Final answer:
An inverting amplifier with an input resistance of 20kΩ and a gain of 10 requires an input resistor (Rin) of 20kΩ and a feedback resistor (Rf) of 200kΩ. The gain is determined by the ratio -Rf/Rin, ensuring the circuit meets the design specifications.
Step-by-step explanation:
To design an inverting amplifier with an input resistance of 20kΩ and a gain of 10, we need to choose resistor values that meet these conditions. The input resistance, known as Rin, will be the resistance seen by the input signal. Therefore, Rin should be 20kΩ. Now, the gain of the inverter amplifier (Φ) is given by the formula -Rf/Rin, where Rf is the feedback resistor. To achieve a gain of 10, the feedback resistor must be 10 times the input resistance, which is 20kΩ × 10 = 200kΩ.
By applying Ohm's law to determine the correct values for resistors, we can ensure the designed amplifier achieves the desired input resistance and gain. A typical circuit diagram of an inverting amplifier includes a resistor connected from the input signal to the inverting input of the operational amplifier (op-amp), and a feedback resistor connected from the output of the op-amp back to the inverting input. The non-inverting input is connected to the ground.
Remember, it's essential to choose an op-amp that can handle the desired signal voltage range and has an appropriate frequency response for the application.