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JAJSUV0 June 2024 LM5171

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7.1.1.2 Current Loop Compensation

Equation 36 indicates that the power plant is basically a first-order system. A Type-II compensator as shown in Figure 7-1 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 current loop compensation gain is determined by :

Equation 37.

G_{c i} (s) = G_{m} \times [R_{G M}‖ Z_{c o m p} (s)]

where

A_CS is the current sense amplifier gain, that is 40;
G_m is the trans-conductance of the gm error amplifier, which is 100μA/V;
Z_COMP(s) is the equivalent impedance of the compensation network seen at the COMP pin (see Figure 7-1)

Equation 38.

Z_{C O M P} (s) = \frac{1}{C_{H F} + C_{C O M P}} \times \frac{1 + s \times R_{C O M P} \times C_{C O M P}}{s \times (1 + s \times R_{C O M P} \times \frac{C_{H F} \times C_{C O M P}}{C_{H F} + C_{C O M P}})}

Considering C_HF << C_COMP, Equation 38 can be simplified to :

Equation 39.

Z_{C O M P} (s) = \frac{1}{C_{C O M P}} \times \frac{1 + s \times R_{C O M P} \times C_{C O M P}}{s \times (1 + s \times R_{C O M P} \times C_{H F})}

Because R_GM is > 5MegΩ, and the frequency range for loop compensation is usually above a few kHz, the effects of R_GM on the loop gain in the interested frequency range becomes negligible. Therefore, substituting Equation 39 into Equation 37, and neglecting R_GM, one can get the following:

Equation 40.

G_{c i} (s) = \frac{G_{m}}{C_{C O M P}} \times \frac{1 + s \times R_{C O M P} \times C_{C O M P}}{s \times (1 + s \times R_{C O M P} \times C_{H F})}

From Figure 7-2, the open-loop gain of the inner current loop can be found as:

Equation 41.

T_{i} (s) = G_{c i} (s) \times \frac{1}{V_{M}} \times G_{i d} (s) \times R_{f}

where

Equation 42.

V_{M} = V_{H V} \times K_{F F}

Equation 43.

R_{f} = R_{C S} \times A_{C S}

K_FF is the ramp generator coefficient. For LM5171, K_FF=0.03125.

Substituting Equation 40 and Equation 36 into Equation 41, T_i(s) can be written as:

Equation 44.

T_{i} (s) = \frac{1}{s {\times K_{F F} \times L}_{m}} \times \frac{R_{f} \times G_{m}}{C_{C O M P}} \times \frac{1 + s \times R_{C O M P} \times C_{C O M P}}{s \times (1 + s \times R_{C O M P} \times C_{H F})}

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

Equation 45.

f_{p 1} = 0

Equation 46.

f_{p 2} = \frac{1}{2 π \times R_{C O M P} \times C_{H F}}

Equation 47.

f_{z} = \frac{1}{2 π \times R_{C O M P} \times C_{C O M P}}

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

The zero f_z is placed at around 1/5 of target crossover frequency f_CI,
The pole f_p2 is placed at approximately 1/2 of switching frequency f_SW,
The total open-loop gain is set to unity at f_CI, namely,

Equation 48.

|T_{i} (2 i \times π \times f_{C I})| = 1

Therefore, the compensation components can be derived from the above equations, as shown in Equation 49.

Equation 49.

\{\begin{matrix} R_{C O M P} = \frac{K_{F F}}{A_{C S} \times R_{C S} \times G_{m}} \times |2 i \times π \times f_{C I} \times L_{m}| \\ C_{C O M P} = \frac{1}{|2 i \times π \times \frac{f_{C I}}{5} \times R_{C O M P}|} \\ C_{H F} = \frac{1}{|2 i \times π \times \frac{f_{S W}}{2} \times R_{C O M P}|} \end{matrix}

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7.1.1.2 Current Loop Compensation