An engineer commissioning an LDO test board argues as follows: "The output pole from…

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Semiconductor devices and analogue circuits · Semiconductor devices and analogue circuits

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Problem

An engineer commissioning an LDO test board argues as follows: "The output pole from

R_L \parallel r_o = 20\,\Omega

and

C_{\rm out} = 22\,\mu\mathrm{F}

sits at only a few hundred hertz, far below my crossover of tens of kilohertz, so the capacitor's ESR is a parasitic loss that cannot matter". On this basis they choose a

22\,\mu\mathrm{F}

ceramic capacitor with

R_{\rm ESR} = 3\,\mathrm{m\Omega}

in place of the specified

22\,\mu\mathrm{F}

tantalum part with

R_{\rm ESR} = 0.3\,\Omega

, and reports the board oscillating. The loop has DC gain

T_0 = 2000

, an error-amplifier pole at

500\,\mathrm{Hz}

, a pass-device pole at

500\,\mathrm{kHz}

, and the output pole and ESR zero set by

R_L \parallel r_o = 20\,\Omega

and

C_{\rm out} = 22\,\mu\mathrm{F}

as stated. All poles and the zero may be treated as simple first-order terms. ((a)) Find the output pole frequency and, treating the loop as dominated by the error-amplifier pole and the output pole below crossover, estimate the crossover frequency. ((b)) Find the phase margin with the tantalum capacitor and with the ceramic capacitor. ((c)) State precisely where the engineer's reasoning fails.

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