Design and Modeling Analysis of Two-Stage Wide Input DC/DC Converter

1 Introduction
With the widespread application of switching power supplies in various industries, the demand for DC/DC converters has become a symbol of economic development. For single-stage converters, due to the constant output voltage, the pulse width waveforms at both ends of the semiconductor device in the circuit are very different under different input voltage conditions. The higher the input voltage, the shorter the switch tube conduction time, and the higher the voltage it withstands during the off period. The rectifier diode in the circuit will withstand high-voltage narrow pulses during the switch tube conduction period. The average value of the current flowing through the switch device remains unchanged, and the effective value increases, resulting in a sharp rise in the temperature of the switch tube, rectifier tube, filter capacitor and other devices, large switch tube conduction loss, reduced converter efficiency, and even permanent damage. The difference between the input and output voltages of each stage of the two-stage DC/DC converter is smaller than the difference between the input and output voltages of the single-stage DC/DC converter, which can reduce the burden of the single-stage converter when working in a wide voltage range and greatly enhance its adaptability to a wide range of voltage inputs. However, the two-stage converter is large in size, complex to control, and has poor circuit stability.
The two-stage Buck wide-input DC/DC converter designed here has the advantages of a two-stage converter and reduces the switching loss of power devices when the output current is large. A control strategy of open loop in the front stage and closed loop in the back stage is adopted, and the stability of the system is improved through the compensation network. The converter has the advantages of high efficiency, simple control, high system stability, and wide input voltage range.

2 Introduction to wide-input converter topology
The main circuit topology of the dual-Buck cascade wide-input DC/DC converter is shown in Figure 1. When fully loaded, the converter works in continuous current mode, with an input voltage range of 19 to 150 V. When working in closed loop, the output voltage is 30 V, and the maximum output power is 500 W.

Uin, Ug, Uo are the input voltage of the converter, the output voltage of the front-stage Buck circuit and the output voltage of the converter, VS1 and VS2, VD1 and VD2, L1 and L2 are the switch power tubes, freewheeling diodes and inductors of the front-stage and rear-stage Buck circuits, iL1 and iL2 are the currents flowing through L1 and L2, Ro is the equivalent load resistance, and Io is the load current. Gvd1(s) and Gvd2(s) are the control and output transfer functions of the front-stage and rear-stage circuits, respectively, Gm(s) is the PWM transfer function, Gc(s) is the voltage controller transfer function, H(s) is the voltage sampling network transfer function, and D1 is the front-stage duty cycle.

[page] The working conditions of the circuit under different input voltage ranges are shown in Table 1. In the voltage range of 30 to 75 V, only the post-stage Buck circuit works, at this time the output power Po = 500 W, Uin = Ug, Uo = 30 V, VS2 duty cycle D2 is 0.4 to 1, switching frequency fs2 = 100 kHz, and the maximum output current Iomax = Po/Uo = 16.7A.

Gm(s) is equal to the inverse of the sawtooth wave amplitude Um in PWM, that is, Gm(s)=1/Um, H(s) is equal to the ratio of the voltage reference Uref to Uo, that is, H(s)=Uref/Uo. Then the expression of Gvd2(s) is:

The voltage controller adopts PID regulator, and the expression of its transfer function Gc(s) is:

3.2 Impact of disturbance on converter
In working modes I and II, the circuit operation is relatively simple. To analyze the impact of the front and rear circuits on the closed-loop system, we can discuss the input voltage mutation and load mutation in working mode III, that is, when the front and rear circuits work at the same time.

When the two stages work simultaneously, the duty cycle of the front-stage power tube is fixed, the voltage reference is a certain value, and when the input voltage suddenly changes, the load current change is set to zero, and when the load suddenly changes, the input voltage change is set to zero. According to Figure 2, the system block diagrams for the two cases are simplified, as shown in Figure 4. As can be seen from the figure, the closed-loop transfer function of the system when the input suddenly changes and the load suddenly changes, no matter what the case, the closed-loop system is a high-order system, and its damping ratio ξ is proportional to the output power. Therefore, the greater the power, the more intense the transient oscillation of the system, and the greater the ξ, the smaller the overshoot and adjustment time of the system.
At the moment when the input voltage rises to 75 V, D1 suddenly changes. At this time, the converter system is acted upon by two disturbances at the same time, namely the input disturbance and the front-stage duty cycle disturbance.

[page]4 Analysis of experimental results
An experimental platform was built and used as the power supply for the avionics controller. The circuit starts working when the input voltage is higher than 19 V. When the input is lower than 30 V, the front and rear circuits are directly connected. When the input is lower than 75 V, the rear converter is controlled to work in a closed loop. When it is higher than 75 V, the front and rear stages work together. The front stage uses a square wave generator composed of 555 to generate a driving signal with a fixed duty cycle, and the rear stage uses a voltage-type PWM control circuit based on SG3525. Figure 5 shows the external characteristic curve of the converter when the input is 150 V. After adding full load, the output voltage drops by 0.6 V, and the converter voltage accuracy is 2%. According to GJB1412-94, the voltage accuracy of the low-voltage DC power supply on the ground of aerospace should be less than 3%, which meets the requirements.

The input is directly connected to the input end of the subsequent Buck circuit, and the control strategy is appropriately adjusted. The two-stage wide input converter is transformed into a single-stage converter. At this time, the device parameters and closed-loop control strategy are the same as those of the two-stage converter, and the voltage and current meet the rated parameters of the switching device. The efficiency curves of the two converters changing with the input voltage are measured under 300 W and 1 W load conditions, respectively, as shown in Figure 7.

Under light load conditions, the current in the circuit is very small, and the inherent loss of the two-stage circuit is greater than that of the single-stage circuit. Even in the single-stage working mode, the direct pass of the front-stage Buck circuit will also cause losses in the circuit. Therefore, when the output power is 1 W, the efficiency of both converters is very low, and the efficiency of the two-stage converter is even lower than that of the single-stage converter. Under heavy load conditions, the current in the circuit is very large. When the two-stage converter works in the single-stage mode, the current and voltage stresses borne by the components of the rear-stage circuit are the same as those of the components in the single-stage converter, and the direct pass of the front stage also produces inherent losses. Therefore, in this case, the efficiency of the two-stage converter is still lower than that of the single-stage converter. When the input voltage increases and the two-stage converter enters the two-stage working mode, the voltage stress of the rear-stage circuit is reduced, and the increase in the effective value of the current flowing through the circuit switch device is curbed. The inherent loss of the circuit is less than the inherent loss of the single-stage converter, so the efficiency of the two-stage converter is higher than that of the single-stage converter.

5 Conclusion
The working principle of the two-stage wide input DC/DC converter is introduced, and the experimental and simulation waveforms of input mutation and load mutation are given through modeling analysis, and the stability of the circuit is verified. By comparing the relevant performance of the two-stage and single-stage converters, it is shown that the dual-Buck cascade wide input DC/DC converter reduces the switching loss and voltage stress of the device under a wide range of input voltage conditions compared to the single-stage Buck converter, and the control is simple, which can reduce the circuit cost and extend the service life.