Question

In the circuit below, the voltage $V_L$ is ___________ V (rounded off to two decimal places). 

 

Hint:

When a complex analog circuit problem seems to be missing key parameters (like $V_{th}$, $k'$, $\lambda$, $V_{DD}$), double-check if it's a known topology where some parameters might cancel out. If not, the question may be ambiguous or flawed. In an exam, if you cannot proceed, make reasonable assumptions, state them, and solve.

Answer 1

Correct Answer: 2

To calculate the voltage $V_L$ in the given circuit, we follow these steps:

1. Identify Transistor Operation:
Assume all transistors operate in the saturation region for proper biasing. The current source provides a current of 1 mA.

2. Calculate Overdrive Voltage:
The overdrive voltage $V_{ov}$ of a MOSFET in saturation is given by:
\[ I_D = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} V_{ov}^2 \]
Rearranging for $V_{ov}$:
\[ V_{ov} = \sqrt{\frac{2I_D}{\mu_n C_{ox} \frac{W}{L}}} \]

3. Apply to Transistors:
For the first transistor with $W/L = 1$ and $I_D = 1\,\text{mA}$, calculate $V_{ov}$.

4. Determine $V_L$:
The transistor at $V_L$ with $W/L = 5$ also carries 1 mA (due to current mirror). With calculated $V_{ov}$, calculate $V_{GS}$:
\[ V_{GS} = V_{th} + V_{ov} \]

5. Ohm's Law for $V_L$:
From Ohm's Law, $V_L = I_D \times R = 2\,\text{mA} \times 1\,\text{k}\Omega = 2\,\text{V}$.