Analog VLSI Basics: Passive Circuits and First-Order RC/RL Questions Quiz

Test your understanding of key Analog VLSI interview questions on passive circuits, focusing on first-order RC and RL circuits. This easy quiz will help you practice essential concepts such as time constants, voltage behavior, and intuitive analysis relevant to analog circuit interviews.

1. Time Constant Calculation in RC Circuits

   What is the time constant (τ) of an RC circuit consisting of a 1 kΩ resistor and a 1 μF capacitor connected in series?

   1. 1 microsecond
   2. 10 milliseconds
   3. 1 millisecond
   4. 1 second

   Explanation: The time constant τ for an RC circuit is given by τ = R × C. Here, R = 1 kΩ and C = 1 μF, giving τ = 1000 × 0.000001 = 0.001 seconds or 1 millisecond. 1 microsecond is incorrect as it is too small, 1 second is too large, and 10 milliseconds is ten times the correct value.

2. Output Exceeding Supply Voltage

   Is it possible for the output voltage (Vout) of an RC circuit to exceed the supply voltage (VDD) in practical scenarios, and under what basic condition?

   1. Yes, during fast switching with inductive effects
   2. No, it is never possible
   3. Yes, with capacitor charging to a negative value
   4. Yes, if there is resonance

   Explanation: In certain practical cases, such as rapid switching or with inductive kick-back, Vout can temporarily exceed VDD due to energy stored in inductors. Resonance does not typically occur in simple RC circuits, so option A is wrong. Saying it is 'never possible' ignores real transient behaviors. Capacitors cannot charge to a value more negative than the supply without active circuits, making option D incorrect.

3. Transfer Function Intuition

   For a series RC circuit, the zero in the transfer function is intuitively located at which frequency?

   1. -1/(RC)
   2. -RC
   3. 1/(RC)
   4. RC

   Explanation: The zero of the transfer function in a standard RC circuit is at s = -1/(RC) in the Laplace domain. RC or -RC are not frequencies and do not represent the location of the zero. 1/(RC) is positive, missing the negative sign required for a stable system zero.

4. Voltage Behavior in a Charging Capacitor

   What happens to the voltage across the capacitor in an RC circuit when a DC step input is suddenly applied (e.g., 0V to 5V)?

   1. It rises gradually toward 5V, following an exponential curve
   2. It instantly jumps to 5V
   3. It decreases toward zero
   4. It remains at zero

   Explanation: A capacitor's voltage cannot change instantly; it increases gradually, approaching the final value according to the RC time constant. Instant jumping is physically impossible. It does not remain at zero or decrease toward zero unless a reverse scenario is described, so those options are incorrect.

5. Intuitive Drawing of Vout for Discharging

   After charging, when the supply voltage is removed from an RC circuit, how does Vout behave over time?

   1. It oscillates
   2. It increases rapidly
   3. It stays constant at the previous voltage
   4. It decays exponentially to zero

   Explanation: Upon disconnecting the supply, the capacitor discharges through the resistor, causing Vout to decay exponentially toward zero. The voltage does not increase or stay constant. Oscillations do not occur in simple RC circuits without additional reactive components.

6. Effect of Adding Additional Capacitor

   If a second identical capacitor is added in parallel to an existing one in an RC circuit, what will be the new time constant?

   1. It will double
   2. It remains the same
   3. It becomes zero
   4. It will halve

   Explanation: Adding a second capacitor in parallel increases the total capacitance (C_total = C1 + C2). This doubles the capacitance, so the time constant τ = R × C_total also doubles. Halving would occur if resistance was decreased, not capacitance, so that choice is incorrect. It never becomes zero and does not remain the same.

7. Voltage Divider in RC Circuits

   At steady state (long after the input is applied), the capacitor in an RC circuit behaves electrically as what?

   1. A current source
   2. A short circuit
   3. An open circuit
   4. A variable resistor

   Explanation: In DC steady state, the capacitor charges fully and blocks direct current, behaving as an open circuit. Treating it as a short circuit applies only to AC at very high frequencies. It isn’t a variable resistor or current source, so those options are not appropriate.

8. Current Through the Resistor Initially

   Immediately after a DC voltage step is applied to a series RC circuit, what is true about the current through the resistor?

   1. It stays constant regardless of time
   2. It slowly increases
   3. It is at its maximum value
   4. It is zero

   Explanation: At the instant a step input is applied, the capacitor initially behaves like a short circuit, so the entire supply voltage appears across the resistor, causing maximum current. The current is not zero or slowly increasing; rather, it decreases over time. It does not stay constant either.

9. Order of an RC Circuit

   What is the order of a simple RC circuit?

   1. Third order
   2. Zeroth order
   3. Second order
   4. First order

   Explanation: An RC circuit has one energy storage element (the capacitor), so it is a first-order circuit. Second order requires two storage elements. Zeroth and third orders do not apply to this configuration.

10. Effect of Large Time Constant

    If the time constant τ of an RC circuit is made very large, what is the effect on the output voltage Vout in response to a sudden input?

    1. Vout immediately reaches the final value
    2. Vout changes very slowly
    3. Vout changes very rapidly
    4. Vout becomes unstable

    Explanation: A larger time constant means the capacitor charges or discharges more slowly, so Vout changes gradually after a step input. It definitely does not reach its final value immediately or change very fast. Instability is not typical in such passive circuits, making option C incorrect.