Varactor Diode

The varactor diode is a reverse-biased p-n junction diode specially designed so that its junction capacitance varies in a controlled and predictable manner with applied reverse voltage. This voltage-dependent capacitance makes it the fundamental tuning element in voltage-controlled oscillators, phase-locked loops, and RF tunable filters.

Core Concept Explanation

Every reverse-biased p-n junction has a depletion region that is free of mobile carriers and acts as the dielectric of a parallel plate capacitor. The p-side and n-side neutral regions act as the conducting plates. When reverse bias is increased, the depletion region widens, effectively increasing the plate separation and decreasing the capacitance. When reverse bias is reduced, the depletion region narrows and capacitance increases.

In ordinary diodes this capacitance change is a parasitic effect. In a varactor, the doping profile is precisely engineered to give a specific and repeatable capacitance-voltage relationship. Varactors are operated only in reverse bias to prevent forward conduction which would destroy the capacitive behavior and introduce noise.

The tuning ratio of a varactor is defined as the ratio of maximum to minimum capacitance achievable over its operating voltage range. A high tuning ratio allows a wider frequency tuning range in a VCO. Typical silicon varactors achieve tuning ratios of 3:1 to 10:1.

Mathematical Expression

The junction capacitance of a varactor as a function of applied reverse voltage VR is expressed as:

Cj(VR) = C0 / (1 + |VR| / Vbi)^n, where C0 is the zero-bias junction capacitance, Vbi is the built-in potential of the junction (typically 0.6 to 0.7 V for silicon), and n is the grading coefficient. For an abrupt (step) junction n = 0.5, and for a linearly graded junction n = 0.33. Hyperabrupt varactors have n > 0.5, sometimes as high as 2, giving a much steeper capacitance variation and wider tuning range for a small voltage swing.

Practical Understanding

Varactors are the primary tuning elements in voltage-controlled oscillators (VCOs) used in PLLs inside FM tuners, mobile phones, and satellite receivers. The LC tank circuit of the oscillator uses the varactor as the capacitor. Changing the control voltage shifts the resonant frequency electronically with no mechanical parts.

An important figure of merit is the Q factor of the varactor, which reflects how lossy the capacitor is. At microwave frequencies, series resistance of the diode reduces Q significantly. High-Q varactors use gallium arsenide which has higher electron mobility and lower series resistance than silicon.

Given:
Silicon varactor: C0 = 20 pF, Vbi = 0.7 V, n = 0.5 (abrupt junction)
Applied reverse voltage VR = 4 V

Why this formula applies:
Junction capacitance decreases with reverse bias due to depletion width increase

Formula:
Cj = C0 / (1 + |VR| / Vbi)^n

Substitution:
Cj = 20 / (1 + 4 / 0.7)^0.5
Cj = 20 / (1 + 5.714)^0.5
Cj = 20 / (6.714)^0.5

Calculation:
Cj = 20 / 2.591

Final Answer: Cj = 7.72 pF at VR = 4 V

Exam Tip: For an abrupt junction varactor n = 0.5, so Cj is proportional to (Vbi + VR)^(-0.5). If n = 0.33 it is a linearly graded junction. Hyperabrupt means n > 0.5. GATE often tests which junction type gives larger capacitance variation for the same voltage change.

• Increasing reverse bias pushes majority carriers away from the junction, widening the depletion region (acts as increasing plate separation).
• Capacitance Cj = epsilon * A / W decreases as depletion width W increases.
• Abrupt junction: Cj proportional to (Vbi + VR)^(-0.5). Linearly graded: exponent is -0.33. Hyperabrupt: exponent greater than -0.5.
• Varactor is always operated in reverse bias; forward bias collapses the depletion region and introduces large forward current, eliminating capacitive operation.
• In a VCO, increasing control voltage increases reverse bias, decreases Cj, increases resonant frequency f = 1 / (2*pi*sqrt(LC)).

Quick Revision

• Varactor operates under reverse bias only; capacitance decreases as reverse voltage increases.
• Formula: Cj = C0 / (1 + |VR|/Vbi)^n
• n = 0.5 for abrupt junction, n = 0.33 for linearly graded, n > 0.5 for hyperabrupt.
• Tuning ratio = Cmax/Cmin; hyperabrupt gives highest tuning ratio.
• Applications: VCO tuning in PLL, FM tuners, RF filters.
• Exam trap: Varactor is not used in forward bias. Forward conduction kills its capacitive behavior.
• Q factor reduces at high frequency due to series resistance; GaAs varactors preferred at microwave frequencies.