A bipolar cascode current source is biased at

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

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

Problem

I = 0.5\,\mathrm{mA}

, with

\beta_F = 150

V_A = 80\,\mathrm{V}

and

V_T = 25.7\,\mathrm{mV}

for both transistors. This source forms the tail of a differential pair. ((a)) Derive the cascode's output resistance from its small-signal model: the lower transistor presents a resistance

r_{o1}

at the emitter node of the upper transistor, in parallel with the upper transistor's own

r_{\pi 2}

(its base is held at AC ground); use the standard result that an emitter resistance

R_E

boosts a transistor's output resistance to

r_o(1+g_mR_E)

. State the numerical value of the cascode's output resistance. ((b)) This cascode supplies the full tail current

I_{\rm tail}=0.5\,\mathrm{mA}

of the pair. Using the fact (established for the long-tailed pair) that the transfer stays within about

1\,\%

of its linear approximation provided

|v_{id}|\lesssim 10\,\mathrm{mV}

, independent of

I_{\rm tail}

, state the maximum safe differential input. ((c)) Calculate the single-ended common-mode rejection ratio of the pair,

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

, using the cascode's output resistance as

R_{\rm tail}

and the pair's own

g_m

per side at this tail current. Express the result both as a ratio and in decibels.

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