Figure 2-1 shows the simplified schematic for the PCM buck converter.

Figure 2-1 Simplified Schematic for PCM Buck Converter

Figure 2-2 Overall Control Implementation

Figure 2-2 shows the overall control block model where:

• G_di(s) is the duty cycle to i_L transfer function.
• Z_O(s) is the transfer function of output impedance.
• G_div(s) is the gain of the feedback resistor network.
• G_EA(s) is the transfer function of the error amplifier with certain compensation.
• F_m is the gain of PCM PWM comparator.
• R_i is the current sensing resistor.
• H_e(s) is the transfer function model of inductor current sampling-hold effect.

Equation 1 shows the transfer function from the inductor current to the output voltage.

Equation 1.

G_di(s) is the duty cycle to i_L transfer function.

Equation 2.

The internal loop compensation is designed so that the crossover frequency is much higher than the corner frequency, 1/(2π√LC_O). For crossover frequency and higher frequency, Equation 2 can be simplified as Equation 3.

Equation 3.

The sensed inductor current, external ramp, and the output of error amplifier V_COMP are compared, which determines when to turn off the high side MOSFET, hence the duty cycle is determined. F_m is the comparator gain. f_SW is the switching frequency. S_n is the on-time slope of the sensed-current waveform and S_e is the external ramp slope.

Equation 4.

where

H_e(s) is the transfer function model of inductor current sampling-hold effect. [2]2:

Equation 5.

Equation 6 shows the transfer function of the feedback.

Equation 6.

Equation 7 shows the transfer function of the error amplifier with certain compensation.

Equation 7.