JAJSDX2C September 2017 – October 2021 LM5150-Q1
PRODUCTION DATA
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The open-loop transfer function of a boost regulator is defined as the product of modulator transfer function and feedback transfer function.
The modulator transfer function of a current mode boost regulator including a power stage with an embedded current loop can be simplified as a one load pole (FLP), one ESR zero (FZ_ESR), and one Right Half Plane (RHP) zero (FRHP) system, which can be explained as follows.
Modulator transfer function is defined as follows:
where
RESR is the equivalent series resistance (ESR) of the output capacitor which is specified in the capacitor data sheet.
RCOMP, CCOMP, and CHF (see Figure 9-3) configure the error amplifier gain and phase characteristics to produce a stable voltage loop with fast response. This compensation network creates a dominant pole at low frequency (FDP_EA), a mid-band zero (FZ_EA), and a high frequency pole (FP_EA).
The feedback transfer function is defined as follows:
where
RO (≈ 10 MΩ) is the output resistance of the error amplifier and Gm (≈ 2 mA/V) is the transconductance of the error amplifier.
Assuming FLP is canceled by FZ_EA, FRHP is much higher than crossover frequency (FCROSS), and FZ_ESR is either canceled by FP_EA or FZ_ESR is much higher than FCROSS, the open-loop transfer function can be simplified as follows:
Because |T(s)| = 1 at the crossover frequency, the crossover frequency can be simply estimated using those assumptions.