How Hot Do Those Isolation Resistors Get?

Figure 9 superimposes this worst-case temperature increase for R1 onto the derating response shown in Figure 2. While the temperature/power point remains within the safe operating area for the resistor, there is not much room for error. This means the R1 resistor cannot be stressed much further while maintaining reliable operation.

Figure 9 The worst-case condition for Example 1.

PHASE MISMATCH EXAMPLE 2

In this second example, amplifiers A1 and A3 were paired together, as were amplifiers A2 and A4. In this case, the phase difference was set to 30 degrees, which is 50 percent higher than in Example 1. This results in a more severe power degradation scenario, as shown in Figure 10. Now, the output power for the out-of-phase case decreases by approximately 5 W. Dissipating 5 W in a single resistor at an 85°C baseplate temperature in this combiner would result in failure. Fortunately, in this example, the dissipated power is spread across isolation resistors R2, R3, R4 and R5 as shown in the schematic of Figure 4b.

Figure 10 Power output profile from Example 2 phase mismatch.

Figure 11 Power dissipated in resistors R2, R3, R4 and R5 from Example 2 phase mismatch.

The power dissipation profiles for the four “hot” resistors are shown in Figure 11. The power dissipation in these resistors is not equal. The worst-case dissipation across the 6 to 18 GHz operating band of the four-way combiner occurs at 18 GHz, where R3 and R5 dissipate 2.15 W. However, Example 1 has shown that this is a safe level of dissipation at an 85°C baseplate temperature.

These results suggest several key conclusions. First, phase mismatches should be minimized. This is especially true for phase mismatches that affect R1. This is most critical because R1 does not share its thermal load with a second resistor, unlike the R2/R3 and R3/R4 resistor pairs.

EXPERIMENTAL VERIFICATION OF RESISTOR SURVIVAL

Mismatching the phase of the high-power amplifiers needed to test the resistor temperature model could be a costly and complicated endeavor. Additionally, measuring resistor temperatures inside a combiner would require removing the isolation lids, which would negatively impact RF performance. As a result, a simpler, indirect method was developed to stress the combiner resistors to the edge of their safe operating area and demonstrate survivability.

This method involved modifying a B2B combiner to simulate a graceful degradation of a failed amplifier. The B2B combiner is illustrated in Figure 12a. The diagram in Figure 12b illustrates an RF path that has been laser-cut to create an open circuit, simulating a failed amplifier.

Figure 12 (a) B2B combiner with cut path. (b) Laser-cut circuit diagram to replicate failed amplifier.

A simplified schematic of the B2B network with the circuit cut is shown in Figure 13, which identifies the resistor nomenclature. The left side of the structure is designated the “divider,” while the right side is the “combiner” function. To measure the heating effects, a high-power CW signal was injected into the combiner input port on the right side of the diagram. RF connectors on the evaluation board introduce loss, but this is accounted for using a connector model with loss proportional to the square root of the frequency.

Figure 13 Schematic of B2B combiner with cut path.

Two-port S-parameters of the B2B network were evaluated before and after the modification, as shown in Figure 14. Disconnecting one path reduced return loss and increased insertion loss as expected. Much of the increased loss is due to power being dissipated in the isolation resistors.

Figure 14 B2B S₁₁ (top) and S₂₁ (bottom) combiner performance before and after cutting the path.

Figure 15 Small-signal modeled and measured S₁₁ (top) and S₂₁ (bottom).

Figure 15 compares the small-signal response of the cut B2B network with that of the hybrid HFSS/MWO model. There is a close correlation between the modeled and measured S₁₁ and S₂₁ magnitudes. This serves to illustrate the accuracy of the hybrid modeling approach.

Resistor dissipation is strongly dependent on frequency. For this experiment, a 40 W signal was injected at 15 GHz and the HFSS/MWO model was used to predict resistor dissipation. Figure 16 shows the modeled results, with R4 and R9 dissipating 2.37 W at 15 GHz. This is more than double the dissipation seen in R1, R5, R6 and R10. Resistors R2, R3, R7 and R8 are not in line with the cut path and therefore do not dissipate any power.

Figure 16 Predicted resistor dissipations in cut B2B combiner for divider resistors (top) and combiner resistors (bottom).

A summary of the modeled power dissipation during the cut B2B experiment is shown in Figure 17. The total power dissipation for the resistors is 9.13 W, while the connectors dissipate 5.13 W. Accounting for a reflected power of 0.99 W, since S₁₁ is not perfectly matched and 19.75 W power output, this means 5 W is dissipated in the PolyStrata coax transmission lines. These lines can easily handle this thermal load.

Figure 17 Predicted cut B2B combiner power dissipation.

Figure 18 Predicted combiner resistor temperatures.

The network was heated to a baseplate temperature of 70°C and subjected to increasing power levels at 15 GHz. The resulting resistor temperatures, subjected to an input power of 40 W CW to the cut path B2B combiner for 30 minutes, are shown in Figure 18. R4 in the combiner and R9 in the divider sections dissipate an equal amount of power and these two resistors show a worst-case temperature of 151°C in response to the 40 W input power.

Performing the same analysis as earlier, Figure 19 plots the R4 and R9 temperature and power conditions against the safe operating area. At 150°C, the resistor is rated at zero power, so the cut B2B operating condition of 151°C is outside the safe operating range of the resistor. After the power exposure, the part was re-evaluated and no change in performance was observed. Although it did not fail, continued operation at this point would constitute a reliability concern.

SUMMARY

This article examines the impact of phase imbalances on power dissipation in Wilkinson power divider and combiner architectures. Using a Nuvotronics PolyStrata combiner as an example, a straightforward, inexpensive method is presented for predicting the temperature increase of an isolation resistor using a physical model of a power combiner. The article also presents the modeled results when the PolyStrata combiner/divider is subjected to various input powers and phase imbalance relationships. Rather than an exercise in modeling and matching modeled results to actual results, the experiments described in the article highlight constraints and potential challenges that arise when isolation resistors are stressed to the limit of their safe operating range.