Topic 6 The Non

Topic 6 The Non-Inverting Amplifier

At the end of this topic you should be able to:

Draw and recognise the non-inverting amplifier circuit.
Use the formula gain = 1 + (Rf/Ra).
Know that the input resistance is equal to that of the op-amp.
Draw and recognise a voltage follower based on the non-inverting op-amp.
Show that the follower has a gain of 1.
Describe and explain the use of a voltage follower.
Describe the effects of positive and negative feedback in op-amps.

In this circuit the input voltage is applied to the non-inverting input.

Notice that:

This amplifier uses negative feedback to the inverting input.
There is no difference in the voltage between the inverting and non-inverting inputs, so we can say that the voltage at the non-inverting and the inverting input is the same. So we can say that the voltage at P is V_in.
Since no current is drawn by the inverting input, the current in R_a is the same as the current in R_f. So we can treat the two resistors as a potential divider and apply the potential divider equation.

We can therefore write:

V_in = V_out (__R_a___)

R_f + R_a

Rearranging gives:

V_out = R_f + R_a

V_in R_a

The term Vout/Vin is the gain. The term R_f + R_a can be rewritten R_f+ R_a

R_a R_a R_a

Therefore:

V_out = 1 + R_f

V_in R_a

If we look at the input, we see that there is no feedback resistor in the input, therefore we can say that the input resistance is that of the op-amp. The input resistance is very high indeed, and very little current is taken.

Question 1 Why can we say that the voltage at P is Vin? ANSWER

The problem with the inverting amplifier used as a voltage follower is that the output is at 180^o out of phase with the input. A voltage follower can be based on the non inverting circuit with 100 % negative feedback to the inverting input, and input resistance is very high indeed.

The voltage gain of the op-amp in this configuration is about 1. This because of the feedback factor (the fraction fed back), given the code b (beta, a Greek letter ‘b’) is 1.

We can show this by considering the open loop gain Ao. The actual gain A is given by

A = ___Ao___

1 + bAo

If b is 1, and Ao is very large, we can say that A is approximately 1.

The main use of the voltage follower is as a buffer amplifier, which matches a high input impedance with a low input load. You would come across such a circuit in the input stage of a digital multimeter, which has a very high input impedance, allowing the voltage read to be the same as the voltage that should be there.

Question 2. What is the gain of a non-inverting amplifier with a feedback resistor of 10000 ohms and Ra value of 100 ohms? ANSWER

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