A weather-station power module rectifies its transformer's secondary with a diode bridge

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

Electronics for Measurement, Ch Power supplies: holding a rail steady

Problem

A weather-station power module rectifies its transformer's secondary with a diode bridge, each diode modelled as a fixed

0.6\,\mathrm{V}

drop (

1.2\,\mathrm{V}

in the conducting path, already counted in the measured sag below), and stores the direct output on a

2200\,\mathrm{\mu F}

reservoir capacitor. The transformer's off-load secondary is rated

16.0\,\mathrm{V}

rms at

230\,\mathrm{V}

mains. Under the module's

0.60\,\mathrm{A}

load, the combined sag of the transformer's winding resistance and the diode drops is measured to be a constant

3.0\,\mathrm{V}

, subtracted from the peak of the rectified waveform and essentially independent of the mains voltage. Mains frequency is

50\,\mathrm{Hz}

, so the reservoir is refreshed at

100\,\mathrm{Hz}

. ((a)) Find the loaded peak voltage on the reservoir, the peak-to-peak ripple, and the trough voltage, at nominal mains (

230\,\mathrm{V}

rms) and at the low-mains limit of

-10\%

(

207\,\mathrm{V}

rms). ((b)) The reservoir feeds a

9\,\mathrm{V}

linear regulator whose dropout is

2.5\,\mathrm{V}

(its input must stay at least

2.5\,\mathrm{V}

above

9\,\mathrm{V}

at every instant). Using the trough at

-10\%

mains, find the margin above dropout and decide whether the regulator stays in regulation. ((c)) The same raw rail also feeds a buck converter delivering

3.3\,\mathrm{V}

1.0\,\mathrm{A}

to a sensor board, switching at

250\,\mathrm{kHz}

with a

68\,\mathrm{\mu H}

inductor. Taking the converter's input as the mean loaded voltage at nominal mains (the loaded peak of part (a) minus half the ripple), find the duty cycle and the inductor's peak-to-peak ripple current. ((d)) The buck converter's output is smoothed by a

100\,\mathrm{\mu F}

capacitor with

30\,\mathrm{m\Omega}

of series resistance. Find the peak-to-peak output ripple voltage and state which of the capacitor's two contributions dominates.

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