Design of dual-switch forward parameters and control loop based on SABER simulator

0 Introduction
At present, forward converters are widely used in medium and high power applications, but the switch tube of a single-tube forward converter bears twice the input voltage stress and cannot be used in higher input applications. The dual-tube forward converter solves this problem. The voltage stress of its switch tube is equal to the input voltage, and there will be no leakage inductance spike when it is turned off. In addition, it has a simple structure and high reliability, and is widely used in medium and high power applications with high input voltage.
In the design process of switching power supplies, the quality of the control loop design is related to the stability of the system. Therefore, an excellent control loop is crucial to the switching power supply system. For the control loop of the PWM converter, the traditional method uses the state space averaging method to obtain a small signal model to design the control loop. This method has a large amount of calculation and low efficiency, which is not conducive to engineering applications.
An efficient method is to use simulation software to obtain the circuit open-loop BODE diagram to design the control loop. There are many simulation softwares on the market with powerful functions, such as Matlab, Pspice, etc. However, the convergence algorithm of Pspice software is not good, which brings a lot of inconveniences; Matlab software modeling is complex, and its compensator is a transfer function or state equation, which needs to be converted into a specific circuit using electrical network theory, which is very inconvenient.
Compared with other simulation softwares, SABER has a richer component library and more accurate simulation description capabilities, and better authenticity. Especially in the field of power supply, its inherent advantages can shorten the time to market of power supply products with its powerful simulation functions. At present, it is rare to design control loops with SABER software. Based on this, it is proposed to use SABER simulation to design dual-tube forward parameters and control loops.

1 Circuit structure
The dual-tube forward topology is shown in Figure 1. The working principle is: VT1 and VT2 are turned on and off at the same time; when VT1 and VT2 are turned on, the power supply outputs energy to the load through the high-frequency transformer T and the fast recovery diode VD3, and charges C through L; when VT1 and VT2 are turned off, the output current is continued by the fast recovery diode VD4, and the excitation current of the primary winding of the transformer feeds back energy to the power supply through VD1-UiN-VD2. Due to the clamping of VD1 and VD2, the switch stress of VT1 and VT2 is equal to the power supply voltage. Compared with the single-tube forward circuit, one more switch tube is used, the voltage stress is half of that of a single tube, there is no leakage inductance spike, and the transformer does not need a flux reset winding, which is suitable for medium and large power level occasions with higher input voltage.

2 Control loop design method
System stability conditions: The open-loop BODE diagram of the system loop has an amplitude slope of -20dB/dec at the shear frequency and a phase margin of at least 45°.
Control loop design steps:
(1) Design the main circuit according to the application requirements.
(2) Obtain the BODE diagram of the main circuit using the SABER simulator.
(3) Determine the shear frequency ωc according to actual requirements and constraints. For power products, the shear frequency is usually 1/4 or 1/5 of the switching frequency.
(4) Determine the type and frequency points of the compensation amplifier according to the system steady-state accuracy requirements and the shear frequency. Make the low-frequency gain high. Generally, the low-frequency band of power products is designed as a type I system to ensure steady-state accuracy; the slope at the mid-frequency bandwidth is -20dB/dec, and there is sufficient phase margin (i.e. y>45°); the high-frequency gain decays quickly to reduce high-frequency interference; use SABER to obtain the open-loop frequency response curve of the compensated loop to verify the stability of the system.

3 Main circuit parameter setting
Since the output filter parameters of the main circuit are related to the setting of the control loop, the compensator should be adjusted according to the output filter parameters. This article uses a 250W power supply as an example to illustrate the design of the control loop.
1) Main technical requirements
Input: AC220V (DC=265V (220~310V))
Output: 48V 0.5~5A;
ripple voltage: 0.1V; ripple current: 1A;
efficiency: ≥0.85; switching frequency: 100kHz;
transformer primary-to-secondary ratio n=2; Uout=48.85V (diode); duty cycle:
2) Output filter parameters
The output filter is designed according to the required ripple current and ripple voltage values. The ripple current determines the inductance value, and the ripple current and ripple voltage jointly determine the capacitance value.
(1) Filter inductance
The current waveform flowing through the filter inductor is shown in Figure 2. The peak-to-peak value of the ripple current depends on the minimum allowable current value. When the load current is less than 0.5A, it enters the current discontinuous mode.

To prevent the converter from entering discontinuous mode, the current flowing through L cannot drop to zero during Toff.

(2) Filter capacitor
The capacity of the filter capacitor is discussed in the following two cases:
① Using ordinary aluminum electrolytic capacitors. According to literature [3], when the switching frequency of this type of capacitor is lower than 500kHz and RoCo is greater than half of the switch-off and on-time of the switch tube, the output ripple is only determined by ESR (Ro).

This method has become impractical with the advancement of technology. It is best to obtain the ESR value of the capacitor from the manufacturer or test.
② The filter capacitor uses zero ESR or low ESR capacitors. The zero point (1/2πRest×C) formed by its own resistance and capacitance is high, but it has little effect on the loop design; if the low ESR capacitor uses a large capacity, the zero point formed by its own resistance and capacitance makes the high-frequency attenuation near the bandwidth insufficient, which may cause oscillation and increase the difficulty of compensator design. As shown in Figures 3 and 4.

Considering the effect of heat generation on the life of the capacitor, 22μF is used.
The maximum value of the ESR value of the capacitor is
ESR(max)=△U/△I=0.1/l=0.1Ω.
When ESR exceeds 0.1Ω, the ripple voltage will increase.

4 Use SABER for open-loop simulation
The average mode dual-tube forward model is established in SABER, as shown in Figure 5.
The following table shows the main modules and parameters used in the model in Figure 5:

The open loop BODE diagram is shown in Figure 6. The phase angle at the shear frequency is -160°, the phase margin is 20°, and the amplitude slope at the shear frequency is -40dB/dec, so compensation is required. In addition, the amplitude at 25kHz (1/4 switching frequency) is -35.5dB.

5 Design the compensator based on the open-loop BODE diagram
The dual-tube forward compensator uses a type 2 error amplifier circuit. As shown in Figure 7.
Its transfer function is:

One zero point fz = 1/2πR2C1, one pole fp = 1/2πR2C2; when designing, set the shear frequency to 1/4 of the switching frequency; the zero frequency is set to 1/4 of the filter resonant frequency to increase the phase margin in the mid-frequency band; the pole frequency is set to the capacitance frequency of the filter capacitor itself to increase the attenuation in the high-frequency band. R2/R1 is set to the negative gain at 1/4 of the switching frequency; RS1 and RS2 are designed according to the sampling network, so:

Calculation results, using national standard series values:

The open-loop BODE diagram after compensation obtained by using SABER is shown in Figure 8. Note that before SABER performs small signal analysis, the duty cycle reference voltage needs to be fine-tuned to make the static operating point of the comparator inverting input terminal at 5V, otherwise it may be saturated.
It can be seen that the system has been corrected to type I, with a shear frequency of 25kHz, an amplitude slope of -20dB/dec, and a phase margin much greater than 45°.

SABER is used to perform time domain analysis to observe the system performance when the input voltage and load are disturbed, as shown in Figures 9 and 10.

6 Conclusion
SABER software is the most advanced simulation software in the world today. With the vigorous promotion of Analogy, SABER software will be more and more widely used in the power supply field. Through the auxiliary design of SABER software, the time to market of power supply products is shortened and the speed, stability and steady-state accuracy of product control performance are improved.