Choose ESR to ensure linear regulator stability

April 10, 2021

Output stability is a critical issue for any power supply design. Because linear regulators are easy to use (most linear regulators have only three pins), it's easy to forget the importance of this. While there are currently many techniques to ensure output stability, the simplest and most cost effective solution is to add or use the equivalent series resistance (ESR) of the output capacitor.

Here is an example of a low dropout positive adjustable regulator LM1084 with a 5V output. The LM1084 is capable of delivering 5A to the load and can function in the presence of large current spikes. It is also a quasi-regulator, ie the pass transistor is a single NPN transistor driven by a PNP transistor, as shown in Figure 1. Due to its internal architecture, some ESR is typically required in the output capacitor of the quasi-regulator to ensure stability.

Choose ESR to ensure linear regulator stability

Figure 1: Simplified schematic diagram of the internal quasi-regulator

In general, the ESR of tantalum capacitors and electrolytic capacitors is sufficient to ensure stability, but due to the increasingly limited space requirements of the design, smaller ceramic capacitors are ideal. Since ceramic capacitors have almost no ESR, adding an external series resistor is only used to simulate its behavior. In this article, I will use the LM1084 to demonstrate how to estimate the best ESR value in the output and how to test its effectiveness in the lab.

Method of testing stability

The traditional method of testing stability is to introduce a small sinusoidal signal into the feedback loop and measure the gain and phase response crossover frequency by means of a frequency response network analyzer. This approach requires the feedback loop to be turned off, so it is often not possible to test a fixed output regulator with a feedback loop built into an integrated circuit (IC). This method is cumbersome to set up, requires additional laboratory equipment, and improper precautions can cause errors.

The simple method is to perform a load transient test and then observe the ringing of the output. Figure 2 is a setup example that provides a 50mA~1A load transient for a 5V regulator output. The function generator sends a rectangular wave to the gate of the N-channel FET. When the N-channel FET is driven, the effective value of the total load resistance is 5 Ω. When the N-channel FET is not driven, the load resistance is 100Ω, which is just enough to meet the minimum load requirement.

Choose ESR to ensure linear regulator stability

Figure 2: Load Transient Test Setup

Observe the output ringing

The regulator can be determined to be stable by observing the output ringing of the load transient. Figure 3 is a schematic illustration of a LM1084 with a ceramic output capacitor and no external ESR added. Figure 4 is its load transient response. As shown in Figure 4, there is a case of excessive ringing, and you can add a partial ESR to the output capacitor for suppression. But how much ESR do you need to add?

Choose ESR to ensure linear regulator stability

Figure 3: Schematic of the LM1084 - no ESR

Choose ESR to ensure linear regulator stability

Figure 4: Load Transient Response - No ESR

Calculation of ESR value

You can measure the appropriate ESR value by Equation 1:

Choose ESR to ensure linear regulator stability

This equation can be used to calculate the minimum ESR when the output ringing or oscillation frequency is zero. During the load transient test, the output ringing frequency indicates that the 0db intersection is close to this frequency, so the phase limit needs to be slightly increased to suppress the output response. Setting this to zero at this frequency will increase the phase limit you need. Below we calculate according to the examples in Figures 3 and 4.

The oscillation frequency in Figure 4 is approximately 50 kHz and the output ceramic capacitance is 22 μF. Substituting these numbers into Equation 1 yields a minimum ESR of 145mΩ:

Choose ESR to ensure linear regulator stability

Adding a 145mΩ ESR to the output response works as follows. Figure 5 is a schematic diagram of the addition of ESR, and Figure 6 shows the load transient response. Although the ringing has been eliminated, there is a side effect that the effective output capacitance decreases as the ESR increases, so the resistance of the capacitor becomes larger and larger, resulting in a larger drop in the original output.

Choose ESR to ensure linear regulator stability

Figure 5: Schematic of the LM1084 with ESR

Choose ESR to ensure linear regulator stability

Figure 6: Load Transient Response - with ESR

In summary, simply add an external resistor to suppress the output ringing caused by the linear regulator. This is useful if there is a ceramic capacitor in the resistor. The calculation method is simple, and there are very few devices that need to be used to test and verify stability.

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