A current-mode boost converter steps up to with inductor

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Semiconductor devices and analogue circuits · Feedback, operational amplifiers and analogue signal processing

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Problem

A current-mode boost converter steps

9\,\mathrm{V}

up to

24\,\mathrm{V}

with inductor

L = 22\,\mu\mathrm{H}

, delivering

I_o = 0.5\,\mathrm{A}

. Its compensated loop is designed so that near crossover

T(s) \approx (\omega_c/s)(1-s/\omega_z)

, with

\omega_c = 2\pi f_c

set by the compensator at the nominal crossover

f_c = 8\,\mathrm{kHz}

and the right-half-plane zero at

\omega_z = (1-D)^2 R_L/L

R_L = V_o/I_o

. Because the zero lifts

|T(j\omega_c)|

slightly above one, estimate each phase margin at

f_c

. ((a)) Find the duty cycle

D

and the zero frequency

f_z

I_o = 0.5\,\mathrm{A}

, and the resulting phase margin at

f_c = 8\,\mathrm{kHz}

. ((b)) Find the new zero frequency and phase margin if the load current doubles to

I_o = 1.0\,\mathrm{A}

(same

f_c

). ((c)) Using the Nyquist criterion for a non-minimum-phase loop with a single unity-gain crossing, show that the loop remains stable at both loads by evaluating the high-frequency limit of

|T|

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