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Electronics and (for?) Data Acquisition Lecture: Measurement Techniques Uni Bern, Fall Semester 2008 M.S. Weber M.S. Weber, Fall 20081

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Analysis Sensors Detectors DAQ Storage M.S. Weber, Fall 20083

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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 Some material / sources H. Spieler, LBL, C. De La Taille, LAL,

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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, … M.S. Weber, Fall 20085

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Signals M.S. Weber, Fall 20086

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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 s 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 electronics for separate optimization. – Different sensitivity to electronics elements, RC or RL – = RC; small RC good for fast signals, but show high distortions to slow signals – Sometimes signals are split to separately optimized lines. M.S. Weber, Fall 20087

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More characteristics of 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 shapes M.S. Weber, Fall More on detectors later in this lecture

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The next two weeks: “Electronics for DAQ” M.S. Weber, Fall Acquire an electrical signal (typically a current pulse) Digitize and prepare for storage First, some electronics basics

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Fundamentals M.S. Weber, Fall 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 M.S. Weber, Fall 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) The next several slides are about

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RESISTANCE R I Symbol, American Symbol, Europe IEC M.S. Weber, Fall

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CAPACITANCE C M.S. Weber, Fall Stores charge: Q [Coulombs] Impedance II ~

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RC CIRCUIT M.S. Weber, Fall τ

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Exercise Calculate the voltage U1 across R1 for step-wise rise in voltage U What is the rise time of U1, with R2>>R1 ? M.S. Weber, Fall U t U R2 R1C U1

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INDUCTANCE L M.S. Weber, Fall Heinrich Lenz

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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 M.S. Weber, Fall The next several 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

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Matrix form M.S. Weber, Fall 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 V and a single series resistor R Thevenin, 1883 Helmholz, 1853 – a single current source I and a single parallel resistor R Norton, 1926 Mayer, 1926 M.S. Weber, Fall

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Two-port networks (“Vierpole”) M.S. Weber, Fall

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Simple examples (Derive as exercise) M.S. Weber, Fall

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Combination Example T: M.S. Weber, Fall

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More combinations M.S. Weber, Fall Series: Z = Z 1 + Z 2 Parallel: Y = Y 1 + Y 2

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Exercises M.S. Weber, Fall 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 M.S. Weber, Fall The next several slides are about So far we have covered electronics 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 M.S. Weber, Fall Cutoff frequency Output reduced by a factor of 2 (3dB) in power -3dB Power -6dB Gain (- 3dBV). -3dBV A V in V out

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Transfer functions of FILTERS M.S. Weber, Fall Low pass filter High pass filter Combination: Band pass filter Band reject (notch) filter e.g. 50 Hz Frequency Amplitude Frequency Amplitude

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SIMPLE PASSIVE LOW PASS FILTER M.S. Weber, Fall Recall the voltage divider, As f increases, A=V OUT /V IN (the transfer function) decreases. Thus high frequencies are attenuated.

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SIMPLE PASSIVE HIGH PASS FILTER M.S. Weber, Fall Recall the voltage divider, As f increases, A=V OUT /V IN (the gain/transfer function) increases. Thus low frequencies are attenuated.

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DIODE M.S. Weber, Fall I Forward bias, conducting Reverse bias, non conducting I PN P, N is the “doping” of silicon to carry P (+) or N (-) charge)

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TRANSISTORS Transistors are made typically from Silicon (Si): Bipolar junction transistor BJT I E = I B typically analog Wide range of currents, voltages, frequencies Field effect transistor FET I DS = V GS ) 2 both analog and digital; high impedance. MOS or CMOS; digital, high speed and low power, respectively M.S. Weber, Fall Transistor as amplifier (or switch) Small current (voltage) at the base (gate) is amplified to produce large current at collector (drain) and emitter (source).

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Evolution of technologies M.S. Weber, Fall First transistor (1949) (Brattain-Bardeen Nobel 56) 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) M.S. Weber, Fall Basic and most common circuit building device. 1.V out =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 on pole integrals of Nyquist plot (2D plot with amplitude and phase Bode plots) M.S. Weber, Fall

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Feedback on OpAmp VOLTAGE FOLLOWER M.S. Weber, Fall V + = V IN By virtual ground, V - = V + Thus V out = V - = V + = V IN 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 V IN. 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 M.S. Weber, Fall V - = V + As V + = 0, V - = 0 As no current can enter V - and from Kirchoff’s Ist law, I 1 =I 2 = I I = V IN /R 1 I = -V OUT /R 2 => V OUT = -I 2 R 2 Therefore V OUT = (-R 2 /R 1 )V IN

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NON – INVERTING AMPLIFIER M.S. Weber, Fall V - = V + 2.As V + = V IN, V - = V IN 3.As no current can enter V - and from Kirchoff’s Ist law, I 1 =I I 1 = V IN /R 1 5. I 2 = (V OUT - V IN )/R 2 => V OUT = V IN + I 2 R 2 6. V OUT = I 1 R 1 + I 2 R 2 = (R 1 +R 2 )I 1 = (R 1 +R 2 )V IN /R 1 7. Therefore V OUT = (1 + R 2 /R 1 )V IN

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Acquiring a signal Typically, the “signal” we want is a charge generated in some time interval This usually is seen as 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 M.S. Weber, Fall The next several slides are about

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M.S. Weber, Fall If R i is small (R i (C i +C d ) small), then the detector will discharge and the amplifier will sense the signal current If R i 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 But: Voltage depends on detector capacitance: very involved calibrations necessary ! Better Use feedback circuits

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Ideal integrating amplifier M.S. Weber, Fall Virtual ground for A= , Z i =0 90% of all front-ends (but almost always re-built with custom circuits/design…) 90% of all front-ends (but almost always re-built with custom circuits/design…)

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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 (w 0 /2 )should be 1.6GHz. M.S. Weber, Fall

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“Ideal” vs. “real” M.S. Weber, Fall 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 M.S. Weber, Fall

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M.S. Weber, Fall Gain: Constant at low frequency Decay linearly with /2 phase shift

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At low frequency: At higher frequency: M.S. Weber, Fall

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Frequency domain & time domain Frequency domain : – V(ω,t) = A sin (ωt + φ) Described by amplitude and phase (A, φ) – Transfer function : H(ω) – V out (ω) = H(ω) V in (ω) M.S. Weber, Fall Correspondance through Fourier transforms H( ω ) = F { h(t) } = ∫ h(t) exp(iωt)dt H(ω) v in (ω) v out (ω) h(t) v in (t) v out (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 v in (t) is obtained by convolution : V out (t) = v in (t) * h(t) = ∫ v in (u) * h(t-u) du

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Summary and preview Detectors produce signals of O(10 4 ) electrons with rise time between ns and 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 The next several slides are about

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