Loop Response Measurement Options When the Top Feedback Resistor is Inaccessible

Abstract

This article will detail how to measure the loop response of a power supply when there is no obvious injection point (that is, inaccessible or missing a top feedback resistor). There are two scenarios where this can occur. A power supply module can have either an inaccessible internal top feedback resistor or it can have an output sense pin with no top feedback resistor.

Introduction

For a power supply to be stable, a certain gain and phase margin is needed. Typically, a phase margin target of at least 45° and a gain margin target of at least 10 dB is required for a power supply to be considered stable. These values are usually measured by inserting a small resistor between the V_OUT node and the top feedback resistor. A perturbation signal is applied across this added resistor and the loop response is measured across the desired frequency range. This conventional approach is preferred for its simplicity, assuming the user has access to the top feedback resistor.

But how can the loop response be measured when the top feedback resistor is inaccessible within a molded module? And how is the loop response measured when a device does not require a top feedback resistor and instead uses an output voltage sense pin? These questions will be answered by comparing bode plots of the loop response for the conventional measurement approach to that of these novel measurement approaches.

Where Is the Top Feedback Resistor?

As shown in Figure 1, the conventional method for measuring loop response is to insert a small value resistor between the V_OUT node and the top feedback resistor. This method can only be used if the top feedback resistor is accessible.

Figure 1. Schematic showing the added resistor required to measure the loop response with the LT8608.

There are many power supply modules whose top feedback resistor is inaccessible within the power supply package. With a top feedback resistor hardwired to the V_OUT node, the output voltage should never increase above the voltage set by the feedback resistor divider. If the top feedback resistor is not hardwired, then the V_OUT node could increase as high as the input voltage for a buck regulator if the top feedback resistor is not connected properly or if it breaks. Many of Analog Devices’ line of μModule^® devices have the top feedback resistor molded inside the module for this added protection. But now the loop response cannot be measured using the conventional method. Figure 2 shows the LTM8074 with its inaccessible top feedback resistor.

Figure 2. Example circuit showing an inaccessible top feedback resistor.

Another unique situation occurs when a module uses an output voltage sense pin (V_OSNS) to regulate the V_OUT voltage. As the simplified block diagram shows in Figure 3, there is no top feedback resistor due to this setup using a current reference instead of the typical voltage reference. The LTM4702 uses this current reference circuit to regulate its output voltage.

Figure 3. Simplified block diagram showing V_OSNS circuitry.

Load Transient Response or Bode Plot?

Without a way to measure the loop response of a power supply, one must rely solely on the transient response of the system to determine stability. The transient response test looks at the voltage response of V_OUT when a load step is applied to the V_OUT node. An example transient response is shown in Figure 4. From the waveform, the bandwidth (ƒ_BW) can be estimated by measuring the time from when the load step is applied to when the output voltage starts to recover. The bandwidth of the control loop is the inverse of this recovery time (tr) multiplied by pi. In this example, the recovery time is approximately 4 μs and the bandwidth is 80 kHz.

Equation 1.

Also, the stability can be estimated by looking at the shape of the waveform. The system has an underdamped response when ringing is seen in the waveform (green response). This means the system can be unstable and have a lower phase margin. But how low is the phase margin?

If the recovery time of the waveform takes a significant amount of time, then the response can be considered overdamped (blue response). The system can take much longer for the output voltage to recover than desired. Downstream circuitry may be impacted due to the voltage drooping for a longer duration than preferred.

Although the transient response can give clues to the system’s loop response, the exact phase margin and gain margin can only be determined by measurement.

A Novel Method to Measure Loop Stability

For the scenario where an output voltage sense pin is used, the loop response measurement is similar to the conventional measurement approach. Simply place a small value resistor between the V_OUT node and the V_OSNS pin. The perturbation signal is applied across this resistor as shown in Figure 3 and the loop response is measured.

For the scenario where the top feedback resistor is inaccessible inside a module, the novel loop measurement technique requires a bit more care. As shown in Figure 5, a parallel resistor divider network must be installed, and the perturbation signal is now placed across a resistor inserted between the bottom feedback resistor and ground. Care must be taken to keep the parallel resistor divider network as close as possible to the feedback resistor network to minimize errors.

Figure 5. Novel loop response measurement method.

Step 1:

Insert the 20 Ω R_PERT resistor between R2 and ground. The perturbation signal is applied across R_PERT.

Step 2:

Choose R4 to be in the range of 500 Ω to 1 kΩ. See Note 1.

Step 3:

Calculate the parallel resistor divider network ratio. n = R2/R4.

Step 4:

Calculate R3 and C_FF2 using the ratio, n, from step 3.

Step 5:

Reconstruct the parallel resistor divider network including the feedforward capacitor and the capacitor (C_M) to negate the effects of the added capacitance from the perturbation signal. See Note 2.

Equations:

1. n = R2/R4

2. R3 = R1/n

3. C_FF2 = n × C_FF1

4. C_M = n × C_PERT

Note 1:

Choose R4 so that R2 is 40 to 100 times greater than R4. This will allow the R2 and R3 resistor network to dominate the feedback loop measurement.

Note 2:

If the perturbation signal’s parasitic capacitance cannot be reliably measured, then the C_M capacitance can be determined empirically through iteration.

The novel measurement approach yields the same loop response as the conventional approach as shown in Figure 6.

Figure 6. Bode plot comparison of the conventional and novel measurement methods.

Conclusion

With this novel measurement approach, the user can now determine the loop response without access to the top feedback resistor. The user is no longer mandated to use a compromised approach with limited bandwidth and significant error. And the user does not have to estimate the loop stability from only looking at the load transient response.

References

Zhang, Henry. “Application Note 149: Modeling and Loop Compensation Design of Switching Mode Power Supplies.” Linear Technology, January 2015.