What is Non-Inverting Op Amp Equation

Like inverting op amp, the non-inverting op amp equation is a must for us. The equation is not that different from the inverting one.

Non-Inverting Op Amp Equation

Another important application of the ideal op amp is the non-inverting amplifier shown in Figure.(1).

In this case, the input voltage v_i is applied directly at the non-inverting input terminal, and resistor R₁ is connected between the ground and the inverting terminal. We are interested in the output voltage and the voltage gain.

Application of KCL at the inverting terminal gives

But v₁ = v₂ = v_i. Equation. (1) becomes

The voltage gain is Av = v_o/v_i = 1 + Rf/R1, which does not have a negative sign. Thus, the output has the same polarity as the input.

A non-inverting amplifier is an op amp circuit designed to provide a positive voltage gain.

Again we notice that the gain depends only on the external resistors.

Notice that if feedback resistor R_f = 0 (short circuit) or R₁ = ∞ (open circuit) or both, the gain becomes 1. Under these conditions (R_f  = 0 and R₁= ∞), the circuit in Figure.(1) becomes that shown in Figure.(2), which is called a voltage follower (or unity gain amplifier) because the output follows the input.

Thus, for a voltage follower

Such a circuit has a very high input impedance and is therefore useful as an intermediate-stage (or buffer) amplifier to isolate one circuit from another, as portrayed in Figure.(3). The voltage follower minimizes interaction between the two stages and eliminates interstage loading.

Read also : crossover network

Non-Inverting Op Amp Equation Example

For the op amp circuit in Figure.(4), calculate the output voltage v_o.

Solution:
We may solve this in two ways: using superposition and using nodal analysis.

■ METHOD 1: Using superposition, we let

where v_o1 is due to the 6-V voltage source, and v_o2 is due to the 4-V input. To get v_o1, we set the 4-V source equal to zero. Under this condition, the circuit becomes an inverter. Hence the Equation.(2) in ‘Inverting Op Amp‘ gives

To get v_o2, we set the 6 -V source equal to zero. The circuit becomes a noninverting amplifier so that Equation.(3) applies

Thus,

■ METHOD 2: Applying KCL at node a,

But v_a = v_b = 4, and so

or v_o = –1 V, as before.