1. 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

2. 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

3. 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

4. Non-inverting Amplifier Remember the rules for negative feedback:

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

6. Inverting Amplifier Use the same rules:

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

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

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

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

11. Non-Inverting Summing Amplifier

12. 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.

13. Integrator Like the inverting amp:

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

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

16. 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

17. 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