10 Signal Processing for Particle Detectors
447
Fig. 10.8 Induced charges in
coplanar electrodes:
Q 1 − Q 2 = const
independently of x 0
Fig. 10.9 Induced currents in
coplanar electrodes
(charge), and by the impulse response h(t), i.e., the weighting function w(t) of the
measurement system, the preamplifier and the subsequent readout chain,
σ
2
= n q
2
∞
−∞
h
2 (t)dt = n q
2
∞
−∞
w
2 (t)dt .
(10.3)
The noise variance is determined by the noise process, the rate of impulses
and their area q (charge), and by the impulse response h(t). If we measure the
variance and the h(t), we can determine 2 , but we cannot determine and
q. Only when randomly generated carriers move in one direction, which results in a
mean current I 0 = =n can the rate and the charge of impulses be determined from
σ 2 and I 0 . It is shown in Ref. [9] that 2 equals the mathematical (two-sided)
noise current spectral density, whereas i 2
n = 2 n q 2 equals the physical (singlesided) one, to be used in calculations of the equivalent noise charge (ENC) in Sect.
10.4.2.