Objective: Determine the range required for resistor $R_{1}$ , to realize a differential gain adjustable from 5 to 500.

The instrumentation amplifier circuit is shown in Figure 9.26. Assume that $R_{4} = 2R_{3}$ , so that the difference amplifier gain is 2.

Question

Objective: Determine the range required for resistor [latex]R_{1}[/latex], to realize a differential gain adjustable from 5 to 500.

The instrumentation amplifier circuit is shown in Figure 9.26. Assume that [latex]R_{4} = 2R_{3}[/latex], so that the difference amplifier gain is 2.

Accepted Answer

Assume that resistance [latex]R_{1}[/latex] is a combination of a fixed resistance [latex]R_{1f}[/latex] and a variable resistance [latex]R_{1v}[/latex] , as shown in Figure 9.28. The fixed resistance ensures that the gain is limited to a maximum value, even if the variable resistance is set equal to zero. Assume the variable resistance is a 100 kΩ potentiometer.
From Equation (9.67), the maximum differential gain is

[latex]v_{O} = \frac{R_{4}}{R_{3}} \left(1 + \frac{2R_{2}}{R_{1}} \right) (v_{I 2} − v_{I 1}) [/latex] (9.67)

[latex]500 = 2 \left( 1 + \frac{2R_{2}}{R_{1 f}} \right) [/latex]

and the minimum differential gain is
[latex]5 = 2 \left( 1 + \frac{2R_{2}}{R_{1 f} + 100} \right) [/latex]

From the maximum gain expression, we find that
[latex]2R_{2} = 249 R_{1 f}[/latex]
Substituting this [latex]R_{2}[/latex] value into the minimum gain expression, we have
[latex]1.5 = \frac{2R_{2}}{R_{1 f} + 100} = \frac{249 R_{1 f}}{R_{1 f} + 100}[/latex]
The resulting value of [latex]R_{1 f}[/latex] is [latex]R_{1 f} = 0.606 k \Omega[/latex], which yields [latex]R_{2} = 75.5 k \Omega[/latex].
Comment: We can select standard resistance values that are close to the values calculated, and the range of the gain will be approximately in the desired range.
Design Pointer: An amplifier with a wide range of gain and designed with a potentiometer would normally not be used with standard integrated circuits in electronic systems. However, such a circuit might be very useful in specialized test equipment.

Question 9.8: Objective: Determine the range required for resistor R1, to ...

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