As is well known, any closed-loop system with a unity gain of 1 and an internal phase shift of 360° with frequency will have the potential for instability. Therefore, almost all switching power supplies have a closed-loop feedback control system to achieve better performance. In negative feedback systems, the connection of the control amplifier intentionally introduces a 180° phase shift. If the feedback phase remains within 180°, the control loop will always be stable. Of course, this is not the case in reality. Due to various switching delays and reactances introducing additional phase shifts, without appropriate loop compensation, these phase shifts can also lead to instability in the switching power supply . Stability Indicators The indicators for measuring the stability of a switching power supply are phase margin and gain margin. Phase margin refers to the phase corresponding to a gain drop to 0dB. Gain margin refers to the gain magnitude (actually attenuation) corresponding to a zero phase. 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 process of 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, 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 change 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 switching power supply control block, which consists of the following three parts. [img=352,273]http://cms.cn50hz.com/files/RemoteFiles/20090213/444284001.jpg[/img] (1) Power converter section, mainly includes square wave driven power switch, main power transformer and output filter; (2) Pulse width adjustment section, mainly includes PWM pulse width comparator and 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 in 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). 2. 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, and the phase will be the same as the original phase. Therefore, the interference will persist, and the system will oscillate at this frequency. As shown in Figure 2, typically, control amplifiers use feedback compensation components Z2 to reduce the gain at higher frequencies, ensuring the switching power supply remains stable at all frequencies. [img=327,281]http://cms.cn50hz.com/files/RemoteFiles/20090213/444284002.jpg[/img] The Bode plot corresponds to the system's response to a small-signal (theoretically, the small signal is infinitesimally small) disturbance; 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 that the circuit can achieve. When these factors affect the system response, the original system will exhibit nonlinearity, and the transfer function method can no longer be used. Therefore, although small-signal stability is essential, it is not enough to guarantee the stable operation of the power supply. Therefore, when designing power supply loop compensation, it is necessary to consider not only the response characteristics of the signal power supply system, but also to properly handle the large-signal response characteristics of the power supply system. The quality of a power supply system's response to large signals can be judged by its load transient response and input voltage transient response. These two characteristics are strongly correlated; a good load transient response generally indicates a good input voltage transient response. 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 load transient response waveform. 3. Stability Test Test conditions: (1) Non-inductive resistor; (2) Load variation range of 10% to 100%; (3) Adjustable load switching frequency (the higher the switching frequency, the better, under the condition of obtaining the same ideal response waveform); (4) The load switching current variation rate is limited to 5A/μs or 2A/μs. Transient response curves without specifying the load current magnitude and variation rate are meaningless. Figure 3(a) shows the transient load waveform. Figure 3(b) shows the damped response, with the control loop oscillating after the transient edge. This indicates that the power supply with this response has very small gain margin and phase margin, and can only be stable 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. [img=353,627]http://cms.cn50hz.com/files/RemoteFiles/20090213/444284003.jpg[/img] 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 and phase margins. Symmetrical waveforms are required for both positive and negative spikes. Therefore, it can be seen that the control section and the power supply section have a center line within the control loop, and their oscillation rates are the same when the load increases or decreases. The above introduces two stability criteria for the switching power supply control loop: determining the phase margin of the switching power supply control loop under small signals through the Bode plot and determining the stability of the switching power supply control loop under large signals through the transient response waveform of the load jump. The following introduces four design methods for control loop stability. 4. Stability Design Methods 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 is unlikely that all parameters will be exactly equal to 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, the transfer characteristics of the pulse width modulator and power converter are measured. Then, the "differential technique" is used to determine the necessary characteristics of the compensation control amplifier. It is unlikely that the actual amplifier will perfectly meet the optimal characteristics; the main goal is to achieve a close approximation. 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 is less than 315° (phase margin is at least 45°) within the range up to equal the crossing frequency; (2) Find the frequency corresponding to the EsR zero in the open-loop curve, and introduce poles around the corresponding frequency in the compensation network (otherwise, these zeros will flatten the gain characteristics and will not decrease as expected); (3) If the low-frequency gain is too low and the expected DC correction cannot be obtained, a pair of zero poles can be introduced to improve the gain at low frequencies. In most cases, "fine-tuning" is required, and the best way is to use the transient load measurement method. 4.3 The control loop uses an overcompensated control amplifier with a low-frequency dominant pole to form a closed loop to obtain initial stability. Then, the transient pulse load method is used to dynamically optimize the compensation network. This method is fast and effective. Its disadvantage is that the optimal performance cannot be determined. [b]4.4 Calculation and measurement combination method[/b] In summary, the above three points mainly depend on the skills and experience of the designer. For a power supply designed using the above method, the Bode plot of the closed-loop switching power supply system can be measured using the following method. The measurement steps are as follows. Figure 4 shows a commonly used method for measuring the gain and phase of the Bode plot of a closed-loop power supply system. The advantage of this method is that it does not require modification of the original circuit. [img=387,303]http://cms.cn50hz.com/files/RemoteFiles/20090213/444284004.jpg[/img] 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, and 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 voltage gain of the system. The phase difference is the phase shift of the entire loop (after taking into account the fixed 180° negative feedback anti-phase). The input signal level must be small enough so that the entire control loop operates within its normal linear range. [b]4.5 Measurement Equipment[/b] The measurement equipment for the Bode plot is as follows: (1) An adjustable frequency oscillator V3 with a frequency range from 10 Hz (or lower) to 50 kHz (or higher); (2) Two narrow-band voltmeters V1 and V2 that can selectively display peak or RMS values, with the same applicable frequency range as 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 position in the control loop shown in Figure 4 or Figure 5. The position of T1 in Figure 4 meets 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 meets this criterion; it is located between the low-output amplifier A1 and the high-input-impedance pulse-width modulator in Figure 5. [img=394,373]http://cms.cn50hz.com/files/RemoteFiles/20090213/444284005.jpg[/img] **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-isolation start + post-PWM control. Specific block diagrams are shown in Figures 6 and 7. [img=397,475]http://cms.cn50hz.com/files/RemoteFiles/20090213/444284006.jpg[/img] Most DC/DC power supply designs, both domestically and internationally, employ 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 utilize this control method. The loop stability compensation design of this type of power supply topology mainly focuses on the following parts: (1) Loop compensation design of sampling and comparison circuit with integrated circuit U2 as the core; (2) Loop compensation design with the internal voltage comparator of the pre-PWM integrated circuit as the core; (3) The output filter design mainly considers the output voltage/current characteristics and is only for reference in the loop stability compensation design of isolated power supply; (4) Other parts such as power tube drive and main power transformer do not need to be considered in the loop stability compensation design of isolated power supply. As shown in Figure 7, the output voltage stabilization process of the post-isolation start + post-PWM control method is: output error sampling → PWM circuit error comparison → PWM width modulation → isolation drive → output voltage regulation. The loop stability compensation design of this type of power supply topology mainly focuses on the following parts: (1) Loop compensation design with the internal voltage comparator of the post-PWM integrated circuit as the core; (2) The output filter design mainly considers the output voltage/current characteristics and is only for reference in the loop stability compensation design of isolated power supply. (3) Other parts, such as isolated startup and main power transformer, do not need to be considered in the design of isolated power supply loop stability compensation. Comparing the control methods and loop stability compensation designs in Figures 6 and 7, it can be seen that the advantages of the post-isolated startup + post-PWM control method in Figure 7 are as follows: (1) It reduces the sampling, comparison, amplification and optocoupler of the later stage, and the control loop is simple; (2) Only the voltage comparator inside the post-PWM integrated circuit needs to be designed for loop compensation, and the response frequency of the control loop is wider; (3) Large phase margin; (4) Good load transient characteristics; (5) Good input transient characteristics; (6) Strong radiation resistance. Experiments have shown that even if the optocoupler is hardened for radiation resistance, its total radiation dose will not exceed 2x104 Rad (Si), which is not suitable for the application requirements of high reliability and long life of aerospace power supplies. 6 Conclusion There are two key points in the design of switching power supplies: one is the magnetic circuit design, which focuses on solving the voltage and power conversion problem from input to output. The other is the stability design, which focuses on solving the quality problem of output voltage. The quality of a switching power supply's stability design directly determines its startup characteristics, input voltage jump response characteristics, load jump response characteristics, high and low temperature stability, and ease of production and debugging. Applying the aforementioned switching power supply stability design methods and conclusions to the research and development of switching power supplies will undoubtedly yield twice the results with half the effort.