The power supply employs negative feedback from the output back to the error amplifier to ensure proper voltage regulation under various operating conditions (load variations, temperature variations, and input voltage variations, etc.). Like any stable closed-loop system, the power supply must ensure that the closed-loop gain is less than 1 at the operating frequency or under risky oscillations and/or other unsuitable characteristics. The power supply's negative feedback condition must be completely out of phase with the input or generate a gain less than 1 to ensure correct operation.
A typical voltage regulator IC provides the necessary phase margin within the device to ensure stable operation. Like all engineers, IC designers need to make operating limit assumptions and often provide control mechanisms to adjust the internal phase delay to accommodate various load limits. A regulator can be designed to provide a 90-degree phase margin with the rated output impedance. However, if that impedance is more capacitive than expected, the phase delay may increase to the same phase point as the internal feedback point (also the phase point returning from the power supply output). This phase reversal produces positive feedback with a gain greater than 1 (oscillator formula). We all know this is undesirable in voltage regulator circuits.
Many voltage regulators offer mechanisms for adjusting internal phase delay, typically implemented through an external compensation network with several passive components. However, in some cases, regulators do not provide this mechanism and must be used within specific operating limits (minimum/maximum output impedance under various load limits). In either case, proper circuit analysis is essential to determine if design adjustments are necessary. While loop characteristics can be simulated, accurately modeling actual system-level characteristics such as PCB and connector impedances is challenging, especially with lower-cost simulation tools. Therefore, actual stability measurements are necessary to understand the actual stability of the loop.
Admittedly, I have witnessed many instances where systems, after being put into production, became unstable later in production due to environmental changes and/or operating limits. In these cases, the prototype may have functioned well, but the phase and gain margins within the power supply were not tested during prototype testing. If designers were able to test the power supply's stability, they could identify and correct the problem before it causes significant production cost issues.
1. Stability Indicators
The metrics for measuring the stability of a switching power supply are phase margin and gain margin. Phase margin refers to the phase at which the gain drops to 0dB. Gain margin refers to the gain at which the phase is zero (actually, it's attenuation). In practical switching power supply design, gain margin is only considered when designing flyback converters; it is generally not used when designing other converters.
In switching power supply design, phase margin has two independent functions: one is to dampen the dynamic processes that occur in the converter during load step changes; the other is to ensure system stability even when component parameters change. Phase margin can only guarantee "small-signal stability." During load step changes, the power supply inevitably enters the "large-signal stability" range. In engineering practice, we consider the loop phase margin to be greater than 45° under room temperature, standard input, and normal load conditions. This phase margin is sufficient to ensure system stability under various parameter variations and errors. If the load changes or the input voltage range varies greatly, the loop and phase margin should be greater than 30° under all loads and input voltages.
Figure 1 shows a schematic diagram of the control block of a switching power supply. The control loop of the switching power supply consists of the following three parts.
(1) The power converter section mainly includes a square wave driven power switch, a main power transformer, and an output filter;
(2) The pulse width adjustment section mainly includes a PWM pulse width comparator and a totem-pole power amplifier;
(3) Sampling, control, comparison and amplification section, mainly includes output voltage sampling, comparison and amplification (such as TL431), error amplification and transmission (such as optocoupler) and voltage comparator integrated inside PWM integrated circuit (the compensation design of these amplifiers determines the stability of the switching power supply system to the greatest extent, and is the key and difficult point of the design).
II: Stability Analysis
As shown in Figure 1, suppose an interference wave is introduced at node A. The energy contained in this square wave is distributed into an infinite number of odd harmonic components. If the real system is detected to respond to the increasing harmonics, it can be seen that the gain and phase shift also change with increasing frequency. If at a certain frequency the gain is equal to 1 and the total additional phase shift is 180° (this phase shift plus the originally set 180° phase shift, the total phase shift is 360°), then there will be enough energy returning to the system input with the same phase as the original phase, so the interference will persist, and the system will oscillate at this frequency. As shown in Figure 2, typically, the control amplifier uses a feedback compensation device Z2 to reduce the gain at higher frequencies, so that the switching power supply remains stable at all frequencies.
A Bode plot corresponds to the system's response to a small-signal disturbance (theoretically, a small signal is infinitesimally small). However, if the disturbance is large, the system's response may not be determined by the linear part of the feedback, but rather by the nonlinear part, such as the op-amp's slew rate, gain bandwidth, or the minimum and maximum duty cycles achievable in the circuit. When these factors affect the system response, the original system will exhibit nonlinearity, and the transfer function method can no longer be used. Therefore, while small-signal stability is essential, it is insufficient to guarantee stable power supply operation. Thus, when designing power supply loop compensation, it is necessary to consider not only the signal response characteristics of the power supply system but also its large-signal response characteristics. The quality of the power supply system's large-signal response characteristics can be judged by its load jump response characteristics and input voltage jump response characteristics. There is a strong correlation between these two characteristics; a good load jump response characteristic necessarily indicates a good input voltage jump response characteristic.
The theoretical analysis of the stability criteria for switching power supply loops is complex because the transfer function changes with load conditions. The effective inductance values of various wire-wound power components typically change with load current. Furthermore, when considering large-signal transients, the control circuit operates in a nonlinear mode, making a complete state description impossible using only linear analysis. The following section details how to determine the stability of a switching power supply loop through analysis of the transient response waveform to load jumps.
Three: Stability Testing
Test conditions:
(1) Non-inductive resistor;
(2) The load variation range is 10%~100%;
(3) The load switching frequency is adjustable (the higher the switching frequency, the better, under the condition of obtaining the same ideal response waveform);
(4) The load switch current change rate is limited to 5A/μs or 2A/μs. Transient response curves without specifying the load current magnitude and change rate are meaningless.
Figure 3(a) shows the transient load waveform.
Figure 3(b) shows the damped response, where the control loop oscillates after the transient edge. This indicates that the power supply with this response has very small gain and phase margins and can only stabilize under certain specific conditions. Therefore, this type of response should be avoided as much as possible, and the compensation network should be adjusted to slip at a slightly lower frequency.
Figure 3(c) shows the overdamped response, which is relatively stable, but its transient recovery performance is not optimal. The slip frequency should be increased.
Figure 3(d) shows the ideal response waveform, which is close to the optimal situation. In most applications, the transient response is stable and performs well, with sufficient gain margin and phase margin.
For both positive and negative spikes, a symmetrical waveform is required. Therefore, it can be seen that the control section and the power supply section have a center line within the control, and their oscillation rate is the same when the load increases or decreases.
The above section introduced two stability criteria for switching power supply control loops: determining the phase margin of the control loop under small-signal conditions using a Bode plot, and determining the stability of the control loop under large-signal conditions using the transient response waveform of a load jump. The following section introduces four design methods for control loop stability.
IV: Stability Design Method
4.1 Analytical Method
Analysis is performed based on the theory, mathematics, and circuit model of the closed-loop system (computer simulation). In practice, it's unlikely that all parameters will precisely equal their specified values during overall analysis, especially the inductance value, which cannot remain constant across the entire current variation range. Similarly, large transient responses that can alter the linear operation of the system are difficult to predict.
4.2 Trial and error method
First, measure the transfer characteristics of the pulse width regulator and power converter sections, and then use the "differential technique" to determine the characteristics that the compensation control amplifier must have.
It is unlikely that a practical amplifier will perfectly meet its optimal characteristics; the main goal is to get as close as possible. The specific steps are as follows:
(1) Find the frequency corresponding to the zero-crossing point of the pole in the open-loop curve, and introduce zeros around the corresponding frequency in the compensation network. Then, the phase shift will be less than 315° (phase margin is at least 45°) up to the crossover frequency.
(2) Find the frequency corresponding to the zero of EsR in the open-loop curve, and introduce poles around the corresponding frequency in the compensation network (otherwise these zeros will flatten the gain characteristic and will not decrease as expected);
(3) If the low-frequency gain is too low and the desired DC correction cannot be obtained, a pair of zeros and poles can be introduced to improve the low-frequency gain.
In most cases, "fine-tuning" is required, and the best way to do this is by using the transient load measurement method.
4.3 Empirical Method
This method uses an overcompensated control amplifier with a low-frequency dominant pole to form a closed loop in the control circuit to achieve initial stability. Then, a transient pulse load method is used to dynamically optimize the compensation network. This method is fast and effective. Its drawback is that it cannot determine the optimal performance.
4.4 Combined Calculation and Measurement Method
In summary, the key factor is the designer's skills and experience.
The Bode plot of a closed-loop switching power supply system designed using the above method can be measured using the following method, with the measurement steps as follows.
Figure 4 shows a common method for measuring the gain and phase of a closed-loop power supply system's Bode plot. The advantage of this method is that it does not require modification of the original circuit.
As shown in Figure 4, the oscillator introduces a small series voltage V3 into the loop through transformer T1. The effective AC voltage flowing into the control amplifier is measured by voltmeter V1, while the AC voltage at the output is measured by voltmeter V2 (capacitors C1 and C2 act as DC current blockers). V2/V1 (in decibels) is the system voltage gain. The phase difference is the phase shift of the entire loop (after considering the fixed 180° negative feedback anti-phase).
The input signal level must be low enough so that all control loops operate within their normal linear range.
4.5 Measuring equipment
The measuring equipment for Bode plots is as follows:
(1) An adjustable frequency oscillator V3, with a frequency range from 10Hz (or lower) to 50kHz (or higher);
(2) Two narrow-band voltmeters, V1 and V2, which can be selected to display peak or RMS values, and whose applicable frequency range is the same as that of the oscillator;
(3) Professional gain and phase measurement instruments.
Test point selection: Theoretically, Bode plot measurements can be performed at any point in the loop. However, to obtain good measurement accuracy, the selection of the signal injection node must consider two factors: low power supply impedance and high input impedance of the next stage. Furthermore, a single signal path is required. In practice, the measurement transformer is typically connected to the location of the measurement transformer in the control loop shown in Figure 4 or Figure 5.
The position of T1 in Figure 4 satisfies the above criteria. The power supply impedance (in the direction of signal injection) is the low output impedance of the power supply section, while the input impedance of the next stage is the high input impedance of the control amplifier A1. The second signal injection position in Figure 5 also satisfies this criterion; it is located between the low-output amplifier A1 and the high-input-impedance pulse-width modulator in Figure 5.
5: Optimal Topology
Whether in foreign or domestic DC/DC power supply circuit design, the isolation methods can be summarized into two basic forms: pre-start + pre-PWM control and post-isolated start + post-PWM control. The specific structural block diagrams are shown in Figures 6 and 7.
Most domestic and international DC/DC power supply designs adopt a pre-start + pre-PWM control method. The subsequent stage uses a switch to transmit the sampled and compared error signal to the pre-stage PWM circuit via optocouplers for pulse width adjustment, thereby achieving overall DC/DC power supply voltage regulation. As shown in Figure 6, the pre-start + pre-PWM control block diagram illustrates the output voltage stabilization process: output error sampling → comparison → amplification → opto-isolated transmission → PWM circuit error comparison → PWM pulse width adjustment → output voltage regulation. Interpoint's MHF+ series, SMHF series, MSA series, MHV series, and other products all belong to this control method. The loop stability compensation design for this type of topology power supply products mainly focuses on the following parts:
(1) Loop compensation design of sampling and comparison circuit based on integrated circuit U2;
(2) Loop compensation design based on the internal voltage comparator of the pre-PWM integrated circuit;
(3) The output filter design mainly considers the output voltage/current characteristics and is for reference only when designing the stability compensation of isolated power supply loops;
(4) Other components, such as power transistor drivers and main power transformers, do not need to be considered in the design of isolated power supply loop stability compensation.
As shown in Figure 7, the block diagram of the post-isolated startup + post-PWM control method shows that the output voltage stabilization process is as follows: output error sampling → PWM circuit error comparison → PWM pulse width modulation → isolation drive → output voltage regulation. The loop stability compensation design for this type of power supply topology mainly focuses on the following parts:
(1) Loop compensation design based on the internal voltage comparator of the post-PWM integrated circuit;
(2) The output filter design mainly considers the output voltage/current characteristics and is only for reference in the design of isolated power supply loop stability compensation.
(3) Other parts, such as isolated start-up and main power transformer, do not need to be considered in the design of isolated power supply loop stability compensation.
Why is it necessary to test power supply stability?
The power supply is one of the core components of a computer, providing stable voltage and current to other hardware. An unstable power supply can cause the computer to malfunction or even damage other hardware. Therefore, testing power supply stability is crucial.
II. How to test power supply stability?
1. Use a voltmeter to test.
Using a voltmeter to test the output voltage and current of a power supply can help determine its stability. During testing, stable voltage and current settings should be selected to avoid inaccurate results due to load variations.
2. Use load testing tools
Load testing tools can simulate computer loads and test power supply stability. During testing, an appropriate load should be selected to avoid overloading the power supply.
3. Use software testing
Some software programs can test a computer's power supply stability, such as AIDA64 and OCCT. When testing, appropriate test options should be selected to avoid overloading the power supply due to excessive test load.
III. Precautions
1. A stable environment should be selected during testing to avoid excessively high or low temperatures affecting the test results.
2. When testing, a suitable load should be selected to avoid overloading the power supply.
3. When testing, appropriate testing tools should be selected to avoid inaccurate test results.
4. Safety precautions should be taken during testing to avoid overloading the power supply and damaging the computer.
In summary, power supply stability testing is an indispensable part of computer hardware testing. This article introduces how to accurately test power supply stability, as well as common testing methods and precautions. We hope this article is helpful to you.
