VCO Tuning Sensitivity

KVCO = Δf / ΔV

Quick answer

This calculator solves KVCO = Δf / ΔV for VCO Gain. With Frequency Change 22 MHz, Tuning Voltage Change 12 V, the result is 1.83 × 10⁶ Hz/V. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

VCO Gain (MHz)
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Formula

KVCO = Δf / ΔV

Description

The VCO (voltage-controlled oscillator) tuning sensitivity or gain constant KVCO describes how much the oscillation frequency changes per volt of tuning voltage change. It is a critical parameter in PLL design because it directly affects the loop gain and stability. High KVCO allows wide tuning range but makes the VCO more sensitive to noise on the tuning voltage, degrading phase noise. Low KVCO gives better noise performance but limits tuning range. Modern PLL ICs often use multi-band VCOs with calibration to maintain moderate KVCO across a wide frequency range.

Variables

  • KVCO — VCO tuning sensitivity (Hz/V)
  • Δf — Frequency change (Hz)
  • ΔV — Tuning voltage change (V)

Practical Notes

Typical KVCO values: LC VCO 10-100 MHz/V, ring oscillator 100-1000 MHz/V. The PLL loop gain is proportional to KVCO, so variations in KVCO across the tuning range affect loop dynamics. The total frequency range should require less than 80% of the available tuning voltage range to ensure lock over temperature and supply variations.

Symbols and units

Symbol Meaning Default unit Accepted units
KVCO VCO Gain MHz Hz/V
df Frequency Change MHz Hz, kHz, MHz, GHz
dV Tuning Voltage Change V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Frequency Change 22 MHz, Tuning Voltage Change 12 V
  2. 2. The relation: KVCO = Δf / ΔV
  3. 3. Substitute: df = 22 MHz, dV = 12 V
  4. 4. Result: VCO Gain = 1.83 × 10⁶ Hz/V

Worked examples

Minimum range

Given: Frequency Change 0.22 MHz, Tuning Voltage Change 0.33 V

Result: VCO Gain = 666700 Hz/V

Low range

Given: Frequency Change 2.2 MHz, Tuning Voltage Change 3.3 V

Result: VCO Gain = 666700 Hz/V

Typical

Given: Frequency Change 22 MHz, Tuning Voltage Change 12 V

Result: VCO Gain = 1.83 × 10⁶ Hz/V

High range

Given: Frequency Change 0.22 GHz, Tuning Voltage Change 0.23 kV

Result: VCO Gain = 956500 Hz/V

Maximum range

Given: Frequency Change 2.2 GHz, Tuning Voltage Change 2.3 kV

Result: VCO Gain = 956500 Hz/V

Solving for each variable

Solve for VCO Gain

Frequency Change 0.22 MHz, Tuning Voltage Change 0.33 V → 666700 Hz/V

Solve for Frequency Change

VCO Gain 0.1 Hz/V, Tuning Voltage Change 0.33 V → 0.033 Hz

Solve for Tuning Voltage Change

VCO Gain 0.1 Hz/V, Frequency Change 0.22 MHz → 2200 kV

How VCO Gain changes with Frequency Change

Frequency Change (input) VCO Gain (result)
4.84 MHz 183300 Hz/V
12.1 MHz 458300 Hz/V
24.2 MHz 916700 Hz/V
36.3 MHz 1.37 × 10⁶ Hz/V
48.4 MHz 1.83 × 10⁶ Hz/V
72.6 MHz 2.75 × 10⁶ Hz/V
96.8 MHz 3.67 × 10⁶ Hz/V
0.1936 GHz 7.33 × 10⁶ Hz/V
0.3388 GHz 1.28 × 10⁷ Hz/V
0.484 GHz 1.83 × 10⁷ Hz/V

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Frequently asked questions

How do you calculate VCO Tuning Sensitivity?

Use KVCO = Δf / ΔV. With Frequency Change 22 MHz, Tuning Voltage Change 12 V, VCO Gain works out to 1.83 × 10⁶ Hz/V.

What is the formula for VCO Tuning Sensitivity?

The formula is KVCO = Δf / ΔV. The VCO (voltage-controlled oscillator) tuning sensitivity or gain constant KVCO describes how much the oscillation frequency changes per volt of tuning voltage change.

How do you find Frequency Change when you know the other values?

Rearrange for Frequency Change: with VCO Gain 0.1 Hz/V, Tuning Voltage Change 0.33 V, Frequency Change is 0.033 Hz.

How do you find Tuning Voltage Change when you know the other values?

Rearrange for Tuning Voltage Change: with VCO Gain 0.1 Hz/V, Frequency Change 0.22 MHz, Tuning Voltage Change is 2200 kV.

Related Concepts

All Timing & Oscillators formulas →
555 Timer Astable 555 Timer Monostable Crystal Load Capacitance RC Oscillator Frequency Crystal Frequency Stability PLL Lock Time VCO Tuning Sensitivity Jitter from Phase Noise

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