CERN Technical Training 2005 ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS PART 2 Francis ANGHINOLFI January 20, 2005 Francis.Anghinolfi@cern.ch

ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS – Part 2 Noise in Electronic Systems Noise in Detector Front-Ends Noise Analysis in Time Domain Conclusion

Noise in Electronic Systems Signal frequency spectrum Circuit frequency response Noise Floor f Amplitude, charge or time resolution What we want : Signal dynamic Low noise

Noise in Electronic Systems Power EM emission Crosstalk System noise EM emission Crosstalk Ground/power noise Signals In & Out All can be (virtually) avoided by proper design and shielding Shielding

Noise in Electronic Systems Fundamental noise Physics of electrical devices Detector Unavoidable but the prediction of noise power at the output of an electronic channel is possible What is expressed is the ratio of the signal power to the noise power (SNR) Front End Board In detector circuits, noise is expressed in (rms) numbers of electrons at the input (ENC)

Noise in Electronic Systems Current conducting devices Only fundamental noise is discussed in this lecture

Noise in Electronic Systems Current conducting devices (resistors, transistors) Three main types of noise mechanisms in electronic conducting devices: THERMAL NOISE SHOT NOISE 1/f NOISE Always Semiconductor devices Specific

Noise in Electronic Systems THERMAL NOISE Definition from C.D. Motchenbacher book (“Low Noise Electronic System Design, Wiley Interscience”) : “Thermal noise is caused by random thermally excited vibrations of charge carriers in a conductor” R The noise power is proportional to T(oK) The noise power is proportional to Df K = Boltzmann constant (1.383 10-23 V.C/K) T = Temperature @ ambient 4kT = 1.66 10 -20 V/C

Noise in Electronic Systems THERMAL NOISE Thermal noise is a totally random signal. It has a normal distribution of amplitude with time.

Noise in Electronic Systems THERMAL NOISE R The noise power is proportional to the noise bandwidth: The power in the band 1-2 Hz is equal to that in the band 100000-100001Hz Thus the thermal noise power spectrum is flat over all frequency range (“white noise”) P h

Noise in Electronic Systems THERMAL NOISE Bandwidth limiter R G=1 Only the electronic circuit frequency spectrum (filter) limits the thermal noise power available on circuit output Circuit Bandwidth P h

Noise in Electronic Systems THERMAL NOISE R The conductor noise power is the same as the power available from the following circuit : R * Et is an ideal voltage source R is a noiseless resistance <v> gnd

Noise in Electronic Systems THERMAL NOISE R * RL=h gnd The thermal noise is always present. It can be expressed as a voltage fluctuation or a current fluctuation, depending on the load impedance. R * RL=0 gnd

Noise in Electronic Systems Some examples : Thermal noise in resistor in “series” with the signal path : For R=100 ohms For 10KHz-100MHz bandwidth : Rem : 0-100MHz bandwidth gives : For R=1 Mohms For 10KHz-100MHz bandwidth : As a reference of signal amplitude, consider the mean peak charge deposited on 300um Silicon detector : 22000 electrons, ie ~4fC. If this charge was deposited instantaneously on the detector capacitance (10pF), the signal voltage is Q/C= 400mV

Noise in Electronic Systems Thermal Noise in a MOS Transistor Ids Vgs The MOS transistor behaves like a current generator(*), controlled by the gate voltage. The ratio is called the transconductance. The MOS transistor is a conductor and exhibits thermal noise expressed as : G : excess noise factor (between 1 and 2) or (*) : physics of MOS current conduction is discussed in another session

Noise in Electronic Systems Shot Noise I q is the charge of one electron (1.602 E-19 C) Shot noise is present when carrier transportation occurs across two media, as a semiconductor junction. As for thermal noise, the shot noise power <i2> is proportional to the noise bandwidth. The shot noise power spectrum is flat over all frequency range (“white noise”) P h

Noise in Electronic Systems Shot Noise in a Bipolar (Junction) Transistor Ic Vbe The current carriers in bipolar transistor are crossing a semiconductor barrier  therefore the device exhibits shot noise as : The junction transistor behaves like a current generator, controlled by the base voltage. The ratio (transconductance) is : or

Noise in Electronic Systems 1/f Noise Formulation 1/f noise is present in all conduction phenomena. Physical origins are multiple. It is negligible for conductors, resistors. It is weak in bipolar junction transistors and strong for MOS transistors. 1/f noise power is increasing as frequency decreases. 1/f noise power is constant in each frequency decade (i.e. from 0 to 1 Hz, 10 to 100Hz, 100MHz to 1Ghz)

Noise in Electronic Systems 1/f noise and thermal noise (MOS Transistor) 1/f noise Circuit bandwidth Thermal noise Depending on circuit bandwidth, 1/f noise may or may not be contributing

Noise in Detector Front-Ends Circuit Note that (pure) capacitors or inductors do not produce noise Detector How much noise is here ? (detector bias) As we just seen before : Each component is a (multiple) noise source

Noise in Detector Front-Ends Circuit Rp Circuit equivalent voltage noise source Ideal charge generator Detector gnd Passive & active components, all noise sources en A capacitor (not a noise source) noiseless in Rp gnd Circuit equivalent current noise source

Noise in Detector Front-Ends gnd Noiseless circuit en in Av Rp From practical point of view, en is a voltage source such that: when input is grounded in is a current source such that: when the input is on a large resistance Rp

Noise in Detector Front-Ends In case of an (ideal) detector, the input is loaded by the detector capacitance C Detector gnd Noiseless circuit en iTOT Av Cd Detector signal node (input) ITOT is the combination of the circuit current noise and Rp bias resistance noise : The equivalent voltage noise at the input is: (per Hertz)

Noise in Detector Front-Ends gnd Noiseless circuit en iTOT Av Cd input The detector signal is a charge Qs. The voltage noise <einput> converts to charge noise by using the relationship (per Hertz) The equivalent charge noise at the input, which has to be ratioed to the signal charge, is function of the amplifier equivalent input voltage noise <en>2 and of the total “parallel” input current noise <iTOT>2 There are dependencies on C and on

Noise in Detector Front-Ends gnd en iTOT Av Cd Noiseless circuit (per Hertz) For a fixed charge Q, the voltage built up at the amplifier input is decreased while C is increased. Therefore the signal power is decreasing while the amplifier voltage noise power remains constant. The equivalent noise charge (ENC) is increasing with C.

Noise in Detector Front-Ends Now we have to consider the TOTAL noise power over circuit bandwidth Detector en Noiseless circuit, transfer function Av Cd iTOT gnd Eq. Charge noise at input node per hertz Gp is a normalization factor (peak voltage at the output for 1 electron charge)

Noise in Detector Front-Ends gnd Noiseless circuit en iTOT Av Cd In some case (and for our simplification) en and iTOT can be readily estimated under the following assumptions: The <en> contribution is coming from the circuit input transistor Input node Active input device The <iTOT> contribution is only due to the detector bias resistor Rp Rp (detector bias)

Noise in Detector Front-Ends gm Rp Input signal node Cd gnd Av (voltage gain) of charge integrator followed by a CR-RCn shaper : t~n.RC Step response

Noise in Detector Front-Ends For CR-RCn transfer function, ENC expression is : Rp : Resistance in parallel at the input gm : Input transistor t : CR-RCn Shaping time C : Capacitance at the input Series (voltage) thermal noise contribution is inversely proportional to the square root of CR-RC peaking time and proportional to the input capacitance. Parallel (current) thermal noise contribution is proportional to the square root of CR-RC peaking time

Noise in Detector Front-Ends Fp, Fs factors depend on the CR-RC shaper order n 1.27 1.16 1.11 0.99 0.95 0.84 0.92 Fs 7 6 5 4 3 2 1 n 0.34 0.36 0.40 0.45 0.51 0.63 0.92 Fp 7 6 5 4 3 2 1 n CR-RC2 CR-RC CR-RC3 CR-RC6

Noise in Detector Front-Ends “Series” noise slope “Parallel” noise (no C dependence) ENC dependence to the detector capacitance

Noise in Detector Front-Ends The “optimum” shaping time is depending on parameters like : C detector Gm (input transistor) R (bias resistor) optimum Shaping time (ns) ENC dependence to the shaping time (C=10pF, gm=10mS, R=100Kohms)

Noise in Detector Front-Ends Example: Dependence of optimum shaping time to the detector capacitance C=15pF C=10pF C=5pF Shaping time (ns) ENC dependence to the shaping time

Noise in Detector Front-Ends ENC dependence to the parallel resistance at the input

Noise in Detector Front-Ends The 1/f noise contribution to ENC is only proportional to input capacitance. It does not depend on shaping time, transconductance or parallel resistance. It is usually quite low (a few 10th of electrons) and has to be considered only when looking to very low noise detectors and electronics (hence a very long shaping time to reduce series noise effect)

Noise in Detector Front-Ends Analyze the different sources of noise Evaluate Equivalent Noise Charge at the input of front-end circuit Obtained a “generic” ENC formulation of the form : Series noise Parallel noise

Noise in Detector Front-Ends The complete front-end design is usually a trade off between “key” parameters like: Noise Power Dynamic range Signal shape Detector capacitance

Noise Analysis in Time Domain A class of circuits (time-variant filters) are used because of their finite time response These circuits cannot be represented by frequency transfer function The ENC estimation is possible by introducing the “weighting function” for a time-variant filter

Noise Analysis in Time Domain Detector gnd en iTOT W(t) Cd Example : Ileak Rp

Noise Analysis in Time Domain Detector gnd en iTOT W(t) Cd input device gm Example : RS

Noise Analysis in Time Domain For time invariant filter (like CR-RC filters), W(t) is represented by the mirror function in time of the impulse response h(t) : h(Tm-t) (Tm is signal measurement time) Example : RC circuit If noise hit occurs at measurement time t=Tm, contribution is h(0) (maximum) If noise hit occurs at t=RC before Tm, contribution is 1/e the maximum If noise hit occurs at t>Tm, contribution is zero

Noise Analysis in Time Domain For time variant filter, W(t) represents the “weight” of a noise impulse occurring at time t, whereas measurement is done at time Tm switch Example : Gated integrator C TM-TG TG TM If noise hit occurs at time between t=Tm-TG and Tm, contribution is maximum If noise hit occurs before Tm-TG or after Tm, contribution is zero Remark : a perfect gated integrator would give ENCs negligible Practically, rise and fall time are limited. They are in fact limited on purpose to predict and optimize the total ENC

Noise in Analysis Time Domain Example : Trapezoidal Weighting Function T2 T1 T1 The formulation can be compared to Obtained in case of a continuous time CR-RC quasi-Gaussian filter with t peaking time

Conclusion Noise power in electronic circuits is unavoidable (mainly thermal excitation, diode shot noise, 1/f noise) By the proper choice of components and adapted filtering, the front-end Equivalent Noise Charge (ENC) can be predicted and optimized, considering : Equivalent noise power of components in the electronic circuit (gm, Rp …) Input network (detector capacitance C in case of particle detectors) Electronic circuit time constants (t, shaper time constant) A front-end circuit is finalized only after considering the other key parameters Power consumption Output waveform (shaping time, gain, linearity, dynamic range) Impedance adaptation (at input and output)

CERN Technical Training 2005 ELEC-2005 Electronics in High Energy Physics Winter Term: Introduction to electronics in HEP ANALOG SIGNAL PROCESSING OF PARTICLE DETECTOR SIGNALS PART 2 Francis ANGHINOLFI January 20, 2005 Francis.Anghinolfi@cern.ch