Signal Induced by a Moving Charge Example l Parallel Plate lon Chamber Anode(A) Ael-".A(P) q Applying E Green's VA(P d q Theorem P v A constant induced current flows in the external circuit Cathode(C) dQ dx d dt Luciano musa
Beijing, January 2008 Luciano Musa 6 Signal Induced by a Moving Charge + − d x E Vb i QA,el = -q V’A(P) V’A = -q x d QA,ion = q V’A(P) V’A = q x d Anode (A) Cathode (C) A constant induced current flows in the external circuit i = dQA,el dt = - q d dx dt Parallel Plate Ion Chamber Applying Green’s Theorem Example I P(x)
Signal Induced by a Moving Charge Example Cylindrical Proportional Chamber Charged Avalanche particle eglo primary (amplification) ionization cathode inode Electron cloude lectron -ion E≠0 =io/(1tt0) Luciano musa
Beijing, January 2008 Luciano Musa 7 anode cathode Avalanche region (amplification) Charged particle electron – ion pair E ≠ 0 primary ionization Ion cloude Electron cloude gas Signal Induced by a Moving Charge Cylindrical Proportional Chamber i(t) = i0 / (1+t/t0) Example II
Detector Signal Processing Model senes serles white noise 1/ noise noiseless preamplifier e2Fc/fl A signal processor Q. s(t) d 12=b 12 =d f arallel fs()=8(t) para A(Q/(Cd+ci)) hite noise f nois noise power spectral density Ax[a+blo(cd+Ci)2 The detector is modeled as a current source, delivering a current pulse with time profile s(t) and charge Q, proportional to the energy released across the parallel combination of the detector capacitance Cd and the preamplifier input capacitance Ci Beijing January 2008 Luciano musa
Beijing, January 2008 Luciano Musa 8 Q Cd Ci ·s(t) A noiseless preamplifier Detector Signal Processing Model The detector is modeled as a current source, delivering a current pulse with time profile s(t) and charge Q, proportional to the energy released, across the parallel combination of the detector capacitance Cd and the preamplifier input capacitance Ci . signal processor i 2 W=b e 2 W=a parallel white noise series white noise e 2 f=c/|f| i 2 f=d·f series 1/f noise parallel f noise noise power spectral density Ax[a+b/w(Cd+Ci)2] A(Q/(Cd+Ci)) If s(t) = d(t)
Electronic Signal Processing Signal Processor F(n h(f) F(f U(f fo Noise flo f Improved fO Signal/Noise Ratio Example of signal filtering-the figure shows a"typical case of noise filtering In particle physics, the detector signals have very often a very large frequency spectrum The filter(shaper) provides a limitation in bandwidth, and the output signal shape is different with respect to the input signal shape. Beijing January 2008 Luciano musa
Beijing, January 2008 Luciano Musa 9 Electronic Signal Processing F(f) U(f) F(f) f U(f) f h(f) f Noise floor f0 f0 f0 Improved Signal/Noise Ratio Example of signal filtering - the figure shows a “typical” case of noise filtering In particle physics, the detector signals have very often a very large frequency spectrum The filter (shaper) provides a limitation in bandwidth, and the output signal shape is different with respect to the input signal shape. Signal Processor
Electronic Signal Processing AF U(t h(f) t) u(t Noise floor fo Improved fo f Signal/Noise ratio The output signal shape is determined, for each application, by the following parameters Input signal shape(characteristic of detector Filter(amplifier-shaper) characteristic The output signal shape is chosen such to satisfy the application requirements Time measurement Amplitude measurement Pile-up reduction Optimized signal-to-noise ratio Luciano musa
Beijing, January 2008 Luciano Musa 10 Electronic Signal Processing F(f) U(f) f(t) f u(t) f h(f) f Noise floor f0 f0 Improved Signal/Noise Ratio The output signal shape is determined, for each application, by the following parameters: • Input signal shape (characteristic of detector) • Filter (amplifier-shaper) characteristic The output signal shape is chosen such to satisfy the application requirements: • Time measurement • Amplitude measurement • Pile-up reduction • Optimized Signal-to-noise ratio