A differential probe is specified with a CMRR at low frequency

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

Inside the Instrument, Ch The differential pair and the current mirror

Problem

A differential probe is specified with a CMRR

= 86\,\mathrm{dB}

at low frequency, falling to

60\,\mathrm{dB}

200\,\mathrm{kHz}

. Its front end is a bipolar long-tailed pair biased at

I_{\rm tail} = 600\,\mu\mathrm{A}

, whose single-ended CMRR is set by the tail's output resistance as

\mathrm{CMRR} \approx g_mR_{\rm tail}

. Take

V_T = 25.9\,\mathrm{mV}

. ((a)) Find

g_m

and, from the

86\,\mathrm{dB}

figure, the tail resistance

R_{\rm tail}

this implies. ((b)) The probe is used at

200\,\mathrm{kHz}

on a supply line carrying a common-mode voltage of

4\,\mathrm{V}

(peak) together with a genuine differential signal of

1\,\mathrm{mV}

(peak). Find the equivalent input error this common-mode voltage produces, and express it as a percentage of the genuine signal.

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