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9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 1
Introduction to Electronics for High
Energy Physics
C. de LA TAILLE LAL Orsay
CERN Summer school 2003
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 2
Outline
Course 1 : The art of electronics : is there something beyond Ohm’s law ?
Course 2 : Learning to decipher a schematic
Course 3 : Electronics in high energy physics
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 3
Introduction
Speak “electronician” in just 3 lessons… “Did you cascode your charge preamp to increase your open loop gain ?” “Did you find an FPGA with LVDS I/Os for your digital filter ?” A lot of vocabulary (and abreviations…) to get used to, but :
Little prerequisite knowledge required : Ohm’s law : U = Z I Some basics of Fourier (or Laplace) transforms cannot hurt for signal theory
Many more details are given in the transparencies -> don’t be scared !
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 4
Electronics in experiments
A lot of electronics in the experiments… Readout electronics : amplification, filtering… : Analog electronics (A,V,C) Processing & Trigger electronics : Digital electronics (bits) [see lecture of
Cittolin]
The performance of electronics often impacts on the detectors
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 5
Detector
Overview of readout electronics
Most front-ends follow a similar architecture
Preamp Shaper Analog memory
ADC
Very small signals (fC) -> need amplification Measurement of amplitude and/or time (ADCs, discris,
TDCs) Several thousands to millions of channels
fC V bitsFIFODSP…
V V
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 6
Readout electronics : requirements
Low cost !
(and even less)
Radiation hardness
High reliability
High speed
Large dynamic
range
Low power
Low material
Low noise
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 7
The foundations of electronics
Voltage generators or source
RS → 0
Ideal source : constant voltage, independent of current (or load)
In reality : non-zero source impedance RS
Current generators Ideal source : constant current,
independent of voltage (or load) In reality : finite output source impedance
RS
Ohms’ law Z = R, 1/jωC, jωL Notice the sign convention
Z
Vi
V
RS → ∞i
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 8
Frequency domain & time domain
Frequency domain : V(ω,t) = A sin (ωt + φ)
• Described by amplitude and phase (A, φ) Transfer function : H(ω) [or H(s)] = The ratio of output signal to input signal in the
frequency domain assuming linear electronics
Vout(ω) = H(ω) Vin(ω)
Time domain Impulse response : h(t) = the output signal for an impulse (delta)
input in the time domain The output signal for any input
signal vin(t) is obtained by convolution * :
Vout(t) = vin(t) * h(t) = ∫ vin(u) * h(t-u) du Correspondance through Fourier transforms
X(ω) = F { x(t) } = ∫ x(t) exp(jωt)dt a few useful Fourier transforms in appendix below
H(ω) vin(ω) vout(ω)
h(t) vin(t) vout(t)
F -1
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 9
Appendix 1 : a few useful Fourier Transforms
H(ω) = 1<-> h(t) = δ(t) (impulse) H(ω) = 1/jω h(t) = S(t) = (step) H(ω) = 1/(1+jωT) h(t) = exp(-t/T) (low pass filter, exponential) H(ω) = 1/jω (1+jωT) h(t) = 1 - exp(-t/T) H(ω) = 1/(1+jωT)n h(t) = 1/n! (t/T)n-1 exp(-t/T) …
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 10
Using Ohm’s law
Example of photodiode readout Used in high speed optical links Signal : ~ 10 µA when illuminated Modelisation :
• Ideal current source Iin• pure capacitance Cd
I in C d
Simple I to V converter : R ! R = 100 kΩ gives 1V output for 10
µA
Speed ? Transfer function H(ω) = vout/iin H has the dimension of Ω and is
often called « transimpedance » and even more often (improperly) « gain »
H(ω) = R/(1 + jω RCd)
-1/jRCd is called a « pole » in the transfer function
light
volts
10 Gb/s optical receiver (Orx)
100K
Vout
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 11
Frequency response
Bode plot Magnitude (dB) = 20 log |H(jw)| -3dB bandwidth : f-3dB = 1/2πRC
• R=105Ω, C=10pF => f-3dB=160 kHz
• At f-3dB the signal is attenuated by 3dB = √2, the phase is -45°
Above f-3dB , gain rolls-off at-20dB/decade
(or -6dB/octave)
100 dBΩ
80 dBΩ
Magnitude
Phase
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 12
Time response
Step response : rising exponential H(t) = F -1 { 1/jω R/(1+jωRC) }
= R [ 1 - exp(-t/ τ) ] Rise time : t10-90% = 2.2 τ « eye diagramm »
Impulse response h(t) = F -1 { R/(1+jωRC) }
= R/ τ exp(-t/τ) τ (tau) = RC = 1 µs : time
constant
Speed : ~ 10 µs = 100 kb/s ! Still 5 orders ofmagnitude away
from a 10 Gb/s link !
pulse response
tr 10-90%
Impulse response10Gb/s eye diagram (10 ps/div)
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 13
Current preamplifiers in theory
Improve with an opamp Vout = G(vin+- vin-) G >> 1 : « open loop gain » Vin+ = 0 ; iin- = 0
Transimpedance configuration Rf between input and output (« shunt-shunt
feedeback ») -> « current preamp » (PAI) Transfer function :
• Vout - vin = - Rf if• Vin = (iin - if)/ jω Cd = - vout/G
Bandwidth improvement by G >>1 Example with LM741, (G0=2 105) => BW = 3.2 THz ! Looks great !
Current preamplifierarchitecture
vout/iin = - Rf /(1 + jω RfCd/G)
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 14
Current preamp in practice
With an old LM741
Oscillations : ω0 = 500 kHz
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 15
Current preamp in practice
Trying a more modern opamp… (OP 620 GBW=300 MHz) More (but faster) oscillations
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 16
Stability in current preamps
What happens ? Opamp open loop gain varies with
frequency G(ω) = G0/(1 + j ω/ω0)
• G0 : low frequency gain
• ω0 : dominant pole
• 90° phase shift above ω0 90° Phase shift in opamp + 90° phase
shift on detector capacitance = 180° => oscillations
Also with the maths : H(jω) = -Rf / (1 + jω RfCd/G(ω)) = -
Rf / [1 + jω RfCd(1/G0 + jω/G0w0)] = - Rf / (1 + jω RfCd/G0 - ω2 RfCd
/G0w0) 2nd order system
Open loop frequency response of OP620
frequency response of 2nd order
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 17
Current preamp seen from the input
Input impedance Zin
Zin = vin/iin = Rf/(G+1) -> small Low input impedance = « virtual
ground » Current sensitive input
Inductive behaviour With G(jω) = G0/(1 + j ω/ω0)
Zin = Rf/ G0 + j ω Rf/G0ω0
Virtual inductance : Leq = Rf/G0ω0
• Ex : LM741 (G0ω0=107) : Leq = 10 mH
• Ex : OP620 (G0ω0=109) : L = 100 µH
RLC circuit with capacitive detector Resonant frequency : fres = 1/2π √LeqCd
Quality factor : Q = R / √Leq/Cd Q > 1/2 -> ringing
• Ex : LM741 : Q=105 √10-2/10-11 = 3• Ex : OP620 : Q=105 √10-4/10-11 = 31 !
Input impedance of PAI
Cd10pF
Rf100kΩ
Leq100µH
Equivalent circuit on the input
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 18
Stabilisying the current preamp
Damping the oscillations: Need a resistor such as Q=1/2 R = 0.5 √Cd/Leq -> 1.5k Resistor on the input : OK but
noisy -> Virtual resistor :
Capacitance in feedback : Cf
Resistive input impedance Req = 1/ G0ω0 Cf
• Virtual resistor (noiseless)
Q = 1/Cf √(Cd/Rf G0ω0) Q=1/2 => Cf=2 √(Cd/Rf G0ω0)
Example :• LM741 (G0ω0=107) :
Cf=10pF
• OP620 (G0ω0=109) : Cf=0.5pF
Speed : ~ 200 ns = 5 Mb/S Only 3 more orders of
magnitude to gain for the 10 Gb/s link !
Cf
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 19
Charge preamps (1)
Capacitive feedback Transimpedance configuration Similar to current preamp : Rf -> Cf
Vout(ω)/iin(ω) = - Zf = - 1/jω Cf
Integrator : vout(t) = -1/Cf ∫ iin(t)dt
Charge sensitive preamplifier (PAC) Output proportionnal to the incoming
charge « Gain » : 1/Cf
Cf = 1 pF -> 1 mV/fC Transforms a short pulse into a long one The front-end of 90% of particle physics
detectors
Charge preamplifierarchitecture
vout(t) = - Q/Cf
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 20
Charge preamps (2)
Input impedance Zin = 1/jω G0Cf + 1/ G0ω0 Cf
Low resistive input impedance
Rin = 1/ G0ω0 Cf
G0ω0 is given by the preamp design
Determines the risetime at the output :ReqCd
Good stability (…!)• Low sensitivity to detector
capacitance• Small crosstalk
Input impedance of a PAC
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 21
Charge preamp example
Monolithic circuit
Cf
Input
Output
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 22
Zf
Z0
Charge preamps in practice
D0 Lar calorimeter charge preamplifer
2”
FET
driverpreamp
InputOutput
9-11 july 2003 C. de La Taille Electronics CERN Summer School 2003 23
10 Gb/s transimpedance amplifier
« Simple architecture »