Final answer:
An inverting amplifier with a gain of -15 can be designed using an operational amplifier with a feedback resistor (Rf) of 15 kΩ and an input resistor (Rin) of 1 kΩ, resulting in the gain formula A = -Rf/Rin.
Step-by-step explanation:
Designing an Inverting Amplifier with a Gain of -15
To design an inverting amplifier with a gain of -15, you need to select resistors for the input and feedback path of an operational amplifier (op-amp). The gain (A) of an inverting amplifier is given by the formula A = -Rf/Rin, where Rf is the feedback resistor and Rin is the input resistor.
To achieve a gain of -15, you could choose, for example, a feedback resistor (Rf) of 15 kΩ and an input resistor (Rin) of 1 kΩ. The negative sign indicates that the output signal will be inverted relative to the input.
The circuit configuration will include the selected resistors connected to an op-amp, with the input resistor connected to the input signal and the inverting input of the op-amp, and the feedback resistor connected between the output and the inverting input of the op-amp. You must also provide appropriate power supply voltages to the op-amp.