Measure power-supply loop transfer
Using a function generator and an oscilloscope, you can measure gain and phase shift versus frequency in a power supply’s control loop.
By Frederik Dostal, National Semiconductor -- Test & Measurement World, 9/1/2008
Power supplies use control-loop circuits to produce constant voltage or current. The transfer function—gain and phase as a function of frequency—provides valuable information about a control loop’s speed and stability. Knowing a control loop’s transfer function, as well as the poles and zeros of the transfer circuit, can help you select the right compensation and power-stage components.
| See "Good connections," a Web-exclusive sidebar that explains how to modify a regulator IC evaluation board and provides a video of the test procedure. |
To perform the measurements, you inject a small AC signal into the power supply’s control-loop circuit and measure the loop’s gain and phase shift. By measuring the gain and phase, you can plot them with a Bode plot. The gain and phase differences between the injected signal and the control loop’s output is the transfer function.
Prepare the circuit
Figure 1 shows a typical step-down switch-mode regulator with the required measurement setup. Start by breaking the loop of the power supply’s regulator circuit (highlighted area in Figure 1) so you’ll have a point at which to inject the small signal and measure the loop’s response. You can break the loop at the low-impedance output node above the high side feedback resistor (R1) in the feedback path.
 Figure 1. This measurement setup lets you compare an injected sine wave to the signal as it rides on a power supply’s output (VOUT). |
You must electrically isolate the measurement points, A and B, by placing a small resistance, such as 20 Ω, in the control loop’s feedback path. A 20-Ω resistor in the control loop will have a negligible effect on the power supply’s output voltage (VOUT).
To inject the signal into the control loop and make the measurements, you need a sound measurement structure. See “Good connections,” a sidebar that explains how to modify a regulator IC evaluation board for these measurements. The sidebar includes a 7-min video of the test procedure.
The injected signal must be small in relation to the output voltage so it won’t change the way the power supply handles large signals. Yet, the injected signal must be large enough that you can recognize it in the control loop. The injected signal must not trigger a voltage protection threshold at a regulator IC’s feedback pin (FB in Figure 1).
You should inject a sine wave with an amplitude between 30 mV and 100 mV across the 20-Ω resistor in Figure 1. The exact signal amplitude you need may change depending on the control loop’s gain, and the amplitude will vary with frequency. Start by injecting a small signal and then increase its amplitude as needed until you can see it on an oscilloscope screen. This will ensure that the signal is still small relative to the loop’s DC output.
The injection transformer, T1 in Figure 1, prevents DC from entering the control loop. Look for a transformer that offers a flat voltage transmission over a wide frequency band. If you don’t have such a transformer, you can compensate for frequency variations in your transformer’s flatness by adjusting the signal generator’s output amplitude.
Connect the signal generator to the transformer’s primary side, then turn on the generator. Measure the injected signal across the 20-Ω resistor using two calibrated oscilloscope probes. (Attach the ground leads of both probes to a common ground point on the power supply under test.) To make the measurement, you’ll need to view the difference between the signals on channel A and channel B.
Adjust the signal generator’s amplitude so the transformer’s output voltage won’t drive the control-loop circuit into nonlinear operation. Set the DC offset of the signal generator’s output to 0 V so you don’t introduce DC into the measurement circuit.
To prevent switching noise from filling the oscilloscope’s screen and covering the waveform of interest, set the oscilloscope for bandwidth limiting. You can ensure a well-triggered waveform by connecting a third oscilloscope channel to the signal generator’s output and triggering on the output signal.
Set up the power supply
Next, you should power up the control-loop circuit, attach a load, and make a stability measurement by looking for oscillations in VOUT. Repeat this measurement under different load and line conditions. At low output loads, most power supplies will go into discontinuous current-conduction mode, which will change the control loop’s characteristics. In voltage mode, a power supply’s loop characteristics will change with input voltage.
After setting up the equipment and powering the control loop, you should see a line on the channel connected to VOUT (probe A in Figure 1) and a noisy sine wave on the other channel. If you don’t see a sine wave, then set the oscilloscope to the highest amplitude resolution (typically 20 mV/div) or increase the amplitude of the signal generator’s output.
 Figure 2. When control loop gain = 1 (0 dB), the amplitude of the injected signal (upper trace) will equal the amplitude of the output signal (lower trace). |
Once you see a sine wave, change its frequency by adjusting the signal generator. You will see a change in amplitude on channel A. Look for a frequency where the sine waves of channel A and channel B have equal amplitude—this is the point where the gain of the control loop is 1 (0 dB). This frequency is the loop’s 0-dB crossover frequency (Figure 2).
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Table 1. Commonly used decibel values for voltage ratios.  |
You can successfully make these loop measurements on a control loop that doesn’t oscillate or is in some sort of hysteretic overvoltage protection mode. If the error amplifier is a transconductance amplifier, you can achieve a stable loop design by placing a capacitor from the regulator IC’s compensation pin to ground. If the error amplifier is a standard voltage-to-voltage error amplifier, then place a capacitor from the compensation pin to the FB pin. A 1-µF capacitor will typically work well. It will set a pole at very low frequencies and force the gain to drop quickly so that the 0-dB crossover is at a very low frequency. In current-mode control designs, the phase margin at very low frequencies is usually enough to yield a stable circuit.
The Bode plot
To generate a Bode plot, you must sweep the signal generator’s frequency across the frequency range of interest and measure the gain and the phase shift between the input signal (probe B in Figure 1) and the output signal (probe A). For very large and very small gains, you might have a difficult time seeing results on the oscilloscope screen. At 30-dB gain, for example, it’s difficult to see a voltage relationship between channel A and channel B.
For typical designs, you can easily and accurately measure the most important points of a Bode plot such as the 0-dB crossover point. At high gain frequencies, you might have a difficult time viewing the exact decibel value, but you can make a quantitative observation such as “the gain is very high and probably above 30 dB.” Figure 3 shows the control loop’s 0-dB gain crossover frequency, where the blue trace crosses 0 dB.
 Figure 3. A Bode plot shows the point where gain (blue trace) is 0 dB and also shows the corresponding phase offset (yellow vertical line indicated by the arrow). |
You can consider loop bandwidth as a combination of the level of DC gain and the frequency of the 0-dB crossover. This measurement—the control loop’s phase margin—can indicate the control loop’s stability margin. Depending on the design, you need a minimum phase margin of 45° to 50°. More is better.
 Figure 4. This measurement setup lets you measure the compensation signal of the voltage regulator IC (probe B). |
Besides using the measurement setup in Figure 1, you can connect the oscilloscope channel that was measuring injected signal (probe B) to the compensation pin of a power-supply regulator IC (Figure 4). In this setup, you can measure the transfer function of the control loop without the influence of the compensation network (the capacitor connected to the regulator’s compensation pin). With the information you obtain about the power stage with this measurement, you can easily select optimized compensation components for a desired control-loop bandwidth and phase margin.
Good connections
To inject a test signal into a power supply's regulator circuit, you must first break the feedback path in the circuit (Figure A) and soldering a 20-Ω resistor across the gap. Some regulator IC evaluation boards already have this gap for the stability measurement resistor. On other boards, you can easily cut the feedback trace on the PCB and reconnect it through a 20-Ω resistor. For the connection of the two voltage probes as well as the signal injection cables, use a twisted cable as shown in Figure A.
A small twisted pair works very well because it minimizes loops and thus avoids noise pickup, which is critical for a good measurement. The tight connected twisted wires can be up to about 2 in. long without a problem. Such a connection will help reduce the mechanical stress on the PCB that can come from the voltage probes and the signal injection connector while not influencing the measurement. Connect the ground leads of the oscilloscope probes to a single ground connection on the power-supply board to avoid ground loops. Figure B shows the two oscilloscope probe connections to the board.—Frederik Dostal
CLICK ON FIGURE A OR FIGURE B TO VIEW A 7-MIN VIDEO OF THIS TEST PRODEDURE.  Figure A. Twisted-pair wires minimize interference caused by wire loops. |
 Figure B. A transformer isolates DC from a signal generator (not shown) from entering the control loop circuit under test. |
Frederik Dostal is an applications engineer for the Power Management Group at National Semiconductor. His responsibilities include product development and technical support for switching regulators, linear regulators, and controllers. He holds a degree in electrical engineering (Dipl.-Ing) from the Friedrich-Alexander Universität in Erlangen, Germany.
