**2.2 Pulse modulation gain:** *F***<sup>m</sup>**

Because the switching converter is controlled by the pulse width modulation (PWM) signal corresponding to the duty ratio, it is necessary to modulate the control signal from the compensator to the PWM signal. **Figure 3** shows the correspondence between the control signal and the PWM signal. In an analog circuit, a comparator is used for comparing the control signal *V*<sup>c</sup> to a sawtooth wave (or a triangular wave) *V*tri. Therefore, it is ON when *V*<sup>c</sup> > *V*tri and OFF when *V*<sup>c</sup> < *V*tri.

**Figure 3.** *PWM modulation* F*m.*

*Power Balance Mode Control for Boost-Type DC-DC Converter DOI: http://dx.doi.org/10.5772/intechopen.82787*

The ratio per switching cycle of this relationship is the duty ratio. When a small disturbance Δ*V*c(*s*) occurs in the control voltage *V*c, a small disturbance Δ*D*(*s*) is generated in the duty ratio *D* in the steady state. The relationship between these is equal to the slope of the sawtooth wave in one switching cycle. Accordingly, when the amplitude of the sawtooth wave is *V*p-p, the transfer function of the PWM gain *F*<sup>m</sup> is expressed by Eq. (5).

$$F\_{\rm m} = \frac{\Delta D(s)}{\Delta V\_{\rm C}(s)} = \frac{1}{V\_{\rm p\cdot p}}\tag{5}$$

From Eq. (5), when the amplitude of the sawtooth wave is *V*p-p = 1 V, the PWM gain *F*<sup>m</sup> can be neglected.
