LM5146 datasheet(32/55 Pages) TI

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associated with the output LC filter and a zero related to the ESR of the output capacitor. The DC (and low

frequency) gain of the modulator and power stage is VIN/VRAMP. The gain from COMP to the average voltage at

the input of the LC filter is held essentially constant by the PWM line feedforward feature of the LM5146 (15 V/V

or 23.5 dB).

Complete expressions for small-signal frequency analysis are presented in Table 9-3. The transfer functions are

denoted in normalized form. While the loop gain is of primary importance, a regulator is not specified directly

by its loop gain but by its performance related characteristics, namely closed-loop output impedance and audio

susceptibility.

Table 9-3. Buck Regulator Small-Signal Analysis

TRANSFER FUNCTION

EXPRESSION

Open-loop transfer function

comp

Öv

(s) Öv (s)

d(s)

T (s)

G (s) G (s) F

v (s)

(s)

d(s)

Duty-cycle-to-output transfer function

Öv (s) 0

Öi (s) 0

Öv (s)

G (s)

Öd(s)

ESR

Compensator transfer function(1)

comp

mid

Öv

(s)

G (s)

Öv (s)

¹©

·§

¸¨

¹©

Modulator transfer function

comp

RAMP

Öd(s)

Öv

(s)

(1)

Kmid = RC1/RFB1 is the mid-band gain of the compensator. By expressing one of the compensator zeros in inverted zero format, the

mid-band gain is denoted explicitly.

Figure 9-2 shows the open-loop response gain and phase. The poles and zeros of the system are marked with

x and o symbols, respectively, and a + symbol indicates the crossover frequency. When plotted on a log (dB)

scale, the open-loop gain is effectively the sum of the individual gain components from the modulator, power

stage, and compensator (see Figure 9-3). The open-loop response of the system is measured experimentally by

breaking the loop, injecting a variable-frequency oscillator signal, and recording the ensuing frequency response

using a network analyzer setup.

-40

-20

-180

-135

-90

-45

100

1000

Frequency (kHz)

Loop

Gain

(dB)

Loop

Phase

(°)

Complex

LC Double

Pole

Compensator

Poles

Output

Capacitor

ESR Zero

Crossover

Frequency, fc

Compensator

Zeros

Loop

Phase

Loop

Gain

Figure 9-2. Typical Buck Regulator Loop Gain and Phase With Voltage-Mode Control

LM5146

SNVSBV0A – JUNE 2021 – REVISED JUNE 2021

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