Varactor Diode

A varactor diode acts as a voltage-controlled capacitor, and that single property makes it the tuning element inside every FM radio, PLL synthesizer, and voltage-controlled oscillator. Changing the reverse bias voltage by a few volts tunes a receiver across the entire FM band.

Core Concept

A varactor diode (also called a varicap) exploits the voltage-dependent capacitance of a reverse-biased p-n junction. When reverse voltage increases, the depletion region widens. This acts like pulling the plates of a parallel-plate capacitor further apart, reducing C_j.

The BB910 and MV2109 are standard varactor diodes used in TV tuner circuits. A typical device provides a capacitance range of 5 pF to 50 pF as reverse voltage varies from 8V down to 1V. This 10:1 range is enough to tune an LC oscillator over a wide frequency band.

The grading coefficient n controls how quickly capacitance falls with voltage. An abrupt junction has n = 0.5. A hyperabrupt junction has n = 1 to 2, giving a larger tuning range. Hyperabrupt varactors are preferred in wideband VCO designs because their tuning sensitivity dC/dV is higher.

Key Equations

Junction capacitance: C_j = C_0 / (1 + V_R/V_0)^n where C_0 is zero-bias capacitance in pF, V_R is reverse voltage in V, V_0 is built-in potential (0.7V for silicon), and n is grading coefficient (0.5 for abrupt, 1 for hyperabrupt).

Resonant frequency with varactor: f_r = 1 / (2π √(L × C_j)) where L is the inductor in series with the varactor in the tank circuit.

Tuning ratio: C_max / C_min = (1 + V_max/V_0)^n / (1 + V_min/V_0)^n this ratio determines how wide the frequency tuning range will be.

Given:
  C_0 = 60 pF (zero-bias capacitance)
  V_0 = 0.7 V (built-in potential for silicon)
  n = 0.5 (abrupt junction)
  V_R1 = 2 V, V_R2 = 8 V
  Inductor L = 1 µH = 1×10^-6 H

Why this formula:
  C_j depends on reverse voltage via the depletion approximation.

Formula:
  C_j = C_0 / (1 + V_R/V_0)^n

Substitution at V_R = 2V:
  C_j1 = 60 / (1 + 2/0.7)^0.5
       = 60 / (1 + 2.857)^0.5
       = 60 / (3.857)^0.5
       = 60 / 1.964

Substitution at V_R = 8V:
  C_j2 = 60 / (1 + 8/0.7)^0.5
       = 60 / (1 + 11.43)^0.5
       = 60 / (12.43)^0.5
       = 60 / 3.526

Calculation:
  C_j1 = 30.5 pF
  C_j2 = 17.0 pF

  f1 = 1 / (2π √(1×10^-6 × 30.5×10^-12))
     = 1 / (2π × 5.52×10^-9)
     = 28.8 MHz

  f2 = 1 / (2π √(1×10^-6 × 17.0×10^-12))
     = 1 / (2π × 4.12×10^-9)
     = 38.6 MHz

Final Answer:
  C_j at 2V = 30.5 pF, f_r = 28.8 MHz
  C_j at 8V = 17.0 pF, f_r = 38.6 MHz
  Tuning range = 28.8 MHz to 38.6 MHz

Exam Tip: GATE tests the exponent n carefully. For an abrupt junction n = 0.5, for a linearly graded junction n = 1/3, and for hyperabrupt n > 0.5. Many students substitute n = 1 for all cases and get wrong capacitance values. Also remember: varactor is always operated in reverse bias only. Forward bias destroys the capacitive behavior and causes large forward current.

Key Properties

• Varactor diodes are operated exclusively in reverse bias. Forward bias causes forward current and the device stops functioning as a capacitor.
• A typical BB910 varactor provides C_j from 2 pF to 10 pF as V_R varies from 28V to 1V, with n ≈ 0.5.
• Abrupt junction (n = 0.5) gives moderate tuning range. Hyperabrupt junction (n = 1 to 2) gives wider tuning range and is preferred in VCO designs.
• Quality factor Q of a varactor is typically 50 to 200 at 100 MHz. Lower Q adds phase noise to oscillator circuits.
• Series resistance r_s (0.5 Ω to 2 Ω) limits Q at high frequencies and must be minimized in RF designs.
• Varactors are used in PLLs, AFC (automatic frequency control), parametric amplifiers, and frequency multipliers.

Quick Revision

• Varactor = voltage-controlled capacitor using reverse-biased p-n junction.
• C_j = C_0 / (1 + V_R/V_0)^n: capacitance decreases as V_R increases.
• Abrupt junction: n = 0.5. Linearly graded: n = 1/3. Hyperabrupt: n > 0.5.
• Built-in potential V_0 = 0.7V for silicon, 1.2V for GaAs.
• Wider reverse bias: wider depletion region, lower C_j, higher resonant frequency.
• Applications: FM tuner, VCO, PLL, parametric amplifier.
• BB910 and MV2109 are industry-standard varactor diodes for RF tuning.
• Exam trap: Students use n = 1 for all varactor problems. Use n = 0.5 for abrupt junction unless the problem explicitly states hyperabrupt or linearly graded.