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Electronic Instrumentation Experiment 8 * Op Amp Circuits Review * Voltage Followers and Adders * Differentiators and Integrators * Analog Computers

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Op Amp Circuits Review w Inverting Amplifier w Non-inverting Amplifier w Differential Amplifier w Op Amp Analysis

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Inverting Amplifier

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Non Inverting Amplifier

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Differential Amplifier

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Op Amp Analysis w Golden Rules of Op Amp Analysis 1) The current at the inputs is 0 2) The voltage at the two inputs is the same w These are theoretical assumptions which allow us to analyze the op-amp circuit to determine what it does. w These rules essentially allow us to remove the op amp from the circuit.

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General Analysis Example(1) w Assume we have the circuit above, where Zf and Zin represent any combination of resistors, capacitors and inductors.

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w We remove the op amp from the circuit and write an equation for each input voltage. w Note that the current through Zin and Zf is the same, because equation 1 is a series circuit. General Analysis Example(2)

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w Since I=V/Z, we can write the following: w But V A = V B = 0, therefore: General Analysis Example(3)

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w For any op amp circuit where the positive input is grounded, as pictured above, the equation for the behavior is given by: General Analysis Conclusion

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Voltage Followers and Adders w What is a voltage follower? w Why is it useful? w Voltage follower limitations w Adders

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What is a voltage follower?

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Why is it useful? w In this voltage divider, we get a different output depending upon the load we put on the circuit. w Why?

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w We can use a voltage follower to convert this real voltage source into an ideal voltage source. w The power now comes from the +/- 15 volts to the op amp and the load will not affect the output.

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Voltage follower limitations w Voltage followers will not work if their voltage or current limits are exceeded. w Voltage followers are also called buffers and voltage regulators.

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Adders

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Weighted Adders w Unlike differential amplifiers, adders are also useful when R 1 <>R 2. w This is called a “Weighted Adder” w A weighted adder allows you to combine several different signals with a different gain on each input. w You can use weighted adders to build audio mixers and digital-to-analog converters.

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Analysis of weighted adder I2 I1 If

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Differentiators and Integrators w Ideal Differentiator w Ideal Integrator w Miller (non-ideal) Integrator w Comparison of Integration and Differentiation

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Ideal Differentiator

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Analysis in time domain

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Problem with ideal differentiator Circuits will always have some kind of input resistance, even if it is just the 50 ohms from the function generator. RealIdeal

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Analysis of real differentiator Low FrequenciesHigh Frequencies ideal differentiatorinverting amplifier

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Comparison of ideal and non-ideal Both differentiate in sloped region. Both curves are idealized, real output is less well behaved. A real differentiator works at frequencies below c =1/R in C in

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Ideal Integrator

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Analysis in time domain

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Problem with ideal integrator (1) No DC offset. Works ok.

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Problem with ideal integrator (2) With DC offset. Saturates immediately. What is the integration of a constant?

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Miller (non-ideal) Integrator w If we add a resistor to the feedback path, we get a device that behaves better, but does not integrate at all frequencies.

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Low FrequenciesHigh Frequencies inverting amplifiersignal disappears w The influence of the capacitor dominates at higher frequencies. Therefore, it acts as an integrator at higher frequencies, where it also tends to attenuate (make less) the signal. Behavior of Miller integrator

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Analysis of Miller integrator Low FrequenciesHigh Frequencies inverting amplifier ideal integrator

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Comparison of ideal and non-ideal Both integrate in sloped region. Both curves are idealized, real output is less well behaved. A real integrator works at frequencies above c =1/R f C f

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Problem solved with Miller integrator With DC offset. Still integrates fine.

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Why use a Miller integrator? w Would the ideal integrator work on a signal with no DC offset? w Is there such a thing as a perfect signal in real life? noise will always be present ideal integrator will integrate the noise w Therefore, we use the Miller integrator for real circuits. Miller integrators work as integrators at > c where c =1/R f C f

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Comparison w The op amp circuit will invert the signal and modify the mathematical amplitude by RC (differentiator) or 1/RC (integrator)

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Analog Computers (circa. 1970) Analog computers use op-amp circuits to do real-time mathematical operations.

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Using an Analog Computer Users would hard wire adders, differentiators, etc. using the internal circuits in the computer to perform whatever task they wanted in real time.

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Analog vs. Digital Computers w In the 60’s and 70’s analog and digital computers competed. w Analog Advantage: real time Disadvantage: hard wired w Digital Advantage: more flexible, could program jobs Disadvantage: slower w Digital wins they got faster they became multi-user they got even more flexible and could do more than just math

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Now analog computers live in museums with old digital computers: Mind Machine Web Museum: Analog Computer Museum:

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