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).

non-inverting op amp
Figure 1. The non-inverting amplifier.

In this case, the input voltage vi 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

Non-Inverting Op Amp Equation

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

Non-Inverting Op Amp Equation

The voltage gain is Av = vo/vi = 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 Rf = 0 (short circuit) or R1 = ∞ (open circuit) or both, the gain becomes 1. Under these conditions (Rf  = 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.

non-inverting op amp
Figure 2. The voltage follower.

Thus, for a voltage follower

Non-Inverting Op Amp Equation

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.

non-inverting op amp
Figure 3. A voltage follower used to isolate two cascaded stages of a circuit

Read also : crossover network

Non-Inverting Op Amp Equation Example

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

Non-Inverting Op Amp Equation
Figure 4


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

METHOD 1: Using superposition, we let

Non-Inverting Op Amp Equation

where vo1 is due to the 6-V voltage source, and vo2 is due to the 4-V input. To get vo1, 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

Non-Inverting Op Amp EquationTo get vo2, we set the 6 -V source equal to zero. The circuit becomes a noninverting amplifier so that Equation.(3) applies

Non-Inverting Op Amp Equation


Non-Inverting Op Amp Equation

METHOD 2: Applying KCL at node a,

Non-Inverting Op Amp Equation

But va = vb = 4, and so

Non-Inverting Op Amp Equationor vo = –1 V, as before.

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