IFB270 Advanced Electronic Circuits Chapter 12: The operational amplifier Prof. Manar Mohaisen Department of EEC Engineering
Review of the Precedent Lecture Introduce the four layer diode Introduce the silicon-controlled controlled rectifier (SCR) Introduce the light-activated SCR (LASCR) Introduce several applications of the SCR/LASCR Introduce the diac and triac Introduce the Unijunction Transistor (UJT) and Programmable UT 2
Lecture Objectives Introduction Op-amp operation modes and parameters Op-amp circuits with a negative feedback Effects of the negative feedback on the op-amp impedances Open-loop p frequency response of an op-amp p Closed-loop frequency response of an op-amp 3
Operational Amplifier (op-amp) Introduction Early op-amps were used to perform operations such addition, subtraction, integration, etc. These op-amps were constructed using vacuum tubes Today s op-amps are linear integrated circuits (ICs) Reliable, low dc supply, ppy, and inexpensive 4
The ideal op-amp has Infinite voltage gain Infinite bandwidth Infinite input impedance (open) Zero output impedance The practical op-amp Introduction Ideal vs. practical op-amp It falls short of these ideal standards (does not fulfill.) 5
Introduction The practical op-amp Characteristics and limitations Peak-to-peak voltage is limited to slightly less than the two supply voltages Current is limited by the maximum power dissipation and rating Very high voltage gain Very high input impedance Very low output impedance 6
Introduction The practical op-amp contd. Internal block diagram of an op-amp Differential amplifier: Amplifies the difference between the two inputs Voltage amplifier: Class A amplifier that provides additional gain Some op-amps might have more than one voltage amplifier Push-pull amplifier: A switching circuit 7
Op-amp Input Modes & Parameters Input signal modes Differential mode Case I: One signal is applied to an input and the other input is grounded (a) The signal is applied at the inverting input (with - sign) The output is an inverted amplified version of the input (b) The signal is applied at the non-inverting input (with + sign) The output is a non-inverted amplified version of the input 8
Op-amp Input Modes & Parameters Input signal modes Double-ended differential mode contd. Case II: Two opposite-polarity signals are applied to the inputs (a) Two out-of-phase of signals are applied to the input and the output is an amplified version of their difference (b) is a different representation of the circuit in (a) 9
Common mode Op-amp Input Modes & Parameters Input signal modes Two signals with the same phase, amplitude, and frequency are applied to the inputs The output is the difference between inputs The output = 0 V This action is referred to as common-mode rejection When an unwanted signal appears at both inputs, It is important to suppress (cancel) this signal Common-mode signals are usually kinds of noise 10
Op-amp Input Modes & Parameters Input signal modes Common mode (rejection ratio) Desired signals appear at the inputs with opposite polarities Therefore, they are amplified and appear at the output Undesired signal appears at both inputs with the same polarity Therefore, it is cancelled out (blocked) and does not appear at the output Common-mode rejection ratio (CMRR) The measure of an amplifier s ability to reject undesired signals Ideally, CMRR = infinity. However, practically it is given by CMRR = A A ol cm A ol : Open-loop differential voltage gain,» The gain when there is no external components> The value depends on the internal design A cm : common-mode gain 11
Op-amp Input Modes & Parameters contd. Maximum output voltage swing (V O(p-p) ) Without input, the output is the quiescent output voltage = 0 When an input is applied Ideally, the peak-to-peak voltage is ±V CC However, practically the peak-to-peak value is less than the ideal values The value directly yproportional p to the value of the load resistance Example I: Fairchild KS741 datasheet shows that V O(p-p) = ±13 V for V CC = ±15 and R L = 2 kω Example II: Fairchild KS741 datasheet shows that V O(p-p) = ±14 V for V CC = ±15 and R L = 10 kω 12
Op-amp Input Modes & Parameters contd. Input offset voltage Ideally, the op-amp produces zero output for a zero input voltages However, practically a non-zero input should be applied to obtain a zero output This is due to the mismatch of the base-emitter voltages of the differential amplifier In datasheets, this offset is given as V OS which is in the range of 2 mv or less Input bias current It is the input dc current required to operate the first stage (differential amplifier) These currents are connected to the bases of the two transistors. differential amplifier 13
Op-amp Input Modes & Parameters contd. Input Impedance Differential input impedance The total resistance between the inverting and the non-inverting inputs It is measured by measuring the change in the bias current for a given change in the differential input voltage Common-mode input impedance The resistance between each input and the ground It is measured by determining the change in the bias current for a given change in the common-mode input voltage 14
Op-amp Input Modes & Parameters contd. Input offset current Ideally, the two input bias currents are equal so the offset is equal to zero In practice, the input offset current is given by I = I I OS 1 2 The offset voltage developed due to the input offset current V = I R I R = ( I I ) R = I R OS 2 in 1 in 1 2 in OS in This error at the input is amplified by the voltage gain, so that the output error becomes V = A V = A I R OUT(error) v OS v OS in 15
Op-amp Input Modes & Parameters contd. Output impedance The resistance seen from the output of the op-amp 16
Op-amp Input Modes & Parameters contd. Slew rate The maximum rate of change of the output voltage in response to a step input voltage It depends on the high-frequency response of the amplifier (why?) The slew rate is then given by (in V/μs) Slew rate = ΔV Δt t out 17
Negative Feedback Negative feedback A portion of the output is fed back out of phase with the input to stabilize the op-amp Advantages of the negative feedback configuration Precise values of voltage gain can be set up V V A ol OUT = IN = (1 mv)(100,000) = 100V This is never possible Both input and output impendences and bandwidth can be controlled 18
Negative Feedback contd. Op-amp with feedback vs. without feedback Voltage gain Input Z Output Z BW Without negative feedback A ol is too high Relatively high Relatively low Relatively narrow (small BW) With negative feedback A cl is set to desired value by feedback circuit Can be increased or reduced to a desired value Can be reduced to a desired value Significantly wider 19
Op-amps with Negative Feedback Closed-loop voltage gain contd. Noninverting amplifier The input is applied to the noninverting (+) input of the op-amp A part of the output is fed back to the input and applied to the inverting (-) input The fed back voltage is given by R V i f = Vout = BV out Ri + Rf The output-input relation is given by ol V = A V V out ol in f ( in out ) = Aol V BV = A V A BV in Therefore, the non-inverting closed loop gain A out v(ni) Vin 1 ol out V A = = ol + A B ol 1 R + R f i, for Aol B 1 B = R >> i 20
Op-amps with Negative Feedback Closed-loop voltage gain contd. Noninverting amplifier contd. Example 12-3 Find the closed-loop loop gain of the noninverting amplifier A v(ni) Rf = 1+ = 1+ 100 = 22.3 R 4.7 i 21
Voltage-follower Op-amps with Negative Feedback Closed-loop voltage gain contd. The input is applied to the noninverting input (+) The output is fully fed back to the inverting input (-) Voltage gain A ( V V ) = V A ol in out out V A = out ol 1 V = A + 1 = 1 v(vf) in ol Characteristics High input impedance and low output impedance It is thus suitable for interfacing high impedance sources and low loads Therefore, VF op-amp does not affect neither the source impedance nor the load resistance 22
Op-amps with Negative Feedback Closed-loop voltage gain contd. Inverting amplifier The input is applied to the inverting (-) input of the op-amp through the resistance R i The output is fed back to the input and applied to the inverting (-) input through the resistance R f The noninverting input is grounded Note that ideally, The input impedance is infinite Therefore, the input current = 0 and both inputs are at the ground level The inverting input is considered as a virtual ground 23
Inverting amplifier contd. From Figure (b), Op-amps with Negative Feedback Closed-loop voltage gain contd. I f = I V out = R f Therefore, the closed-loop gain of the inverting amplifier is A cl(i) in V R in i Rf = R i Note that the closed-loop gain of the inverting amplifier gain is independent of the open-loop pgain 24
Op-amps with Negative Feedback Closed-loop voltage gain contd. Inverting amplifier contd. Example 12.4: Find R f so that the closed-loop gain = -100 Therefore A cl(i) Rf = R i R = A (100)(2.2 k ) 220 k ( ) R i = Ω = Ω f cl I 25
Effects of the NF on the Op-amp Impendences Impedances of the noninverting amplifier Input impedance NF: Negative feedback Since the input impedance is not infinite There is a small voltage difference between the two inputs such that V = V + V = V + BV in d f d Since V out = A ol V d, and V d = I in Z in, it turns out that Therefore, the overall input impedance is given by out V = V + BA V = (1 + A B) I Z Z in d ol d ol in in in V (NI) = in = (1 + Aol B) Z I in in 26
Effects of the NF on the Op-amp Impendences Impedances of the noninverting amplifier contd. Output impedance From the Figure V = A V Z I Since V out = I out Z out(ni), out ol d out out A ( Vin V ), for A V >> Z ol f ol d out I = A V BA V ol in ol out out A V ol in = (1 + A ol B) V out = (1 + A B) I out Z ol out(ni) Also, without feedback, A ol V in = V out. This means that Therefore, Z V = = (1 + A B) Z out out I ol out(ni) out Z Z = + A B out(ni) 1 out ol 27
Effects of the NF on the Op-amp Impendences Impedances of the Voltage-follower amplifier contd. Voltage follower amplifier, It is a special case of the noninverting amplifier with B = 1 Noninverting amplifier Voltage follower amplifier Z in = (1 + A B) Z (NI) ol in Z = (1 + A ) Z in(ni) ol in Z Z Z = Z = + A B out(ni) 1 out + A out(ni) 1 out ol ol 28
Effects of the NF on the Op-amp Impendences Impedances of the inverting amplifier contd. Input impedance Since the inverting input is at virtual ground, the source only sees R i as input resistance, therefore Z R in(i) i As with the noninverting amplifier, the output impedance is given by Z Z = + A B out(i) 1 out ol 29
Inverting amplifier Ideally, when V in = 0 Bias Current and Offset Voltage Effect of input bias current The inverting input has a zero voltage and there is no feedback current (I 1 = 0) However, practically, The internal transistors of the op-amp must be biased Therefore, the bias current coming from the output does not equal zero (I 1 0) As a consequence, there will be an output voltage error of I 1 R f 30
Voltage-follower amplifier Ideally, when V in = 0 Bias Current and Offset Voltage Effect of input bias current contd. The noninverting input has a zero voltage and there is no bias current (I 1 = 0) However, practically, The internal transistors of the op-amp must be biased Therefore, the bias current leads to a drop on the source resistance, R s, (I 1 0) As a consequence, there is an output voltage error of -I 1 R s 31
Noninverting amplifier Ideally, when V in = 0 Bias Current and Offset Voltage Effect of input bias current contd. The noninverting input has a zero voltage and there is no bias current (I 1 = 0). Therefore, the voltage at the inverting terminal is also zero. However,,practically, The internal transistors of the op-amp must be biased Therefore, the bias current leads to a drop on the R f, (I 1 0) As a consequence, there is an output voltage error of I 1 R f 32
Bias Current and Offset Voltage Bias current compensation in a VF op-amp Compensation method Adding a feedback resistance, equal to the source resistance R f is selected such that I 1 = I 2 and therefore the output voltage = 0 Even if I 2 does not equal I 1, the error is reduced to VF: Voltage Follower V = I I R = I R OUT(error) 1 2 s OS s 33
Bias Current and Offset Voltage Bias current compensation in other op-amp configurations Compensation method Adding a resistance R c in the circuit. R = R R c i f 34
Open-loop Response Review of op-amp gains The open-loop gain is set by the internal design However, the closed-loop gain is specified by the external resistances 35
Bandwidth limitations Open-loop Response contd. The op-amp does not have a lower critical frequency. Therefore, the upper critical frequency is referred to as f c. q y f c Therefore, the op-amp is a dc amplifier 36
Open-loop Response contd. The compensated op-amp representation Due to the concatenation of the pure gain (A ol(mid) ) and the RC circuit, The overall gain is the product of the gains of the two circuits RC circuit analysis V X = = out C Vin R2 + X 2 2 C R 1 + X C 1 f f c 1 X = = (2 π RC) f R C V out = 1 Vin 1 + ( f / f ) 2 c A ol = A ol( mid) 1 + ( f / f ) 2 c 37
Example 12-8 Open-loop Response contd. Determine A ol for the following values of f. Assume f c(ol) = 100 Hz and A ol(mid) = 100,000. Find the open-loop pgain at the following frequencies. 0 Hz 10 Hz 100 Hz 1000 Hz A A A ol ol ol A = = 100,000 = 100,000 1 + / 1+ 0 ol( mid ) f 2 f 2 c A = = 100,000 = 99,503 1 + / 1 + (0.1) ol( mid) f 2 f 2 c 2 A = = 100,000 = 70,710 1 + / 1 + (1) ol( mid) f 2 f 2 c 2 A ol A = = 100,000 = 9950 1 + / 1 + (10) ol( mid) f 2 f 2 c 2 38
Phase Shift Open-loop Response contd. θ = tan 1 R = tan 1 XC f c f 39
Open-loop Response contd. Overall frequency response (example 12-10) N θ tan 1 tot f / f = ci i = 1 40
Closed-loop Response contd. Negative feedback affects the midrange gain A 1 cl(ni) + Rf A R cl (I) i Rf = 1 R A cl (VF) = i Effect of negative feedback on bandwidth f = f (1 + B A ) c( cl) c( ol) ol( mid) BW = BW (1 + B A ) ccl ( ) col ( ) olmid ( ) Gain bandwidth product A f = A f cl c ( cl ) ol c ( ol ) 41
Example 12-12 Closed-loop Response contd. Find the BW of each of the amplifiers in the Figure. Both op-amps have an open-loop gain of 100 db and a unity gain bandwidth of 3 MHz. R f A = 1 + f = 67.77 A 47 cl cl = = R R i R f i ft 3M f f = BW = = = 44.3kHz T 3M ccl ( ) cl f 7 = BW = = = 63.8kHz A 67.7 ccl ( ) cl A 47 cl cl 42
Keywords and terms Op-amp Inverting amplifier Noninverting amplifier Voltage-follower amplifier Closed-loop gain of an op-amp Open-loop gain of an op-amp Effect of negative feedback on gain Effect of negative feedback on BW Keywords Effect of negative feedback on input/output impedances Unity-gain frequency Effect of the bias current on output voltage error Differential mode of operation Common mode of operation 43
Lecture Summary Op-amp operation modes and parameters Op-amp circuits with a negative feedback Effects of the negative feedback on the op-amp impedances Open-loop frequency response of an op-amp Closed-loop frequency response of an op-amp p 44