Sneaky Peak: Covert feedback pathways that destabilize an otherwise stable feedback loop

For a long time I believed that electrons were smarter than people. Even the best engineers can fall prey to subtleties that electrons will easily act on, especially when it comes to finding hidden feedback paths that can really screw up an otherwise stable feedback loop. Here we consider a case study.

There was one DC power supply with multiple outputs whose design was occasionally unstable on the circuit and I was looking for the cause and looking for a solution. I have set up an injected signal, I call it “E-test” as shown in Figure 1 so by examining E2 in relation to E1 I can look at the gain and phase properties of the feedback.

Figure 1 Basic Test Plan for E-Test Circuit Amplification.

There was a galvanic isolation barrier in the project, so the test setup was set up as follows (Figure 2):

Figure 2 A more detailed circuit gain test plan.

Now we consider how the isolation barrier circuit is configured (Figure 3):

Figure 3 The Isolation Barrier Circuit with variable action clamping action.

The input signal voltage, E (left), is transferred to the output signal voltage, E (right), by having a DC source that drives the secondary center tap of the transformer to induce alternating clamping action through the two diodes of the transformer primary . We lose a little level because of V_cesat of the two NPN transistors and the forward voltage drops of the four diodes, but a linear transfer function from the input to the output is achieved very closely. A more detailed circuit is shown in Figure 4.

Figure 4 The isolation barrier circuit with clamping alternate action in a little more detail from Figure 3.

Please note the 8 volt supply of the 1N4623 zener diode. We shall return to consider the nature of these two parts a little later.

This pair of curves shown in Figure 5 shows the output of the isolation barrier circuit and the subsequent PWM control signal output relative to the input to the isolation barrier circuit. For the sake of feedback control, that’s all we need.

Figure 5 Linearity of the isolation barrier circuit.

Although it has now been replaced, the Hewlett-Packard 4395A network analyzer was used for loop testing (Figure 6).

Figure 6 On the left, the HP 4395A network analyzer used for our electronic test. Right, its attachment to the unit under test (UUT).

The 4395A was attached to the UUT via a 1:1 interface transformer shown in Fig Figure 7. The braid of the coaxial cable serves as the primary of the test transformer, while the center conductor of the cable serves as the secondary of the test transformer. The two 100 Ω resistors provide an almost 50 Ω load for the RF output of the analyzer, while the 100 Ω and 10 Ω resistors create a very small E-test to keep the power supply operating as close to normal as possible while we do our measurements.

Figure 7 The test transformer and its attachment to the HP 4395A network analyzer.

We ran our circuit gain tests at various E-test excitation levels and got a big surprise.

As the test signal level from the analyzer was taken from 0 dBm down to -12 dBm, we had different test results (Figure 8).

Figure 8 Loop gain Seen for (a) 0 dBm, (b) -3 dBm, (c) -6 dBm, (d) -9 dBm, (e) -10 dBm, and (f) -12 dBm excitation from the network analyzer .

While the gain roll-off characteristic of the circuit looked good at first when the network analyzer was set to an output level of 0 dBm, the roll-off characteristic changed dramatically as the excitation level changed.

The culprit was discovered as follows (Figure 9):

Figure 9 The hidden feedback path.

The 8 volt power was obtained from the same inverter that the PWM controlled, resulting in a feedback loop as shown above. The included zener diode resistance made it easier this time and, I suspect, R_zener different from the test excitation which led to the strange test results.

The zener was replaced with an active IC as follows (Figure 10):

Figure 10 Remove hidden feedback path.

By using the LM136 with its extremely low dynamic resistance and replacing a single resistor to restore the Q-point of the PNP transistor, the hidden feedback path was eliminated.

The test results became the following (Figure 11):

Figure 11 Loop gain and loop phase with hidden path removed.

With the hidden feedback path disconnected, the results in the boost phase were good and consistent at all levels of test driving.

We had incorrectly assumed that the power supply was a linear system. Due to the behavior of zener generators, the power supply was a truly non-linear system.

Starting from scratch so to speak, circuit gain and circuit phase tests should always be run at different excitation levels to see if the test results match each other at each excitation level. If they don’t, you have a nonlinearity somewhere that could cause problems for you and/or your end user.

John Dunn is an electronics consultant and graduate of Brooklyn Polytechnic Institute (BSEE) and New York University (MSEE).

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