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Lecture 3 Operational AmplifiersNon-ideal behavior 1

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Goals Study non-ideal op amp behavior. Demonstrate circuit analysis techniques for non-ideal op amps. Understand frequency response limitations of op amp circuits. 2

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v i2 = 0 v + = 0 = v -, v o(1) = -R 2.v i1 (inverting amplifier) R 1 V i1 = 0 V + = R 4. v i2, v o(2) = (1+ R 2 /R 1 ). R 4.v i2 R 3 + R 4 R 3 +R 4 non-inverting amplifier v o = v o(1) + v o(2) = (1+ R 2 ). R 4 v i2 - R 2.V i1 R 1 R 3 + R 4 R 1 Difference Amplifier Assume an ideal op-amp Use the superposition theory

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Difference Amplifiers In order to provide equal gain for both inputs v o = -R 2 /R 1 (v 1 – v 2 ) (1 + R 2 ). R 4 = R 2 R 1 R 3 + R 4 R 1 R 4 /R 3 = R 2 /R 1 Balance Condition

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Difference Amplifier Also called a differential subtractor, amplifies difference between input signals. R in2 is series combination of R 1 and R 2 because i + is zero. For v 2 =0, R in1 = R 1, as the circuit reduces to an inverting amplifier. For general case, i 1 is a function of both v 1 and v 2. For R 2 = R 1 5

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Difference Amplifier v icm, and v id are another representation for the inputs v o = A d v id + A cm v icm Differential gain Common-mode gain For the ideal case, v o = -R 2 /R 1 (v 1 – v 2 ) = (-R 2 /R 1 ).v id + 0 A d = -R 2 /R 1, and A cm = 0 If balance condition is not satisfied, (R 4 /R 3 R 2 /R 1 ) Then A cm 0 v id = v 1 – v 2 differential input voltage v icm = (v 1 + v 2 )/2 Common-mode input voltage Define

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Difference Amplifier FOM

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Integrator Feedback resistor R 2 in the inverting amplifier is replaced by capacitor C. The circuit uses frequency-dependent feedback. Since i c = i s Voltage at the circuits output at time t is given by the initial capacitor voltage integral of the input signal from start of integration interval, here, t=0. Integration of an input step signal results in a ramp at the output. 8

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Differentiator Input resistor R 1 in the inverting amplifier is replaced by capacitor C. Derivative operation emphasizes high- frequency components of input signal, hence is less often used than the integrator. Since i R = i s Output is scaled version of derivative of input voltage. 9

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Operational Amplifier Complete Model Represented by: A= open-circuit voltage gain v id = (v + -v - ) = differential input signal voltage R id = amplifier input resistance R o = amplifier output resistance 3

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Non-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 error –Nonzero output resistance –Finite input resistance –Finite CMRR –Common-mode input resistance – DC error sources – Output voltage and current limits 11

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V o +VS -VS AV in V+V+ V-V- V in = V + - V - v o = A (v + - v - ) = A.v in |v + - v - | > 0 Finite Open-loop Gain Example 1, Inverting Amplifier S S V-V- V+V+ i i 12

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DC Error Sources: Input-Offset Voltage v o =A(v + -v - ), if v + = v - Then v o = 0 (Ideal case) For real op-amp an input dc offset exists that can saturates the output. We can bring the output back to zero by applying an external voltage equal in magnitude but opposite in direction to the offset voltage 14

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Finding the error in the output voltage produced by the offset (v os ) Consider only the offset voltage. i.e set any input signal to zero V oe = output error due to v os If an input signal is connected to R1 Total output = Desired output error FOR LF351, v os = 5mV (typical) 15

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DC Error Sources: Input-Offset Voltage (Example) Problem: Find quiescent dc voltage at output. Given data: R 1 =1.2 k, R 2 = 99 k Assumptions: Ideal op amp except for nonzero offset voltage. Output voltage is given by Actual sign of V OS is unknown as only upper bound is given. Note: Offset voltage of most IC op amps can be manually adjusted by adding a potentiometer as shown. 16

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Bias currents I B1 and I B2 ( base currents in BJTs or gate currents in MOSFETs or JFETs) are similar in value with directions depending on internal amplifier circuit type + - IBIB IBIB I os /2 I B2 I B1 Ideal -opamp Equivalent circuit model Sign of offset current is unknown as only upper bound is given. DC Error Sources: Input-Bias and Offset Currents 17

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DC Error Sources: Input-Bias and Offset Currents In inverting amplifier shown, I B1 shorted out by ground connection. Since,inverting input is at virtual ground, amplifier output is forced to supply I B2 through R Set v in =0, v - = v + = 0 (virtual gnd) i 1 =0, i 2 =I B2 i1i1 i2i2 This poses a limitation on the value of R 2

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Numerical Example 19

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DC Error Sources: Input-Bias and Offset Currents - Bias Current Compensation Bias current compensation resistor R B is used in series with non-inverting input. Output due to I B1 alone is By superposition, if. Since, offset current is typically 5.10 times smaller than individual bias currents, dc output voltage error can be reduced by using bias compensation. 20

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DC Error Sources: Input-Bias and Offset Currents - Errors in Integrator At t<0, reset switch is closed, circuit becomes a voltage- follower, At t=0, reset switch is opened, circuit starts integrating its own offset voltage and bias current. Using superposition analysis, Output becomes ramp with slope determined by V OS and I B2 and saturates at one of the power supplies. 21

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