JAJSNC5 データシート

JAJSNC5 april 2023 LM5171-Q1

ADVANCE INFORMATION

パッケージ・オプション

メカニカル・データ（パッケージ｜ピン）

PHP|48
- MPQF051B

サーマルパッド・メカニカル・データ

発注情報

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8.1.1.3 Voltage Loop Small Signal Model

When the current loop compensator is designed, the outer voltage loop can then be analyzed. Figure 8-4 shows the outer voltage control loop and inner current loop.

Figure 8-4 Voltage Loop and Current Loop Block Diagram

We can get the close loop transfer function from ISET to the output voltage (v_O) as:

Equation 49.

G_{v s} (s) = \frac{{\hat{v}}_{L V}}{{\hat{v}}_{I S E T}} = \frac{G_{c i} (s) \times \frac{1}{V_{M}} \times G_{v d} (s)}{1 + T_{i} (s)}

When selecting the crossover frequency of the buck voltage loop lower than the current loop crossover frequency, G_vs(s) can be simplified. For the denominator, T_i(s) dominates, Equation 49 can be written as:

Equation 50.

G_{v s} (s) = \frac{{\hat{v}}_{L V}}{{\hat{v}}_{I S E T}} = \frac{G_{c i} (s) \times \frac{1}{V_{M}} \times G_{v d} (s)}{T_{i} (s)} = \frac{G_{v d} (s)}{G_{i d} (s) \times A_{C S} \times R_{C S}}

The buck power plant transfer function from the duty cycle (d) to the output voltage (v_LV) is determined by the following:

Equation 51.

G_{v d_B K} (s) = \frac{{\hat{v}}_{L V}}{\hat{d}} = V_{H V} \times \frac{1 + \frac{s}{ω_{Z_v l_B K}}}{1 + \frac{s}{ω_{0_B K} \times Q_{B K}} + \frac{s^{2}}{{ω_{0_B K}}^{2}}}

where

Equation 52.

ω_{Z_v l_B K} = \frac{1}{R_{E S R_B K} \times C_{O U T_B K}}

Substituting Equation 51 into Equation 50, a simplified transfer function from the ISET voltage to the Output voltage (V_LV) is determined by the following:

Equation 53.

G_{v s_B K} (s) = \frac{{\hat{v}}_{L V}}{{\hat{v}}_{I S E T}} = K_{d c_B K} \times \frac{1 + \frac{s}{ω_{Z_v l_B K}}}{1 + \frac{s}{ω_{Z_i l_B K}}}

where

Equation 54.

K_{d c_B K} = \frac{R_{O U T_B K}}{A_{C S} \times R_{C S}}

Similarly, the boost power plant transfer function from the duty cycle (d) to the output voltage (v_HV) is determined by the following:

Equation 55.

G_{v d_B S T} (s) = \frac{{\hat{v}}_{H V}}{\hat{d}} = \frac{V_{L V}}{{(1 - D)}^{2}} \times \frac{(1 + \frac{s}{ω_{Z_v l_B S T}}) (1 + \frac{s}{ω_{R H P Z}})}{1 + \frac{s}{ω_{0_B S T} \times Q_{B S T}} + \frac{s^{2}}{{ω_{0_B S T}}^{2}}}

where

Equation 56.

ω_{Z_v l_B S T} = \frac{1}{R_{E S R_B S T} \times C_{O U T_B S T}}

Equation 57.

ω_{R H P Z} = \frac{R_{O U T_B S T} \times (1 - D)}{L_{m}}

Substituting Equation 55 into Equation 50, a simplified transfer function from the ISET voltage to the output voltage (V_HV) is determined by the following:

Equation 58.

G_{v s_B S T} (s) = \frac{{\hat{v}}_{H V}}{{\hat{i}}_{s e t}} = K_{d c_B S T} \times \frac{(1 + \frac{s}{ω_{Z_v l_B S T}}) (1 - \frac{s}{ω_{R H P Z}})}{1 + \frac{s}{ω_{Z_i l_B S T}}}

where

Equation 59.

K_{d c_B S T} = \frac{R_{O U T_B S T} \times (1 - D)}{{2 \times A}_{C S} \times R_{C S}}