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# Operational amplifiers (opamps)

Extracts from this document...

Introduction

1. Introduction:

Operational amplifiers (opamps) are usually used in two different modes, mainly the positive feedback mode and the negative feedback mode. These two modes have very different effects on the input-output relationship of  opamps. This report will be looking at the effects of negative feedback on inverting and non-inverting operational amplifiers, the extent of proportionality of the input-output relationship of an opamp with negative feedback, and the Schmitt trigger and oscillator to illustrate the non-linear input-output relationships of opamps.

2. Theory:

An ideal op-amp draws no current and the output voltage is only dependent on the difference between the two input voltages. The output voltage is determined by: VOUT = A(V+ - V-),  where A is open loop voltage gain. The open loop voltage gain is defined as the gain of the opamp when the output terminal is not connected to any of the input terminals. For the ideal case, the difference of voltage between the two input terminals is zero, and the gain of the opamp is infinite.

An opamp has negative feedback when the output of the opamp is connected to back to the negative input, usually through some intermediary components. A basic opamp with negative feedback is shown below in figure1:

Middle

Graph 2: The output voltage (VOUT) plotted against the input voltage (VIN) for an inverting amplifier with negative feedback and a gain of  -10. As can be seen, the linearity of an opamp with negative feedback is limited to the region where the output voltage is between the supply voltages (in this case, +15V and -15V).

The output voltage was measured from the oscilloscope to be -15V. This was because the input was 0V and the gain of the opamp had to be infinite because of the negative feedback. However, the circuit also had to satisfy the constraint that the magnitude of the maximum and minimum allowable voltages were +15V and -15V respectively. Since this was an inverting opamp, the output was driven to -15V.

3.2 Negative feedback in a non-inverting amplifier:

Similar to an inverting amplifier, the output of a non-inverting amplifier with negative feedback can also be shown to be proportional to its input. A basic non-inverting amplifier is as shown below in  figure 4:

Figure 4: A non-inverting opamp with negative feedback.

For the opamp above, VOUT = (1+RF/R)VIN , where VIN and VOUTare the input and output voltages of the opamp respectively.

Conclusion

Appendix 2:

Derivation of formulae for the output voltage of an inverting opamp with negative feedback:

Figure 9: An inverting opamp with negative feedback

Using  figure 9, the current going into the negative terminal’s input will be zero. The voltage at the negative input terminal will be zero as it will tend to follow the positive terminal’s input voltage for an ideal opamp. Applying Kirchoff’s Current Law at the negative input terminal will give us:

-VIN / R + (-VOUT / RF) = 0

=>                     VOUT =-(RF / R)VIN

Derivation of formulae for the output voltage of a non-inverting opamp with negative feedback:

Figure 10: An inverting opamp with negative feedback

Using figure 10 the current going into the negative terminal’s input will be zero. The voltage at the negative input terminal will be equal to VINas it will tend to keep the differential input voltage to zero. Applying Kirchoff’s Current Law at the negative input terminal will give us:

VIN /R + (VIN- VOUT) / RF = 0

=>                            VOUT = (1+RF/R)

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