How an IMPATT generates negative resistance. Two delays are deliberately stacked. First, avalanche multiplication does not follow the field instantaneously — the carrier population builds up, so the injected current lags the voltage by about 90°. Second, the generated carriers must drift across the depletion region at saturated velocity, adding a further transit-angle delay

\(\theta=\omega\tau=\dfrac{\omega L}{v_s}\)

Together the two delays push the terminal current towards 180° out of phase with the voltage, and a device in which current and voltage are in antiphase presents a negative resistance to the external circuit.

Examine the assertion — true. The magnitude of that negative resistance depends on the transit angle. Beyond π the phase relationship moves further towards antiphase and the negative resistance grows rapidly as θ approaches 3π/2, which is the standard result for the small-signal IMPATT analysis. The optimum design point is generally taken near \(\theta=\pi\), i.e. a drift-region length of about half a transit wavelength, and the negative resistance climbs steeply past it.

Examine the reason — true. The IMPATT structure — typically n⁺-p-i-p⁺ in the Read diode form — does indeed place a thin, heavily doped avalanche region where the field is highest, followed by a lightly doped drift region across which the carriers travel at saturation velocity. This is a correct description of the device.

Does the reason explain the assertion? No. The reason describes the device's construction; the assertion is a statement about how the negative resistance varies with transit angle. The structure explains why a negative resistance exists at all, but it says nothing about the functional dependence on θ — that comes from the small-signal impedance analysis, not from the doping profile. So both statements are true but (R) does not explain (A): code 2.

Context worth carrying. IMPATT diodes are the most powerful solid-state sources at millimetre wavelengths, delivering watts at tens of gigahertz, but the avalanche process makes them noisy — which is why the quieter TRAPATT and Gunn devices are preferred where noise matters.

Hence, both (A) and (R) are true, but (R) is not the correct explanation of (A).