VIEWS: 9 PAGES: 51 POSTED ON: 12/14/2011 Public Domain
Amplifiers BASIC AMPLIFIER CONCEPTS Ideally, an amplifier produces an output signal with identical waveshape as the input signal, but with a larger amplitude. vo t Av vi t Inverting Amplifiers Inverting amplifiers have negative voltage gain, and the output waveform is an inverted version of the input waveform. Non-inverting Amplifiers Non-inverting amplifiers have positive voltage gain amplify the input signals. Voltage-Amplifier Model Ri: input resistance Ro: output resistance Avo: Open loop voltage gain ( vo / vi ) Voltage-Amplifier Model Ri: input resistance Ro: output resistance Avo: Open loop voltage gain ( vo / vi ) Ri vi vs Ri RS if Ri , vi vS and ii 0, then power delivered by vS 0. 1. It will ensure vs is not degraded. 2. It enhances the power efficiency as limited power is drawn from the signal source. Voltage-Amplifier Model Ri: input resistance Ro: output resistance Avo: Open loop voltage gain ( vo / vi ) RL vo Avovi RL Ro if Ro 0, vo Avovi it will not reduce the amplified signal. A zero output resistance will maintain the gain. Current Gain io vo RL Ri Ai Av ii vi Ri RL Power Gain Av Ai Av Po Vo I o 2 Ri G Pi Vi I i RL CASCADED AMPLIFIERS Av Av1 Av 2 1500 vi 2 200vi1 150vi1 1500 500 100 vo 2 100vi 2 50vi 2 50 150vi1 100 100 7500vi1 Avo=Avo1*Avo2=200*100=20000 Not agree with the calculation Why? As Ro1≠0, Ro2 ≠0 If Ro1=Ro2=0 1500 vi 2 200vi1 200vi1 1500 100 vo 2 100vi 2 100vi2 100 200vi1 100 20000vi1 Desirable output resistance as small as possible. Operational Amplifier 1. Ideal Op-Amp and its analysis 2. Practical Op-Amp and its limitations 3. Application of Op-Amp IDEAL OPERATIONAL AMPLIFIERS Power Supply Connection of Op-amp Characteristics of Ideal Op Amp Infinite gain for the differential input signal Infinite input impedance Zero output impedance Zero gain for the common-mode input signal Infinite bandwidth OP-Amp Model Ideal OP-Amp •Rin = ∞, so that it will not draw any power from the input signals •Rout = 0 so that it will not degrade the signal due to the output resistance •Avd = ∞ it is to amplify the differential signals •Avcommon = 0 it is to reject any common mode input signals Bandwidth = ∞ so that it can be used for any signal spectrum i1 V- _ i1 i2 i2 + V+ Ideal op-amp rule 1. No current ever flows into either input terminal. i1, i2 = 0 2. There is no voltage difference between the two input terminals v- = v+ We call this Summing Point Constraint Ideal Op-Amp vs v vout v is , iF , iin 0 Rs RF is i F , is i F 0 vs v vout v 0 Rs RF Since, v 0, vout Av o ( v v ) Av o v vout v Av o vs v vout v vs v vout v v As 0, 0, and v out Rs RF Rs Rs RF RF Av o vs v v v out out out 0 Rs Av o Rs RF Av o RF vs v v v v v R ( out out out ), If Av o , s out , vout F vs Rs Av o Rs RF Av o RF Rs RF Rs RF v Avc , Also v out 0 Avc is the closed loop gain Rs Av o Negative Feedback Effect • The effect of the feedback connection from the output to the inverting input is to force the voltage at the inverting input to be equal to that at the non-inverting input. v- = v+ It is called ; • summing point constraint, or • virtual ground concept Illustration of the principle of summing point constraint As i- and i+ are both zero, then, i1 = i2 vin 0 vo vo i1 i2 R1 R2 R2 vo R2 Avc vin R1 INVERTING AMPLIFIERS vo R2 Av vin R1 Practical Design Difficulty Design an inverting amplifier with gain -100, R1 = 50K, then R2 = 5M , too much for real practical resistor v x vo i4 Vx R4 0 v x vx i2 R2 R2 0 vx i3 R3 vx ii 0 R3 vin i1 R1 vx vx v v i2 , i3 , i4 x o R2 R3 R4 i2 i 3 i4 v x v x v x vo vin vx R2 R 3 R4 i1 i2 R1 R2 R2 1 1 1 vo vin R R R R R1 2 4 v x 0 i2 R2 3 4 vo R2 R4 R4 R2 Av 1 vin vin R1 R3 R2 R1 Av = -100, R1 = 50K vo R2 R4 R4 Av 1 vin R1 R3 R2 vo R4 R4 R2 Av 1 vin R1 R3 R1 R2 R4 R4 8, and 10.5 R1 R1 R3 R1 50 K , R2 R4 400 K R3 38.1K NON-INVERTING AMPLIFIER v1 v1 vo At node A, 0 i- R1 R2 Node A vin vin vo As vin v1 , 0 R1 R2 vin R2 R1vin R1vo 0 vi 0, ii 0, i 0 vin ( R2 R1 ) R1vo and vin v1 vo ( R2 R1 ) R2 1 Avc vin R1 R1 NON-INVERTING AMPLIFIER iF iS iin Since ideal op amp, Rin iin 0 v vS v v vout v iS , iF , i F iS RS RF v vout v v v vS S out RS RF RS RF RF vS RS ( vout vS ) RF vS RS vS RS vout vS ( RF RS ) R vout vS (1 F ) RS RS vout RF Avc (1 ) vS RS Summer iF i1 i2 i3 ..iN 0 vS 1 vS 2 vSj vout i1 , i2 ,... i j .., and i F RS1 RS 2 RSj RF vS 1 vS 2 vSj vSN vout .. .. RS1 RS 2 RSj RSN RF RF RF RF RF RF vout vS 1 vS 2 vS 3 ... vSj ... vSN RS 1 RS 2 RS 3 RSj RSN N RF vSi i 1 RS i Voltage Follower vout vS Differential Amplifier v1 v vout v i1 i2 0 R1 R2 v1 v v vout R1 R2 R2 v1 R2 v R1v R1vout R1vout R2 v1 R1v R2 v R2 R2 vout v1 v v R1 R1 R2 v v2 v R2 R2 R2 R2 R1 R2 v1 v2 v2 R1 R1 R2 R1 R1 R2 2 R2 R2 R2 v1 v2 v2 R1 R1 R2 R1 ( R1 R2 ) Common Mode Rejection _ + Vo Vo Acm Vcm + Vcm + - _ Common Mode Voltage Gain An op-amp is a differential amplifier. It is desirable to reject any signal in common to V_ and V+ terminal. In other words, Acm should be as small as possible. The quality of rejecting the common mode signal is defined by CMMR (Common mode rejection ratio) Avo Avo or 20 log10 Acm Acm Common Mode Rejection CMMR f v1= 2 + 3 sin10tV v2= 2V The common component of the two input signal is 2V. It is desirable for the amplifier to amplify the difference of v1 and v2, that is 3 sin10t, and not to amplify the common component 2V. How good the amplifier does to reject the common component is defined by the CMMR. OP-AMP IMPERFECTIONS IN THE LINEAR RANGE OF OPERATION Real op amps have several categories of imperfections compared to ideal op amps. Real op amps have finite input impedance, nonzero output impedance and finite open loop gain Ri ≠ ∞, Avo ≠ ∞, Ro ≠ 0 iin ≠ 0 Bandwidth Bandwidth = fH-fL Idea op-amp, the bandwidth is infinity, so that signal at any frequency can be amplified by the amplifier. Practical op-amp, the bandwidth is limited. That is, the gain is not uniform. The gain at frequency higher than the fBOL is diminished gradually at a -20dB rate of decline. The unit bandwidth product is to define how good is the frequency response of the amplifier, i. e, how wide is it bandwidth. Unity bandwidth product = Avo*fBOL LINEAR WAVEFORM DISTORTION If the gain of an amplifier has a different magnitude for the various frequency components of the input signal, a form of distortion known as amplitude distortion occurs. Due to bandwidth limitation. Phase Distortion If the phase shift of an amplifier is not proportional to frequency, phase distortion occurs. NONLINEAR LIMITATIONS The output voltage of a real op amp is limited to the range between certain limits that depend on the internal design of the op amp. When the output voltage tries to exceed these limits, clipping occurs. Slew-Rate Limitation Another nonlinear limitation of actual op- amp is that the magnitude of the rate of change of the output voltage is limited. dvo SR dt DC IMPERFECTIONS