# The Non-inverting Op Amp Stage

**The Non-inverting Op Amp Stage**

The non-inverting op amp stage, also known as a voltage follower with gain, or simply voltage follower.

This op amp stage processes the input V_{IN} by a gain of G, so a generalized expression for gain is:

G =

Feedback network resistances R_{F} and R_{G} set the stage gain of the follower. For an ideal op amp, the gain of this stage is:

G =

For clarity, these expressions are also included in the figure. Comparison of this figure and the more general shows R_{F} and R_{G} here as a simple feedback network, returning a fraction of V_{OUT} to the op amp (−) input (note that some texts may show the more general symbols Z_{F} and Z_{G} for these feedback components— both are correct, depending upon the specific circumstances).

In fact, we can make some useful general points about the network R_{F} – R_{F}. We will define the transfer expression of the network as seen from the top of R_{F} to the output across R_{G} as β. Note that this usage is a general feedback network transfer term, not to be confused with bipolar transistor forward gain. β can be expressed mathematically as:

β =

So, the feedback network returns a fraction of V_{OUT} to the op amp (–) input. Considering the ideal principles of zero offset and infinite gain, this allows some deductions on gain to be made. The voltage at the (–) input is forced by the op amp’s feedback action to be equal to that seen at the (+) input, V_{IN}. Given this relationship, it is relatively easy to work out the ideal gain of this stage, which in fact turns out to be simply the inverse of β.

### Thus an ideal non-inverting op amp stage gain is simply equal to 1/β, or:

G =

This non-inverting gain configuration is one of the most useful of all op amp stages, for several reasons. Because V_{IN} sees the op amp’s high impedance (+) input, it provides an ideal interface to the driving source. Gain can easily be adjusted over a wide range via R_{F} and R_{G}, with virtually no source interaction.

A key point is the interesting relationship concerning R_{F} and R_{G}. Note that to satisfy the conditions, only their ratio is of concern. In practice this means that stable gain conditions can exist over a range of actual R_{F} – R_{G} values, so long as they provide the same ratio.

If R_{F} is taken to zero and R_{G} open, the stage gain becomes unity, and V_{OUT} is then exactly equal to V_{IN}. This special non-inverting gain case is also called a unity gain follower, a stage commonly used for buffering a source.

Note that this op amp example shows only a simple resistive case of feedback. As mentioned, the feedback can also be reactive, i.e., Z_{F}, to include capacitors and/or inductors. In all cases however, it must include a DC path, if we are to assume the opamp is being biased by the feedback (which is usually the case).

To summarize some key points on op amp feedback stages, we paraphrase from Reference 2 the following statements, which will always be found useful:

The summing point idiom is probably the most used phrase of the aspiring analog artificer, yet the least appreciated. In general, the inverting (−) input is called the summing point, while the non-inverting (+) input is represented as the reference terminal. However, a vital concept is the fact that, within linear op amp applications, the inverting input (or summing point) assumes the same absolute potential as the non-inverting input or reference (within the gain error of the amplifier).