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Electronics and (for?) Data Acquisition
Lecture: Measurement TechniquesUni Bern, Fall Semester 2008
M.S. Weber
M.S. Weber, Fall 2008
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Safety first !
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Analysis
SensorsDetectors
DAQ
Storage
M.S. Weber, Fall 2008
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Overview• Detector signals• Electronics components• Circuit analysis• Filters, amplifiers• Signal transmission• Noise• Signal discrimination• Time (TDC) and charge (ADC) conversion• Integrated electronics• Logic gates, EPLD
M.S. Weber, Fall 2008
Some material / sourcesH. Spieler, LBL, http://www-physics.lbl.gov/~spieler/C. De La Taille, LAL, http://indico.cern.ch/conferenceDisplay.py?confId=a062747
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Signals
• Measure electrical signals• Convert to digital information if the signal is analog
• “Direct” electrical detectors– e.g. wire chambers, semiconductor
detectors, ionization chambers
• “Indirect” detectors (sensor ?)– detection of light, which has to be converted
to electrical signal, e.g. scintillators, cerenkov– Temperature, pressure, …
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Signals
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Fast / Slow signals• Fast: rise time of ns
– Timing information– High counting rates difficult to keep stable through the DAQ
• Slow: rise time of ms Easier to keep stable:– Good for precise energy (integral), pulse height information
• Very slow: sampling at once per second
• Slow and fast signals need different treatment in the electronicsfor separate optimization. – Different sensitivity to electronics elements, RC or RL– t = RC; small RC good for fast signals, but show high distortions to slow signals– Sometimes signals are split to separately optimized lines.
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More characteristicsof signals from detectors
• Analog signals• Signal speed
(relevant for processing time and for time measurements)• Rates• Noise• Response function and offset
(Energy measurement)– Pedestal– Calibration
• Dead time• Efficiency• Robustness of signal shapesM.S. Weber, Fall 2008
More on detectors later in this lecture
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The next two weeks:“Electronics for DAQ”
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Acquire an electrical signal (typically a current pulse)Digitize and prepare for storage
First, someelectronics basics
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Fundamentals
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PASSIVE: Resistors, capacitors, transformer/inductor etc. Their properties do not depend actively on currents/voltages applied.
ACTIVE: Diodes, Transistors (various types; analog/digital such as bipolar, field effect used in analog circuit and MOS/CMOS used in digital circuits), LED/ photo-detector, OpAmp, digital integrated circuits.
ANALOG: The component response is continuously and proportionally dependent on the input (may be linear or nonlinear).Example: amplifier
DIGITAL: The component response is essentially 1 or 0 (ON or OFF).Usually used in digital circuits, computer memory and processors.Example: microprocessor
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The basics: Electronic Circuits
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• Passive elements: R, C, L, …
• Ohm’s law – links voltage with current and resistance• Voltage, current , impedance, energy, power
• Kirchhoff’s laws• Analyze complex circuits: mesh rule, nodal analysis• Voltages at any node or current in any branch
• Thevenin and Norton equivalent circuits• Combine sources of signal
(voltage or current, as well as indirectly resistance)
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are about
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RESISTANCE RI
2 2
Ohm's law
Power (1/4 W to many W)
/
U RI
P I RIU R U
Symbol, American
Symbol, Europe IEC
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CAPACITANCE C
d dU
d d
d1
Q CU
QI C
t t
U I tC
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Stores charge:Q [Coulombs]
0
0
/
1
1
i t
i t
U U e
U I C
i e IC
U Ii
U
C
1CZ i CImpedance
I I
~
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RC CIRCUIT
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τ/
dU
d
/
1
(1 )
·
10
( ) t RC
U
R
U URC
I U R
t C
eU t V
/0
Discharge:
( ) t RCV t V e
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Exercise
• Calculate the voltage U1 across R1for step-wise rise in voltage U
• What is the rise time of U1, with R2>>R1 ?
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U
t
U
R2
R1 C
U1
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INDUCTANCE L
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d
d
dI
d
·
·Udt L I
I L
Ut
U Lt
ò
Heinrich Lenz
0
0
·
·
·
1
i t
i t
U U e
Udt L I
e L IiU i I
U
L
LZ i L
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Analysis of linear circuits
• Definition of linear circuit:– Current is a linear function of the applied voltage
• Ideal components or small voltages applied
– Superposition: currents and voltages are combined without interacting
• Mesh rules and nodal analysis
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The nextseveral slides
are about
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Mesh rules
• Mesh: a loop that does not contain an inner loop.1. Count the number of “window panes” in the circuit.
Assign a mesh current to each window pane.2. Write Kirchhoff equations for every mesh whose current is unknown.
3. Solve the resulting equations
M.S. Weber, Fall 2008
1 1 2 2 2
2 3 4 2 1 2 3 4
3 4 4
1
5 2 2
( )
( ) 0
( )
I R R I R U
I R R R I R I R
I R R I R U
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Matrix form
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1 1 2 2 2
2 3 4 2 1 2 3 4
3 5 4 2 4 2
1 2 2 1 1
2 3 4 2 4 2
4 5 4 3 2
1( )
( ) 0
( )
0
·
0
0
I R R I R U
I R R R I R I R
I R R I R U
R R R I U
R R R R R I
R R R I U
Z I U
Z = Impedance matrix
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Equivalent circuits• Theorem of Thevenin and Norton
any combination of voltage sources, current sources and resistors with two terminals is electrically equivalent to:
– a single voltage source Vand a single series resistor RThevenin, 1883Helmholz, 1853
– a single current source Iand a single parallel resistor RNorton, 1926Mayer, 1926
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Two-port networks (“Vierpole”)
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1 11 1 12 2
2 21 1 22 2
Mesh
·
·
e
·
r l
·
u
I IU Z Z
U Z ZI I
1 1
2 2
1 1
2 2
1
2
2
1
impedance matrix :
admittance matrix :
transmission matrix :
·
·
·
U
U
I
IZ Z
U
I U
U U
I
Y Y
AI
A
I
determinant
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Simple examples
(Derive as exercise)
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1
0 1
RA
1 0
1/ 1A
R
1 11 2 12 2
1 21 2 22 2
Trans
·
·
t
·
p r
·
o
U IU A A
I A AU I
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Combination
Example T:
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1 2·A A A
1 1 0 1
0 1 1/ 1 0 1
R RA
R
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More combinations
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Series:
Z = Z1 + Z2
Parallel:
Y = Y1 + Y2
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Exercises
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A ? Z ?
A ? Z ?
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More ingredients needed…
Next:• Transfer functions• Filters:
– high-pass– low-pass
• Diodes• Transistors• OpAmp • Feedback loops• Amplifiers
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are about
So far we have coveredelectronics basics
• R, C, L• RC• Circuit analysis•Mesh rules• Two-poles
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Transfer Function (or gain):
Bode plot (in magnitude):The log of the transfer function plotted versus log frequency
A complete Bode plot also includes a graph versus phase
TRANSFER FUNCTION
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Cutoff frequencyOutput reduced by a factor of 2 (3dB)in power
-3dB Power -6dB Gain (- 3dBV).
-3dBV
/out inA V V
AVin Vout
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Transfer functions of FILTERS
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• Low pass filter
• High pass filter
•Combination:
• Band pass filter
• Band reject (notch) filtere.g. 50 Hz
Frequency
Amplitude
Frequency
Amplitude
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SIMPLE PASSIVE LOW PASS FILTER
12
12
1
1 2
OUT IN
IN
i fCV V
Ri fC
Vi fRC
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Recall the voltage divider,
As f increases, A=VOUT/VIN (the transfer function) decreases.Thus high frequencies are attenuated.
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SIMPLE PASSIVE HIGH PASS FILTER
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Recall the voltage divider,
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2
1 2
OUT IN
IN
RV V
Ri fC
i fRCV
i fRC
As f increases, A=VOUT/VIN (the gain/transfer function) increases.Thus low frequencies are attenuated.
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DIODE
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R
VVI ON
I
Forward bias, conducting
Reverse bias, non conducting
I
P N
P, N is the “doping” of silicon to carry P (+) or N (-) charge)
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TRANSISTORSTransistors are made typically from Silicon (Si):
• Bipolar junction transistor BJT IE = b IB
• typically analog
• Wide range of currents, voltages, frequencies
• Field effect transistor FET IDS = (b VGS )2
• both analog and digital; high impedance.
• MOS or CMOS; digital, high speed and low power, respectively
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Transistor as amplifier (or switch) Small current (voltage) at the base (gate) is amplified to produce large current at collector (drain) and emitter (source).
Evolution of technologies
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First transistor (1949)(Brattain-Bardeen Nobel 56)
5 µm MOSFET (1985) 15 nm MOSFET (2005)
SiGe Bipolar in 0.35µm monolithic process
Molecular electronics
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Operational Amplifier (OpAmp)
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Basic and most common circuit building device.
1. Vout=A(V+ - V-) with A →∞
2. No current can enter terminals V+ or V-. Infinite input impedance.
3. Can draw infinite current at the ouput. Zero ouput impedance
4. An opamp needs separate power.
5. In a circuit with feed-back: V+=V-
A
Many uses of OpAmps ! With and w/o feedback.
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Feedback loop
• some proportion of a system's output is returned (fed back) to the input
• used to control the dynamic behavior of the system• Changes the transfer function
• Feedback is usually passive,can be active (control systems)
• Stability is an issue:Nyquist stability criterion, based onpole integrals of Nyquist plot(2D plot with amplitude and phase Bode plots)
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Feedback on OpAmpVOLTAGE FOLLOWER
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V+ = VIN
By virtual ground, V- = V+
Thus Vout = V- = V+ = VIN
So, what’s the point ?Due to the infinite input impedance of an op amp,no current at all can be drawn from the circuit before VIN.The output signal is fed from the OpAmp power.
No input signal distortion, input isolated from input.
Very useful for interfacing to high impedance sensors
(possibly the simplest front-end…)
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INVERTING AMPLIFIER
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V- = V+
As V+ = 0, V- = 0
As no current can enter V- and from Kirchoff’s Ist law, I1=I2 = I
I = VIN/R1
I = -VOUT/R2 => VOUT = -I2R2
Therefore VOUT = (-R2/R1)VIN
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NON – INVERTING AMPLIFIER
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1. V- = V+
2. As V+ = VIN, V- = VIN
3. As no current can enter V- and from Kirchoff’s Ist law, I1=I2.
4. I1 = VIN/R1
5. I2 = (VOUT - VIN)/R2 => VOUT = VIN + I2R2
6. VOUT = I1R1 + I2R2 = (R1+R2)I1 = (R1+R2)VIN/R1
7. Therefore VOUT = (1 + R2/R1)VIN
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Acquiring a signal• Typically, the “signal” we want
is a charge generatedin some time interval
• This usually is seenas a current pulse
• We need to integrate• E.g. energy measurement
• Integration can be done at different stages:– At the sensor capacitance– Use an integrating pre-amplifier– Amplify the signal and integrate at the ADC– Rapidly sample the signal and use software
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E Q Idt
The nextseveral slides
are about
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• If Ri is small (Ri (Ci +Cd) small), then the detector will discharge and the amplifier will sense the signal current
• If Ri is large enough (i.e. the input time constant is large, compared to the signal = current pulse), the charge is integrated and a voltage is measured at the amplifier output
si
d i
QV
C C
But: Voltage depends on detector capacitance: very involved calibrations necessary ! Better Use feedback circuits
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Ideal integrating amplifier
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-+
Virtual ground for A=, Zi=0
0
1( ) ( )
( )
out inf
outf
V
V t I t dtC
QV t
C
90% of all front-ends(but almost always re-built with custom circuits/design…)
0
0
0d
d
1 (
( 1)
( 1)
1) 1 )
(
i
f i i
f i
i
i f i f
i f
v
Q
v Av
v v v A v
Q Q C A v
Av
C A CvA
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• Sensor capacitance is discharged by the resistive input impedance of the feedback circuit with time constant:
• Feedback capacitance should be much smaller than the detector capacitance.For 10ns rise time signal, the bandwidth (w0/2p)should be 1.6GHz.
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0
1·i i d df
C CRC
0/100 100 /f d iC C
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“Ideal” vs. “real”
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We used here “ideal” components…life is a bit more complicated (interesting ?)with “Real” electronic elements
Get the help of experts !
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Simple realistic amplifier
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0 0
0
d d
d d
1 1 1
1/
Lv m L
i i
R C
L L
v i
v v
ZA g Z
i i i
Z i CR
11
v mL
A gR
Ci
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Gain:• Constant at low frequency• Decay linearly with p/2 phase shift
11
v mL
A gR
Ci
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• At low frequency:• At higher frequency:
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v m LA g R
0
0
0
;
1
mv v
mv
cong
stC
A A
gA
i
C
Frequency domain & time domain• Frequency domain :
– V(ω,t) = A sin (ωt + φ)• Described by amplitude and phase (A, φ)
– Transfer function : H(ω)– Vout(ω) = H(ω) Vin(ω)
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• Correspondance through Fourier transforms• H(ω) = F {h(t)} = ∫ h(t) exp(iωt)dt
H(ω) vin(ω) vout(ω)
h(t) vin(t) vout(t)
F -1
H(ω) = 1 -> h(t) = δ(t) (impulse)H(ω) = 1/jω -> h(t) = S(t) (step)H(ω) = 1/jω (1+jωT) -> h(t) = 1 - exp(-t/T)H(ω) = 1/(1+jωT)-> h(t) = exp(-t/T) H(ω) = 1/(1+jωT)n-> h(t) = 1/n! (t/T)n-1 exp(-
t/T)
• 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
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Summary and preview
• Detectors produce signals of O(104) electrons with rise time between ns and m s.
• The signals are mostly a current pulse• Signals needs to be amplified and possibly integrated• Signals are typically shaped• Learned about basic electronics components, amplifiers,
integrators, shapers
• Next: signal/noise, signal transmission, signal shaping
M.S. Weber, Fall 2008
The nextseveral slides
are about