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Standard Op Amp Feedback Hookups

Virtually all op amp feedback connections can be categorized into just a few basic types. These include the two most often used, non-inverting and inverting voltage gain stages, plus a related differential gain stage. Having discussed above just the attributes of the ideal op amp, at this point it is possible to conceptually build basic gain stages. Using the concepts of infinite gain, zero input offset voltage, zero bias current, etc., standard op amp feedback hookups can be devised. For brevity, a full mathematical development of these concepts isn't included below (but this follows in a subsequent section). The end-of section references also include such developments.
The Non-inverting Op Amp Stage
The op amp non-inverting gain stage, also known as a voltage follower with gain, or simply voltage follower, is shown below in Figure 1-3.
The non-inverting op amp stage (voltage follower)
Figure 1-3: The non-inverting op amp stage (voltage follower)
This op amp stage processes the input VIN by a gain of G, so a generalized expression for gain is:
Feedback network resistances RF and RG set the stage gain of the follower. For an ideal op amp, the gain of this stage is:
For clarity, these expressions are also included in the figure. Comparison of this figure and the more general Figure 1-2 shows RF and RG here as a simple feedback network, returning a fraction of VOUT to the op amp (−) input (note that some texts may show the more general symbols ZF and ZG for these feedback components— both are correct, depending upon the specific circumstances).
In fact, we can make some useful general points about the network RF – RG. We will define the transfer expression of the network as seen from the top of RF to the output across RG 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:
So, the feedback network returns a fraction of VOUT 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, VIN. 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. This is apparent from a comparison of equations 1-2 and 1-3.
Thus an ideal non-inverting op amp stage gain is simply equal to 1/β, or:
This non-inverting gain configuration is one of the most useful of all op amp stages, for several reasons. Because VIN 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 RF and RG, with virtually no source interaction.
A key point is the interesting relationship concerning RF and RG. Note that to satisfy the conditions of Equation 1-2, only their ratio is of concern. In practice this means that stable gain conditions can exist over a range of actual RF – RG values, so long as they provide the same ratio.
If RF is taken to zero and RG open, the stage gain becomes unity, and VOUT is then exactly equal to VIN. 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., ZF, to include capacitors and/or inductors. In all cases however, it must include a DC path, if we are to assume the op amp 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 (Reference 2: Walter Borlase, An Introduction to Operational Amplifiers (Parts 1-3), September 1971, Analog Devices Seminar Notes, Analog Devices, Inc) 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). In short, the amplifier tries to servo its own summing point to the reference.
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