Final answer:
A difference amplifier with a gain of 7.5 can be designed by selecting the feedback resistor (Rf) and the input resistor (Rin) such that Rf is 7.5 times Rin. If Rin is 10kΩ, Rf should be 75kΩ. It is important to match resistors accurately and use precision components for stable operation.
Step-by-step explanation:
Designing a Difference Amplifier with a Gain of 7.5
To design a difference amplifier with a gain of 7.5, begin by selecting appropriate resistor values. The gain in a difference amplifier is given by the ratio of the feedback resistor to the input resistor. Therefore, if we designate Rf as the feedback resistor and Rin as the input resistor, the gain (A) formula is A = Rf / Rin.
In this case, if we want a gain of 7.5, and if we choose Rin to be 10kΩ, then Rf should be 75kΩ (since 75kΩ / 10kΩ = 7.5). It is essential to properly match both the inverting and non-inverting inputs with resistors of the same values to maintain the balance of the amplifier. The precision of the resistors will affect the accuracy of the gain.
Additionally, to ensure stable operation of the amplifier and minimize offset errors, you might consider using precision resistors and implementing good PCB layout practices. Remember that real-world components have tolerances, so the exact gain might slightly vary from the ideal calculated value.