Operational Amplifiers

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1 Operational mplifiers lektronikseminar Georg Wirth Institt für Laser Physik rd March 8

2 Otline Introdction General characteristics Basic operation The ideal op-amp The Concept of Feedback Basic idea of feedback The noninverting and inverting amplifier Circit xamples Smming and differential amplifier Integrator and Differentiator Nonlinear applications eal op-amps Freqency esponse and Slew ate Inpt Offset Voltage and Bias Crrent Practical Hints Good (GND connections voiding noise from power spply Georg Wirth, Institt für Laser-Physik

Pros and Cons of op-amps Basic idea: Use integrated circit (black box internal realiation nknown as a modlar device to maniplate signals,

dvantages of op-amps Versatility - operation only determined by external srronding circit No bias crrent needed to determine operation

range TO-99 (transistorsingle-otline SOIC-8 (small-otlineintegrated-circit Disadvantages low otpt crrents de to small package higher

3 Pros and Cons of op-amps Basic idea: Use integrated circit (black box internal realiation nknown as a modlar device to maniplate signals, so that behavior of the circit is prely characteried by external elements. circit symbol Why not se a transistor? dvantages of op-amps Versatility - operation only determined by external srronding circit No bias crrent needed to determine operation point High inpt impedance, low otpt impedance High intrinsic gain Very linear and precise amplification over broad voltage an freqency range TO-99 (transistorsingle-otline SOIC-8 (small-otlineintegrated-circit Disadvantages low otpt crrents de to small package higher noise de to mltiple amplifier stages lower ct-off-freqency than single-stage transistor amplifiers CDIP / PDIP (dal-inline-package Georg Wirth, Institt für Laser-Physik

4 Basic operation and wiring Typical pin assignment inverting (- and noninverting ( inpt (, voltage difference D - - between inpts is amplified linearly by factor (open-loop-gain to otpt ( - - (6 every potential is measred relatively to grond potential (sally GND or V two connections (4,7 for power spply V ± (sally ±5V no separate grond connection, otpt grond reference by for - - (for ideal op-amp sally two extra pins for external offset compensation (8, V - V - µv µv 5 D D V- - V satration linear satration Georg Wirth, Institt für Laser-Physik 4

5 The ideal op-amp Parameter Symbol Ideal eal (OP7 Inpt Impedance Differential-Mode Inpt Impedance Common-Mode D, - 4 MΩ pf GΩ pf i Inpt Bias Crrent Inpt Offset Voltage Otpt Impedance Unity Gain Bandwidth i, i - ±5 n µv 7 Ω f ( - db 8 MH D i D ~ virtal GND Open-Loop-Gain d /d D 6 db Common-Mode ejection atio / d /d( - 6 db real GND Slew rate max(d /dt.8 V/µs Georg Wirth, Institt für Laser-Physik 5

6 Basic idea of feedback Problem open-loop-gain too high, inpt voltage range of µv to small amplification not adjstable gain determined by device (and hence differs between varios devices, instabilities Soltion op-amp feed factor k F of otpt signal back into inpt signal experiences certain amplification / attenation and phase shift while passing the loop, effect determined by phase difference at inpts inpt error ± feedback plant controller otpt Conseqences redced gain, bt improved linearity, freqency response, bandwidth and stability more negative feedback reslts in less dependency on device parameters in general, feedback can be freqency-dependant (eqaliers and filters or amplitde-dependant (logarithmic amplifiers or mltipliers The golden rles concerning op-amps. The otpt attempts to do whatever is necessary to make the voltage difference between the inpts ero (infinite open-loop-gain.. The inpts draws no crrent (infinite inpt impedance. Georg Wirth, Institt für Laser-Physik 6

7 Georg Wirth, Institt für Laser-Physik 7 The noninverting amplifier realie controller by voltage divider -, rising otpt voltage hinders inpt difference - - ( ( ( short- circit virtal from feedback OP- mp ideal closed-loop- gain signal otpt feedback negative becase generally >>, the inpt voltage difference tends to ero (virtal short-circit (complies with st golden rle high inpt impedance ( Ω, low otpt impedance ( Ω for and the closed-loop-gain, op-amp works as bffer (voltage follower

8 Georg Wirth, Institt für Laser-Physik 8 The inverting amplifier connect inpt signal to lower end of feedback voltage divider - assme inpt voltage V, bt no otpt V since noninverting inpt is connected to GND V, op-amp sees high inpt nbalance this forces the otpt to go negative, ntil both inpt are on GND - V ( ω ( ω i i ( ( ( ( ( ( ( ω ω ω ω ω ω ω di d i i i i D D D impedance inpt closed loop gain high op- amp impedance open loop gain jnction rle kirchhoff's freqency-dependant (bt linear feedback provides active filters, integrators, differentiators non-linear feedback allows to bild amplitde-dependant devices, i.e. exponential or logarithmic amplifiers

9 The smming amplifier Problem smming crrents is easy, bt since all potentials are gronded, how to add potentials? Soltion take inverting amplifier and add crrents in feedback loop assme that high inpt impedance i - and virtal GND - kirchhoff's jnction rle assme eqal inpts i i F i n i F n n n F n n i n i i n F i F closed-loop- gain F ( n Georg Wirth, Institt für Laser-Physik 9

10 The differential amplifier Problem measre voltage drop over some impedance, what if none of both connections has GND contact? Soltion se featres from both inverting and noninverting amplifier virtal short - circit kirchhoff's jnction rle i i N P P N N insert N N P P if ( N and P N Cation assme N α and thereby the closed-loop-gain -α, resistors have tolerance Δα CM d d( α ( α Δ α error, if resistor vales differ different inpt impedances reqire sorce with low otpt impedance better reslts with instrmentation amplifier Georg Wirth, Institt für Laser-Physik

11 The integrator freqency response se inverting amplifier with C-high-pass C - filter in feedback strong negative feedback for high freqencies (respectively weak feedback for low freqencies reslts in low-pass-characteristic se closed loop gain ( ω ( ω ( ω ( ω and ( ω ( C iωc iω( C ( iωc iω( C i C i missing feedback at ω makes circit instable, insertion of bypass limits feedback at low freqencies attenation ( < at high freqencies can be avoided by insertion of i assme lower limit lower ct -off pper ct-off pper limit ( ω ( ω ( ( ω ( ω << << DC DC ω ( ω ( ( ( C C log ( ( ω DC integrating range ω ω db/dec log( ω Georg Wirth, Institt für Laser-Physik

12 The integrator operating method closed loop gain ( ω ( ω ( ω iωc iω( C kirchhoff's jnction rle i i i C d( dt i C pproximations i for freqencies far above lower limit ω >> ω, crrent i / can be neglected (shortened by C for freqencies far beneath pper limit ω << ω, impedance of C - is dominated by condensator, so the voltage change d /dt over can be neglected i d C ( t dt C t ( t dt ( integration constant ( Q / C is determined by initial condensator charge and capacity inpt bias crrent i - and inpt offset voltage reslt in additional condensator crrent / i -, which changes otpt voltage by i C d dt i - µ reslts with C µf in a change of V per second (offset compensation Georg Wirth, Institt für Laser-Physik

13 The differentiator freqency response swap condensator and resistor in integrator C-low-pass filter -C delivers in high negative feedback for low freqencies, reslting in a high-pass characteristic se ( ω iωc iωc iωc ( ω iωc closed loop gain ( ω ( ω iω C and ( ω at high freqencies ω, missing feedback makes circit nstable HF noise is strongly amplified, circit tends to oscillate de to phase delay of op-amp and feedback gain limiting at high freqencies can be achieved by insertion of assme lower limit lower ct-off pper ct -off pper limit ( ( ω ( ω ( ω ( ω << ω ω DC C C log i ( ( ω C db/dec i differentiating range ω ω log( ω Georg Wirth, Institt für Laser-Physik

14 The differentiator operating method closed loop gain kirchhoff's jnction rle ( ω iωc ( ω ( ω iω C i i d( C dt C i pproximation i for freqencies far beneath pper limit ω << ω, impedance of -C is dominated by condensator, so the voltage change d /dt over can be neglected d d C ( t C dt dt differentiator is bias-stable, optional roll-off-condensator in feedback can redce bandwidth (bandpass capacitive inpt impedance draws crrent from sorce, problems possible at high freqencies Georg Wirth, Institt für Laser-Physik 4

15 The logarithmic amplifier Problem measred signal has large dynamic range Idea instead of linear characteristic crve i / of a resistor, se exponential I-U-dependency of semicondctors se collector crrent i C of a bipolar transistor i C C B i C i CS C ( ln( i i ( T, exp B T B T C CS > i CS T kt/e reverse leakage crrent thermal voltage since B, i C T ln ics (for > no error de to collector-base-crrent i CB, since CB, bt temperatre drift with appropriate transistor and op-amp with low bias-crrent, sally nine decades available swap resistor and transistor: exponential amplifier mltiply / divide signals by taking logarithm, add / sbtract, take exponential vale Georg Wirth, Institt für Laser-Physik 5

16 The comparator Problem device for comparison of two signals, which decides if voltage is below / above some threshold Soltion se op-amp withot feedback to compare voltages (comparator becase of high open-loop-gain, circit is sensitive to small voltage differences D and switches between satrated vales - max and max in satration no virtal short-circit between inpts, i.e. - D max max for for > < max sefl for regeneration of digital signals or as trigger special devices for fast applications D D t satration max satration Georg Wirth, Institt für Laser-Physik 6

17 The noninverting Schmitt trigger Problem comparator has no well-defined otpt for small inpt signals D different switching vales for high an low state desired Soltion se positive feedback to create hysteresis for switching assme high positive inpt, so that otpt is max with falling inpt voltage, otpt remains nchanged ntil -, where,off - ( / max pper switching point lower switching point hysteresis,on,off Δ T max max max max,on D,off, on t,off max Georg Wirth, Institt für Laser-Physik 7

18 The real op-amp differential open-loop-gain d /d D is sally not infinite -> error in approx. even with shortened inpts - -, opamp amplifies common-mode voltage -, sally expressed by ratio of differential open-loop-gain to d /d( - -> common-mode rejection ratio finite inpt impedance draws crrent from sorce, common-mode inpt impedance (inpt to GND sally negligible, effect compensated if adjsted nonero otpt impedance negligible, since decrease of otpt by otpt load is compensated by feedback transistors as well as resistors prodce noise, which is amplified towards the otpt Parameter Symbol Ideal eal (OP7 Inpt Impedance Differential-Mode Inpt Impedance Common-Mode Inpt Bias Crrent Inpt Offset Voltage Otpt Impedance Unity Gain Bandwidth D, - 4 MΩ pf GΩ pf i, i - ±5 n µv 7 Ω f ( - db 8 MH Open-Loop-Gain d /d D 6 db Common-Mode ejection atio / d /d( - 6 db Slew rate max(d /dt.8 V/µs Georg Wirth, Institt für Laser-Physik 8

19 eal op-amps - freqency response real op-amps are mlti-stage transistor-amplifiers every single stage represents a low-pass filter with a particlar ct-off-freqency ω, that redces the gain by - db per decade and adds a certain phase shift of maximal φ π/ (sbseqent stages sally have increasing bandwidths if (ω is open-loop-gain, and k F is feedback factor, reqirement for oscillation is (negative inpt adds phase shift φ π k F ( ω ( ω kf ϕ arg F ( k,π,... to prevent oscillation at ω C, feedback factor has to be maximal k F / (ω C (signal gain in one loop passage mst be smaller than one If an op-amp is not internally freqencycompensated (and by that not nity-gain stable, external freqency compensation or minimal closed-loop-gain is necessary. (ω C log ϕ π π π ( ( ω - db/dec ω ω ω ω C -4 db/dec -6 db/dec log( ω Georg Wirth, Institt für Laser-Physik 9

20 Comparison OP7 OP7 OP7 (nity-gain stable OP7 (not nity-gain stable Georg Wirth, Institt für Laser-Physik

21 Bandwidth freqency-compensated op amps can be regarded as st order low-pass DC ( ω ω i ( ω ω C for freqencies ω >> ω above ct-off, openloop gain is approximately ( ω ( ω DC ω ω DC i gain-bandwidth-prodct (nity - gain bandwidth i i i Ci sally DC is in the range of db, bt ctoff freqency very low ω / π H se closed-loop gain from noninverting amplifier with feedback factor k F / ( to calclate new freqency response ( ω ( ω ( ω k ( ω F insert ( ω DC log( (ω for ω << ω ( ω i ( ω ω i( ω ω for ω >> ω (DC closed-loop gain kf ω k ω closed-loop ct - off freqency F DC / k F ω log( (ω ω log( ω Georg Wirth, Institt für Laser-Physik

22 Slew ate internal capacities and freqency compensation act as a low-pass, whose otpt for a nit-step inpt is a (more or less fast exponential fnction otpt transistors and capacities need driving crrent from (previos driving stage, whose otpt crrent is limited otpt change rate is limited to the slew rate S max(d /dt image sine-wave inpt signal d max sin ω dt ( ω t max ( ω max amplitde-dependant distortion freqency-dependant distortion t slew rate limits amplitde of ndistorted sine-wave otpt swing above some critical freqency (power bandwidth t S max ω Georg Wirth, Institt für Laser-Physik

23 Inpt offset voltage and bias crrent Offset voltage otpt signal even for no inpt signal -, de to nsymmetrical differentialamplifier at inpt (sally several µv amplified towards otpt can be compensated by potentiometer at extra pins problem is temperatre drift of sally µv/ C V 7-8 k V- Bias crrent inpt transistors need constant base- or gatecrrent for operation, which is delivered by power spply Bipolar Darlington FT n n p can be compensated by additional bias resistor B B B Georg Wirth, Institt für Laser-Physik

Practical Hints - Good (GND connections Soldering in general, work with soldering temperatre as high as possible, bt as low as necessary (semicondctors sally stand ~ C for 5 seconds.

24 Practical Hints - Good (GND connections Soldering in general, work with soldering temperatre as high as possible, bt as low as necessary (semicondctors sally stand ~ C for 5 seconds. clean srfaces, remove oxide film. heat p all participants above melting point of solder-tin. melt solder-tin at hot parts, so that flx covers all srfaces 4. capillary actions draws liqid solder-tin into joint Grond connections 5 H GND is reference for all signals (i.e. noise on this connection is spread nearly everywhere if possible, connect every device/component starlike to one common grond reference condctive track have nonero resistance, so flowing crrents prodce a voltage drop (grond shift -> separate signal grond from consmer grond avoid grond-loops, since magnetic stray-fields from transformers indct 5 H noise i con chassis i con chassis Georg Wirth, Institt für Laser-Physik 4

25 voiding noise from power spply se shielded cables for power spply, separate shield grond from signal grond se CLC-filters to filter noise from power spply inpt capacitor to shorten cable indctivity LC-low pass with electrolytic capacitor to filter HF-noise small n capacitors directly at op-amp pins avoid crosstalk or oscillating between different devices n µ m µ V V- - - n µ m µ Georg Wirth, Institt für Laser-Physik 5

26 eferences lectronics U. Tiete, C. Schenk,. Gamm: Halbleiter Schaltngstechnik, Springer, Berlin P. Horowit, W. Hill: The rt of lectronics, Cambridge University Press 989 T. Matsyama: Vorlesngsskript lektronik nd, Hambrg 5 Op-amp circits on Mancini: Op mps for veryone. Design eference. flage. lsevier, Oxford ( Walter G. Jng: OP MP pplications. Firmenschrift nalog Devices, Norwood ( Wikipedia ( Datasheets / Manfactrers National Semicondctor ( NLOG DVICS ( Texas Instrments / Brr Brown ( Georg Wirth, Institt für Laser-Physik 6

ELECTRONIC SYSTEMS. Basic operational amplifier circuits. Electronic Systems - C3 13/05/ DDC Storey 1

ELECTRONIC SYSTEMS. Basic operational amplifier circuits. Electronic Systems - C3 13/05/ DDC Storey 1 Electronic Systems C3 3/05/2009 Politecnico di Torino ICT school Lesson C3 ELECTONIC SYSTEMS C OPEATIONAL AMPLIFIES C.3 Op Amp circuits» Application examples» Analysis of amplifier circuits» Single and