INFN Laboratori Nazionali di Legnaro, Marzo 2007 FRONT-END ELECTRONICS PART 2

Transcription

1 INFN Laboratori Nazionali di Legnaro, 6-30 Marzo 007 FRONT-END ELECTRONICS PART Francis ANGHINOLFI Wednesday 8 March 007 Francis.Anghinolfi@cern.ch v1 1

2 FRONT-END Electronics Part A little bit about signal & circuit representation Noise in systems & components Noise analysis for detector and front-end circuit Some examples

3 Signal & Circuit Representation Time domain : X(t) H Y(t) Electronic signals, like voltage, or current, or charge can be described in time domain. H in the above figure represents an object (circuit) which modifies the (time) properties of the incoming signal X(t), so that we obtain another signal Y(t). H can be a filter, transmission line, amplifier, resonator etc... If the circuit H has linear properties like : if X1 ---> Y1 through H if X ---> Y through H then X1+X ---> Y1+Y The circuit H can be represented by a linear function of time H(t), such that the knowledge of X(t) and H(t) is enough to predict Y(t) 3

4 Signal & Circuit Representation X(t) H(t) Y(t) In time domain, the relationship between X(t), H(t) and Y(t) is expressed by the following formula : Where Y(t) = H(t)*X(t) H(t)*X(t) = H(u)X(t - u)du This is the convolution function, that we can use to completely describe Y(t) from the knowledge of both X(t) and H(t) Time domain prediction by doing convolution is not so easy 4

5 Signal & Circuit Representation What is H(t)? δ(t) δ(t) H H(t) H(t) (Dirac function) H(t) = H(t)* δ (t) If we inject a dirac function to a linear system, the output signal is the characteristic function H(t) H(t) is the transfer function in time domain, of the linear circuit H. 5

6 Signal & Circuit Representation Frequency domain : The electronic signal X(t) can be represented in the frequency domain by x(f), using the following transformation x(f) = X(t).exp(- jπft). dt (Fourier Transform) This is *not* an easy transform, unless we assume that X(t) can be described as a sum of exponential functions, of the form : X(t) = c k exp( jπf k t) The conditions of validity of the above transformations are precisely defined. We assume here that it applies to the signals (either periodic or not) that we will consider later on 6

7 Example : X(t) Signal & Circuit Representation = exp( at ) For (t >0) X(t) x(f) = 0 exp (-at). exp (-jπft).dt x(f) = exp(-(a + jπf)t).dt x(f) x(f) = The frequency representation x(f) is in complex numbers. a + 1 j π f Arg(x(f)) 7

8 Signal & Circuit Representation x(f) h(f) y(f) With the frequency domain representation (signals and circuit transfer function mapped into frequency domain by the Fourier transform), the relationship between input, circuit transfer function and output is simple: Example : cascaded systems y(f) = h(f).x(f) x(f) h1(f) h(f) h3(f) y(f) y(f) = h1(f). h(f). h3(f). x(f) 8

9 Signal & Circuit Representation x X ( f ( t ) ) x(f) = 1 j π f = ν ( t ) h(f) 1 h(f) = 1 + j π f RC lowpass filter y(f) 1 y(f) = j π f(1 + Y( t) = 1 exp( t) j π f) R t C

10 Signal & Circuit Representation x(f) h(f) Frequency representation can be used to predict time response X(t) ----> x(f) (Fourier transform) H(t) ----> h(f) (Fourier transform) h(f) can also be directly formulated from circuit analysis Apply y(f) = h(f).x(f) Then y(f) ----> Y(t) (inverse Fourier Transform) y(f) h(f) Fourier Transform - j Π. f.t = H(t).e. dt Inverse Fourier Transform H(t) j Π.f.t = h(f).e. df 10

11 Signal & Circuit Representation x(f) y(f) h(f) X(t) H(t) Y(t) THERE IS AN EQUIVALENCE BETWEEN TIME AND FREQUENCY REPRESENTATIONS OF SIGNAL or CIRCUIT THIS EQUIVALENCE APPLIES ONLY TO A PARTICULAR CLASS OF CIRCUITS, NAMED TIME-INVARIANT CIRCUITS. IN PARTICLE PHYSICS, CIRCUITS OUTSIDE OF THIS CLASS CAN BE USED : ONLY TIME DOMAIN ANALYSIS IS APPLICABLE IN THIS CASE 11

12 Signal & Circuit Representation y(f) = h(f).x(f) δ(f) h(f) h(f) δ(f) Dirac function frequency representation f h(f) f x(f) In frequency domain, a system (h) is a frequency domain shaping element. In case of h being a filter, it selects a particular frequency domain range. The input signal is rejected (if it is out of filter band) or amplified (if in band) or shaped if signal frequency components are altered. x(f) h(f) y(f) y(f) f h(f) f f 1

13 noise vni(f) Unlimited noise power distribution Signal & Circuit Representation f y(f) = h(f).x(f) h(f) The noise is also filtered by the system h vno(f) Noise components (as we will see later on) are often white noise ie : constant distribution over all frequencies (as shown above) So a filter h(f) can be chosen so that : f Noise power distribution cut by filter It filters out the noise frequency components which are outside of the frequency range of the signal 13

14 Signal & Circuit Representation x(f) x(f) f0 Noise floor f h(f) pass cut f0 cut f y(f) y(f) f0 Improved Signal/Noise Ratio f Example of signal filtering : the above figure shows a «typical» case, where only noise is filtered out. In particle physics, the input signal, from detector, is often a very fast pulse, similar to a Dirac pulse. Therefore, its frequency representation is over a large frequency range. The filter (shaper) provides cuts in the signal bandwidth and therefore the output signal shape is different from the input signal shape. 14

15 x(f) Signal & Circuit Representation x(f) y(f) h(f) y(f) Noise floor f0 f f0 Improved S/N DC component cut 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, different form the input detector signal, is chosen for the application requirements: Time measurement Amplitude measurement Pile-up reduction Optimized Signal-to-noise ratio f f 15

16 Signal & Circuit Representation f0 f Filter cuts noise. Signal BW is preserved f Filter cuts inside signal BW : modified shape 16

17 NOISE in Electronics Systems Signal frequency spectrum Circuit (Amplifier, shaper) response Noise Floor f Amplitude, charge or time resolution What we want : Signal dynamic Low noise 17

18 NOISE in Electronic System EM emission Power System noise Crosstalk EM emission Crosstalk Ground/power noise All can be (virtually) avoided by proper design and shielding Shielding Signals In & Out 18

19 NOISE in Electronics Systems Fundamental noise Detector Front End Board Physics of electrical devices 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) In detector circuits, noise is expressed in (rms) numbers of electrons at the input (ENC) 19

20 NOISE in Electronics Systems Current conducting devices Only Fundamental Noise is discussed in this lecture 0

21 NOISE in Electronics Components 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 General 1

22 NOISE in Electronics Components 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 v i = 4kTR. f 1 = 4kT. f R K = Boltzman constant ( V.C/K) T = ambient 4kT = V/C The noise power is proportional to T( o K) The noise power is proportional to f

23 NOISE in Electronics Components THERMAL NOISE Thermal noise is a totally random signal. It has a normal distribution of amplitude with time. 3

24 NOISE in Electronics Components THERMAL NOISE R v = 4kTR. f i 1 = 4kT. f R The noise power is proportional to the noise bandwidth: The power in the band 1- Hz is equal to that in the band Hz Thus the thermal noise power spectrum is flat over all frequency range ( white noise ) P 0 h 4

25 NOISE in Electronics Components THERMAL NOISE R G=1 Bandwidth limiter v = 4kTR. BW tot noise The electronic circuit frequency spectrum (filter) limits the thermal noise power available on circuit output P Circuit Bandwidth 0 h 5

26 NOISE in Electronics Components THERMAL NOISE R v = 4kTR. f The conductor noise power is the same as the power available from the following circuit : R * Et = 4kTR. f <v> Et is an ideal voltage source R is a noiseless resistance gnd 6

27 NOISE in Electronics Components THERMAL NOISE R * Et = 4kTR. f RL = v = 4kTR. f * gnd R Et = 4kTR. f i R L =0 4kT =. f R The thermal noise is always present. It can be expressed as a voltage fluctuation or a current fluctuation, depending on the load impedance. gnd 7

28 Some examples : NOISE in Electronics Components Thermal noise in resistor in serie with the signal path : v = 4kTR. f For R=100 ohms v = 1.8nV / Hz For 10KHz-100MHz bandwidth : v = 1.88µV Rem : 0-100MHz bandwidth gives : v = 1.80µV rms rms For R=1 Mohms For 10KHz-100MHz bandwidth : v = 1. 8mV rms As a reference of signal amplitude, consider the mean peak charge deposited on 300µm Silicon detector : 000 electrons, ie ~4fC. If this charge was deposited instantaneously on the detector capacitance (10pF), the signal voltage is Q/C= 400µV 8

29 NOISE in Electronics Components Thermal Noise in a MOS Transistor Vgs Ids The MOS transistor behaves like a current generator(*), controlled by the gate voltage. The ratio is called the transconductance. i d = 4kT. Γ. gm. f 3 I gm = V The MOS transistor is a conductor and exhibits thermal noise expressed as : or v G DS GS = 4kT 3. Γ. gm 1. f Γ : excess noise factor (between 1 and ) (*) : physics of MOS current conduction is not discussed there 9

30 NOISE in Electronics Components Shot Noise I i shot = qi f q is the charge of one electron (1.60 E -19 C) Shot noise is present when carrier transportation occurs across two medium, as a semiconductor junction. As for thermal noise, the shot noise power <i > is proportional to the noise bandwidth. The shot noise power spectrum is flat over all frequency range ( white noise ) P 0 h 30

31 NOISE in Electronics Components Shot Noise in a Bipolar (Junction) Transistor Vbe Ic IC gm = Vbe The current carriers in bipolar transistor are crossing a semiconductor barrier therefore the device exhibits shot noise as : i col = qic f The junction transistor behaves like a current generator, controlled by the base voltage. The ratio (transconductance) is : gm = qic / kt 1 = 4kT gm. f i col or v kt gm f B =

32 NOISE in Electronics Components 1/f Noise Formulation v f A =. f α f 1/f noise is present in all conduction phenomenon. Physics 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) 3

33 NOISE in Electronics Components 1/f Noise and thermal noise (MOS Transistor) 1/f noise Circuit bandwidth Thermal noise 1/f noise may be removed by special circuit technique (correlated double sampling) 33

34 Noise in Detector & Front-Ends Detector Circuit How much noise is here? Note that (pure) capacitors or inductors do not produce noise (detector bias) As we just seen before : Each component is a (multiple) noise source 34

35 Noise in Detector & Front-Ends Detector Cd R p Circuit Detector Circuit equivalent voltage noise source Ideal charge generator gnd A capacitor, (not a noise source) Passive & active components, all noise sources gnd R p e n i n Circuit equivalent current noise source noiseless 35

36 Noise in Detector & Front-Ends Detector e n Noiseless circuit From practical point of vue, e n is a voltage source such that: Cd R p A v e n Vnomeas =. f A v i n when input is grounded gnd i n is a current source such that: i Vnomeas 1 n =. Av Rp f when the input is on a large resistance R p 36

37 Noise in Detector & Front-Ends In case of an (ideal) detector, the input is loaded by the detector capacitance C and a biasing resistance Rp Detector gnd Cd Detector signal node (input) e n R p i TOT A v Noiseless circuit I TOT is the combination of the Rp bias resistance noise and of the equivalent current noise of the amplifier: i p TOT 1 = 4kT. R n p i = i + i p The equivalent voltage noise at the input is: e input = en + C d TOT i ( ) jω (Per hertz) 37

38 Noise in Detector & Front-Ends Detector Cd input R p e n i TOT A v Noiseless circuit The detector signal is a charge Qs. The voltage noise <e input > converts to charge noise by using the relationship q = C d.v gnd q input = en. Cd + i TOT ( jω) (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 <e n > and of the total parallel input current noise <i TOT > There are dependencies on C and on ω = πf 38

39 Noise in Detector & Front-Ends Detector e n Noiseless circuit Cd R p A v gnd i TOT q input = en. Cd + i TOT ( jω) (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. 39

40 Noise in Detector & Front-Ends Now we have to consider the TOTAL noise power over circuit bandwidth Detector e n Noiseless circuit, transfer function Av(ω) Cd R p A v i TOT gnd Eq. Charge noise at input node per hertz i ENC 1 TOT tot = en. Cd.. G + p ( jω) 0 [ Av( ω) ] dω G p is a normalization factor (peak voltage at the output for 1 electron charge) 40

41 Noise in Detector & Front-Ends Detector e n Noiseless circuit i ENC 1 TOT tot = en. Cd.. G + p ( jω) 0 [ Av( ω) ] dω Cd R p A v i TOT In some case (and for our simplification) e n and i TOT can be readily estimated under the following assumptions: gnd The <e n > contribution is coming from the circuit input transistor Input node Active input device The <i TOT > contribution is only due to the detector bias resistor R p R p (detector bias) 41

42 Noise in Detector & Front-Ends Detector e n = 4kT 3 gm Input signal node gm Cd Rp i 1 n = 4kT Rp gnd 1 1 4kT 1 ENCtot = 4kT. gm. Cd... G + p 3 ( jω) Rp 0 [ Av( ω) ] dω Av (voltage gain) of charge integrator followed by a CR-RC n shaper : Av( ω) = RC. jω (1 + RC. jω) n τ~n.rc Step response 4

43 Noise in Detector & Front-Ends For CR-RC n transfer function, ENC expression is : ENC 4 4kT 1 Cd kt = Fs. gm + Fp. q 3 τ q R p τ Rp : Resistance in parallel at the input gm : Input transistor 4kT 1 Cd ENC = Fs. gm. + q 3 τ 4kT Fp. q R p. τ τ : CR-RC n Shaping time C d : Capacitance at the input Serie (voltage) thermal noise contribution is inversely proportional to the square root of CR-RC n peaking time and proportional to the input capacitance. Parallel (current) thermal noise contribution is proportional to the square root of CR- RC n peaking time 43

44 Noise in Detector & Front-Ends Fp, Fs factors depend on the CR-RC shaper order n n Fs n Fp CR-RC CR-RC CR-RC CR-RC

45 Noise in Detector & Front-Ends Serie noise slope Parallel noise (no C dependance) ENC dependance to the detector capacitance 45

46 Noise in Detector & Front-Ends optimum The optimum shaping time is depending on parameters like : C detector Gm (input transistor) R (bias resistor) Shaping time (ns) ENC dependence to the shaping time (C=10pF, gm=10ms, R=100Kohms) 46

47 Noise in Detector & Front-Ends C=10pF C=15pF Example: Dependence of optimum shaping time to the detector capacitance C=5pF Shaping time (ns) ENC dependence to the shaping time 47

48 Noise in Detector & Front-Ends ENC dependence to the parallel resistance at the input 48

49 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 10 th 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 serie noise effect) f ENC = K. CD 49

50 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 : ENC 4 4kT Cd = Fs. R s + q τ Fp. q kt R p τ Serie noise Parallel noise 50

51 Some examples The complete frontend design is usually a trade off between key parameters like: Noise Power Dynamic range Signal shape Detector capacitance 51

52 Some examples Charge sensitive Preamplifier BiCMOS technology PMOS transistor input Cascode stage Input Source Follower output stage Feedback capacitance All the rest is biasing Cf Output 5

53 Some examples J. Kaplon et al., 004 IEEE Rome Oct 004, use 0.5 µm CMOS Front-End circuit for Silicon Strip detectors 1000 el. 15ns peaking time, 300uA input current, Cdet = 10pF (6cm strip length of p-n detector). 53

54 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 (τ, shaper time constant) A front-end circuit is finalized only after considering the other key parameters Power consumption Output shape (shaping time, gain, linearity, dynamic range) Impedance adaptation (at input and output) 54