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SNVSCM3 June 2024 LM5171

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7.2.1.2.15 Loop Compensation

Select current loop cross over frequency f_CI to 1/6 of the switching frequency. According to Equation 49, the compensation network for the inner current loop is determined by:

Equation 114.

\{\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}| = \frac{0.03125}{40 \times 1 m Ω \times 100 μ A / V} \times |2 i \times π \times 15 k H z \times 4.7 μ H| = 3.5 k Ω \\ C_{C O M P} = \frac{1}{|2 i \times π \times \frac{f_{C I}}{5} \times R_{C O M P}|} = \frac{1}{|2 i \times π \times \frac{15 k H z}{5} \times 3.5 k Ω|} = 15 n F \\ C_{H F} = \frac{1}{|2 i \times π \times \frac{f_{S W}}{2} \times R_{C O M P}|} = 0.9 n F \end{matrix}

Selecting the closest standard values for the compensation network, namely,

R_COMP1 = R_COMP2 = 3.65kΩ

C_COMP1 = C_COMP2 = 15nF

C_HF1 = C_HF2 = 1nF

Figure 7-11 shows the bode plots of the power plant $\frac{1}{V_{M}} \times G_{i d} (s) \times A_{C S} \times R_{C S}$ , the current loop compensation gain G_ci(s) , and the resulting total open loop gain T_i(s).

Figure 7-11 Bode Plots of the Current Loop

For buck mode, select the voltage loop crossover frequency at 1/10 of the current loop crossover frequency. According to Equation 115, the compensation network for the voltage current loop is determined by:

Equation 115.

\{\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}} = \frac{26.7 k Ω}{\frac{0.4 Ω}{40 \times 1 m Ω} \times |\frac{1 + \frac{2 i \times π \times 1.5 k H z}{250 k H z}}{1 + \frac{2 i \times π \times 1.5 k H z}{6.25 k H z}}| \times 0.8} = 6.1 k Ω \\ C_{L C O M P} = \frac{1}{|2 i \times π \times \frac{f_{C V}}{5} \times R_{C O M P}|} = \frac{1}{|2 i \times π \times \frac{1.5 k H z}{5} \times 6.1 k Ω|} = 86 n F \\ C_{L H F} = \frac{1}{|2 i \times π \times 10 \times f_{C V} \times R_{C O M P}|} = 1.7 n F \end{matrix}

Selecting the closest standard values for the compensation network, namely,

R_LCOMP = 6.2kΩ

C_COMP1 = 100nF

C_HF1 = 1.5nF

Figure 7-12 shows the bode plots of the power plant G_{vs_BK}(s), the voltage loop compensation gain G_cv(s) , and the resulting total open loop gain T_{vs_BK}(s).

Figure 7-12 Bode Plots of the Voltage Loop

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7.2.1.2.15 Loop Compensation