Case 2: VOUT = +mVIN – b

The circuit shown in Figure 4–13 yields a solution for Case 2. The circuit equation is obtained by taking the Thevenin equivalent circuit looking into the junction of R1 and R2. After the R1, R2 circuit is replaced with the Thevenin equivalent circuit, the gain is calculated with the ideal gain equation (Equation 4–37).

Figure 4–13. Schematic for Case 2: VOUT = +mVIN – b

Comparing terms in Equations 4–37 and 4–14 enables the extraction of m and b.

The specifications for an example design are: VOUT = 1.5 V @ VIN = 0.2 V, VOUT = 4.5 V @ VIN = 0.5 V, VREF = VCC = 5 V, RL = 10 kΩ, and 5% resistor tolerances. The simultaneous equations, (Equations 4–40 and 4–41), are written below.

From these equations we find that b = -0.5 and m = 10. Making the assumption that R1||R2<<RG simplifies the calculations of the resistor values.

Let RG = 20 kΩ, and then RF = 180 kΩ.

Select R2 = 0.82 kΩ and R1 equals 72.98 kΩ. Since 72.98 kΩ is not a standard 5% resistor value, R1 is selected as 75 kΩ. The difference between the selected and calculated value of R1 has about a 3% effect on b, and this error shows up in the transfer function as an intercept rather than a slope error. The parallel resistance of R1 and R2 is approximately 0.82 kΩ and this is much less than RG, which is 20 kΩ, thus the earlier assumption that RG >> R1||R2 is justified. R2 could have been selected as a smaller value, but the smaller values yielded poor standard 5% values for R1. The final circuit is shown in Figure 4–14 and the measured transfer curve for this circuit is shown in Figure 4–15.

 

Figure 4–14. Case 2 Example Circuit

Figure 4–15. Case 2 Example Circuit Measured Transfer Curve

The TLV247X was used to build the test circuit because of its wide dynamic range. The transfer curve plots very close to the theoretical curve; the direct result of using a high performance op amp.