Consider the circuit shown in Figure (a). A gate pulse v_g is applied between time instants t₀ and t₁. After t₁, during the MOSFET turn OFF process, it experiences a voltage overshoot. Based on the v_ds waveforms shown in Figure (b), which one of the following options is correct?

The correct option is R3 > R2 > R1.

Step 1: Analyzing the Circuit during MOSFET Turn-OFF

In Figure (a), when the gate pulse $v_g$ is applied between time $t_0$ and $t_1$, the MOSFET turns ON and energy is stored in the inductor $L$.

At time $t=t_1$, the gate pulse is removed, causing the MOSFET to turn OFF. When the MOSFET turns OFF, the current flowing through the inductor cannot change instantaneously. This forces the freewheeling diode $D$ to conduct, establishing a loop containing the DC voltage source $V_{DC}$, the inductor $L$, and the resistor $R_f$.

Step 2: Deriving the Peak Drain-to-Source Voltage ($v_{ds,\text{peak}}$)

Applying Kirchhoff's Voltage Law (KVL) around the loop immediately after turn-OFF at $t=t_1^{+}$, the voltage across the MOSFET is given by:

$v_{ds}=V_{DC}+L\frac{di}{dt}$

Also, across the freewheeling branch with resistor $R_f$ and diode $D$, the voltage drop is:

$v_{ds}=V_{DC}+i·<!--\; \cdot \; -->R_f$

At the instant of turn-OFF ($t=t_1$), the current in the inductor reaches its maximum value, $I_{L0}$. Thus, the maximum (peak) voltage overshoot experienced by the MOSFET is:

$v_{ds,\text{peak}}=V_{DC}+I_{L0}·<!--\; \cdot \; -->R_f$

Step 3: Comparing the Waveforms

From the peak overshoot formula, we observe that the peak value of $v_{ds}$ is directly proportional to the resistance value $R_f$:

$v_{ds,\text{peak}}\propto <!--\; \propto \; -->R_f$

Looking at the waveform graph in Figure (b):

1. The curve with $R_f=R_1$ has the highest peak voltage overshoot.

2. The curve with $R_f=R_3$ has an intermediate peak voltage overshoot.

3. The curve with $R_f=R_2$ has the lowest peak voltage overshoot.

Therefore, comparing the peak overshoots directly gives:

$R_1>R_3>R_2$

Rearranging this inequality in terms of $R_3$ leading the sequence:

$R_3>R_2>R_1$