Tips for designing a stable POWER SUPPLIES: Phase margin

Intuitive understanding of phase margin!

Introduction

First, I would like to explain "phase margin" using a familiar example to help you get an idea of what it means.
Have you ever experienced being unable to control the game as you wanted due to communication lag while playing an online game?
For example, imagine a scene where you are controlling your character and running along a course.

What would happen if there was a one-second delay before your actions were reflected in the game?
Even if you turn left the moment you see a left curve, the game will reflect that action one second later, so the player will continue to turn left.Then, when the curve changes from left to right, even if you turn right, there will still be a one-second delay, so your character will continue to turn left and go off course.
The shorter this one-second delay, the more closely your controls will match your movements in the game, allowing for smoother control and preventing you from going off course.

This "delay time" is closely related to the "phase margin" in control engineering. When a given frequency is input to a system, if there is a delay time until it is reflected in the output, it appears as a phase delay in the output.

Figure 1 is a graph showing how the phase lag increases and the phase margin decreases as the delay time increases.
This "frequency" represents how many times per second the operation of turning left or right (counting each left or right curve as one set) is repeated, in other words, the speed of the change in operation. When calculating the phase margin, think of the crossover frequency as the maximum operation speed at which you can turn your character left or right in one second.

For example, suppose the limit is two left and right turns per second (= 2Hz). In this case, if the delay time is 0.05 seconds, you will be able to control your character as intended and will be less likely to go off course. The phase margin in this case is 144°.

However, if the delay time becomes 0.25 seconds, the phase delay will be 180°, and the operation and reaction will be completely reversed. At this point, the phase margin is 0°. Even if you perform an operation to turn left at the timing of entering a left curve, your character will not actually start turning left until after you have already entered a right curve. In this state, you will definitely go off course.

Thinking about it this way, it's easy to intuitively understand that phase margin is a measure of "how well you can control your character as intended, with ease."

point:

The smaller the delay time at the crossover frequency, the larger the phase margin!
Phase margin is a measure of whether operation can be performed as intended, and the larger it is, the more leeway there is!

We will now explain how to ensure phase margin and design a stable POWER SUPPLIES, using the LT8624S POWER SUPPLIES IC manufactured by Analog Devices as an example.

LT8624S Link

https://www.analog.com/jp/products/lt8624s.html

LT8624S Features

The LT8624S incorporates third-generation Silent Switcher technology and offers three major features:

1. Low noise in low frequency bands
・Low noise even in the extremely low frequency range of 0.1Hz to 100kHz
・Output noise is almost constant regardless of output voltage
2. Low EMI
・Minimizes EMI (electromagnetic noise) even at high-speed SWITCHES (up to 6MHz)
- Built-in bypass CAPACITORS and symmetrical layout dramatically reduce radiated noise
3. High efficiency at high frequencies
- Synchronous rectification method achieves high conversion efficiency
・Minimum on time is short, enabling high-speed response

Link to 3rd Generation Silent Switcher Technical Article

https://www.analog.com/jp/resources/technical-articles/ultra-low-noise-switch-mode-power-supply-with-adi-silent-switcher.html

How to regulate the output voltage: Feedback control

Control Overview

The LT8624S uses feedback control to monitor and regulate the output voltage to the target value.
Figure 2 is the output voltage feedback control block diagram shown on page 28 of the LT8624S datasheet.

Let's take a look at how this feedback control stabilizes the output voltage.

① The output voltage _VOUT is input to the OUTS TERMINALS and connected to the inverting input of the gm amplifier.
② A current of 100 μA flows from the SET TERMINALS to the parallel circuit of R _SET and C _SET, generating a voltage at the SET TERMINALS.
→ This SET TERMINALS voltage is the target value for the output voltage _VOUT.
③ The voltage at the SET TERMINALS is input to the non-inverting input of the gm amplifier.
④ A current equivalent to (SET TERMINALS voltage - OUTS TERMINALS voltage) × gm flows from the output of the gm amplifier to the V _C TERMINALS, then flows through the series circuit of R _C and C _C, generating a voltage at the VC TERMINALS.
→If the OUTS TERMINALS voltage is lower than the SET TERMINALS voltage (= _VOUT target value), a positive current flows to the V _C TERMINALS, causing the V _C TERMINALS voltage to rise.
If the OUTS TERMINALS voltage is higher than the SET TERMINALS voltage, current is drawn from the V _C TERMINALS, causing the V _C TERMINALS voltage to drop.
⑤ The V _C TERMINALS voltage is input to the DRIVERS, and a PWM waveform according to the V _C TERMINALS voltage is output from the SW TERMINALS.
→The higher the _VC TERMINALS voltage, the larger the duty ratio of the PWM waveform, and the lower the voltage, the smaller the duty ratio.
⑥ The PWM waveform is smoothed by INDUCTORS L and CAPACITORS _COUT connected to the SW TERMINALS, and the output voltage _VOUT is obtained.
→ The larger the duty ratio of the PWM waveform, the higher the output voltage VOUT will be, and the smaller the duty ratio, the lower the output voltage _VOUT will be.

By configuring this type of feedback loop, the SET TERMINALS voltage (= _VOUT target value) and output voltage _VOUT are compared, and if _VOUT is higher than the _VOUT target value, _VOUT is lowered, and if it is lower, VOUT is raised.
This is how the output voltage is regulated.
Similar control is used in the online game example above.

In the "Control your character according to the course conditions" block in Figure 3, the control that controls your character along the course can be thought of as operating in a similar manner to the LT8624S's control that compares the target _VOUT value with the output voltage _VOUT and adjusts _VOUT.
Earlier, we explained that "the smaller the delay time at the crossover frequency, the larger the phase margin!" Where does the delay time occur in the LT8624S block diagram in Figure 4?

The answer is the A and β blocks surrounded by red frames.
Block A generates a PWM waveform according to the _VC TERMINALS voltage, and a delay occurs when smoothing it with an LC FILTERS.
In the β block, a delay occurs when the output current of the gm amplifier is converted into the V _C TERMINALS voltage in the series circuit of R _C and C _C.
In the low frequency range, the impedance of C _C becomes larger than that of R _C, and the impedance of C _C becomes dominant in the combined impedance of the series circuit of R _C and C _C.
This causes a delay time equivalent to the charging time of C _C. At high frequencies, the impedance of C _C becomes smaller than R _C, and the impedance of R _C becomes dominant in the combined impedance of the series circuit of R _C and C _C. As a result, almost no delay time occurs.

Simulation using LTspice

In control engineering, the crossover frequency is defined as the frequency when the gain is 0dB. In the online game example, I wrote that you should think of the crossover frequency as the maximum speed at which you can move your character left and right in one second to turn a corner.
Let's think about this in the same way. The crossover frequency is the frequency at which the output can be controlled to increase by 0 dB, or 1x (0.1V) when the output voltage drops by 0.1V.
At frequencies higher than this, the output will increase by less than 0.1 V in response to a 0.1 V drop, making it impossible to maintain the target voltage. Therefore, the crossover frequency can be said to be the limit frequency at which the output voltage can be appropriately corrected.

Now, to reduce the delay time in the β block at the crossover frequency, let's increase the capacitance of C _C and lower the impedance of C _C.
Figure 5 shows a simulated Bode diagram of the feedback control using LTspice, a circuit simulator provided free of charge by Analog Devices.

In order to reduce the delay time by reducing the effect of the impedance of C _C in the combined impedance of the series circuit of R _C and C _C at the crossover frequency, the capacitance of C _C is increased from 2 nF to 3.9 nF.At 2 nF, the phase margin at a crossover frequency of 62 kHz increases from 37° to 54° (delay time from 6.4 μs to 5.6 μs), and we can see that the delay time has decreased.

However, a closer look reveals that when the capacitance of _CC is 3.9nF, the gain also decreases, lowering the crossover frequency. This is because the impedance of _CC at the crossover frequency decreases, and the combined impedance of the series circuit of R _C and _CC also decreases, resulting in a decrease in the conversion gain when converting the gm amplifier output current to the _VC TERMINALS voltage.
Let's try increasing the resistance of R _C to increase the total impedance.

Figure 6 shows the Bode plot when the R _C capacitance is increased from 500 Ω to 1500 Ω. It can be seen that the gain increases and the crossover frequency becomes higher.

In this way, by adjusting the combined impedance of the R _C and C _C series circuit, we were able to improve the crossover frequency from 62 kHz to 79 kHz and the phase margin from 37° to 89°.
In POWER SUPPLIES control, increasing the crossover frequency increases stability against higher frequency disturbances.
For example, the amount of change in output voltage is small in response to a step change in load current that contains higher frequency components.
Furthermore, if a phase margin of 60° or more is ensured, the magnitude and duration of output voltage ringing in response to step changes in load current will be reduced.
When improving feedback control, it is a good idea to imagine the expected change in voltage in response to a step change in load current.

LT8624S Development Resources

Explore development resources for the LT8624S.

Evaluation board

EVAL-LT8624S

https://www.analog.com/jp/resources/evaluation-hardware-and-software/evaluation-boards-kits/eval-lt8624s.html#eb-overview
This is a synchronous step-down POWER SUPPLIES equipped with the LT8624S, with an input voltage of 2.7 to 18V and an output of 1V/4A.

Simulation Tools

■LTspice

https://www.analog.com/jp/resources/design-tools-and-calculators/ltspice-simulator.html

LTspice is a fast, free circuit simulator. To create the Bode diagram for POWER SUPPLIES, we used the Frequency Response Analysis (FRA) function, a new feature of LTspice® 24.
For a more detailed explanation, please watch the webinar (in English) at the link below.

https://ez.analog.com/webinar/c/e/766

Summary

Table 1 summarizes the information provided to help you intuitively understand phase margin.
Control engineering deals with various controls in the frequency domain, so understanding the frequency domain is essential, but to gain an intuitive understanding, it is best to think about it in terms of the more familiar time domain.

Item	Online games	POWER SUPPLIES
Causes of time delay	Communication lag, etc.	A, β phase lag
Crossover Frequency	Limit number of operations per second	Frequency at 0dB gain
Phase margin	Measure of smooth operation	Stability against disturbances
Improvement measures	Improved communication lag	Adjustment of R _C and C _C of the β block