In the below photo-sensor conditioning circuit, the photo current I(Ph) of photo

Question

In the below photo-sensor conditioning circuit, the photo current I(Ph) of photo sensor diodes is a function of both the incident photon flux (Ph) and temperature T. I(Ph, T) = Io exp(T/T0) + A times Ph A shielded reference photo sensor (similar to the photo sensor) is used to cancel the effect of temperature on the output voltage. Show that Vout is a function of incident photon flux Ph only, and not temperature. If Io = 1 mu A, VB = 5 V, R = 1 M ohm, T = 300 K, To = 273 K, find the offset voltage in the output for CMRR = 1000, and CMRR = 1000,000.

Explanation / Answer

I(Ph,T) = Io exp(T/To) + A*Ph

output of the Op amp

Vo = 100(V+ - V-)

V- = (5V + I*R) = 5 - R*Io exp(T/To)   = 5 - 1.0e+6 *1.0e-6(exp(300/273)

       = 2.0 V

V+ = (5V - I*R) = 5 - R*{Io exp(T/To) + A*Ph} = 5 - 1.0e+6 * {1.0e-6(exp(300/273) +A*Ph}

       = 2.0 - 1.0e+6*A*Ph

output V0 = 100(-1.0e+6A*Ph

                  = -A*Ph e+8 V

CMRR = 1000

diff G = 100

CMRR = diff G/ Com. G = 1000

com. G = 100/1000 = 0.1

common input = 2.0 V

common out put = 0.2V , required offset = 0.2 V

CMRR = 100000

comm G = 100/1000000 = 1.0e-4

reuired offset = 2.0*1.0e-4 = 0.2 mV

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