5 Solid State Detectors
157
Fig. 5.15 The effect of amplifier serial noise in a detector-amplifier system
noise is represented by a noise current source of density d 2 >/df = 2I·q in parallel
to the detector capacitance C D . To estimate the charge measuring precision one
has to follow separately signal and noise through the complete readout chain and
compare their respective output signals.
The signal produced by the amplifier will usually not be used directly; it will
be further amplified and shaped, in order to optimize the ratio of signal to noise
and to reduce the interference between subsequent signals. We will only consider
a few very simple cases, the simplest being an idealized charge-sensitive amplifier
followed by an RCCR filter. For a more elaborate treatment, the reader is referred
to the literature (e.g. [15]).
The arrangement of a CSA followed by an RCCR filter is shown in Fig. 5.16. The
output of the CSA is a voltage step given for very high amplification as Q/C f . The
shaper does an RC integration followed by a CR differentiation. This procedure
results in a signal peak, which for the same integration and differentiation time
constant τ = R 1 C 1 = R 2 C 2 has the shape U out (t) = (Q/C f )·(t/τ )·exp(−t/τ ) with
a peak value U peak = (Q/C f )·exp(−1). The height of this peak is a measure of the
signal charge. Superimposed on the signal is the noise voltage, and we are interested
in the signal-to-noise ratio, which is defined as the ratio of the height of the peak
value to the root-mean-square value of the noise voltage measured at the same point
in the circuit.
In order to find the noise voltage at the output, each noise source in the circuit has
to be traced to the output and the resulting voltages added in quadrature. Doing so,
one finds the important result that, for white (thermal) serial noise, the ratio of noise
to signal (N/S) decreases with the square root of the shaping time constant τ , while
for 1/f noise this ratio remains constant. Parallel noise, given as a time integral over
current fluctuations, increases with the square root of the shaping time.
More sophisticated continuous time filtering methods use (for example) Gaussian
shape filtering, which can be approximated by several sequential RC integration
and differentiation steps. Especially important in integrated electronics are the
157
Fig. 5.15 The effect of amplifier serial noise in a detector-amplifier system
noise is represented by a noise current source of density d 2 >/df = 2I·q in parallel
to the detector capacitance C D . To estimate the charge measuring precision one
has to follow separately signal and noise through the complete readout chain and
compare their respective output signals.
The signal produced by the amplifier will usually not be used directly; it will
be further amplified and shaped, in order to optimize the ratio of signal to noise
and to reduce the interference between subsequent signals. We will only consider
a few very simple cases, the simplest being an idealized charge-sensitive amplifier
followed by an RCCR filter. For a more elaborate treatment, the reader is referred
to the literature (e.g. [15]).
The arrangement of a CSA followed by an RCCR filter is shown in Fig. 5.16. The
output of the CSA is a voltage step given for very high amplification as Q/C f . The
shaper does an RC integration followed by a CR differentiation. This procedure
results in a signal peak, which for the same integration and differentiation time
constant τ = R 1 C 1 = R 2 C 2 has the shape U out (t) = (Q/C f )·(t/τ )·exp(−t/τ ) with
a peak value U peak = (Q/C f )·exp(−1). The height of this peak is a measure of the
signal charge. Superimposed on the signal is the noise voltage, and we are interested
in the signal-to-noise ratio, which is defined as the ratio of the height of the peak
value to the root-mean-square value of the noise voltage measured at the same point
in the circuit.
In order to find the noise voltage at the output, each noise source in the circuit has
to be traced to the output and the resulting voltages added in quadrature. Doing so,
one finds the important result that, for white (thermal) serial noise, the ratio of noise
to signal (N/S) decreases with the square root of the shaping time constant τ , while
for 1/f noise this ratio remains constant. Parallel noise, given as a time integral over
current fluctuations, increases with the square root of the shaping time.
More sophisticated continuous time filtering methods use (for example) Gaussian
shape filtering, which can be approximated by several sequential RC integration
and differentiation steps. Especially important in integrated electronics are the