Interview questions & answers
Q1. State Thevenin's theorem and explain how to find the Thevenin equivalent.
Thevenin's theorem states that any linear two-terminal network can be replaced by a single voltage source Vth in series with a single resistance Rth, where Vth is the open-circuit voltage across the terminals and Rth is the equivalent resistance seen from the terminals with all independent sources deactivated. For a circuit with a 12V source, 4Ω and 6Ω resistors in a voltage divider feeding a load: Vth = 12 × 6/(4+6) = 7.2V and Rth = 4||6 = 2.4Ω. The Thevenin equivalent is most powerful in amplifier design where the source resistance of a sensor determines the gain and noise loading of the next stage.
Follow-up: How do you find Rth when the circuit contains a dependent source?
Q2. State Norton's theorem and explain the relationship between Norton and Thevenin equivalents.
Norton's theorem states that any linear two-terminal network can be replaced by a single current source In in parallel with a resistance Rn, where In is the short-circuit current and Rn equals the Thevenin resistance. For the same 12V, 4Ω, 6Ω circuit: In = Vth/Rth = 7.2/2.4 = 3A and Rn = 2.4Ω. Converting between Norton and Thevenin is simply source transformation: Vth = In × Rn, making them completely interchangeable and the choice purely a matter of which form simplifies subsequent analysis.
Follow-up: When is the Norton equivalent more convenient than the Thevenin equivalent?
Q3. State the Maximum Power Transfer theorem and derive the condition.
Maximum power is transferred from a source to a load when the load resistance equals the Thevenin resistance of the source network, delivering P_max = Vth²/(4Rth). For an audio amplifier with Thevenin output resistance 8Ω, connecting an 8Ω speaker maximizes acoustic power delivery; connecting a 4Ω speaker or 16Ω speaker each reduces transferred power. The efficiency at maximum power transfer is exactly 50%, meaning the source dissipates as much power internally as the load receives — which is acceptable in communications but unacceptable in power systems.
Follow-up: In a power transmission system, is the maximum power transfer condition desirable? Why or why not?
Q4. State the Superposition theorem and describe its application procedure.
The superposition theorem states that in a linear circuit with multiple independent sources, the response (voltage or current) at any element is the sum of the individual responses caused by each source acting alone with all other independent sources deactivated (voltage sources replaced by short circuits, current sources by open circuits). To find the current through a 10Ω resistor in a circuit with a 20V source and a 5A current source: find I' with only the 20V source, find I'' with only the 5A source, and sum I = I' + I''. Superposition fails for power calculations because power is nonlinear (P = I²R), so you must find total current first then calculate power — not sum individual powers.
Follow-up: Why does the superposition principle not apply to power calculations?
Q5. State the Reciprocity theorem and give a practical example.
The reciprocity theorem states that in a linear passive bilateral network, if a voltage source V in branch A produces a current I in branch B, then moving the source to branch B produces the same current I in branch A, with the same source and network topology. An antenna radiating from point A and receiving at point B has the same transfer function as radiating from B and receiving at A, which is why the same antenna element can be used for both transmit and receive in RADAR systems. Reciprocity holds only for passive networks with no dependent sources, controlled sources, or magnetically anisotropic materials like ferrite isolators.
Follow-up: Does reciprocity hold in a circuit containing a transistor amplifier? Why?
Q6. What is Millman's theorem and when is it useful?
Millman's theorem gives the voltage at a common node connected to multiple voltage sources through resistors as V = (V1/R1 + V2/R2 + ... + Vn/Rn) / (1/R1 + 1/R2 + ... + 1/Rn), effectively combining parallel branches with sources into a single Thevenin equivalent. A three-phase unbalanced load analysis with neutral displacement is solved directly by Millman's formula without setting up three simultaneous KCL equations. It is a shortcut for any parallel combination of voltage sources with series resistances, which appears repeatedly in battery parallel connection analysis and op-amp summing amplifier derivations.
Follow-up: How would you use Millman's theorem to find the neutral shift voltage in an unbalanced three-phase load?
Q7. What is the Substitution theorem?
The substitution theorem states that any branch in a network carrying a known current I or having a known voltage V can be replaced by an independent current source of value I or an independent voltage source of value V without affecting any other voltage or current in the network. In an amplifier analysis, once the base current of a BJT is determined by the surrounding network, the transistor branch can be substituted by a current source equal to that base current for the purpose of finding the effect on the rest of the circuit. This theorem is the theoretical foundation for small-signal equivalent circuit substitution in transistor amplifier analysis.
Follow-up: What is the key restriction on applying the substitution theorem?
Q8. State the Compensation theorem.
The compensation theorem states that if the resistance of a branch in a network changes from R to R + ΔR, the change in all other branch currents and voltages can be found by inserting a compensation voltage source of value ΔV = I × ΔR in series with the original branch (where I is the original current) with all other sources deactivated. If a 10Ω resistor in a network carrying 2A changes to 12Ω, the compensation source is 2 × 2 = 4V, and its effect on all other branches is calculated by superposition with the original network at zero excitation. This theorem is used in sensitivity analysis of filters and power systems to quantify the effect of component tolerance on circuit performance.
Follow-up: How is the compensation theorem used in sensitivity analysis of filter components?
Q9. How do you find Rth when the circuit contains dependent sources?
When a circuit contains dependent sources, deactivating all independent sources and applying an external test voltage Vt (or test current It) at the terminals allows Rth to be calculated as Rth = Vt/It, because the dependent source will respond to the test signal. Apply 1V test source, find the resulting current It, and Rth = 1/It in siemens converted to ohms. You cannot simply series/parallel combine resistances in the presence of dependent sources because the dependent source can effectively create or cancel resistance.
Follow-up: Can Rth be negative? What physical situation causes a negative Thevenin resistance?
Q10. What is the difference between a unilateral and bilateral network, and which theorems require bilaterality?
A bilateral network has identical transmission properties in both directions (passive resistors, capacitors, and inductors), while a unilateral network transmits differently in each direction (diodes, transistors, and amplifiers). Reciprocity and the network theorems involving Thevenin and Norton equivalents in their standard form assume bilateral, linear, passive networks. Thevenin's theorem can be extended to active circuits but requires treating dependent sources carefully; reciprocity fails entirely in unilateral networks, which is why RADAR isolators use ferrite circulators.
Follow-up: Can Thevenin's theorem be applied to a circuit containing a transistor? If so, how?
Q11. What is source transformation and when do you use it?
Source transformation converts a voltage source Vs in series with resistance Rs into an equivalent current source Is = Vs/Rs in parallel with the same Rs, or vice versa, leaving the external circuit completely unaffected. In a complex circuit with a mix of voltage and current sources, systematically converting all sources to the same type (all current sources for node analysis) simplifies the equation setup. Source transformation cannot be applied to an ideal voltage source with no series resistance or an ideal current source with no parallel resistance, because the transformed equivalent would have infinite or zero resistance.
Follow-up: What is the limitation of source transformation when the source resistance is zero?
Q12. How is Thevenin's theorem applied in amplifier design?
In amplifier design, the Thevenin equivalent of the signal source (sensor output resistance plus wiring) determines how much signal is delivered to the amplifier input: if the source Thevenin resistance is 600Ω and the amplifier input resistance is 600Ω, exactly half the open-circuit voltage is applied to the input. For a microphone with 150Ω source impedance feeding a 47kΩ input op-amp, the loading error is less than 0.4%, which is negligible. Impedance matching using Thevenin analysis is the first design step for any RF receiver front-end where source resistance equals load resistance for maximum power.
Follow-up: In an op-amp voltage follower used as a buffer, what is the Thevenin output resistance?
Q13. What is the significance of Norton's theorem in current mode circuits?
Norton's theorem is naturally suited to current-mode circuits like transimpedance amplifiers, photodiode interfaces, and current mirrors because the current source plus parallel resistance model directly represents how these devices behave. A photodiode is best modeled as a Norton source: it generates a current proportional to incident light and has a high parallel shunt resistance of 100 MΩ or more. The transimpedance amplifier converts this Norton current source to a voltage output, and the design directly uses In and Rn values from the photodiode datasheet.
Follow-up: What is the transimpedance gain of an op-amp with feedback resistor Rf connected to a Norton source?
Q14. State the Tellegen theorem and explain how it differs from conservation of energy.
Tellegen's theorem states that the sum of instantaneous power in all branches of a network is zero (ΣVkIk = 0), which follows from KVL and KCL simultaneously and holds for any lumped network regardless of element types or values. Conservation of energy (power in = power out) is a specific case of Tellegen's theorem for passive networks, but Tellegen's theorem is stronger: it holds even for topologically identical networks with entirely different element values, making it useful for proving network identities without knowing element types. In practice, engineers use it to verify circuit simulation results by checking that the sum of all branch powers is identically zero.
Follow-up: Can Tellegen's theorem be applied to a nonlinear network? Why?
Q15. How do you use superposition to analyze AC circuits with sources at different frequencies?
In circuits with AC sources at different frequencies, superposition is mandatory because impedances (especially capacitors and inductors) are frequency-dependent, so a single set of equations cannot represent both frequencies simultaneously. Analyze the circuit at each frequency separately with only that source active, calculate voltage or current phasors at the element of interest, convert back to time domain, then add the time-domain expressions algebraically. A circuit with a 1 kHz source and a 3 kHz source requires two separate impedance calculations: the capacitor has different XC at each frequency, so the response at both frequencies must be found independently before adding.
Follow-up: Why can't you add phasor voltages at different frequencies directly?
Common misconceptions
Misconception: Maximum power transfer requires the load resistance to be as large as possible.
Correct: Maximum power transfer requires load resistance to equal the source Thevenin resistance, not to be maximized; a larger load reduces current more than it increases voltage, resulting in less power.
Misconception: Superposition can be used to calculate power by summing powers from individual sources.
Correct: Power is proportional to the square of current or voltage, which is nonlinear, so superposition cannot be applied to power; total current must be found first, then power computed from it.
Misconception: Thevenin's theorem does not apply to circuits with dependent sources.
Correct: Thevenin's theorem applies to circuits with dependent sources, but Rth must be found by applying a test source at the terminals rather than by simple resistance combination.
Misconception: The reciprocity theorem applies to all electronic circuits.
Correct: Reciprocity applies only to linear, passive, bilateral networks; circuits with transistors, op-amps, or other active components violate the bilateral passive condition.