Q4Microwave Engineering 2

(a) Equivalent Circuit, Construction, and Operation of Varactor Diode

A varactor (variable reactor/varactor) diode is a specially-constructed pn-junction (or Schottky-barrier) diode designed to exploit the voltage-dependent junction capacitance that exists in any reverse-biased diode junction, deliberately optimized to provide a well-controlled, predictable, and reasonably large capacitance variation as a function of applied reverse bias voltage.

Equivalent circuit: the varactor diode's small-signal equivalent circuit consists primarily of a voltage-dependent junction capacitance Cj(V) (representing the depletion-region capacitance, which decreases as reverse bias voltage increases, since a larger reverse bias widens the depletion region and hence reduces its capacitance, analogous to increasing the plate separation of a parallel-plate capacitor) in series with a small series resistance Rs (representing the resistance of the undepleted bulk semiconductor material and the ohmic contacts), with this series resistance being an important non-ideal parameter since it introduces loss and limits the diode's achievable quality factor (Q) at high frequencies.

Construction: a varactor diode is typically fabricated as an abrupt or hyperabrupt pn junction (or Schottky junction) in silicon or gallium arsenide, with the doping profile specifically engineered (particularly in hyperabrupt varactors, where doping concentration is deliberately graded to increase sharply near the junction) to achieve a desired, often more strongly non-linear, capacitance-versus-voltage relationship than would result from a simple uniformly-doped abrupt junction, allowing the diode to be tailored for specific tuning-range or linearity requirements in a given application.

Operation: as the reverse bias voltage applied across the varactor diode is increased, the width of the depletion region at the junction increases correspondingly, and since junction capacitance is inversely related to depletion width (analogous to a parallel-plate capacitor's capacitance decreasing as plate separation increases), the diode's capacitance decreases as reverse bias increases, following an approximately Cj(V) = Cj0 / (1+V/Vbi)^n relationship, where Cj0 is the capacitance at zero bias, Vbi is the junction's built-in potential, and n is an exponent (typically 0.5 for an abrupt junction, or a higher value such as 1 to 2 for a hyperabrupt junction) determined by the specific doping profile. This voltage-controlled capacitance behavior makes the varactor diode extremely useful as an electronically-tunable reactive element in voltage-controlled oscillators (VCOs), electronically-tunable filters, and parametric frequency multiplier circuits, where an applied DC tuning voltage allows the resonant frequency (or other frequency-dependent characteristic) of a circuit to be adjusted electronically, without requiring any mechanically-variable component.

(b) Gunn Diode - Operation, Modes, and Oscillating Modes

The Gunn diode is a two-terminal, bulk (no pn junction) semiconductor device made from a compound semiconductor material exhibiting the transferred-electron effect (also called the Ridley-Watkins-Hilsum effect), most commonly n-type gallium arsenide (GaAs) or indium phosphide (InP), used to generate microwave oscillations without relying on any avalanche or minority-carrier injection mechanism (unlike the IMPATT diode discussed in the preceding answer).

Transferred-electron effect and negative differential mobility: in certain compound semiconductors such as GaAs, the conduction band has two distinct energy sub-bands (valleys) with different electron effective mass and mobility characteristics — a lower-energy central valley with high electron mobility, and a higher-energy satellite valley with substantially lower electron mobility. At low applied electric field, essentially all conduction electrons remain in the high-mobility central valley, giving normal, field-proportional current behavior; but as the applied field is increased beyond a critical threshold value, an increasing fraction of electrons gain sufficient energy to transfer into the higher-energy, low-mobility satellite valley, and since this transfer reduces the electrons' average mobility as field increases further, the material's overall drift velocity (and hence current, for a given cross-sectional area) can actually decrease as the applied field increases further — this negative differential mobility characteristic is the fundamental physical basis of Gunn diode operation.

Basic operation and domain formation: when a DC bias voltage exceeding the material's threshold field is applied across a Gunn diode sample, this negative-differential-mobility region causes any small local non-uniformity in doping or field distribution (which naturally exists in any real semiconductor sample) to grow rather than dissipate, nucleating a localized region of high electric field known as a 'domain,' which then travels (drifts) from the cathode toward the anode at a velocity roughly equal to the material's saturated drift velocity. As this domain reaches the anode and is absorbed (extinguished), a new domain nucleates near the cathode and the process repeats periodically, producing a corresponding periodic (oscillating) current variation in the external circuit at a frequency approximately equal to the reciprocal of the domain's transit time across the sample (f approximately equal to vsat/L, where vsat is the saturated drift velocity and L is the sample length) — this transit-time-determined oscillation is the basis of the Gunn diode's most common operating mode.

Basic Modes of Operation

• Gunn (transit-time) mode: the standard operating mode described above, in which a single high-field domain forms, transits the sample, and is absorbed at the anode, with oscillation frequency determined primarily by the sample length and material drift velocity (f is approximately vsat/L).
• Delayed domain mode: the resonant circuit connected to the diode is designed such that the domain is deliberately not allowed to fully form and transit before the RF cycle causes the field to drop below the sustaining threshold, effectively 'quenching' the domain formation process before completion, allowing the oscillation frequency to be set by the external resonant circuit rather than purely by the sample's own transit time, providing a useful degree of external frequency control.
• Quenched domain mode: the external circuit's oscillation actively quenches (extinguishes) each domain before it reaches the anode, and no new domain forms until the RF voltage cycle brings the field back above threshold, again allowing external-circuit-determined oscillation frequency, potentially higher than the natural transit-time frequency, since the domain need not complete its full transit before quenching.
• LSA (Limited Space-charge Accumulation) mode: the bias field is switched high and low so rapidly (at a frequency well above the natural transit-time frequency) that no significant space-charge domain has time to nucleate and grow at all during each RF cycle, allowing the entire bulk of the material to contribute to negative-resistance-based power generation more efficiently across a wider range of operating frequencies (rather than the power generation being localized within the relatively narrow travelling high-field domain of the standard transit-time mode), making the LSA mode capable of higher output power and higher operating frequency than the standard Gunn mode, at the cost of requiring more careful, precisely-tuned external circuit design to sustain this specific mode of operation.

The specific operating mode a given Gunn diode circuit exhibits depends on the interaction between the semiconductor sample's intrinsic transit-time frequency, the doping-length product of the device, and the impedance/resonant characteristics of the external circuit in which the diode is mounted, giving circuit designers meaningful flexibility to tailor Gunn diode oscillator performance (frequency, power, tuning range) to a specific microwave application's requirements through appropriate choice of both device parameters and external circuit design.