A photodiode of capacitance

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Feedback, operational amplifiers and analogue signal processing · Sensors, detectors and experimental instrumentation

Inside the Instrument, Ch Low-noise front ends and noise measurement

Problem

A photodiode of capacitance Cd=50 pFC_d = 50\,\mathrm{pF}, wiring and amplifier input capacitance included, is read through Rf=1 MΩR_f = 1\,\mathrm{M}\Omega by an amplifier with fu=10 MHzf_u = 10\,\mathrm{MHz}, en=5 nV/Hze_n = 5\,\mathrm{nV}/\sqrt{\mathrm{Hz}} and in=10 fA/Hzi_n = 10\,\mathrm{fA}/\sqrt{\mathrm{Hz}}, at 300 K300\,\mathrm{K}. Model the amplifier as A(s)=ωu/sA(s) = \omega_u/s. ((a)) Choose CfC_f by the working rule for ζ≈0.5\zeta \approx 0.5. ((b)) With that CfC_f, find the frequency at which the loop gain T=AβT = A\beta crosses unity, and the phase margin there. ((c)) Find the frequency above which the amplifier's voltage noise acting on CdC_d exceeds the feedback resistor's own current noise. ((d)) Over a brick-wall band of 100 kHz100\,\mathrm{kHz}, find the rms input-referred noise current of each of the three terms and their total, and name the dominant term.

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