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Chapter 4: Problem 23

To achieve an output of \(10 \mathrm{~V}\) with an input of \(300 \mathrm{mV}\), what voltage gain is required?

Short Answer

Expert verified
The required voltage gain to achieve an output of 10 V with an input of 300 mV is approximately \(A_v = 33.3\).

Step by step solution

01

Understand the voltage gain formula.

The voltage gain formula is given by: \( Voltage\ Gain (A_v) = \frac{Output\ Voltage (V_o)}{Input\ Voltage (V_i)} \) We'll use this formula to find the voltage gain required for the given output voltage (10 V) and input voltage (300 mV).
02

Convert input voltage to volts.

The input voltage is given in millivolts (mV). We need to convert it to volts (V) to use it in the voltage gain formula: \( V_i = 300\ mV = 300 \times 10^{-3} V = 0.3\ V \)
03

Calculate the voltage gain.

Now, plug the output voltage (10 V) and the converted input voltage (0.3 V) into the voltage gain formula to find the required voltage gain: \( A_v = \frac{V_o}{V_i} = \frac{10\ V}{0.3\ V} \)
04

Solve for the voltage gain.

Divide the output voltage by the input voltage to find the required voltage gain: \( A_v = \frac{10}{0.3} = 33.\overline{3} \) So, the voltage gain required to achieve an output of 10 V with an input of 300 mV is approximately 33.3.

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