Characterize optocouplers in the feedback loop of high-frequency power converters
Optocouplers will add a phase shift that can make your power supply unstable. Here is how you can measure and compensate the loop.
By John Bottrill, Texas Instruments -- EDN, June 19, 2009
A difficult challenge in power-supply design is tailoring the response of the control loop. With the loads dynamically changing at a much higher frequency, the control loop has to keep up. To handle higher load dynamics and take full advantage of smaller components, you need faster control loops. With switching frequencies increasing to 200 kHz and higher, you'll need to cross the 0-dB gain point at a frequency much greater than the old 3-kHz range. According to accepted theory, a 200-kHz switcher under worst-case line and load conditions needs a unity gain point at 40 kHz.
Crossing the 0-dB gain at this relatively high frequency allows you to use smaller output capacitors, despite higher dynamic-load changes. This is because the converter's response with a higher gain crossover is faster, and the output capacitors do not have to hold the voltage up for quite as long during load transients. The control circuit adjusts the power transferred to compensate and control the output voltage. The circuit does not need to rely on the output capacitors to ride through the load or line transients. Additionally, the magnetic components get smaller as the switching frequency increases, saving even more space.
There are, of course, some disadvantages to fast switching frequencies. Switching losses increase when using traditional circuits. Thankfully, better-designed components have negated those losses to a great extent. Switching losses are also reduced if you use quasi-resonant topologies such as a phase-shifted, full-bridge topology. In many designs, synchronous switches on the secondary side significantly improve efficiency.
The magnetic components, switches, and output capacitors affect the control-to-output gain as a function of frequency. The feedback control has its own challenges, and the parasitic elements in the feedback circuit play a more important role. At these higher frequencies, these parasitics become a significant problem. With low-frequency switching, the 0-dB crossover is in the neighborhood of 5 kHz or less, and parasitics in the feedback loop were mainly layout related. However, as you get into the 30-kHz crossover designs, other parasitic elements can come into play.
An optocoupler in the feedback loop can introduce enough phase shift, or time lag, to make the power supply oscillate. Recently I encountered this particular issue on a converter running at 400 kHz in a phase-shifted design using a UCC3895 control IC on the primary side. The designer used an optocoupler to cross the primary-to-secondary isolation barrier. At first glance it appeared that everything was taken into account. But for some reason, the loop was unstable, and the output was in low-level oscillation while still maintaining the dc set point. I reviewed the design calculations but found nothing obvious. I then set the converter into a condition where it appeared with dc output with an ac ripple on it and started to probe the circuit.
After significant time and effort, I found that even though the error amplifier on the secondary side was faithfully reproducing the ripple that appeared on the converter's output with the correct (180-degree) phase change, the signal coming through the optocoupler was shifted by approximately 45 degrees from the expected phase at a frequency of about 35 kHz (). This was enough to remove the phase margin at crossover, resulting in the observed oscillations. The optocoupler data sheet made no mention of this phase shift, but optocouplers have a pole at higher frequencies. I reviewed a number of data sheets for various optocouplers, but none of them mentioned a phase shift as a function of frequency.
I built a test circuit to examine the gain and phase relationship across the optocoupler (). I used a network analyzer to measure the data. We performed our first tests using the circuit in . I then plotted the phase and gain of the signals developed across the resistors as a function of frequency. See 
for a dc voltage of 4.3V on the adjustable dc source. I used the voltages across R1 and R2 to establish the phase shift.
When the phase shift is 45 degrees and the gain drops by 3 dB, the pole frequency is approximately 35 kHz. This corresponded to the observed behavior. Additional complex poles and zeros are evident beyond the frequency of interest for this optocoupler, so for this analysis I ignored them.
I increased the dc voltage across the test circuit to 11V () and repeated the measurements for similar results. The pole did not change significantly with increased current through the optocoupler.
Next I tried to compensate for the pole by adding a 1.2-nF capacitor across the 4-kΩ resistor (). I repeated the same tests at both current levels sequentially. This introduced a zero at 35 kHz, which helped compensate for the pole in the optocoupler. In both cases this effectively moves the phase shift where it crosses the 135-degree point out beyond the 100-kHz frequency and kept the gain above the 3-dB point beyond 200 kHz. When I added a zero to the optocoupler circuit in the converter, it was stabilized throughout the entire line and load range.
If you plan to use an optocoupler in a closed feedback loop with a 0-dB crossover in excess of 8 kHz, first test the optocoupler to see what the phase and gain characteristics are. If you don't have access to a network analyzer, build a simple circuit like the one shown in . This will help you to identify the phase and gain with simple components, a variable frequency signal generator with dc offset capability, and power supplies.
By injecting a constant amplitude ac current signal into the LED (voltage measured across R1) and measuring the current out of the photo transistor (voltage across R2), you can tell where the pole is by the amplitude and relative phase of the current out of the photo transistor. At low frequencies, the difference in currents will be the current-transfer ratio (CTR). But as the frequency increases, the current through the transistor decreases. When the ac signal frequency increases to a value that the amplitude of the photo transistor ac signal is half of its previous value, you have identified the pole frequency. From this information you will be able to calculate which components are needed to add a zero in the feedback loop. If these results show an undesirable pole at a frequency within the circuit's operational range before the 0-dB crossover, then add a zero in series with the LED circuit to compensate and retest the optocoupler. The final test, of course, is in the converter under operation.
