Page 250 - Organic Electronics in Sensors and Biotechnology

An Intr oduction to Or ganic Photodetectors 227

Ideal Op-Amp Behavior
In Fig. 6.17b we show a circuit for a transimpedance amplifier, where
we have represented the photodiode in equivalent circuit form and,
for now, we ignore the photodiode capacitance. The current source of
the photodiode generates a current i which is split at node x into two
parts i and i that pass through the shunt and feedback resistances,
sh f
respectively. (Note that no current is able to flow into the inverting
terminal of the op-amp due to its infinite input impedance.) Clearly,
i = i + i
sh f (6.44)

from which it follows directly that
⎛ V − ⎞ 0 ⎛ V − V ⎞
i = ⎜ ⎝ − R sh ⎟ ⎠ + ⎜ ⎝ − R f out ⎟ ⎠ (6.45)

where V is the potential at the inverting terminal. After some rear-
−
rangement, this yields
⎛ R ⎞
V =− iR + ⎜ 1 + f ⎟ V (6.46)
out f −
⎝ R sh⎠
In ideal op-amp theory, feedback ensures there is zero potential dif-
ference between the inverting and non-inverting terminals. Hence,
applying V = V = 0, we obtain
−
+
V =− iR (6.47)
out f
The input current is therefore converted to an output voltage by a
transimpedance gain equal in value to the feedback resistor R .
f
In reality, although we have assumed V = V , a very small poten-
− +
tial difference V /A will exist between the input terminals since the
out
output of an op-amp is related to the potentials at its input terminals
by the gain equation
V = A V −( V )
out + − (6.48)
where A is the open-loop gain. From the perspective of the photodi-
ode, the transimpedance amplifier therefore resembles a load resist-
ance R where
eff
V − V − V / A −− ( iR / ) A R f
f
R = − + = out = = (6.49)
eff
i i i A