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 dualsupply circuits» Threshold comparator Example of applications Summing amplifiers Differential amplifiers Single and dualsupply circuits Analysis of amplifier circuits AC and DC analysis Circuits with several Op Amps Circuits with several inputs Circuits with positive feedback Hysteretic threshold comparator Signal generator 3/05/2009 ElnSysC3 2009 DDC 3/05/2009 2 ElnSysC3 2009 DDC Differential gain Ad high but not infinite; differential input voltage d small but not 0 Input currents I, I small but not 0 Actual Op Amp Nonlinear, frequency dependent transfer function u = f(,, ω, ) Limited bandwidth (Ad decreases for high ω) Influence of external parameters temperature, power supply, Basic operational amplifier circuits Inverting and noninverting amplifiers 5.3 New model to take into account these effects eal Op Amp 3/05/2009 3 ElnSysC3 2009 DDC 5.4 2009 DDC 2006 Storey
Electronic Systems C3 3/05/2009 Generalized feedback amplifiers The transfer function evaluated with is valid also with Z I Z Z2 Z2 β = Z Z2 Z Z 2 U = I = I β Z2 I I = Z = Z2 I2 Z2 I Z 3/05/2009 5 ElnSysC3 2009 DDC Z Z2 = Basic operational amplifier circuits (contd.) When looking at feedback we derived the circuit of an amplifier from first principles Normally we use standard cookbook circuits and select component values to suit our needs In analysing these we normally assume the use of ideal opamps in demanding applications we may need to investigate the appropriateness of this assumption the use of ideal components makes the analysis of these circuits very straightforward 5.6 Other useful circuits In addition to simple amplifiers, opamps can also be used in a range of other circuit The next few slides show a few examples of opamp circuits for a range of purposes The analysis of these circuits is similar to that of the noninverting and inverting amplifiers but (in most cases) this is not included here For more details of these circuits see the relevant section of the course text (as shown on the slides) 5.4 5.7 Functional definition Unit with u = A B 2» Adder Can be generalized as» u = A B 2 C 3. If = 2 = 3 and B = A/2, B = C/2» D/A converter (lesson F3) Adder and differential ampòlifiers if A = B = K» Differential amplifier: u = K( 2) 3/05/2009 8 ElnSysC3 2009 DDC 2 3 2 All these circuits use Op Amps and feedback Σ K(2) u u 2009 DDC 2006 Storey 2
Electronic Systems C3 3/05/2009 A differential amplifier (or subtractor) 5.4.3 Subtracting amplifier o = ( 2 ) Signals can be applied to inverting and noninverting inputs u = u() u(a) A Wrong approach! i is a label or a value? u = / (/ ) a 5.9 3/05/2009 0 ElnSysC3 2009 DDC Differential amplifier An inverting summing amplifier 5.4.4 The output includes two terms u = u() u(2) If a = 4/(4) 2 u = / (/ ) 4/(4) 2 If / = 4/ = A D u = A D (2 ) = A D D The circuit is a differential amplifier. 2 A 4 o = ( 2 ) Wrong! Same problem as before In the following: i label K value 3/05/2009 ElnSysC3 2009 DDC 5.2 2009 DDC 2006 Storey 3
Electronic Systems C3 3/05/2009 Adder with Op Amp Active integrator with Op. Amp. The inverting input receives currents from two or more inputs. Since I = 0, the total current (sum) flows in Current in defines the output voltage u. 2 2 3 _ f Inverting voltage amplifier with: Zi =, Zf = C ( s) = ( s) I C sc ( t) = I ( t)dt C The circuit is an adder N n _ The circuit is an INTEGATO 5.4.5 Can be analyzed also with the virtual ground approach 3/05/2009 3 ElnSysC3 2009 DDC 3/05/2009 4 ElnSysC3 2009 DDC With Zi = C, Zf = we get a DIFFEENTIATO ( s) = ( s) ( t) I sc I = C t ( t) Sensitive to noise Limited bandwidth Less used that integrator Differentiator with Op. Amp. 3/05/2009 5 ElnSysC3 2009 DDC C _ 5.4.6 Key points Operational amplifiers are among the most widely used building blocks in electronic circuits An ideal operational amplifier would have infinite voltage gain, infinite input resistance and zero output resistance Designers often make use of cookbook circuits eal opamps have several nonideal characteristics However, if we choose components appropriately this should not affect the operation of our circuits Feedback allows us to increase bandwidth by trading gain against bandwidth 5.6 2009 DDC 2006 Storey 4
Electronic Systems C3 3/05/2009 Selecting component values Our analysis assumed the use of an ideal opamp When using real components we need to ensure that our assumptions are valid In general this will be true if we: limit the gain of our circuit to much less than the openloop gain of our opamp choose external resistors that are small compared with the input resistance of the opamp choose external resistors that are large compared with the output resistance of the opamp. Generally we use resistors in the range to 00 kω 5.6 5.7 Singlesupply circuits Any electrical network has a reference node (0,GND) Op Amp does not show a GND or 0 pin, but Signals as measured from a reference Dual power supply (examples): symmetric: ± 5, reference 0 (GND) asymmetric : 0, 5, reference 0 or 2,5 Single power supply (example) 0, reference 5 The reference (GND, 0) is related with power supply 3/05/2009 8 ElnSysC3 2009 DDC eference voltage eference with single power supply I Single power supply: An intermediate voltage level is selected as reference voltage ( ). AL AL I Dual power supply: The reference voltage is the power supply reference. AL a b C Signals (variable voltages) are measured from a fixed reference voltage (GND, or another reference voltage Single supply circuits, to allow positive and negative voltage changes, use a reference voltage between GND and the power supply. The reference voltage is obtained from power supply, and must have low equivalent impedance (like a DC voltage source). 3/05/2009 9 ElnSysC3 2009 DDC 3/05/2009 20 ElnSysC3 2009 DDC 2009 DDC 2006 Storey 5
Electronic Systems C3 3/05/2009 Output signals Lesson C3 Dual power supply Single power supply al ef. = GND al al ef. al/2 GND t t Example of applications Summing amplifiers Differential amplifiers Single and dualsupply circuits Analysis of amplifier circuits AC and DC analysis Circuits with several Op Amps Circuits with several inputs Circuits with positive feedback Hysteretic threshold comparator Signal generator 3/05/2009 2 ElnSysC3 2009 DDC 3/05/2009 22 ElnSysC3 2009 DDC Analysis of Op Amp circuits with Z Example : asymptotes in F axis Goal: plot (on axis with values) the response In the frequency domain (Bode) In the time domain (step input) Analysis procedure: two steps Asymptotic behavior (quantitative for amplitude, qualitative for horizontal axis)» Frequency domain (ω = 0 andω ): Bode diagram» Time domain (t = 0 and t ): step response Pole and zeroes position» Evaluate network function (in s or in jω )» Denominator 0s: transfer function poles, time constants» Numerator 0s: transfer function 0s For ω C CC, U = For ω 0 C CA, Frequency response (with gain values on Y) = I I I u/i II D I2 I C ω 3/05/2009 23 ElnSysC3 2009 DDC 3/05/2009 24 ElnSysC3 2009 DDC 2009 DDC 2006 Storey 6
Electronic Systems C3 3/05/2009 Ex. : poles and zeroes position Example : Bode plot I D I I2 II I Z C Z U = Z Z = // C 2 Z = s C 3 I sc = I 3 U = polo : τ zero : τ ( )( sc // ) ( s C ) p z = C = ( // )C 2 3 3 2 2 3 I ω p = /τ p = / 3 C I I I2 II D I C ω ω z = /τ z = / 3 // 2 C 3/05/2009 25 ElnSysC3 2009 DDC 3/05/2009 26 ElnSysC3 2009 DDC Example : unity slope Example : numeric For two points on a unity slope segments the frequency ratio is the same as amplitude ratio ation among asymptote levels (amplitude) [( 3 2 )/ ]/( 2 / ) = ( 3 2 )/ 2 ω z /ω p = ( 3 // 2 )C / 3 C = [( 3 2 )/ 3 2 ] / 3 = ( 3 2 )/ 2 2 3 I Numeric example = 2 kω, = 39 kω, = 20 kω. C = 2,2 nf Solving sequence Av(ω) =? I 2 I I I D C 2 ω p = /τ p = / 3 C ω z = /τ z = /( 3 // 2 C) ω Av(0) =? ω z =? τ z =? Av( ) =? ω p =? τ p =? 3/05/2009 27 ElnSysC3 2009 DDC 3/05/2009 28 ElnSysC3 2009 DDC 2009 DDC 2006 Storey 7
Electronic Systems C3 3/05/2009 Example : results AC Amplifier Numeric example = 2 kω, = 39 kω, = 20 kω. C = 2,2 nf esults Av(0) = 3,25 22,4 db ω z = 5,5 krad/s τ z =? Av( ) = 3,25 0,2 db ω p = 3,79 krad/s τ p =? Plot u(t) for a 200 m step input I 2 I I I D C Define the upper band limit (ω 2 ) Pole towards high frequency: C2 capacitor (P/Z pair) For ω >> ω 3, C3 becomes a Short Circuit Z C2 (0) : Av = / Z C2 ( ) << : for high ω the circuit is a voltage follower ω 3 ω 2 ω I C3 C2 3/05/2009 29 ElnSysC3 2009 DDC 3/05/2009 30 ElnSysC3 2009 DDC AC amplifier b Av(ω) for the AC amplifier emove DC component at input Highpass cell at input» C removes DC from input signal (zero at f = 0 pole)» The feedback Op Amp still has DC gain C C C2 C / G (db) I I ω ω 2, ω 3 ω total 0. 0 000 0 5 ω (rad/s) 3/05/2009 3 ElnSysC3 2009 DDC 3/05/2009 32 ElnSysC3 2009 DDC 2009 DDC 2006 Storey 8
Electronic Systems C3 3/05/2009 u(t) for the AC amplifier Comparison among AC amplifiers C T (ms) Inverting circuit can be removed (bias current Ib flows in ) C2 C Ib Low pass response caused by C2 High pass response caused by C and/or C3 Noninverting circuit is mandatory, to get a DC path for the noninverting input C Ib C3 C2 If wide pole separation, looks like a squarewave 3/05/2009 33 ElnSysC3 2009 DDC 3/05/2009 34 ElnSysC3 2009 DDC Test 2: AC amplifier Test 2 b = 0 kω, = 50 kω = 2 kω C = 47 µf C2 = 00 pf C3 = 0 µf 2/i = Av = u/2 = Z2 = //C2 = Z3 = /sc3 = separate the analysis for input cell (C) and the Op Amp circuit C C 2 C3 i u = 0 Av(ω) C2 Bode diagram (C ) C / G (db) 0 ω A = /τ A ω B = /τ B C ω (rad/s) C3 ω A = ω B = Av = C2 (C ) 3/05/2009 35 ElnSysC3 2009 DDC 3/05/2009 36 ElnSysC3 2009 DDC 2009 DDC 2006 Storey 9
Electronic Systems C3 3/05/2009 Test 2 c Lesson C3 Transient response C () = 0,63 C C2 C3 τ B = τ A = (C ) Example of applications Summing amplifiers Differential amplifiers Single and dualsupply circuits AC amplifiers Analysis of amplifier circuits AC and DC analysis Circuits with several Op Amps Circuits with several inputs 0 50 t = τ2 50 t (ms) t = τ Threshold comparator Effects of positive feedback 3/05/2009 37 ElnSysC3 2009 DDC 3/05/2009 38 ElnSysC3 2009 DDC oltage comparators Open loop Op Amp A circuit with analog input and digital output (binary) Compare input signal with a threshold S The output state indicates if > < S S An open loop Op Amp (without feedback) can be used as voltage comparator S d = S = A d d H H d H ~ AL L ~ AL L L 3/05/2009 39 ElnSysC3 2009 DDC 3/05/2009 40 ElnSysC3 2009 DDC 2009 DDC 2006 Storey 0
Electronic Systems C3 3/05/2009 Notinverting comparator circuit Inverting comparator circuit S Non inverting comparator: Se I > S: U = H Se I < S: U = L S Inverting comparator: Se I > S: U = L Se I < S: U = H S S 3/05/2009 4 ElnSysC3 2009 DDC 3/05/2009 42 ElnSysC3 2009 DDC Input signal with noise Hysteretic comparator Noise causes multiple threshold crossing Two switched threshold can remove the effects of noise hysteresis S S S2 3/05/2009 43 ElnSysC3 2009 DDC 3/05/2009 44 ElnSysC3 2009 DDC 2009 DDC 2006 Storey
Electronic Systems C3 3/05/2009 Double threshold How to get a double threshold ule for switching S when = H; S2 when = L The threshold voltage S is obtained combining a reference voltage and the output voltage : S = ( 2 )/( 2 ) S S2 I S 2 H L 3/05/2009 45 ElnSysC3 2009 DDC 3/05/2009 46 ElnSysC3 2009 DDC Inverting hysteretic comparator Notinverting hysteretic comparator S, has two values, depending on the output state The two S values are the two thresholds When = H : S = S = ( H 2 )/( 2 ) When = L : S = S2 = ( L 2 )/( 2 ) S 2 Same approach: 2 Two values of two values of two thresholds S = H : = ( H 2 S )/( 2 ) S = ( 2 ) H )/ 2 = L : = ( L 2 S2 )/( 2 ) S2 = ( 2 ) L )/ 2 3/05/2009 47 ElnSysC3 2009 DDC 3/05/2009 48 ElnSysC3 2009 DDC 2009 DDC 2006 Storey 2
Electronic Systems C3 3/05/2009 Negative and Positive feedback Which function for the Op Amp? Amplifiers: Hysteretic comparator: negative feedback from U to in positive feedback from U to in Effects of positive feedback: Any minimum change is amplified and fed to input with the same polarity The only stable output states are H e L The Op Amp is always saturated (unless at switching) Positive feedback increases switching speed. Threshold assumes two values (hysteresis) Amplifier: Negative feedback (also in DC) Differential input voltage d = 0 ( tracks ) Input currents I, I = 0 Output linear within the range limits: max > > min Comparators Positive feedback (to get hysteresis) Can have any differential input voltage Output switches when d crosses 0 (or = 0) Output always saturated at max or min (unless during switching) 3/05/2009 49 ElnSysC3 2009 DDC 3/05/2009 50 ElnSysC3 2009 DDC A hysteretic comparator is also called SCHMITT TIGGE Integrated hysteretic inputs Inputs with hysteresis are named trigger inputs Use the hysteresis symbol Fixed thresholds Comparators are available as ICs (like Op Amps) Fast response Flexible output (Open Collector) Logic inverter with trigger input: Digital oscillators for example the relaxation oscillator.2.4 3/05/2009 5 ElnSysC3 2009 DDC 5.52 2009 DDC 2006 Storey 3
Electronic Systems C3 3/05/2009 Lesson C3: final test Which voltage levels can we get from the output of an Op Amp with 5 and 0 supply voltages? How can we evaluate the behavior of an electrical network for f = 0? And for very high frequencies? Which is the value of the DC at the output of an AC amplifier? Draw the schematic diagram of a 3input adder (analog). Which are the benefits of differential signals? Write as differential and common mode values two voltages, respectively 3,5 and 4,5 towards GND. Which are the parameters of a threshold comparator? Why do we add hysteresis to voltage comparators? How can we distinguish an amplifier from a voltage comparator? 3/05/2009 53 ElnSysC3 2009 DDC 2009 DDC 2006 Storey 4