Page 256 - Organic Electronics in Sensors and Biotechnology

An Intr oduction to Or ganic Photodetectors 233

where t = time
i = current generated by the current source of the pho-
todiode
i and i = currents that flow through the shunt resistance
sh f
and the feedback resistance, respectively
−
i = input bias current, i.e., the current that flows into
B
the inverting input of the op-amp
The current that flows through the feedback capacitor is propor-
tional to the rate of change of the potential difference across it.
it() = C d [ V − V ()]
t
f dt − out (6.59)
Hence, from Eqs. (6.58) and (6.59), we can write
V − 0 d
it() = − + C [ V − V ()] − i − (6.60)
t
R dt − out B
sh
which, on integrating over a measurement time τ, yields
τ τ ⎧ V ⎫ ⎪
∫ it dt = ⎨ ∫ − + C d [ V − V ()] − ⎬ dt (6.61)
−
i
t
()
−
B
out
0 0 0 ⎩ R sh dt ⎭
The left-hand side can be equated with the total charge Q created by
the photodiode current source. Hence, we can write
τ V
Δ
Q = − − CV − i τ − (6.62)
R out B
sh
where
ΔV = V ()τ − V ( )0 (6.63)
out out out
which rearranges to give
ΔV =− Q + ετ (6.64)
out C

where
1 ⎛ V ⎞
ε= ⎜ − − i − ⎟ (6.65)
C ⎝ R sh B ⎠

Ignoring ε for a moment, we can see that the voltage change ΔV is
out
proportional to the total amount Q of charge generated by the current
source of the photodiode over the measurement time τ. And ε is an
error term arising from the non-ideal behavior of the amplifier (namely,
the effects of the DC offset voltage and the input bias current) and