Clapp Oscillator Calculator
Calculate and design an ideal Clapp oscillator tank using L, C1, C2, and the added C3 series tuning capacitor. The calculator solves effective capacitance, frequency, C3, divider capacitor references, inductance, sensitivity, reactance, and tolerance range.
This page is Clapp-specific. It extends the Colpitts capacitor divider with C3 dominance analysis, target C3 solving, and careful boundaries for feedback, parasitics, and startup.
Engineering tool
Clapp Oscillator Calculator
Analyze and design the ideal Clapp oscillator tank using L, C1, C2, and the added C3 series tuning capacitor.
Mode
Parameter panel
Optional. Leave blank to evaluate reactance at ideal f0.
Result console
- Oscillation Frequency
- 5.513289 MHz
- Equivalent Capacitance
- 83.333333 pF
- Colpitts C12 Ref
- 500 pF
- Period
- 181.379936 ns
- C1/C3 Ratio
- 10
- C2/C3 Ratio
- 10
- Ceq/C3
- 0.833333
- XL
- 346.410162 Ω
- XCeq
- 346.410162 Ω
- Dominance Status
- C3-Dominant Approximation
Clapp Formula Audit
- Adopted Tank Topology
- Ideal Clapp tank: Colpitts-style C1/C2 divider plus series tuning capacitor C3 with L.
- C1 Definition
- C1 is one capacitor in the feedback divider, not the only tank capacitance.
- C2 Definition
- C2 is the second feedback-divider capacitor.
- C3 Definition
- C3 is the added series tuning capacitor that often dominates frequency when C1 and C2 are much larger.
- Equivalent Capacitance
- 1/Ceq = 1/C1 + 1/C2 + 1/C3.
- Oscillation Frequency
- f0 = 1 / (2π√(LCeq)).
- Reactance Identity
- At ideal f0, XL = XCeq.
- C3 Solver
- C3 = 1 / (1/Ceq - 1/C1 - 1/C2), requiring a positive denominator.
- C1/C2 Solver
- Divider capacitor references require enough known constraints and a positive reciprocal denominator.
- Colpitts Limit
- As C3 becomes very large, Ceq approaches C1C2/(C1 + C2).
- Dominant-C3 Limit
- As C1 and C2 become much larger than C3, Ceq approaches C3.
- Sensitivity Model
- Frequency sensitivity is computed by deterministic +1% perturbation for each capacitor.
- Tolerance Model
- Worst-case corners recompute series Ceq; no averaged capacitor tolerance shortcut.
- Feedback Boundary
- C1/C2 feedback ratio is topology and node dependent; no universal beta is claimed.
- Startup Boundary
- Tank resonance is not a guaranteed startup condition.
- Formula Used
- 5.513289 MHz with Ceq 83.333333 pF.
Formula reference
Clapp Oscillator Formulas
The ideal Clapp tank places C1, C2, and C3 in a series-equivalent capacitance network with L.
1/Ceq = 1/C1 + 1/C2 + 1/C3Ceq = C1C2C3 / (C1C2 + C1C3 + C2C3)f0 = 1 / (2π√(LCeq))XL = 2πfLXCeq = 1 / (2πfCeq)At f0: XL = XCeqC3 = 1 / (1/Ceq - 1/C1 - 1/C2)L = 1 / [(2πf0)^2Ceq]Variable definitions
- L
- tank inductance
- C1
- first capacitive divider capacitor
- C2
- second capacitive divider capacitor
- C3
- added series tuning capacitor
- Ceq
- equivalent tank capacitance
- f0
- ideal tank resonant frequency
Clapp Formula Audit
| Adopted Tank Topology | Ideal Clapp oscillator: Colpitts-style C1/C2 divider plus C3 series tuning capacitor with L. |
|---|---|
| C1 Definition | C1 is one capacitive divider capacitor. |
| C2 Definition | C2 is the second capacitive divider capacitor. |
| C3 Definition | C3 is the added series tuning capacitor and often the dominant frequency-setting capacitor. |
| Equivalent Capacitance | 1/Ceq = 1/C1 + 1/C2 + 1/C3. |
| Oscillation Frequency | f0 = 1/(2π√(LCeq)). |
| Reactance Identity | At ideal f0, XL = XCeq. |
| C3 Solver | C3 = 1/(1/Ceq - 1/C1 - 1/C2), requiring denominator > 0. |
| C1 Solver | C1 = 1/(1/Ceq - 1/C2 - 1/C3), requiring denominator > 0. |
| C2 Solver | C2 = 1/(1/Ceq - 1/C1 - 1/C3), requiring denominator > 0. |
| Inductance Solver | L = 1/[(2πf0)^2Ceq]. |
| Colpitts Limit | As C3 becomes very large, Ceq approaches C1C2/(C1 + C2). |
| Dominant-C3 Limit | As C1 and C2 become much larger than C3, Ceq approaches C3. |
| Sensitivity Model | Numerical +1% perturbation for C1, C2, and C3. |
| Tolerance Model | Worst-case corners recompute series Ceq from C1/C2/C3 values. |
| Feedback Boundary | C1/C2 feedback ratio depends on active-device topology and node definitions. |
| Startup Boundary | LC resonance does not guarantee startup. |
Worked Examples
Equivalent capacitance
Known: C1 = 1000 pF, C2 = 1000 pF, C3 = 100 pF
Ceq ≈ 83.3333 pF.
Oscillation frequency
Known: L = 10 µH, Ceq ≈ 83.3333 pF
f0 ≈ 5.51329 MHz.
Reactance identity
Known: At f0
XL and XCeq are equal in the ideal tank.
Equal capacitors
Known: C1 = C2 = C3 = 300 pF
Ceq = 100 pF.
Dominant-C3 limit
Known: C1 and C2 much larger than C3
Ceq approaches C3.
Colpitts limit
Known: C3 very large
Ceq approaches C1C2/(C1 + C2).
Solve C3
Known: Target 10 MHz, L = 10 µH, C1 = C2 = 1 nF
Solved C3 round-trips through analyzer to 10 MHz.
Invalid C3 solve
Known: Target Ceq >= C1/C2 series equivalent
The solver rejects the design.
Solve L
Known: Target f and known C1/C2/C3
L is solved and then recovers the target frequency.
Solve C1
Known: Known C2, C3, L, and target f
C1 is solved from the reciprocal relation.
Solve C2
Known: Known C1, C3, L, and target f
C2 is solved from the reciprocal relation.
C3 sensitivity
Known: Dominant-C3 example
+1% C3 shifts frequency more than +1% C1.
Tolerance
Known: L ±5%, C1/C2 ±5%, C3 ±2%
fmin < fnominal < fmax.
Capacitance units
Known: 1000 pF = 1 nF
Both inputs produce the same result.
Frequency units
Known: 1 MHz = 1000 kHz
Both target inputs solve the same values.
Design round trip
Known: Target -> solve C3 -> analyze
The analyzer recovers the target frequency.
Ceq boundary
Known: Positive C1, C2, C3
Ceq is less than each individual capacitor.
Clapp vs Colpitts
Known: Finite positive C3
Clapp Ceq is less than C1/C2 Colpitts reference.
Engineering Notes
Clapp oscillator
A Clapp oscillator is closely related to the Colpitts oscillator.
Series tuning capacitor
C3 is added in series with the tank capacitance network.
Equivalent capacitance
The ideal tank uses the reciprocal series relation for C1, C2, and C3.
Frequency stability
When C1 and C2 are much larger than C3, C3 largely controls frequency.
Capacitive divider
C1/C2 still participates in the feedback network.
Feedback boundary
No universal beta is stated because node definitions and active topology matter.
Parasitics
Clapp topology can reduce some sensitivity to stray capacitance but cannot eliminate it.
Tank Q
Inductor Q, DCR, capacitor ESR, and load resistance affect startup and phase noise.
Varactor tuning
C3 can be a varactor for tuning, but nonlinear C(V) behavior is outside this V1 model.
Verification
Critical Clapp designs need device models, SPICE, layout review, and measurement.
Common Mistakes
- Treating Clapp as an ordinary Colpitts tank and forgetting C3.
- Using C1 + C2 + C3 instead of the reciprocal series relation.
- Using C1C2/(C1 + C2) while ignoring C3.
- Claiming C3 always equals Ceq regardless of C1/C2 size.
- Claiming C3 dominance without checking ratios or sensitivity.
- Continuing a C3 solve when the denominator is <= 0.
- Calling C1/C2 a universal feedback beta.
- Assuming tank resonance guarantees startup.
- Ignoring active-device capacitance.
- Ignoring inductor Q and winding resistance.
- Ignoring temperature drift.
- Assuming Clapp topology is immune to parasitic capacitance.
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Support reference
FAQ
What is a Clapp oscillator?
A Clapp oscillator is an LC oscillator related to the Colpitts oscillator, but it adds a third series tuning capacitor C3 in the resonant network.
How is a Clapp oscillator different from a Colpitts oscillator?
A Colpitts oscillator uses the C1/C2 capacitive divider. A Clapp oscillator adds C3 in series so the tank capacitance is set by C1, C2, and C3 together.
How do I calculate Clapp oscillator frequency?
First calculate Ceq from 1/Ceq = 1/C1 + 1/C2 + 1/C3, then use f0 = 1/(2π√(LCeq)).
How do I calculate the equivalent capacitance?
Use the reciprocal series-capacitance relation or the equivalent product form C1C2C3/(C1C2 + C1C3 + C2C3).
Why is C3 important in a Clapp oscillator?
When C1 and C2 are much larger than C3, the equivalent capacitance approaches C3, making C3 the dominant frequency-setting capacitor.
When does C3 dominate the oscillation frequency?
C3 dominates when C1/C3 and C2/C3 are large enough that Ceq is close to C3. This calculator reports ratios and sensitivity instead of using a universal cutoff rule.
How do I solve C3 for a target frequency?
Calculate the target Ceq from f0 and L, then solve C3 = 1/(1/Ceq - 1/C1 - 1/C2). The denominator must be positive.
How do I calculate the required inductance?
Calculate Ceq from C1, C2, and C3, then use L = 1/[(2πf0)^2Ceq].
What happens if C3 is very large?
As C3 becomes very large, 1/C3 approaches zero and the Clapp equivalent capacitance approaches the C1/C2 Colpitts series-equivalent capacitance.
What happens if C1 and C2 are much larger than C3?
The equivalent capacitance approaches C3, so frequency sensitivity is dominated by the C3 tuning capacitor and the tank inductance.
How do component tolerances affect frequency?
Low frequency occurs with maximum L and maximum capacitance values. High frequency occurs with minimum L and minimum capacitance values, with Ceq recomputed at each corner.
Why is the Clapp oscillator considered more frequency stable?
With large C1 and C2, C3 can dominate Ceq, reducing the relative influence of some stray and active-device capacitances, though it does not eliminate drift.
Do parasitic capacitances still matter?
Yes. Device capacitance, PCB capacitance, inductor self-capacitance, and probe loading still shift the actual oscillator frequency.
Does LC resonance guarantee oscillator startup?
No. The active circuit must provide enough loop gain or negative resistance to overcome tank losses. This ideal calculator does not model startup margin.