Let's go through the solution to each part of this problem.

Given Data:

• $R_1 = 2 \, \text{k}\Omega$
• $R_f = 6 \, \text{k}\Omega$
• $+V_s = +15 \, \text{V}$
• $-V_s = -15 \, \text{V}$

This circuit is a non-inverting amplifier using an operational amplifier (op-amp).

Solution:

(a) Find the value of $V_o$ if $V_i = 4 \, \text{V}$

For a non-inverting amplifier, the output voltage $V_o$ is given by: $V_o = \left( 1 + \frac{R_f}{R_1} \right) V_i$

1. Calculate the gain: $\text{Gain} = 1 + \frac{R_f}{R_1} = 1 + \frac{6000}{2000} = 1 + 3 = 4$

2. Calculate $V_o$: $V_o = 4 \times V_i = 4 \times 4 = 16 \, \text{V}$

However, since the output of the op-amp is limited by the supply voltages $+V_s$ and $-V_s$, the maximum $V_o$ can be is $+15 \, \text{V}$. Therefore, $V_o = 15 \, \text{V}$ due to saturation.

(b) Draw the graph of $V_o$ with proper labels if $V_i = 4 \sin(\omega t)$

With $V_i = 4 \sin(\omega t)$, we can use the same gain of 4 to determine $V_o$.

$V_o = 4 \times V_i = 4 \times 4 \sin(\omega t) = 16 \sin(\omega t)$

Since $V_o$ is again limited by the supply voltages, the waveform will be clipped at $+15 \, \text{V}$ and $-15 \, \text{V}$.

• The graph of $V_o$ will look like a sinusoidal waveform with peaks clipped at $+15 \, \text{V}$ and $-15 \, \text{V}$.
• Label the y-axis as $V_o (\text{V})$ and the x-axis as $t$.

(c) Draw the graph of $V_o$ with proper labels if $V_i = 6 \sin(\omega t)$

With $V_i = 6 \sin(\omega t)$, we apply the same gain of 4.

$V_o = 4 \times V_i = 4 \times 6 \sin(\omega t) = 24 \sin(\omega t)$

Since $V_o$ exceeds the op-amp's supply limits of $\pm 15 \, \text{V}$, the waveform will be heavily clipped.

• The graph of $V_o$ will have a maximum amplitude of $+15 \, \text{V}$ and a minimum of $-15 \, \text{V}$, resulting in a square wave-like output due to the severe clipping.
• Label the y-axis as $V_o (\text{V})$ and the x-axis as $t$.

Would you like a visual plot of parts (b) and (c) to illustrate the clipping effect?

Additional Questions:

1. How would changing $R_f$ to a different value affect the gain of the amplifier?
2. What would happen if the input signal $V_i$ exceeded the supply voltages significantly?
3. How does the op-amp saturation limit the effectiveness of the amplifier in applications?
4. Could you calculate $V_o$ if $R_f$ and $R_1$ were swapped in the circuit?
5. How would a higher supply voltage affect the clipping of $V_o$?

Tip:

Always consider the supply voltages of an op-amp in your calculations, as they impose limits on the output that can result in signal clipping.