ECEN 325 Electronics


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1 ECEN 325 Electronics Operational Amplifiers Dr. Aydın İlker Karşılayan Texas A&M University Department of Electrical and Computer Engineering
2 Opamp Terminals positive supply inverting input terminal non inverting input terminal output terminal negative supply V V CC SS ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 1
3 Equivalent Circuit inverting input terminal v n i=0 non inverting input terminal v p i=0 A( ) v p v n output terminal ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 2
4 vs. v d V SAT Slope = A v d = v p v n V SAT ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 3
5 Inverting Configuration i 2 Z 2 i 1 Z 1 vo = 1 + Z 2 Z Z 2 A Z 1 A = Z 2 Z 1 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 4
6 Inverting Amplifier i 2 R 2 i 1 R L = R 2 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 5
7 Inverting Integrator i C C i R R = 1 src ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 6
8 Inverting Lossy Integrator i C C i 2 R 2 i 1 vo R 2 = sr 2 C + 1 = K s + 1 ω o, ω o = 1 R 2 C, K = R 2 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 7
9 Inverting Differentiator i R R i C C = src ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 8
10 Inverting Summer v 1 i 1 i f R f i 2 R 2 v 2 i n R n v n = R f v 1 + R f R 2 v R f R n v n ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 9
11 NonInverting Configuration i 2 Z 2 Z 1 i 1 vo = 1 + Z 2 Z Z 2 Z A A = 1 + Z 2 Z 1 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 10
12 NonInverting Amplifier R 2 i 2 i 1 R L = 1 + R 2 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 11
13 UnityGain Buffer v s = v s ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 12
14 Difference Amplifier i 2 R 2 v 1 v 2 i 1 i 3 R 3 i 4 R 4 = 1 + R R 3 R 4 v 2 R 2 v 1 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 13
15 Example i 2 R 2 R 4 i 4 i 3 R 3 i 1 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 14
16 Frequency Dependence Openloop gain 20 log A o (db) 20 db/dec 0 db ω b ωt ω log scale A(s) = A o 1 + s ω b A(jω) = A o 1 + jω ω b ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 15
17 GainBandwidth Product ω ω b A(jω) A o jω ω b A(jω) ω=ωt = 1 ω t = A o ω b A o ω b : GainBandwidth (GBW) Product ω t : Unitygain frequency ω b : Bandwidth A o : DC gain ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 16
18 ClosedLoop Gain Inverting amplifier R 2 A = 1 + R R 2 A(s) A(s) = A o 1 + s ω b ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 17
19 ClosedLoop Gain Inverting amplifier Substitute A(s) into /, = 1 + R s A o ω b 1 + R 2 = R 2 A o R 2 }{{} 1 +s 1 + R 2 ω b A o 0 if A o 1 + R 2 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 18
20 ClosedLoop Gain Inverting amplifier R s A o ω b 1 + R 2 = R s ω o ω o = A oω b 1 + R 2 = ω t 1 + R R 2 ω o = ω t (GBW product or unitygain freq) ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 19
21 ClosedLoop Gain Noninverting amplifier R 2 A = 1 + R R 2 R A(s) A(s) = A o 1 + s ω b ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 20
22 ClosedLoop Gain Noninverting amplifier Substitute A(s) into /, = R s A o ω b 1 + R 2 = R 2 A o 1 + R 2 }{{} 1 +s 1 + R 2 ω b A o 0 if A o 1 + R 2 ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 21
23 ClosedLoop Gain Noninverting amplifier R 2 s A o ω b 1 + R 2 = 1 + R s ω o = G o 1 + s ω o ω o = A oω b 1 + R 2 = ω t 1 + R R 2 ω o = ω t (GBW product or unitygain freq) ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 22
24 Open & Closed Loop Gain 20 log A o (db) 20 log G o (db) 20 db/dec 0 db ω b ω o ωt ω log scale ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 23
25 Slew Rate Slew rate: Maximum rate of change possible at the output of an opamp Find the timedomain output voltage, v O (t) Find the maximum value of rate of change at the output dv O dt max To avoid distortion due to slewrate limitation, the following should be satisfied dv O dt max SR where SR is the slew rate usually specified in the opamp data sheet in units of V/µs. ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 24
26 Slew Rate Example 1 In an amplifier circuit, the opamp has the following slew rate and output voltage: SR = 100 V/µs v O (t) = A sin(ωt) Then dv O dt = Aω cos(ωt) dv O dt max = Aω cos(ωt) max = Aω To avoid distortion due to slewrate limitation, the following should be satistifed Aω 100 V/µs ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 25
27 Slew Rate Example 2 In an amplifier circuit, / is given as (s) = G o 1 + s ω o where v I (t) = A i sin(ω i t) and is the output of the opamp. To avoid distortion, v O (t) = dv O dt max 1 + G o ω i ω o = G oω i A i A i sin(ω i t) ω i ω o 2 SR ECEN 325 Electronics  Aydın İ. Karşılayan  Operational Amplifiers 26
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