(Solved): 1. Derive an expression for the voltage gain, \( A_{v}=\frac{v_{0}}{v_{I}} \), of the inverting am ...

1. Derive an expression for the voltage gain, \( A_{v}=\frac{v_{0}}{v_{I}} \), of the inverting amplifier shown in Figure 1 below. Figure 1. Inverting op-amp circuit 2. Simulate the circuit of Figure 1 in Multisim. Assume \( \mathrm{R} 1=1 \mathrm{k} \Omega, \mathrm{R} 2=10 \mathrm{k} \Omega \), and \( v_{I} \) is a \( 1 \mathrm{kHz} \) sine wave of amplitude \( 100 \mathrm{mV} \). Use the 741 op-amp (Place Component \( \rightarrow \) Group: Analog \( \rightarrow \) OPAMP \( \rightarrow \) 741). Use an oscilloscope to display both the input and output waveforms on the same display. Use the vertical cursors to show the peak value of each of the two waveforms. Use these to calculate the gain. Copy and paste the Multisim circuit and the oscilloscope output below. Show the resulting gain calculation in a textbox beside the oscilloscope display. 3. While leaving the amplitude of \( v_{I} \) the same, change the frequency of the input sinusoid to \( 10 \mathrm{kHz}, 100 \) \( \mathrm{kHz} \), and \( 1000 \mathrm{kHz} \). In each case, compute the resulting gain, and insert the values into Table 1 below. Table 1. Gain of the inverting op-amp circuit for various input frequencies What do you observe about the gain as the input frequency is increased?