(Editor's note: You can also see the author's short video introduction here. )

From the theoretical development in the previous article (Reference 1), basic application circuits can be realized.

This high-gain circuit with a differential input received its name in the days of analog computers. Every mathematical operation required an amplifier to isolate one function from the next. In the simplest form, an operational amplifier (op amp) can be configured for inverting or non-inverting gain (see Figure 1).

Figure 1: Basic gain stages
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The gain equations show that the inverting stage may have a closed loop gain (Acl) of less than one when Ri>Rf. When Ri=Rf, the gain is minus one (inverting). The non-inverting stage can never have a gain less than unity. When Ri is open, the circuit reduces to a unity-gain voltage follower. If a gain less than one is desired, a voltage divider is placed before the amplifier.

Since this is a linear system, the rules of linear superposition apply. Therefore, the next development is the summation of two or more signals (Figure 2).

Figure 2: Weighted signal summation
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To reach these relationships, start by assuming V2=0 and write the equation for Vout as a function of V1. Then assume V1=0 and write the expression for V2. Combine the two terms to get the entire transfer function. More inputs can be added in parallel with those shown here, and the total transfer function can be developed with this superposition technique.

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This ability to add voltages has more value than just the arithmetic. There are times in a design when it is necessary to accomplish a level shift. These circuits will do just that. With these variations on addition it is also possible to accomplish the complementary arithmetic operation, subtraction, Figure 3.

Figure 3: The difference amplifier (diff amp)

Using linear superposition as done above, the general output expression for the difference amp is:

A widely used application is where the desired signal is riding on an interfering signal (see Figure 4). The interference signal is termed the common mode voltage (Vcm) as it is common to both inputs. The desired signal is the differential mode voltage (Vdm). In this case, it is the sum of Vdm1 and Vdm2.

Figure 4: Difference amp application
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If R1=R4 and R2=R3, Vout is given by:
(Editor's note: the above pair of resistor equalities had typographical errors in the original online version of this article; it is now corrected)

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The accuracy with which the interference signal is eliminated is based on two variables: the accuracy of the resistor match; and a parameter of the op amp called common mode rejection ratio (CMRR). With the assumption that the perfect op amp does exist, the calculation of output due to resistor mismatch is a simple spreadsheet exercise.

Table 1: Calculation of output due to resistor mismatch
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Now that we have a suite of basic building blocks, we can next begin to address the various converter options available.

Reference
"SIGNAL CHAIN BASICS: Operational Amplifier--The Basic Building Block", www.planetanalog.com/features/showArticle.jhtml;?articleID=202801320, click here.