Past exam of the physics A course of the University of Cambridge / 2017 / Paper 1 / Section A / 4

Table of contents
- Solution 4

Solution

Use an inverting operational amplifier. Ground the non-inverting input, connect the source to the inverting input through

R_{in}

, and connect

R_{f}

from the output back to that same input.

Figure 1.
An ideal inverting amplifier with 10 kilohm input resistance and 100 kilohm feedback resistance
. Details.

In linear operation the ideal operational amplifier draws no input electric current, and feedback holds the inverting input at the same electric potential as the grounded non-inverting input. This node is a virtual ground. Kirchhoff's current law there gives

\frac{V _{i}}{R _{in}} + \frac{V _{o}}{R _{f}} = 0, \frac{V _{o}}{V _{i}} = - \frac{R _{f}}{R _{in}} .

The source supplies current

I_{i} = V_{i} / R_{in}

, so its input impedance is

R_{in}

. The required design is therefore

R_{in} = 10 kΩ, R_{f} = 100 kΩ, V_{o} = - 10 V_{i} .

Only these two resistors and the single ideal operational amplifier are needed in the signal circuit; its power supplies are implicit. The result assumes an input small enough to keep the output within its linear operating range.

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