Voltage Controlled Oscillator

A voltage-controlled oscillator changes its output frequency in direct response to an input DC voltage. The VCO inside the CD4046 PLL chip is used in FM radio demodulators and clock recovery circuits in digital communications.

Core Concept

A VCO is built around a variable-capacitance or variable-current element that changes the oscillation frequency when a DC voltage is applied. The most common implementation uses a varactor diode (also called a varicap) whose junction capacitance decreases as reverse bias increases. Changing Vc changes C, which shifts the resonant frequency of the LC tank circuit.

In CMOS VCOs (like inside the CD4046), the control voltage steers a current source that charges a timing capacitor faster or slower. A higher Vc means faster charging and a higher output frequency. The CD4046 VCO section covers 1 Hz to 1.4 MHz with just two external components: R1 (or R2) and C1.

The key parameter is the VCO gain constant Kv, measured in Hz/V or rad/s/V. A linear VCO has a straight-line f vs Vc characteristic across its operating range. Non-linearity in this curve causes phase noise and reference spurs when the VCO is used inside a phase-locked loop.

Key Equations

VCO output frequency: f_out = f_0 + Kv * Vc

where f_0 is the free-running frequency at Vc = 0, Kv is VCO gain in Hz/V, and Vc is the control voltage in volts.

VCO gain: Kv = (f_max - f_min) / (Vc_max - Vc_min)

In angular frequency: Ko = 2 * pi * Kv [rad/s/V]

For CD4046 VCO, approximate frequency: f ≈ 1 / (R1 * C1) at mid-range control voltage.

Given:
  VCO with f_min = 500 kHz at Vc = 1V
            f_max = 4.5 MHz at Vc = 8V
  Find: Kv and f_out at Vc = 4V

Why this formula:
  VCO has a linear f vs Vc transfer characteristic.

Formula:
  Kv = (f_max - f_min) / (Vc_max - Vc_min)

Substitution:
  Kv = (4.5e6 - 0.5e6) / (8 - 1)
     = 4e6 / 7

Calculation:
  Kv = 571,428 Hz/V ≈ 0.571 MHz/V

  f_0 (extrapolated to Vc=0):
  f_0 = f_min - Kv * Vc_min
      = 0.5e6 - 571428 * 1
      = -71428 Hz  (not physical; use f_min as lower limit)

  f_out at Vc = 4V:
  f_out = f_min + Kv * (Vc - Vc_min)
        = 0.5e6 + 571428 * (4 - 1)
        = 0.5e6 + 1.714e6

Final Answer:
  f_out = 2.214 MHz at Vc = 4V
  Kv    = 0.571 MHz/V

Exam Tip: In GATE PLL questions, the VCO gain Kv is almost always asked in rad/s/V, not Hz/V. Always convert: Ko = 2 * pi * Kv. A VCO with Kv = 100 kHz/V has Ko = 6.28 * 10^5 rad/s/V. Missing this factor of 2*pi is the single most common error in PLL loop-gain calculations.

Key Properties

• The CD4046 VCO operates from a 3V to 18V supply and covers a frequency range of 1 Hz to 1.4 MHz with R1 = 10 kΩ and C1 = 100 pF.
• VCO gain Kv is expressed in Hz/V for frequency-domain analysis, and as Ko in rad/s/V for PLL loop-filter design.
• A varactor-tuned LC VCO uses the voltage-dependent capacitance of a BB105 or similar diode, typically ranging from 1 pF to 10 pF over a 0V to 10V reverse bias sweep.
• Phase noise in VCOs is measured in dBc/Hz at an offset frequency (e.g., -90 dBc/Hz at 10 kHz offset) and is the dominant quality metric in RF design.
• The free-running frequency f_0 is the output frequency when the control voltage is set to exactly half the supply voltage (Vcc/2) in a symmetrical CMOS VCO.
• In a PLL, the VCO acts as an integrator in the loop transfer function because phase is the integral of frequency, adding a 90-degree phase lag.

Quick Revision

• VCO output: f_out = f_0 + Kv * Vc, linear over operating range.
• Kv in Hz/V; Ko = 2*pi*Kv in rad/s/V used in PLL equations.
• CD4046 has a built-in VCO section; frequency set by R1 and C1.
• Varactor diode (varicap) provides voltage-controlled capacitance for LC-VCOs.
• Higher control voltage means higher output frequency in a standard VCO.
• In a PLL, the VCO acts as an integrator: phase is the integral of frequency.
• Exam trap: Students substitute Kv in Hz/V directly into PLL loop-gain formulas that require Ko in rad/s/V, giving answers that are off by a factor of 2*pi.