Case 1: VOUT = +mVIN+b

The circuit configuration that yields a solution for Case 1 is shown in Figure 4–10. The figure includes two 0.01-µF capacitors. These capacitors are called decoupling capacitors, and they are included to reduce noise and provide increased noise immunity. Sometimes two 0.01-µF capacitors serve this purpose, sometimes more extensive filtering is needed, and sometimes one capacitor serves this purpose. Special attention must be paid to the regulation and noise content of VCC when VCC is used as a reference because some portion of the noise content of VCC will be multiplied by the circuit gain.

Figure 4–10. Schematic for Case1: VOUT = +mVIN + b

The circuit equation is written using the voltage divider rule and superposition.

The equation of a straight line (case 1) is repeated in Equation 4–24 below so comparisons can be made between it and Equation 4–23.

Equating coefficients yields Equations 4–25 and 4–26.

Example; the circuit specifications are VOUT = 1 V at VIN = 0.01 V, VOUT = 4.5 V at VIN =1 V, RL = 10 k, five percent resistor tolerances, and VCC = 5 V. No reference voltage is available, thus VCC is used for the reference input, and VREF = 5 V. A reference voltage source is left out of the design as a space and cost savings measure, and it sacrifices noise performance, accuracy, and stability performance. Cost is an important specification, but the VCC supply must be specified well enough to do the job. Each step in the subsequent design procedure is included in this analysis to ease learning and increase boredom. Many steps are skipped when subsequent cases are analyzed.

The data is substituted into simultaneous equations.

Equation 4–27 is multiplied by 100 (Equation 4–29) and Equation 4–28 is subtracted from Equation 4–29 to obtain Equation 4–30.

The slope of the transfer function, m, is obtained by substituting b into Equation 4–27.

Now that b and m are calculated, the resistor values can be calculated. Equations 4–25 and 4–26 are solved for the quantity (RF + RG)/RG, and then they are set equal in Equation 4–32 thus yielding Equation 4–33.

Five percent tolerance resistors are specified for this design, so we choose R1 = 10 kΩ, and that sets the value of R2 = 183.16 kΩ. The closest 5% resistor value to 183.16 kΩ is 180 kΩ; therefore, select R1 = 10 kΩ and R2 = 180 kΩ. Being forced to yield to reality by choosing standard resistor values means that there is an error in the circuit transfer function because m and b are not exactly the same as calculated. The real world constantly forces compromises into circuit design, but the good circuit designer accepts the challenge and throws money or brains at the challenge. Resistor values closer to the calculated values could be selected by using 1% or 0.5% resistors, but that selection increases cost and violates the design specification. The cost increase is hard to justify except in precision circuits. Using ten-cent resistors with a ten-cent op amp usually is false economy.

The left half of Equation 4–32 is used to calculate RF and RG.

The resulting circuit equation is given below.

The gain setting resistor, RG, is selected as 10 kΩ, and 27 kΩ, the closest 5% standard value is selected for the feedback resistor, RF. Again, there is a slight error involved with standard resistor values. This circuit must have an output voltage swing from 1 V to 4.5 V. The older op amps can not be used in this circuit because they lack dynamic range, so the TLV247X family of op amps is selected. The data shown in Figure 4–7 confirms the op amp selection because there is little error. The circuit with the selected component values is shown in Figure 4–11. The circuit was built with the specified components, and the transfer curve is shown in Figure 4–12.

Figure 4–11.Case 1 Example Circuit

Figure 4–12. Case 1 Example Circuit Measured Transfer Curve

The transfer curve shown is a straight line, and that means that the circuit is linear. The VOUT intercept is about 0.98 V rather than 1 V as specified, and this is excellent performance considering that the components were selected randomly from bins of resistors. Different sets of components would have slightly different slopes because of the resistor tolerances. The TLV247X has input bias currents and input offset voltages, but the effect of these errors is hard to measure on the scale of the output voltage. The output voltage measured 4.53 V when the input voltage was 1 V. Considering the low and high input voltage errors, it is safe to conclude that the resistor tolerances have skewed the gain slightly, but this is still excellent performance for 5% components. Often lab data similar to that shown here is more accurate than the 5% resistor tolerance, but do not fall into the trap of expecting this performance, because you will be disappointed if you do. The resistors were selected in the k-Ω range arbitrarily. The gain and offset specifications determine the resistor ratios, but supply current, frequency response, and op amp drive capability determine their absolute values. The resistor value selection in this design is high because modern op amps do not have input current offset problems, and they yield

reasonable frequency response. If higher frequency response is demanded, the resistor values must decrease, and resistor value decreases reduce input current errors, while supply current increases. When the resistor values get low enough, it becomes hard for another circuit, or possibly the op amp, to drive the resistors.