Page 243 - Organic Electronics in Sensors and Biotechnology

220 Cha pte r S i x

and

⎡ ⎛ t ⎞⎤
−
09V = V 0 ⎢ 1 exp − 2 ⎥ → t = RC ln 10 (6.24)
.
0 ⎜ ⎟ 2
⎣ ⎢ ⎝ RC ⎠ ⎥ ⎦
The rise time Δt is therefore given by
r
Δt = t − t = RCln 9 (6.25)
r 2 1

A similar calculation on the falling edge yields the same value for the
fall time.
The 3 dB cutoff frequency is defined as the frequency at which
the amplitude of the photodiode signal falls to 1/ 2 of its DC value
(Fig. 6.15), and may be straightforwardly determined by illuminating
the photodiode with sinusoidal light of fixed amplitude and sweeping
its frequency f. The cutoff frequency may alternatively be determined
by recording the photodiode’s impulse response, i.e., its transient
behavior in response to an extremely short light pulse. A delta func-
tion contains equal portions of all possible excitation frequencies. The
Fourier transform of the impulse response therefore gives the gain-
49
frequency response of the photodiode, from which the cut-off fre-
quency can be directly determined.

1
f = 2πRC
c

10 0 I (0)
I(f ) =
c
2
10 –1 i
Signal (AU) 10 –2 C i C

10 –3
i
R L RL
10 –4
10 –3 10 –2 10 –1 10 0 10 1 10 2 10 3
Frequency (AU)

FIGURE 6.15 The theoretical signal vs. frequency response of an RC-limited
photodiode. The 3 dB cutoff frequency f occurs when the frequency of the
c
incident light is equal to 1/(2πRC).