# 3. The Non-Inverting Amplifier

*The Non-Inverting Amplifier*

The op-amp can be configured to produce either an inverted or non-inverted output. In the previous section we analyzed the inverting amplifier. We now repeat the analysis for the non-inverting amplifier, as shown in Figure (5).

We analyze this using the basic properties of the ideal op-amp. Since the current through *R _{1}* is zero,

Writing a node equation at the *v _{–}* node yields,

We set *v _{+} = v_{–}*, and substitute for

*v*to obtain,

_{–}The non-inverting gain is then given by,

We analyzed multiple-input inverting op-amps in previous Section (“The Inverting Amplifier”). We now analyze non-inverting op-amps with multiple inputs.

Figure (6) illustrates a circuit with two input voltages. To find *v _{+}*, we apply Kirchhoff’s current law to the non-inverting input terminal to yield (recall that the input current to the op-amp is zero),

Solving then for *v _{+}*, we obtain

The inverting voltage, *v _{–}*, is found from the node equation at

*v*with the result,

_{–}Setting *v _{+}* equal to

*v*, we obtain

_{–}__APPLICATION__

__APPLICATION__Analyze the following circuit using circuit simulation with TINACloud to determine V* _{out}* in terms of the input voltages by clicking the link below.

**1-Two Non-inverting Inputs Circuit Simulation**

In a practical sense, it is important to briefly consider the effects of *loading* on the op-amp. The method we have been using for analysis yields the correct voltage gain, based on the assumption that the current required from the dependent source of the *ideal* op-amp model is within the range set forth by the manufacturer’s data sheet for a *real* op-amp. Although we explore the practical considerations in later chapters, the next two examples illustrate the concept.

When analyzing both the inverting and the non-inverting configurations, we must be certain that the op-amp is capable of supplying sufficient current to drive the load resistor.

__APPLICATIONS__

__APPLICATIONS__Analyze the following circuits using the TINACloud online circuit simulator to determine V* _{out}* in terms of the input voltages by clicking the links below.