The op amp as an amplifier

For the op amp to work as a amplifier the difference between the two input voltages V₂ and V₁ must be less than 150 mV. (More generally it must be less than V_S/A_o.) This is achieved in different ways by the non-inverting and the inverting voltage amplifiers.

The non-inverting voltage amplifier

In this circuit, shown in Figure 1, the input voltage is applied to the non-inverting input (Q), This gives an output voltage that is in phase with the input voltage.

A certain fraction (β) of this output is then fed back to the inverting input. This gives negative feedback and the feedback fraction is given by the equation:

Feedback fraction (β) = R₂ /[R₁ + R₂]





However for negative feedback we have V_o = A_o(v_i - βV_o) but since the closed loop gain (A) is V_o/v_i we can write A = A_o(1 + βA_o).
However since usually βA_o » 1 this gives A is approximately 1/b.
Therefore for the non- inverting amplifier:

Closed loop gain (A) = V_o/Vi = 1/β = 1 + R₁/R₂

This is dependent only on the external resistors R₁ and R₂.

Example problems

Calculate the closed loop voltage gain of a non-inverting voltage amplifier with R₁ = 3 kΩ and R₂ = 1 kΩ.

Closed loop gain (A) = 1 + 3/1 = 4.