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WeeChumlee
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Homework Statement
The circuit of FIGURE 2 is known as a transimpedance circuit used
for the measurement of very small currents. Derive the relationship
between the output voltage V and the input current I; i.e. if V = kI
find k in terms of R1, R2 and Rf.
Homework Equations
The Attempt at a Solution
If current flows from left of Rf to right and V- is 0V then I is negative.
Then Vn (which is the voltage drop over Rf) = -IRfR2 and Rf in parallel have the resistance
R2Rf / (R2 + Rf)We now have a voltage divider:
Vn = {[(R2Rf / (R2 + Rf))] / [ R1 + R2Rf / (R2 + Rf)]} * Vout
Vn = R2Rf / (R1(R2+Rf) + R2Rf) * V
Vn =-IRf
I = -Vn/Rf
I = -[ R2Rf / (R1(R2+Rf) + R2Rf) * V ] / Rf
I = -R2V / (R1(R2+Rf) + R2Rf)
I * (R1(R2+Rf) + R2Rf) = -R2V
V = -[ I * (R1(R2+Rf) + R2Rf) ] / R2V = kI
V / I =k
V / I = -(R1(R2+Rf) + R2Rf) / R2
k = -(R1(R2+Rf) + R2Rf) / R2
The next part states values:
Calculate the current I if Rf = 10 MΩ, R1 = 90 kΩ, R2 = 10 kΩ
and V –0.1 V.
I use these values and plug them into a SPICE program and see that somewhere I am out by a factor of 10.
I just can't find my mistake
If anyone can help I would be much obliged.
Thanks