Derivation of Fm in Current Mode

As slope transfer functions we have derived slope transfer functions for a voltage mode and a current mode, which are representative control methods. Here, we derive a current mode (peak current mode) modulator gain F_m.

When deriving the voltage mode and current mode transfer functions, we explained that a modulator gain F_m is the control voltage change V_C governing a change in the duty cycle D. What is derived here is the F_m for the current mode, but the basic approach is the same, and the following should be read while referring to the transfer functions for the voltage mode and current mode.

Derivation of F_m in current mode

As already explained, coil current information is fed back to the current mode ramp waveform. Hence the ramp waveform when a fixed ramp waveform is not added becomes the feedback component, which is “the ripple current I_ripple × the current sense gain R_S.”

The switch is turned off where this ramp waveform crosses the error amplifier output V_C, and so the coil current information vanishes and the ramp waveform rise stops, becoming zero. This operation is illustrated in Fig. 9.

Here, the ripple current while turned on can be expressed by equation 3-9.

In Fig. 9, upon considering similarity of triangles, equation 3-10 results, and upon substituting D for T:T_ON, equation 3-11 is obtained.


Then, substituting equation 3-9 into equation 3-11, F_m can be expressed as equation 3-12.

Here, if the slope of the ramp waveform due to the coil current is S_n, then S_n can be expressed as in equation 3-13, and the F_m of equation 3-12 can be rewritten as in equation 3-14.


Thus F_m for the current mode has been derived.