Transfer Function

Voltage-Mode Transfer Functions

2017.01.12

Points of this article

・In this section, we first consider transfer functions for voltage-mode control.

Voltage-mode transfer functions

Voltage-mode control in a DC-DC converter is the most basic system. Only the output voltage is fed back through a feedback loop. By using the voltage difference obtained by comparison with a reference voltage using an error amplifier, and further comparing with a slope wave (triangular wave), the pulse width of a PWM signal is determined and the output voltage is controlled.

Fig. 1 shows a block in which the output V_c from the error amplifier and the slope voltage are input to the PWM generator to generate the PWM output.

Here, by comparing a fixed slope wave with V_c, the transfer function of the block F_m, which is PWM controlling the duty D = T_on/T, is derived.

Fig. 2 shows the input waveform and the PWM output waveform. The slope wave rises with a constant slope by V_ramp over one period. Through comparison with V_c, the on and off times of the driver output V_Dout, that is, the duty cycle, is determined. The control conditions are as follows.

When V_c ＞ V_slope , V_Dout = ON
When V_c ＜ V_slope , V_Dout = OFF

Moreover, in Fig. 2:

When V_slope = V_c = ０ , D = 0
When V_slope = V_c = V_ramp , D = 1

Equation 3-1 is obtained from similarity of the triangle formed from V_slope and V_c, and by modifying this equation using D = T_on/T, we obtain equation 3-2.

Moreover, from perturbation of equation 3-2 （ D → D + ?D , V_c → V_c + ?_VC） equation 3-3 is obtained.

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