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Review of Linear Op-Amp Circuits We will quickly review the analysis & design of linear op-amp circuits that use negative feedback: Non-inverting amplifier Inverting amplifier Summing amplifier Integrator Difference amplifier

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Negative Feedback Recap Negative feedback minimises the error signal. If the amplifier gain is very high: the error signal will reduce to zero the output will equal the input

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Adding a Feedback Network Negative feedback still minimises the error signal. If the amplifier gain is very high: the error signal will reduce to zero the output will equal the input times K - + Summing Node Amplifier K Input Error = 0 Output

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Non-inverting Amplifier Remember the rules for negative feedback:

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Example To design a non-inverting amplifier with a voltage gain of +10:

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Inverting Amplifier Use the same rules:

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Input Impedance Unlike the non-inverting amplifier, the input current is non-zero therefore the input impedance is finite:

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Example To design an inverting amplifier with a voltage gain of –10 and an input impedance of 1 k :

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Summing Amplifier Apply Kirchoff’s current law to the V - node: Like the inverting amp, V - = 0

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Input Impedances Input impedance seen by: Input 1 = R 1 Input 2 = R 2 Input N = R N

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Non-Inverting Summing Amplifier

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But… Input current depends on the level of all the other inputs. The effective input impedance is not constant. This can be undesirable. Inverting configuration is usually preferred.

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Integrator Like the inverting amp:

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Difference Amplifier Using superposition: First, set V 1 = 0

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Now set V 2 = 0 Combining the results for arbitrary V 1 and V 2 : So,

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Uses of Linear Op-Amp Circuits Amplifiers Making signals bigger! Summing Amp Mixing (e.g. audio applications) Analogue arithmetic Integrator Analogue computing Active filter design Difference Amp Balanced line receivers

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Ideal Op-Amp Linear Circuit Analysis When negative feedback is applied, the use of these assumptions makes design/analysis much easier (although not necessarily simple!). Of course, they aren’t really true… …more about practical op-amps next time

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