An amplifier using an op-amp with a slew rate of 1v/us has a gain of 40dB. if the amplifier has to faithfully amplify sinusoidal signals from 10 to 20khz without introducing any slew rate induced distortion. (1) . find the input signal. (2). Assuming the op-amp is ideal calculate the output voltage?

Question

Answer

Input Signal Calculation:

- Given slew rate = 1V/us
- Gain = 40dB
- Frequency range = 10kHz to 20kHz

To avoid slew rate distortion, we need to ensure that the rate of change of the output voltage does not exceed the slew rate. This occurs when the product of the gain and the input signal frequency equals the slew rate. Therefore, the input signal frequency can be calculated as follows:

Slew rate = Gain x (2π x f)
1 = 10^(40/20) x (2π x f)
1 = 100 x 2π x f
f = 1 / (200π)
f ≈ 0.0008 kHz

Therefore, the input signal frequency should be less than 0.8 kHz.

Output Voltage Calculation:

- Given an ideal op-amp
- Gain = 40dB
- Input signal frequency = 0.8 kHz

As the op-amp is ideal, it has infinite slew rate, meaning no slew rate distortion will occur. The output voltage can be calculated using the gain formula for a non-inverting amplifier:

Gain = 20log(Vout / Vin)
40 = 20log(Vout / Vin)
2 = log(Vout / Vin)
Vout / Vin = 100

Therefore, the output voltage is 100 times the input voltage. Given that the input signal frequency is within the specified range and the op-amp is ideal, the output voltage will faithfully amplify the input signal without introducing any distortion.

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