Colpitts Oscillator Calculator
Calculate and design the ideal Colpitts oscillator tank using an inductor and a C1/C2 capacitive divider. The calculator solves equivalent capacitance, resonant frequency, C1 or C2, inductance, divider ratios, reactance, and tolerance range.
This page is topology-specific. It intentionally differs from a generic LC resonance calculator by documenting the capacitive divider, solver boundaries, feedback-ratio convention limits, parasitics, and startup boundary.
Engineering tool
Colpitts Oscillator Calculator
Analyze and design the ideal Colpitts LC oscillator tank using C1 and C2 as a capacitive divider.
Mode
Parameter panel
Optional. Leave blank to evaluate reactance at ideal f0.
Result console
- Oscillation Frequency
- 7.11763 MHz
- Equivalent Capacitance
- 50 pF
- Period
- 140.496 ns
- C1:C2 Ratio
- 1
- C2:C1 Ratio
- 1
- Divider Lower Ref
- 0.5V/V
- Divider Upper Ref
- 0.5V/V
- XL
- 447.214 Ω
- XCeq
- 447.214 Ω
- Tank Status
- Near Tank Resonance
Colpitts Formula Audit
- Adopted Tank Topology
- Ideal Colpitts tank: inductor L with a capacitive divider made from C1 and C2.
- C1 Definition
- C1 is one capacitor in the series capacitive divider; node convention affects feedback interpretation.
- C2 Definition
- C2 is the other divider capacitor; C1 and C2 are not parallel tank capacitors.
- Equivalent Capacitance
- Ceq = C1C2 / (C1 + C2), and Ceq must be less than either positive capacitor.
- Resonant Frequency
- f0 = 1 / (2π√(L C_eq)).
- Reactance Identity
- At ideal f0, XL = XCeq.
- Divider Node Definition
- The calculator reports divider references, not a universal loop feedback beta.
- Feedback Boundary
- Colpitts feedback ratio depends on active-device topology, node labeling, loading, and bias network.
- C1 Solver
- C1 = Ceq C2 / (C2 - Ceq), requiring C2 > Ceq.
- C2 Solver
- C2 = Ceq C1 / (C1 - Ceq), requiring C1 > Ceq.
- Inductance Solver
- L = 1 / [(2πf0)^2 Ceq].
- Tolerance Model
- Worst-case corners recompute Ceq from C1 min/max and C2 min/max; no average capacitor tolerance shortcut.
- Startup Boundary
- Tank resonance is not a guaranteed oscillation startup condition.
- Formula Used
- 7.11763 MHz with Ceq 50 pF.
Formula reference
Colpitts Oscillator Formulas
The ideal Colpitts tank uses C1 and C2 as a capacitive divider. Their series-equivalent capacitance sets the LC resonant frequency.
Ceq = C1C2 / (C1 + C2)f0 = 1 / (2π√(LCeq))XL = 2πfLXCeq = 1 / (2πfCeq)At f0: XL = XCeqL = 1 / [(2πf0)^2Ceq]C2 = CeqC1 / (C1 - Ceq)C1 = CeqC2 / (C2 - Ceq)Variable definitions
- L
- tank inductance
- C1
- first capacitive divider capacitor
- C2
- second capacitive divider capacitor
- Ceq
- series-equivalent capacitance of C1 and C2
- f0
- ideal tank resonant frequency
- XL
- inductive reactance
- XCeq
- equivalent capacitive reactance
Colpitts Formula Audit
| Adopted Tank Topology | Ideal Colpitts LC tank with L and a capacitive divider made from C1 and C2. |
|---|---|
| C1 Definition | C1 is one divider capacitor; exact feedback interpretation depends on schematic node convention. |
| C2 Definition | C2 is the other divider capacitor; C1 and C2 are not parallel capacitors. |
| Equivalent Capacitance | Ceq = C1C2/(C1 + C2), always less than either positive capacitor. |
| Resonant Frequency | f0 = 1/(2π√(LCeq)). |
| Reactance Identity | At ideal f0, XL = XCeq. |
| Divider Node Definition | The calculator reports C1:C2, C2:C1, and ideal divider references instead of a universal loop beta. |
| Feedback Boundary | Feedback ratio depends on active-device topology, node labels, loading, and bias network. |
| C1 Solver | C1 = CeqC2/(C2 - Ceq), requiring C2 > Ceq. |
| C2 Solver | C2 = CeqC1/(C1 - Ceq), requiring C1 > Ceq. |
| Inductance Solver | L = 1/[(2πf0)^2Ceq]. |
| Tolerance Model | Ceq corners are recomputed from C1 min/max and C2 min/max; capacitor tolerance is not averaged. |
| Parasitic Boundary | Device capacitance, PCB capacitance, inductor self-capacitance, and probe capacitance are not included. |
| Startup Boundary | LC tank resonance does not guarantee oscillator startup or amplitude stability. |
Worked Examples
Equivalent capacitance
Known: L = 10 µH, C1 = 100 pF, C2 = 100 pF
Ceq = C/2 = 50 pF.
Oscillation frequency
Known: L = 10 µH, Ceq = 50 pF
f0 ≈ 7.11763 MHz.
Reactance identity
Known: At f0
XL and XCeq are equal in the ideal tank model.
Unequal capacitors
Known: C1 = 100 pF, C2 = 200 pF
Ceq ≈ 66.6667 pF.
Target Ceq
Known: Target f = 10 MHz, L = 10 µH
Ceq = 1/[(2πf)^2L] ≈ 25.3303 pF.
Solve C2
Known: Target 10 MHz, L = 10 µH, C1 = 100 pF
C2 is solved from C2 = CeqC1/(C1 - Ceq), then analyzer returns 10 MHz.
Solve C1
Known: Target 10 MHz, L = 10 µH, C2 = 100 pF
C1 is solved symmetrically and the design round-trips to target frequency.
Solve L
Known: Target 10 MHz, C1 = 100 pF, C2 = 200 pF
L = 1/[(2πf)^2Ceq], then analyzer returns 10 MHz.
Invalid preferred capacitor
Known: Known capacitor equals target Ceq
No finite positive solution exists for the other capacitor.
Invalid smaller capacitor
Known: Known capacitor less than target Ceq
The solver rejects the design instead of returning negative capacitance.
Equal capacitor case
Known: C1 = C2 = C
Ceq = C/2.
Tolerance range
Known: L ±5%, C1 ±5%, C2 ±5%
fmin < fnominal < fmax using recomputed Ceq corners.
Increase C1
Known: C2 fixed
Ceq increases and f0 decreases.
Increase C2
Known: C1 fixed
Ceq increases and f0 decreases.
Capacitance units
Known: 1000 pF = 1 nF
Both values produce the same result after unit conversion.
Frequency units
Known: 1 MHz = 1000 kHz
Both target frequency inputs solve the same component values.
Divider reciprocal
Known: C1 = 100 pF, C2 = 200 pF
C1:C2 = 0.5 and C2:C1 = 2.
Design round trip
Known: Target -> solve C or L -> analyze
The analyzer recovers the target frequency within numerical tolerance.
Engineering Notes
Colpitts oscillator
A Colpitts oscillator uses a capacitive divider in its LC resonant network.
Equivalent capacitance
C1 and C2 form a series-equivalent capacitance, not a parallel sum.
Tank resonance
The ideal tank frequency follows f0 = 1/(2π√(LCeq)).
Divider reference
Capacitor ratio affects feedback reference, but exact loop beta depends on the active circuit.
Startup condition
The active device must overcome tank losses; resonance alone is not a startup guarantee.
Tank Q
Inductor Q, capacitor ESR, and loading affect startup, amplitude, stability, and phase noise.
Parasitics
Transistor junction capacitance, PCB capacitance, inductor self-capacitance, and probes shift real frequency.
Inductor SRF
The selected inductor must have self-resonant frequency well above the oscillator frequency.
Supply voltage
Supply voltage does not directly appear in the ideal tank formula, but bias-dependent device capacitance can shift real frequency.
Verification
Critical Colpitts designs need active-device datasheets, SPICE, layout review, and measured validation.
Common Mistakes
Support reference
FAQ
What is a Colpitts oscillator?
A Colpitts oscillator is an LC oscillator that uses an inductor and a capacitive divider made from C1 and C2 as the frequency-selective tank and feedback reference.
How do I calculate Colpitts oscillator frequency?
First calculate the series-equivalent capacitance Ceq = C1C2/(C1 + C2), then use f0 = 1/(2π√(LCeq)).
How do I calculate the equivalent capacitance?
For the ideal Colpitts divider, C1 and C2 form a series-equivalent capacitance: Ceq = C1C2/(C1 + C2). Ceq is always less than either positive capacitor.
Why are C1 and C2 treated as series capacitors?
The two capacitors form the capacitive divider in the tank. Their series-equivalent capacitance, not C1 + C2, sets the ideal LC resonant frequency.
How do I choose C1 and C2 for a target frequency?
Given target frequency and L, calculate the target Ceq. Then choose either C1 or C2 larger than Ceq and solve the other capacitor using C2 = CeqC1/(C1 - Ceq) or C1 = CeqC2/(C2 - Ceq).
How does the capacitor ratio affect feedback?
The capacitor ratio changes the tank divider reference, but the exact loop feedback depends on circuit topology, active device, node labeling, loading, and bias network.
What is the feedback ratio of a Colpitts oscillator?
There is no safe universal beta statement without defining C1/C2 labels and feedback nodes. This calculator reports divider references and avoids claiming a universal loop beta.
Why does feedback-ratio convention depend on the circuit?
Different Colpitts implementations sample different nodes and may use BJT, FET, op-amp, or other active devices. Label conventions also vary between schematics.
How do I calculate the required inductance?
Use L = 1/[(2πf0)^2Ceq] after calculating Ceq from C1 and C2.
How do component tolerances affect frequency?
Worst-case low frequency occurs with maximum L and maximum Ceq. Worst-case high frequency occurs with minimum L and minimum Ceq, with Ceq recomputed from C1 and C2 corners.
How do parasitic capacitances affect a Colpitts oscillator?
Transistor junction capacitance, PCB capacitance, inductor self-capacitance, and probe capacitance add to the effective tank capacitance and can pull the frequency.
Why does inductor Q matter?
Inductor Q affects tank loss, startup margin, amplitude, stability, and phase noise. The ideal LC frequency calculation does not model inductor DCR or core loss.
Does the LC resonant frequency guarantee oscillator startup?
No. Tank resonance is only the frequency-selection condition. The active circuit must provide enough loop gain or negative resistance to overcome tank losses.
What is the difference between this and the LC Resonance Calculator?
The LC Resonance Calculator solves a generic LC frequency relationship. This page is Colpitts-specific and includes the C1/C2 capacitive divider, solver boundaries, divider references, and oscillator design notes.
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Engineering Disclaimer
This calculator models the ideal Colpitts tank and capacitive divider. It does not model transistor bias, active-device negative resistance, tank loss, phase noise, amplitude stabilization, parasitic extraction, or full RF oscillator startup. Validate critical designs with datasheets, SPICE, layout parasitic review, and bench measurement.