibrated using dummy load calorimetry. One would assume that clones of the device would have the same calibration factor. Such clones could then be used at various other points in the transmitter, e.g., at the outputs of each klystron.

3. Standing Waves

None of these waveguide calorimeters is a directional sensor. The dissipation in a waveguide is produced by both the forward wave and any reflected wave. If the dissipation is measured from a section whose length is a multiple of one-quarter of the guide wavelength, the power dissipation in that section will be the sum of the dissipation from the forward wave and the reflected wave as if each were the only wave present in the waveguide. However, this precaution is essentially irrelevant; the S-band transmitter is set up so that reflected waves are negligible and the 430 MHZ transmitter has an "antenna tuner" at its output so that the transmitter power sensor experiences only a forward wave.

4. Thermometry

Most of the calorimetry schemes discussed above require an accurate determination of a temperature difference, T. A thermocouple or thermopile seems the straightforward way of doing this since we need only to measure the difference in temperatures. The conventional way to achieve the necessary accuracy is to use individually calibrated platinum resistance thermometers because of the inherent non-linearity of thermocouples. It would seem, however, that a better system would use a thermocouple together with one resistance thermometer. Knowing the temperature of one end to only moderate accuracy would furnish the proper scaling for the thermocouple reading.

5. Time Constants

All of these calorimeters will have fairly long time constants. This should not be a problem since, in our operations, we routinely transmit for long periods and can arrange a transmission of almost any duration, if needed, to establish a calibration. In the case of the water-cooled calorimeters, the time constant is just the time needed to remove or add heat to the metal structure. (Add calculations to estimate time constants for these various designs).

6. Conclusions

In my opinion, the most promising designs are the Parallel Substitution Calorimeter of Section 2.3 and the Dry Waveguide Calorimeter of section 2.5. Both offer an absolute calibration, i.e., they can provide an estimate of the power without first being calibrated against the dummy load power. Still, we would probably want to verify their operation and determine a correction factor by using them while all the power is diverted into the dummy load calorimeter. The substitution calorimeter needs neither a measured nor constant coolant flow rate and the dry calorimeter uses no coolant flow at all. The parallel substitution calorimeter is appealing in that no absolute measurement is made of T; it is only necessary to adjust the heater until T becomes zero. In addition, the incoming coolant need not be temperature stable. The dry waveguide calorimeter does require absolute measurement of T but, otherwise, is extremely simple. I would recommend that we first construct a prototype of the dry calorimeter and install it close to the dummy load. Once its calibration is corrected using the dummy load, it will become part of the system, providing accurate power measurements with only very infrequent further use of the dummy load and will provide a means to test the stability of the RF readings from the directional coupler. Better yet would be to build also a prototype of the substitution calorimeter. This would let us verify the stability over time of these calorimeters and would show which technique is easiest to implement and maintain.

Appendix 1. Attenuation in S-band waveguide (WR430) at 2380MHz

Appendix 2 . Attenuation in 430MHz waveguide (WR2100) at 430 MHZ