Equation 24 indicates that the power plant is basically a first-order system. A Type-II compensator as shown in Figure 9-3 is adequate to stabilize the loop for both buck and boost mode operations.

Assuming the output impedance of the gm amplifier is R_GM, the gain from the inductor to the output of gm amplifier is determined by Equation 25:

Equation 25.

where

• the coefficient 50 is the current sense amplifier gain;
• Gm is the transconductance of the gm error amplifier, which is 1 mA/V;
• Z_COMP(s) is the equivalent impedance of the compensation network seen at the COMP pin (see Equation 26)

Equation 26.

Usually C_HF is << C_COMP. Thus Equation 26 can be simplified to Equation 27:

Equation 27.

Because R_GM is > 5 MegΩ, and the frequency range for loop compensation is usually above a few kHz, the effects of RGM on the loop gain in the interested frequency range becomes negligible. Therefore, substituting Equation 28 into Equation 25, and neglecting R_GM, one can get the following:

Equation 28.

The total open-loop gain of the inner current loop is the product of H(s) and G(s):

Equation 29.

Or:

Equation 30.

The poles and zeros of the total loop transfer function are determined by:

Equation 31.

Equation 32.

Equation 33.

Equation 34.

To tailor the total inner current loop gain to cross over at f_CO, select the components of the compensation network according to the following guidelines, then fine tune the network for optimal loop performance.

1. The zero f_z is placed at the power stage pole f_p2,
2. The pole f_p3 is placed at approximately two decade higher then f_CO,
3. The total open-loop gain is set to unity at f_CO, namely,

Equation 35.

Therefore, the compensation components can be derived from the above equations, as shown in Equation 36.

Equation 36.