7.4.2 Current Mode Operation

A buck converter using current mode operation can be partitioned into three portions, a voltage divider, an error amplifier and a switching modulator. By linearizing the switching modulator, we can derive the transfer function of the whole system. Because current mode scheme directly controls the inductor current, the modulator can be linearized as shown in Figure 36.

In this example, the inductor is located inside the local feedback loop and its inductance does not appear in the small signal model. As a result, a modulated current source including the power inductor can be modeled as a current source with its transconductance of 1/R_S and the output capacitor represent the modulator portion. This simplified model is applicable in the frequency space up to approximately a half of the switching frequency. One note is, although the inductance has no influence to small signal model, it has influence to the large signal model as it limits slew rate of the current source. This means the buck converter’s load transient response, one of the large signal behaviors, can be improved by using smaller inductance without affecting the loop stability.

Equation 6 describes the total open loop transfer function of the entire system.

Assuming R_L>>ESR, R_O>>R_C and C_C>>C_C2, each transfer function of the three blocks is shown starting with Equation 7.

There are three poles and two zeros in H(s). Each pole and zero is given by the following five equations.

Usually, each frequency of those poles and zeros is lower than the 0 dB frequency, f₀. However, the f₀ should be kept under 1/3 of the switching frequency to avoid effect of switching circuit delay. Equation 15calculates the 0 dB frequency, f₀.