Page 68 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Fundamental Noise Basics and Calculations

Fundamental Noise Basics and Calculations 61

the follower configuration, above a break frequency f 1 the signal output
decreases at -20dB/decade. Writing in the complex frequency (s) domain the
impedance of C f :

1
Z Cf = (3.18)
sCf

f
Z f = RZ Cf (parallel combination of Z Cf and R f ) (3.19)
R f + Z Cf

f 1 = 1 (3.20)
2p RC f
f
That is the photocurrent, feedback resistor thermal current noise, and ampli-
fier current noise outputs decrease together above f 1.
The effect of the circuit configuration on the amplifier’s voltage noise is more
complicated. The voltage noise generator sees an inverting amplifier with a gain
given by the ratio of feedback to input impedances. Hence this noise is ampli-
fied to:
Ê
e n 1 + Z f ˆ ¯ (3.21)
Ë
Z sh
sh
where: Z sh = RZ Cp (parallel combination of C p and R sh )
R sh + Z Cp
C p as before contains all the input capacitances. This contribution to noise
therefore increases at 20dB/decade above a break frequency f 2 where the im-
pedances Z f and Z sh are equal. With large transimpedance resistors and/or
high-capacitance photodiodes this will be typically f 2 = 1/2pR f C p . The various
characteristic frequencies are shown in Fig. 3.10 as a schematic Bode plot. The
numerical values shown assume an R f = 100MW transimpedance, C f = 1.6pF
feedback parasitic capacitance, and a C p = 160pF detector capacitance.
Where large detectors are used with their high capacitance and consequently
low impedance, and high value transimpedances, the magnification of the
voltage noise caused by this effect can easily become the dominant noise source.
As can be seen from Fig. 3.10, the noise gain increase is checked by the para-
sitic capacitance of R f and eventually reduced by the dropping open loop gain of
the amplifier. In between a region of high excess noise is often seen, which is
termed gain peaking. Adding extra capacitance across R f can lower the f 1 break
frequency to reduce the peak, but only at the expense of signal bandwidth.
Given a particular photodiode, large enough to collect most of the signal light,
and a transimpedance to provide adequate signal voltage, there isn’t much we
can do about gain peaking except look for amplifiers that contribute the lowest
possible noise. It is one of the surprising aspects that despite working with nA

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