The open-loop transfer function of a boost regulator is defined as the product of modulator transfer function and feedback transfer function.

The modulator transfer function of a current mode boost regulator including a power stage with an embedded current loop can be simplified as a one load pole (F_LP), one ESR zero (F_{Z_ESR}), and one Right Half Plane (RHP) zero (F_RHP) system, which can be explained as follows.

Modulator transfer function is defined as Equation 15:

Equation 15.

where

R_ESR is the equivalent series resistance (ESR) of the output capacitor which is specified in the capacitor data sheet.

R_COMP, C_COMP, and C_HF (see Figure 9-3) configure the error amplifier gain and phase characteristics to produce a stable voltage loop with fast response. This compensation network creates a dominant pole at low frequency (F_{DP_EA}), a mid-band zero pole (F_{Z_EA}), and a high frequency pole (F_{P_EA}).

The feedback transfer function is defined as Equation 16:

Equation 16.

where

R_O (≈ 10 MΩ) is the output resistance of the error amplifier and Gm (≈ 2 mA/V) is the transconductance of the error amplifier.

Assuming F_LP is canceled by F_{Z_EA}, F_RHP is much higher than crossover frequency (F_CROSS), and if F_{Z_ESR} is either canceled by F_{P_EA} or F_{Z_ESR}, then that is much higher than F_CROSS. The open-loop transfer function can be simplified as Equation 17:

Equation 17.

Because |T(s)|=1 at the crossover frequency, the crossover frequency can be simply estimated using those assumptions.

Equation 18.