A transimpedance preamplifier for a photodiode needs an unusually small tail current,

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_{\rm tail} = 5.0\,\mu\mathrm{A}

, to keep the differential pair's own shot noise small. This current is generated from a reference current

I_{\rm ref}=500\,\mu\mathrm{A}

already available on the same rail. All transistors involved are matched, with Early voltage

V_A = 80\,\mathrm{V}

, current gain

\beta_F = 120

, and a minimum collector-emitter voltage of

V_{CE,\min}=0.2\,\mathrm{V}

for active-region operation (taken as the transistors' saturation limit). Take

V_T = 25.9\,\mathrm{mV}

300\,\mathrm{K}

. ((a)) A Widlar source (a diode-connected reference transistor and a second transistor carrying

I_{\rm tail}

through an emitter resistor

R_E

) steps

I_{\rm ref}

down to

I_{\rm tail}

. Find

R_E

, and the rate of change with temperature at

300\,\mathrm{K}

of the voltage this resistor carries. ((b)) The tail's output resistance must exceed

200\,\mathrm{M}\Omega

. Compute the plain Widlar source's own output resistance

r_{o,\rm Widlar}=r_o(1+g_mR_E)

, then stack an identical-bias cascode transistor above it and compute the resulting output resistance from

r_{\rm out}=r_{o2}+\left(1+g_{m2}r_{o2}\right)\left(r_{o,\rm Widlar}\parallel r_{\pi2}\right),

where subscript 2 refers to the cascode transistor (also biased at

5.0\,\mu\mathrm{A}

). State whether the specification is met. ((c)) The whole tail source (Widlar transistor plus cascode transistor) is allowed at most

1.0\,\mathrm{V}

of headroom, measured from the negative rail up to the pair's common-emitter node. Using

V_{CE,\min}

for the Widlar transistor, the voltage across

R_E

from part (a), and the rule that an optimally biased cascode transistor costs about

0.3\,\mathrm{V}

more of headroom, estimate the minimum headroom this source needs, and state the margin against the

1.0\,\mathrm{V}

budget.

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