Parametric amplifier — what nonlinearity does it exploit for gain? A parametric amplifier achieves amplification by periodically varying a circuit parameter using a high-frequency pump. Which kind of nonlinearity is fundamentally required?

Introduction / Context:
Parametric amplifiers are low-noise RF/microwave/optical devices that achieve gain by periodically varying a circuit parameter with a pump signal. The core idea is energy transfer from the pump to the signal via reactive, time-varying elements rather than by dissipative active devices. This question asks which kind of nonlinearity is essential for true parametric amplification.

Given Data / Assumptions:

• Amplifier is driven by an external high-frequency pump.
• Objective is signal gain through a time-varying circuit parameter.
• Options distinguish resistive vs reactive nonlinearity.

Concept / Approach:
Paramps rely on a nonlinear reactance (capacitance or inductance) whose value depends on instantaneous voltage/current. Classic implementations use varactor diodes (voltage-dependent capacitance) or Josephson junction inductance. When a pump modulates the reactance, mixing occurs between pump, signal, and idler frequencies, enabling power flow from the pump to the signal without ohmic dissipation as the primary mechanism. Purely resistive nonlinearity produces conversion loss and distortion rather than low-noise gain, and it does not implement the parametric energy-exchange principle.

Step-by-Step Solution:

Verification / Alternative check:
Standard small-signal models show gain equations proportional to the pump-induced variation of reactance; dissipation must be minimized to maintain the characteristic low noise temperature associated with paramps.

Why Other Options Are Wrong:

• Non linear resistance: does not realize true parametric energy exchange and adds loss.
• Either (a) or (b): only reactive nonlinearity fits parametric operation.
• Neither: contradicts the definition of a parametric device.

Common Pitfalls:
Confusing mixers based on resistive elements with parametric amplifiers; assuming any nonlinearity suffices for parametric gain.

Final Answer:
non linear reactance