A shielded cable feeds a sensor signal into a bipolar differential pair whose tail…

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 shielded cable feeds a sensor signal into a bipolar differential pair whose tail current is

I_{\rm tail} = 800\,\mu\mathrm{A}

through a tail resistance

R_{\rm tail} = 20\,\mathrm{k}\Omega

. A common-mode current

i_{\rm CM} = 50\,\mathrm{mA}

, of the kind treated on a cable pair in the first chapter, flows along the cable shield and returns through a ground path of resistance

R_g = 0.2\,\Omega

, producing a common-mode voltage

v_{ic} = i_{\rm CM}R_g

that appears at the pair's inputs relative to local ground. A genuine differential sensor signal of

v_{id} = 2\,\mathrm{mV}

(peak) is present at the same time. Take

V_T = 25.9\,\mathrm{mV}

. ((a)) Find the common-mode voltage

v_{ic}

. ((b)) Find the pair's single-ended CMRR, using

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

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

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