Diode Circuit Analysis

In the circuit of FIGURE 1, explain how the relationship between $I_D$, $V_I$, and $R_x$ changes when $V_I$ transitions from a positive to a negative value.

In the context of the diode v-i characteristic from FIGURE 1, how does increasing the saturation current ($I_S$) affect the voltage $V_D$ required to achieve a specific diode current ($I_D$), assuming $n$ remains constant?

For the half-wave rectifier circuit in FIGURE 2a with a sinusoidal input, qualitatively describe the output waveform ($V_O$) that you would expect to see. Assume a constant diode voltage drop of 0.7V.

How does the addition of a capacitor in the half-wave rectifier/filter circuit (FIGURE 2b) affect the shape of the output waveform ($V_O$) compared to the unfiltered rectifier (FIGURE 2a)?

In the limiter circuit (FIGURE 3), what determines the voltage levels at which the output ($V_O$) will be clipped or limited? Explain briefly.

For the voltage clamp circuit (FIGURE 4), explain how the circuit shifts an input signal and what determines the magnitude of the shift.

In the peak detector circuit (FIGURE 5), what is the role of the diode, and how does the capacitor contribute to the circuit's function?

If the input voltage $V_I$ in FIGURE 1 is a 5V peak-to-peak sine wave, and $R_x$ is 10k ohms, what is the peak value of the current $I_D$ when $V_I$ is positive?

In the context of the diode equation $I_D = I_S e^{\frac{V_D}{0.025n}}$, explain how the diode current $I_D$ would change if the temperature of the diode were increased, assuming all other parameters remain constant.

Considering the circuits in FIGURES 2a, 2b, 3, 4, and 5, explain why an op-amp voltage follower (buffer) is necessary when using a function generator with a relatively high source resistance (e.g., 600 ohms).