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Power Supply Design Seminar 2018 technical resources
Considerations for measuring loop gain in power supplies Testing Loop Gain in Power Supplies
Power Supply Design training resources
6.3 Testing Loop Gain in Power Supplies
Now we set up the frequency analyzer and have the correct injection isolator, let's prepare the power supply for loop gain measurement. The static operating point affects a converter frequency response. We need to maintain the same static operating point during measurement. A small resistor is inserted between point A and B to keep the feedback loop closed. Regardless of the isolator and analyzer source output impedance, this resistor values usually from 10 ohms to 100 ohms. By doing this, we can keep the output closely matched to the converters normal operation.
This slide shows a loop gain measurement resulting from a buck converter with the test setup shown in the slide number 21. As can be seen in the graphs, measured crossover frequency and phase margin match the simulation closely. Let's locate the correct voltage injection point. This is the simplified model we used earlier. When impedance Z 2 is not 0, it will affect loop gain measurement. Here's how Z 2 can affect the loop gain measurement. The correct voltage injection point should have Z 2 much smaller than Z 1. Let's use a voltage-mode controlled buck converter as an example and examine each possible injection point.
First is a point between the switching node and the output inductor. The impedance looking backward is the on resistance, or Rds (on) the MOSFET, which is smaller than the impedance of the inductor. The impedance looking forward meets the impedance requirement. However, the switch node voltage is discontinuous and non-linear, so it can't be used for signal measurement.
The second point we'll analyze is between the output and the top of the resistor feedback divider. The impedance looking backward is that of the output capacitors in parallel with the output inductor. The impedance looking forward is the resistor divider. The resistors in the divider are usually in kilohms, which is much greater than the impedance of the output capacitors in parallel with the output inductor. This injection point is the most widely adopted.
The third point is between the midpoint of the resistor divider and the feedback pin. Voltage-mode control converters use type 3 compensation. The feedback pin is virtually shorted to the AC ground. The impedance looking forward can be considered 0, which does not meet the impedance requirement. The fourth point is the point between the output of the error amplifier and the input to the PWM comparator. The output impedance after the error amplifier is very low, and the input impedance of the comparator is very high. It meets the impedance requirement, however, this point is usually buried inside the controller and, thus, is not accessible.
This is a 1 amp LED driver. An LED driver behaves just like a current source. The output impedance of the converter is very high, and the output of the converter is not good as a voltage injection point. As we examine the converter, we notice that the point between the current sensing resistor and the compensator meets the impedance requirement. The impedance looking backward is that of a current sensing resistor, which is only 0.7 ohms. The impedance looking forward is the impedance of R 6, which is 10 kilohms. Here's a measure of loop gain.
We mentioned earlier that the second reason for loop gain measurement is to guide the power supply designer toward improving load transient response. The load transient response performance is determined by the closed loop output impedance. The closed loop output impedance is determined by both the output capacitors and the open loop gain. In the case of a converter with multiple feedback paths, the loop gain is a useful guideline for load transient improvements so long as all feedback paths are included in the measurement. If we measure the loop gain with some feedback paths closed, the resulting measurement may not offer insight into how the loop responds to transients.
A shunt regulator, such as a TL431 is widely used for isolated converters output regulation. Here's a schematic of a compensator for an isolated converter. From the output, there are two feedback paths. One is through the resistor divider and the shunt regulator, and the other path is through the optocoupler pull-up resistor. I've selected a point that will include both feedback paths. Here is the measure of loop gain and corresponding load transient response. The transient response timing matches the loop gain bandwidth.
Here is another example. This example is a buck converter with D-CAP control. To stabilize a converter, D-CAP control injects ripple into the feedback pin during loop measurement. From set up number one, the voltage injection point is between the output and the top of the resistor divider. The measure of the loop bandwidth is only 14 kilohertz, which does not match the transient response. A closer examination shows that there is another output feedback path, which is through the ripple injection circuit in the capacitor CFF. Set up number two selects an injection point to include both of these feedback paths. The loop gain measurement matches the loop transient response in simulation.
In an earlier slide, we emphasized keeping the same DC operating point for loop gain measurement. We also need to maintain a similar AC operating point. This is especially important for advanced control typologies like D-CAP control. The falling slope of the ripple at the feedback pin determines a pulse with modulation gain for D-CAP control. It is important to keep the AC ripple at the feedback pin similar to that of normal operation.
In this example, we insert a 20 ohm resistor R injection for loop gain measurement. At frequencies higher than the switching frequency, we can consider the capacitor C P shorted. The pulsating voltage across the switch node and output will be distributed amongst resistors R P and R injection even though R injection is only 1/100 of R P. The ripple voltage across R injection is still 119 millivolts given an input of 12 volts. The pulsating ripple is coupled through the feedback pin by C FF.
The AC ripple at the feedback pin is greatly distorted, which affects the loop gain measurement. The solution is to add a bypassing capacitor in parallel to our injection. In this example, when I add a 0.1 microfarad capacitor in parallel to R injection, the ripple across R injection is reduced to 1.35 millivolts. This will maintain the AC ripple signal at the feedback pin during measurement.
In this slide, we will talk about the challenges in measuring loop gain for power factor correction converters. First, the control bandwidth is low. It's usually below 10 hertz. We need to select an injection isolator that works in the low frequency range and set the frequency analyzer's intermediate frequency bandwidth or integration time accordingly. Secondly, the output voltage is as high as 400 volts. The frequency analyzer should be able to support a high common mode voltage range.
Finally, the actual input is alternating. We apply DC input for loop gain measurements. Here are the loop gain measurements for the power factor correction SEPIC converter with different DC inputs. If we do not have a frequency analyzer that can support high common voltage, an oscilloscope can be used. Please refer to the reference number five for more details.
February 8, 2018
This video series discusses the theory of open-loop transfer functions and empirical loop gain measurement methods and demonstrates how to configure the frequency analyzer and prepare the power supply under test for accurate loop gain measurements. In this video, we walk through setting up and testing loop gain for your power supply design.
This course is also a part of the following series