Electronics in High Energy Physics Introduction to electronics

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Electronics in High Energy Physics Introduction to electronics in HEP Operational Amplifiers (based on

Electronics in High Energy Physics Introduction to electronics in HEP Operational Amplifiers (based on the lecture of P. Farthoaut at Cern) 1

Operational Amplifiers u u u Feedback Ideal op-amp Applications – – u Non-ideal amplifier

Operational Amplifiers u u u Feedback Ideal op-amp Applications – – u Non-ideal amplifier – – – u u Voltage amplifier (inverting and non-inverting) Summation and differentiation Current amplifier Charge amplifier Offset Bias current Bandwidth Slew rate Stability Drive of capacitive load Data sheets Current feedback amplifiers 2

Feedback u Y is a source linked to X – Y=mx u Open loop

Feedback u Y is a source linked to X – Y=mx u Open loop – x=de – y=mx – s=sy=sdmx u e Closed loop x m d y s s b u u m is the open loop gain bm is the loop gain 3

Interest of the feedback e x m d s s b u In electronics

Interest of the feedback e x m d s s b u In electronics – m is an amplifier – b is the feedback loop – d and s are input and output impedances u If m is large enough the gain is independent of the amplifier 4

Operational amplifier e -A e + u u Gain A very large Input impedance

Operational amplifier e -A e + u u Gain A very large Input impedance very high – I. e input current = 0 u A(p) as shown 5

How does it work? u R 2 Direct gain calculation R 1 u I

How does it work? u R 2 Direct gain calculation R 1 u I - e Feed-back equation + -A e Vout Vin u Ideal Op-Amp 6

Non-inverting amplifier R 2 u Gain R 1 u u I - Called a

Non-inverting amplifier R 2 u Gain R 1 u u I - Called a follower if R 2 = 0 + Input impedance Vout Vin 7

Inverting amplifier R 2 u Gain R 1 u u Input impedance Gain error

Inverting amplifier R 2 u Gain R 1 u u Input impedance Gain error I - Vin + Vout 8

Summation R u Transfer function R 1 V 1 I - Rn Vn In

Summation R u Transfer function R 1 V 1 I - Rn Vn In u If Ri = R + Vout 9

Differentiation R 2 R 1 V 1 I 1 R 1 V 2 I

Differentiation R 2 R 1 V 1 I 1 R 1 V 2 I 1 + Vout R 2 10

Current-to-Voltage converter (1) C R Iin + u u Vout = - R Iin

Current-to-Voltage converter (1) C R Iin + u u Vout = - R Iin For high gain and high bandwidth, one has to take into account the parasitic capacitance 11

Current-to-Voltage converter (2) R 1 R 2 r Iin + Vout u High resistor

Current-to-Voltage converter (2) R 1 R 2 r Iin + Vout u High resistor value with small ones u Equivalent feedback resistor = R 1 + R 2 * (R 1/r) – ex. R 1 = R 2 = 100 k ; r = 1 k ; Req = 10. 2 M u Allows the use of smaller resistor values with less problems of parasitic capacitance 12

Charge amplifier (1) R C u Requires a device to discharge the capacitor –

Charge amplifier (1) R C u Requires a device to discharge the capacitor – Resistor in // – Switch I + Vout 13

Charge amplifier (2) R C I + Input Charge In a few ns V

Charge amplifier (2) R C I + Input Charge In a few ns V 1 C 1 R 2 R 1 Output of the charge amplifier Very long time constant C 2 V 2 Shaping a few 10’s of ns 14

Miller effect u Charge amplifier – – u Vin = e Vout = -A

Miller effect u Charge amplifier – – u Vin = e Vout = -A e The capacitor sees a voltage (A+1) e It behaves as if a capacitor (A+1)C was seen by the input C Vin –Two circuits are equivalent X Z e -A e Vout + Miller’s theorem –Av = Vy / Vx - Y Y X Z 1 Z 2 » Z 1 = Z / (1 - Av) » Z 2 = Z / (1 -Av-1) 15

Common mode u The amplifier looks at the difference of the two inputs –

Common mode u The amplifier looks at the difference of the two inputs – Vout = G * (V 2 - V 1) u The common value is in theory ignored – V 1 = V 0 + v 1 – V 2 = V 0 + v 2 u In practice there are limitations – linked to the power supplies – changes in behaviour u Common mode rejection ratio CMRR – Differential Gain / Common Gain (in d. B) 16

Non-ideal amplifier u Input Offset voltage Vd u Input bias currents Ib+ and Ib.

Non-ideal amplifier u Input Offset voltage Vd u Input bias currents Ib+ and Ib. Ib- u Limited gain u Input impedance u u e Zd Output impedance Common mode rejection Noise Bandwidth limitation & Stability Zc -A e Zout + Vd Ib+ Zc 17

Input Offset Voltage u u “Zero” at the input does not give “Zero” at

Input Offset Voltage u u “Zero” at the input does not give “Zero” at the output In the inverting amplifier it acts as if an input Vd was applied R 2 I R 1 - – (Vout) = G Vd u Notes: – Sign unknown – Vd changes with temperature and time (aging) – Low offset = a few m. V and Vd = 0. 1 m. V / month – Otherwise a few m. V Vd + Vout 18

Input bias current (1) u u u (Vout) = R 2 Ib (Vout) =

Input bias current (1) u u u (Vout) = R 2 Ib (Vout) = - R 3 (1 -G) Ib+ Error null for R 3 = (R 1//R 2) if Ib+ = Ib- R 2 Ib- R 1 + R 3 Ib+ Vout 19

Input bias current (2) u u u In the case of the charge amplifier

Input bias current (2) u u u In the case of the charge amplifier it has to be compensated Switch closed before the measurement and to discharge the capacitor Values – less than 1. 0 p. A for JFET inputs – 10’s of n. A to m. A bipolar Ib- C + R 3 Ib+ Vout 20

Common mode rejection u u u Non-inverting amplifier Input voltage Vc/Fr (Vc common mode

Common mode rejection u u u Non-inverting amplifier Input voltage Vc/Fr (Vc common mode voltage) Same effect as the offset voltage R 2 R 1 Vc/Fr I + Vout 21

Gain limitation R 2 R 1 Vin I - e + u -A e

Gain limitation R 2 R 1 Vin I - e + u -A e Vout A is of the order of 105 – Error is very small 22

Input Impedance R 2 R 1 Zc- + Vin Zd Vout Zc+ u Non-inverting

Input Impedance R 2 R 1 Zc- + Vin Zd Vout Zc+ u Non-inverting amplifier u Zin = Zc+ // (Zd A / G) ~ Zc+ G= (R 1+R 2)/R 1 23

Output impedance u R 2 Non-inverting amplifier R 1 I 0 + Iout -

Output impedance u R 2 Non-inverting amplifier R 1 I 0 + Iout - e -A e + I 0 Iout Z 0 Vout 24

Current drive limitation Maximum Output Swing R 2 R 1 I + Vout RL

Current drive limitation Maximum Output Swing R 2 R 1 I + Vout RL Vin u u u RL*Imax RL Vout = R I = RL IL The op-amp must deliver I + IL = Vout (1/R + 1/RL) Limitation in current drive limits output swing 25

Bandwidth f 3 db= f. T/G f. T u Gain amplifier of non-inverting G(p)

Bandwidth f 3 db= f. T/G f. T u Gain amplifier of non-inverting G(p) = G A(p) / (G + A(p)) – A(p) with one pole at low frequency and -6 d. B/octave » A(p) = A 0 / (p+w 0) – G = (R 1+R 2)/R 1 40 d. B – Asymptotic plot » G < A G(p) = G » G > A G(p) = A(p) 26

Slew Rate u u Limit of the rate at which the output can change

Slew Rate u u Limit of the rate at which the output can change Typical values : a few V/ms A sine wave of amplitude A and frequency f requires a slew rate of 2 p. Af S (V/ms) = 0. 3 f. T (MHz); f. T = frequency at which gain = 1 27

Settling Time u Time necessary to have the output signal within accuracy – ±x%

Settling Time u Time necessary to have the output signal within accuracy – ±x% u Depends on the bandwidth of the closed loop amplifier – f 3 d. B = f. T / G u Rough estimate – 5 t to 10 t with t = G / 2 p f. T 28

Stability u G(p) = A(p) G / (G + A(p)) – A(p) has several

Stability u G(p) = A(p) G / (G + A(p)) – A(p) has several poles u u If G = A(p) when the phase shift is 180 o then the denominator is null and the circuit is unstable Simple criteria – On the Bode diagram G should cut A(p) with a slope difference smaller than -12 d. B / octave – The loop gain A(p)/G should cut the 0 d. B axe with a slope smaller than -12 d. B / octave u -12 d. B/octave Phase margin – (1800 - Phase at the two previous points) u Unstable amplifier The lower G the more problems - Open loop gain A(p) - Ideal gain G - Loop gain A(p)/G 29

Stability improvement -6 d. B/octave Compensation u -6 d. B/octave Pole in the loop

Stability improvement -6 d. B/octave Compensation u -6 d. B/octave Pole in the loop Move the first pole of the amplifier – Compensation u Add a pole in the feed-back u These actions reduce the bandwidth 30

Capacitive load u Buffering to drive lines R 2 R 1 - C =

Capacitive load u Buffering to drive lines R 2 R 1 - C = 20 p. F 10 + u C Load = 0. 5 m. F The output impedance of the amplifier and the capacitive contribute to the formation of a second pole at low frequency – A’(p) = k A(p) 1/(1+r C p) with r = R 0//R 2//R – A(p) = A 0 / (p+w 0) u Capacitance in the feedback to compensate – Feedback at high frequency from the op-amp – Feedback at low frequency from the load – Typical values a few p. F and a few Ohms series resistor 31

Examples of data sheets (1) 32

Examples of data sheets (1) 32

Examples of data sheets (2) 33

Examples of data sheets (2) 33

Current feedback amplifiers e - -A e Zt ie + u Voltage feedback +

Current feedback amplifiers e - -A e Zt ie + u Voltage feedback + u u ie Current feedback Zt = Vout/Ie is called the transimpedance gain of the amplifier 34

Applying Feedback R 2 R 1 I - Zt ie + ie Vout Vin

Applying Feedback R 2 R 1 I - Zt ie + ie Vout Vin u u Non-inverting amplifier Same equations as the voltage feedback 35

Frequency response R 2 R 1 I - Zt ie + ie Vout Vin

Frequency response R 2 R 1 I - Zt ie + ie Vout Vin u The bandwidth is not affected by the gain but only by R 2 – Gain and bandwidth can be defined independently u Different from the voltage feedback – f 3 d. B = f. T / G 36

Data sheet of a current feedback amplifier 37

Data sheet of a current feedback amplifier 37

Data sheet of a current feedback amplifier (cont’) u Very small change of bandwidth

Data sheet of a current feedback amplifier (cont’) u Very small change of bandwidth with gain 38

Transmission Lines u u u Lossless Transmission Lines Adaptation Reflection Transmission lines on PCB

Transmission Lines u u u Lossless Transmission Lines Adaptation Reflection Transmission lines on PCB Lossy Transmission Lines 39

Lossless transmission lines (1) u L, C per unit length x Impedance of the

Lossless transmission lines (1) u L, C per unit length x Impedance of the line Z u Pure resistance u Lx Cx Z 40

Lossless transmission lines (2) u Propagation delay u Pure delay Lx V 1 Cx

Lossless transmission lines (2) u Propagation delay u Pure delay Lx V 1 Cx I V 2 Z 41

Lossless transmission lines (3) u Characteristic impedance pure resistance u Pure delay u Capacitance

Lossless transmission lines (3) u Characteristic impedance pure resistance u Pure delay u Capacitance and inductance per unit of length u Example 1: coaxial cable – Z = 50 – t = 5 ns/m – L = 250 n. H/m; C = 100 p. F/m u Example 2: twisted pair – Z = 100 – t = 6 ns/m – L = 600 n. H/m ; C = 60 p. F/m 42

Reflection (1) Source generator u Zs Zo – V, Output impedance Zs u Line

Reflection (1) Source generator u Zs Zo – V, Output impedance Zs u Line appears as Z 0 u All along the line Vs = Z 0 Is If the termination resistance is ZL a reflection wave is generated to compensate the excess or lack of current in ZL u u V Vs Is ZL The reflected wave has an amplitude 43

Reflection (2) u The reflected wave travels back to source and will also generate

Reflection (2) u The reflected wave travels back to source and will also generate a reflected wave if the source impedance is different from Z 0 – During each travel some amplitude is lost u ZS = 1/3 Z 0 ZL = 3 Z 0 The reflection process stops when equilibrium is reached – VS = V L u u Zs < Z 0 & Z L > Z 0 Dumped oscillation Zs > Z 0 & Z L > Z 0 Integration like ZS = 3 Z 0 ZL = 3 Z 0 44

Reflection (3) u Adaptation is always better – At the destination: no reflection at

Reflection (3) u Adaptation is always better – At the destination: no reflection at all – At the source: 1 reflection dumped 1 transit time » Ex. ZL = 3 Z 0 u Can be used to form signal – Clamping Zs V 2 transit time Zo Vs 45

Transmission lines on PCB u Microstrip u Stripline 46

Transmission lines on PCB u Microstrip u Stripline 46

Lossy transmission lines u Idem with Rs. L instead of L, Rp//C instead of

Lossy transmission lines u Idem with Rs. L instead of L, Rp//C instead of C Rs L C u Rp Characteristic impedance depends on w – Even Rs is a function of w because of the skin effect u u Signal is distorted Termination more complex to compensate cable characteristic 47

Bibliography u The Art of Electronics, Horowitz and Hill, Cambridge – Very large covering

Bibliography u The Art of Electronics, Horowitz and Hill, Cambridge – Very large covering u An Analog Electronics Companion, S. Hamilton, Cambridge – Includes a lot of Spice simulation exercises u Electronics manufacturers application notes – Available on the web » (e. g. http: //www. national. com/apnotes_all_1. html) u For feedback systems and their stability – FEED-2002 from CERN Technical Training 48