VCO Frequency & Gain Calculator
Calculate voltage-controlled oscillator output frequency, KVCO, control voltage, tuning range, deviation, measured linearity, local gain, and tolerance corners using a clear linear reference-point model.
OSC-011 focuses on VCO voltage-to-frequency behavior. PLL divider ratios, phase detector gain, charge pumps, loop filters, bandwidth, lock time, phase noise and jitter integration are intentionally outside this calculator.
Engineering tool
VCO Frequency & Gain Calculator
Analyze linear VCO tuning, KVCO, control voltage, tuning range, and measured linearity.
Calculation mode
Parameter panel
Result console
- Output Frequency
- 110 MHz
- Voltage Offset
- 0.5 V
- Frequency Offset
- 10 MHz
- Frequency Deviation
- 10%
- KVCO
- 20 MHz/V
- Angular KVCO
- 125.664 Mrad/s/V
- Ripple Sensitivity
- 20 kHz
VCO formula audit
| Adopted VCO Model | Linear reference-point model. |
|---|---|
| Reference Frequency | fREF is the output frequency at VREF. |
| Reference Voltage | VREF is the control voltage associated with fREF. |
| Control Voltage | VCTRL is the tuning input voltage. |
| Frequency-Domain KVCO | KVCO = df/dV in Hz/V. |
| Angular KVCO | Kω = 2πKf in rad/s/V. |
| Hz/V ↔ rad/s/V | Never treat MHz/V as Mrad/s/V without the 2π conversion. |
| Frequency Formula | fOUT = fREF + KVCO(VCTRL - VREF). |
| Inverse Voltage | VCTRL = VREF + (fTARGET - fREF)/KVCO. |
| Two-Point KVCO | KVCO = (f2 - f1)/(V2 - V1). |
| Negative KVCO | Positive and negative tuning slopes are both supported. |
| Tuning Range | fmin/fmax use min() and max() so negative KVCO is handled correctly. |
| Center Frequency | fcenter = [f(Vmin) + f(Vmax)]/2 = f(Vcenter) for the linear model. |
| Tuning Span % | (fmax - fmin)/fcenter × 100%. |
| Local KVCO | Adjacent-point slopes after sorting by control voltage. |
| Regression | Least-squares fit of frequency versus control voltage. |
| Residual | Measured frequency minus fitted frequency. |
| R² | Goodness of fit to the entered linear model only. |
| Tolerance Model | Corner enumeration of entered fREF, KVCO, VCTRL and VREF ranges. |
| Extrapolation Boundary | Out-of-range control voltage is reported, not clamped. |
| PLL Scope Boundary | PLL divider, PFD, charge pump, loop filter, bandwidth and lock time are outside V1. |
Formula reference
VCO Frequency and Gain Formulas
The V1 model uses a linear VCO tuning approximation around a reference control voltage and frequency. Use measured tuning curves when the VCO is nonlinear.
KVCO = df/dVKω = 2πKVCOfOUT = fREF + KVCO(VCTRL - VREF)VCTRL = VREF + (fTARGET - fREF)/KVCOKVCO(two-point) = (f2 - f1)/(V2 - V1)Tuning Span % = (fmax - fmin)/fcenter × 100%Local KVCO,i = (fi+1 - fi)/(Vi+1 - Vi)Residual = fmeasured - ffittedΔf ≈ KVCO × ΔVcontrolVariable definitions
- fREF
- output frequency at the reference voltage
- VREF
- reference control voltage
- VCTRL
- applied control voltage
- KVCO
- frequency-domain VCO gain in Hz/V
- Kω
- angular VCO gain in rad/s/V
- fTARGET
- target output frequency
VCO Frequency & Gain Formula Audit
| Adopted VCO Model | Linear reference-point model. |
|---|---|
| Reference Frequency Definition | fREF is the frequency at VREF. |
| Reference Voltage Definition | VREF is the control voltage associated with fREF. |
| Control Voltage Definition | VCTRL is the voltage applied to the tuning input. |
| Frequency-Domain KVCO | KVCO = df/dV in Hz/V. |
| Angular KVCO | Kω = 2πKf in rad/s/V. |
| Hz/V ↔ rad/s/V | Frequency-domain and angular-domain gains differ by 2π. |
| Frequency Formula | fOUT = fREF + KVCO(VCTRL - VREF). |
| Inverse Voltage Formula | VCTRL = VREF + (fTARGET - fREF)/KVCO. |
| Two-Point KVCO | KVCO = (f2 - f1)/(V2 - V1). |
| Negative KVCO Support | Negative tuning slope is valid and supported. |
| Tuning Range | fmin/fmax use min() and max() of endpoint frequencies. |
| Center Frequency | fcenter = [f(Vmin) + f(Vmax)]/2. |
| Tuning Span % | (fmax - fmin)/fcenter × 100%. |
| Local KVCO | Adjacent measured-point slopes after sorting by VCTRL. |
| Regression Model | Least-squares line fit for frequency versus control voltage. |
| Residual | Measured frequency minus fitted frequency. |
| R² | Fit quality for the entered linear model only. |
| Tolerance Model | Corner enumeration of entered fREF, KVCO, VCTRL and VREF ranges. |
| Extrapolation Boundary | Out-of-range control voltage is reported, not clamped. |
| PLL Scope Boundary | PLL loop filter, divider, PFD, charge pump, bandwidth and lock time are not calculated. |
Worked Examples
Positive KVCO
Known: 100 MHz @ 1.5 V, KVCO = 20 MHz/V, VCTRL = 2.0 V
ΔV = 0.5 V, Δf = 10 MHz, fOUT = 110 MHz.
Lower control voltage
Known: Same model, VCTRL = 1.0 V
fOUT = 90 MHz.
Two-point KVCO
Known: 1 V / 90 MHz and 2 V / 110 MHz
KVCO = 20 MHz/V.
Midpoint
Known: Same two points
Midpoint is 1.5 V and 100 MHz.
Target voltage
Known: Target = 105 MHz, 100 MHz @ 1.5 V, KVCO = 20 MHz/V
VCTRL = 1.75 V.
Negative KVCO
Known: 100 MHz @ 1.5 V, KVCO = -10 MHz/V, VCTRL = 2 V
fOUT = 95 MHz.
Negative range ordering
Known: KVCO < 0 with Vmin = 1 V and Vmax = 2 V
Actual fmin/fmax are sorted by value, not assumed from voltage.
Zero KVCO inverse
Known: KVCO = 0
Frequency-to-voltage solver rejects division by zero.
Invalid two-point span
Known: V1 = V2
Two-point characterization rejects zero voltage span.
Invalid tuning range
Known: Vmin >= Vmax
Range analysis rejects the input.
Outside control range
Known: Solved VCTRL beyond Vmin/Vmax
Warning is shown and the voltage is not clamped.
Small-signal ripple
Known: KVCO = 10 MHz/V, ripple = 1 mV
Frequency deviation reference is 10 kHz.
Larger ripple
Known: KVCO = 100 MHz/V, ripple = 10 mV
Frequency deviation reference is 1 MHz.
KVCO units
Known: 1 MHz/V
Equivalent to 1000 kHz/V.
Angular KVCO
Known: 20 MHz/V
Kω = 2πKf = 125.663706 Mrad/s/V.
Perfect fit
Known: Three linear tuning points
R² = 1 and residuals are zero.
Nonlinear fit
Known: Measured point deviates from the line
R² < 1 and residual is nonzero.
Unsorted points
Known: Points entered out of voltage order
Local KVCO is calculated after sorting by VCTRL.
Duplicate voltage
Known: Two points share VCTRL
Rejected because local KVCO is undefined.
Center identity
Known: Linear tuning range
f(Vcenter) equals [f(Vmin)+f(Vmax)]/2.
Round trip
Known: frequency → voltage → frequency
The original target frequency is recovered in the linear model.
Tolerance corners
Known: fREF/KVCO/VCTRL/VREF tolerances entered
Corner enumeration verifies fmin <= fnom <= fmax.
Engineering Notes
| Voltage-Controlled Oscillator | A VCO changes output frequency in response to a control voltage. |
|---|---|
| VCO Gain | KVCO is frequency sensitivity, not voltage gain in V/V. |
| Angular Gain | PLL literature may use rad/s/V; convert with 2π. |
| Control Voltage | Target frequency may require a voltage outside the valid tuning range. |
| Tuning Range | Negative KVCO is supported by sorting endpoint frequencies. |
| Tuning Linearity | Real VCO tuning curves are often nonlinear, so local KVCO may vary. |
| Control Noise | High KVCO increases sensitivity to control-line ripple and noise. |
| Frequency Pushing | Supply pushing is separate from control-voltage KVCO. |
| Load Pulling | Output load changes can shift oscillator frequency and are not modeled. |
| Varactor | Varactor C-V physics is not derived here; use measured or datasheet tuning data. |
| PLL | This is a VCO tuning calculator, not a PLL loop calculator. |
Common Mistakes
- Treating KVCO as voltage gain in V/V.
- Confusing MHz/V with Mrad/s/V.
- Forgetting the 2π angular conversion.
- Requiring KVCO to always be positive.
- Calculating two-point KVCO when V1 equals V2.
- Using KVCO = 0 in an inverse voltage solver.
- Assuming Vmax always gives fmax when KVCO is negative.
- Silently clamping control voltage to the tuning range.
- Treating extrapolation as characterized behavior.
- Assuming KVCO is constant across the full tuning range.
- Using two points to claim perfect VCO linearity.
- Confusing control sensitivity with supply pushing.
- Expanding a VCO calculator into a PLL loop calculator.
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Support reference
FAQ
What is a voltage-controlled oscillator?
A voltage-controlled oscillator is an oscillator whose output frequency changes in response to an applied control voltage.
What is KVCO?
KVCO is the frequency sensitivity of a VCO, defined as df/dV. In this calculator the primary engineering unit is Hz/V or MHz/V.
How do I calculate VCO gain?
For two measured tuning points, calculate KVCO = (f2 - f1)/(V2 - V1).
What units are used for KVCO?
Frequency-domain KVCO is commonly expressed in Hz/V, kHz/V, MHz/V or GHz/V. Some PLL texts use rad/s/V.
What is the difference between Hz/V and rad/s/V?
Angular KVCO in rad/s/V equals 2π times frequency-domain KVCO in Hz/V.
How do I calculate VCO frequency from control voltage?
Use fOUT = fREF + KVCO(VCTRL - VREF) for the linear reference-point model.
How do I calculate the required control voltage for a target frequency?
Use VCTRL = VREF + (fTARGET - fREF)/KVCO. KVCO must be non-zero.
Can KVCO be negative?
Yes. Some VCOs tune downward as control voltage increases, so the calculator supports negative KVCO.
How do I calculate the VCO tuning range?
Calculate f(Vmin) and f(Vmax), then use min and max so both positive and negative KVCO ranges are handled correctly.
What is center frequency?
For a linear tuning range, center frequency is the average of f(Vmin) and f(Vmax), equal to f at the center voltage.
What is local KVCO?
Local KVCO is the slope between adjacent measured tuning points after sorting by control voltage.
Why does KVCO change across the tuning range?
Real VCO tuning curves are often nonlinear because varactor capacitance, device bias and tank behavior are not perfectly linear.
How does control-voltage noise affect a VCO?
Control voltage ripple creates instantaneous frequency deviation approximately equal to KVCO times the ripple voltage.
What is VCO frequency pushing?
Frequency pushing is frequency sensitivity to supply voltage, which is different from control-voltage KVCO.
What is the difference between VCO analysis and PLL design?
This calculator analyzes VCO tuning behavior only. PLL divider ratios, phase detector gain, charge pumps, loop filters, bandwidth and lock time are outside its scope.
Engineering Disclaimer
This calculator provides first-order VCO tuning estimates from entered frequency, voltage and measured data. Critical designs require datasheet tuning curves, control-line noise analysis, temperature characterization, supply pushing and load pulling checks, simulation, and measurement.