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JAJSUV0 June 2024 LM5171

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7.1.1.4 Voltage Loop Compensation

The typical bi-directional application with HV voltage regulation and LV voltage regulation is shown in Figure 7-6. Connect the error voltage of the outer voltage loop error amplifiers (ERRHV and ERRLV) to ISETx as the reference for the inner current loop.

It is advised that the outer voltage loop crossover frequency f_CV should be one decade below that of the inner current loop crossover frequency f_CI. And boost outer voltage loop crossover frequency should also be below 1/5 of the Right-Half-Plane Zero (RHPZ).

Figure 7-6 Outer Voltage Loop Control

Type-II compensator as shown in Figure 7-6 is recommended to stabilize the voltage loop for both buck and boost mode operations.

Buck mode compensation will be analyzed as an example. The transfer function of the compensator of buck mode can be found as:

Equation 71.

G_{c v} (s) = \frac{{\hat{v}}_{I S E T}}{{\hat{v}}_{L V}} \approx \frac{A_{V M} \times ω_{Z E A}}{s} \times \frac{1 + \frac{s}{ω_{Z E A}}}{1 + \frac{s}{ω_{H F}}} \times K_{I S E T}

where

Equation 72.

A_{V M} \approx \frac{R_{L C O M P}}{R_{L F B T}}

Equation 73.

ω_{Z E A} = \frac{1}{R_{L C O M P} \times C_{L C O M P}}

Equation 74.

ω_{H F} \approx \frac{1}{R_{L C O M P} \times C_{L H F}}

Equation 75.

K_{I S E T} = \frac{R_{I S E T B}}{R_{I S E T T} + R_{I S E T B}}

The total open-loop gain of the outer voltage loop of buck mode T_{v_BK}(s) is the product of G_{vs_BK}(s) and G_cv(s):

Equation 76.

T_{v_B K} (s) = G_{v s_B K} (s) \times G_{c v} (s)

Or:

Equation 77.

T_{v_B K} (s) = K_{d c_B K} \times \frac{1 + \frac{s}{ω_{Z_v l}}}{1 + \frac{s}{ω_{Z_i l}}} \times \frac{A_{V M} \times ω_{Z E A}}{s} \times \frac{1 + \frac{s}{ω_{Z E A}}}{1 + \frac{s}{ω_{H F}}} \times K_{I S E T}

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

Choose a value for R_LFBT based on the bias current and power dissipation,
The zero ω_ZEA is placed around 1/5 of target crossover frequency f_CV,
The pole ω_HF is placed at approximately 10 times of f_CV,
The total open-loop gain is set to unity at f_CV, namely,

Equation 78.

|T_{v_B K} (2 i \times π \times f_{C V})| = 1

Therefore, the compensation components can be derived from the above equations as:

Equation 79.

\{\begin{matrix} R_{L C O M P} = \frac{R_{L F B T}}{K_{d c_B K} \times |\frac{1 + \frac{2 i \times π \times f_{C V}}{ω_{Z_v l}}}{1 + \frac{2 i \times π \times f_{C V}}{ω_{Z_i l}}}| \times K_{I S E T}} \\ C_{L C O M P} = \frac{1}{|2 i \times π \times \frac{f_{C V}}{5} \times R_{C O M P}|} \\ C_{L H F} = \frac{1}{|2 i \times π \times 10 \times f_{C V} \times R_{C O M P}|} \end{matrix}

The compensator of boost voltage loop can be designed similarly. Please note that boost voltage loop crossover frequency should also be below 1/5 of the Right-Half-Plane Zero (RHPZ).

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7.1.1.4 Voltage Loop Compensation