Page 252 - Organic Electronics in Sensors and Biotechnology

An Intr oduction to Or ganic Photodetectors 229

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51
operate. The input bias current i at the inverting terminal is split
B
between the feedback resistor and the shunt resistance of the photo-
diode in exactly the same way as the current i generated by the pho-
-
todiode. Therefore i adds directly to i and experiences the same
B
transimpedance gain R , giving rise toa steady systematic offset DV out
f ia
in the output voltage:
−
ΔV out = i R (6.50)
ia B f
Also shown in the equivalent circuit is a small voltage source (or
“input offset voltage”) v at the noninverting terminal, which
OS
accounts for the fact that real op-amps give out a constant output
voltage when their input terminals are shorted. Referring to Eq. (6.46)
and writing V = V = v , the effect of the input offset voltage is to
−
+
OS
generate a systematic offset DV out in the output voltage:
va
⎛ R ⎞
ΔV out = ⎜ 1 + f ⎟ v (6.51)
va OS
⎝ R sh⎠
The amplifier offsets can be minimized by selecting op-amps with
-
the smallest possible values of i and v and by ensuring that the
B OS
shunt resistance R of the photodiode is as high as possible. In addi-
sh
tion, most op-amps allow any remaining offset to be trimmed to
zero using an externally applied voltage, although this is an imper-
fect solution due to natural drift in the offset voltage and bias cur-
rent over time.

Amplifier Noise
The input bias current and the amplifier offset voltage are subject to
noise fluctuations. If we define the input noise current σ to be the noise
Ia
per square root of frequency on the input bias current, then by analogy
with Eq. (6.50), the corresponding noise on the output voltage is given by

σ
σ out = σ R = BR
Ia Ia f Ia f (6.52)
where B is the measurement bandwidth. And if we define the input
noise voltage σ to be the noise per square root of frequency on the
Va
offset voltage, then by analogy with Eq. (6.51), the corresponding
noise on the output voltage is given by

⎛ R ⎞ ⎛ R ⎞

σ out = ⎜ 1 + f ⎟ σ = ⎜ 1 + f ⎟ σ B
Va Va Va (6.53)
⎝ R sh ⎠ ⎝ R sh⎠