2Goals Understand behavior and characteristics of ideal op amps. Demonstrate circuit analysis techniques for ideal op amps.Characterize inverting, non-inverting, summing and difference amplifiers, voltage follower and integrator.Learns factors involved in circuit design using op amps.2
3Ideal Operation Amplifier (Op Amp) Ideal op amps are assumed to haveinfinite voltage gain, andinfinite input resistance.These conditions lead to two assumptions useful in analyzing ideal op amp circuits:1. The voltage difference across the input terminals is zero.2. The input currents are zero.
4Ideal Op Amp Example Writing a loop equation: From assumption 2, we know that i- = 0.Assumption 1 requires v- = v+ = 0.Combining these equations yields:Assumption 1 requiring v- = v+ = 0 creates what is known as a virtual ground.
5Ideal Op Amp Example (Alternative Approach) Writing a loop equation:From assumption 2, we know that i- = 0.Assumption 1 requires v- = v+ = 0.Combining these equations yields:Design Note: The virtual ground is not an actual ground. Do not short the inverting input to ground to simplify analysis.
6Operational Amplifier Complete Model Represented by:A= open-circuit voltage gainvid = (v+-v-) = differential input signal voltageRid = amplifier input resistanceRo = amplifier output resistanceSignal developed at amplifier output is in phase with the voltage applied at + input (non-inverting) terminal and 1800 out of phase with that applied at - input (inverting) terminal.3
7Operational Amplifier Mathematical Model: With Source and Load RL = load resistanceRS = Thevenin equivalent resistance of signal sourcevs = Thevenin equivalent voltage of signal sourceandOp amp circuits are mostly dc-coupled amplifiers. Signals vo and vs may have a dc component representing a dc shift of the input away from Q-point.Op-amp amplifies both dc and ac components.4
8Ideal Operational Amplifier Ideal op amp is a special case of ideal differential amplifier with infinite gain, infinite Rid and zero Ro .andIf A is infinite, vid is zero for any finite output voltage.Vid = 0, v+=v- (Virtual Short Model)Infinite input resistance Rid forces input currents i+ and i- to be zero.Summary, Ideal op amp has following assumptions:A=∞ , Where A is Open-loop gaini- = i+ = 0, Input resistance is infiniteZero output resistanceInfinite bandwidth+VSi-V--VoVid = V+ - V-AV++i+-VS8
9Inverting Amplifier: Configuration Positive input is grounded.Feedback network, resistors R1 and R2 connected between inverting input and signal source and amplifier output node respectively.9
10Inverting Amplifier:Voltage Gain Negative voltage gain implies 1800 phase shift between dc/sinusoidal input and output signals.Gain greater than 1 if R2 > R1Gain less than 1 if R1 > R2Inverting input of op amp is at ground potential (not connected directly to ground) and is said to be at virtual ground.But is=i2 and v-=0 (since vid=v+-v-=0)and10
12Non-inverting Amplifier: Configuration Input signal is applied to the non-inverting input terminal.Portion of the output signal is fed back to the negative input terminal.Analysis is done by relating voltage at v1 to input voltage vs and output voltage vo .12
13Non-inverting Amplifier:Voltage Gain, Input Resistance and Output Resistance Since i-=0 andBut vid =0Since i+=0Rout is found by applying a test current source to amplifier output and setting vs = 0 and is identical to the output resistance of inverting amplifier i.e. Rout =013
14Unity-gain BufferA special case of non-inverting amplifier, also called voltage follower with infinite R1 and zero R2. Hence Av =1.Provides excellent impedance-level transformation while maintaining signal voltage level.Ideal voltage buffer does not require any input current and can drive any desired load resistance without loss of signal voltage.Unity-gain buffer is used in may sensor and data acquisition systems.14
15Summing Amplifier Since i-=0, i3= i1 + i2, Scale factors for the 2 inputs can be independently adjusted by proper choice of R2 and R1.Any number of inputs can be connected to summing junction through extra resistors.This is an example of a simple digital-to-analog converter.Since negative amplifier input is at virtual ground,15
16Difference Amplifier Assume an ideal op-amp vi2 = 0v+ = 0 = v-, vo(1) = -R2.vi1 (inverting amplifier)R1Vi1 = 0V+ = R4. vi2, vo(2) = (1+ R2/R1) . R4.vi2R3 + R R3+R4non-inverting amplifiervo = vo(1) + vo(2)= (1+ R2). R4 vi R2.Vi1R1 R3 + R R1Assume an ideal op-ampUse the superposition theory
17Difference Amplifiers In order to provide equal gain for both inputsvo = -R2/R1 (v1 – v2)(1 + R2 ) . R = R2R1 R3 + R R1R4/R3 = R2/R Balance Condition
18Difference Amplifier For R2= R1 Also called a differential subtractor, amplifies difference between input signals.Rin2 is series combination of R1 and R2 because i+ is zero.For v2=0, Rin1= R1, as the circuit reduces to an inverting amplifier.For general case, i1 is a function of both v1 and v2.18
19Operational Amplifier Complete Model Represented by:A= open-circuit voltage gainvid = (v+-v-) = differential input signal voltageRid = amplifier input resistanceRo = amplifier output resistance3
20Non-ideal Operational Amplifier Various error terms arise in practical operational amplifiers due to non-ideal behavior.Some of the non-ideal characteristics include:√ Finite open-loop gain that causes gain errorNonzero output resistanceFinite input resistanceFinite CMRRCommon-mode input resistance√ DC error sources√ Output voltage and current limits20
21Finite Open-loop Gain vo = A (v+ - v-) = A.vin |v+ - v- | > 0 V- +VSV--VVin = V+ - V-oSV-V+i+V+-AV+in-VSvo = A (v+ - v-) = A.vin|v+ - v- | > 0Example 1, Inverting Amplifier21