Calculator Inputs
Example Data Table
| Case | C1 | C2 | Stray | L | Estimated Frequency | Load Capacitance |
|---|---|---|---|---|---|---|
| Standard crystal tank | 33 pF | 33 pF | 2 pF | 13.7 µH | 9.997 MHz | 18.5 pF |
| Higher divider ratio | 47 pF | 22 pF | 2.5 pF | 10 µH | 12.036 MHz | 17.486 pF |
| Lower inductance trial | 68 pF | 33 pF | 3 pF | 6.8 µH | 12.154 MHz | 25.218 pF |
Formula Used
- Series capacitance: Cseries = C1 × C2 ÷ (C1 + C2)
- Load capacitance: CL = Cseries + Cstray
- Oscillation estimate: f = 1 ÷ (2π√(L × CL))
- Required inductance: L = 1 ÷ ((2πf)² × CL)
- Solve C2: C2 = Cseries × C1 ÷ (C1 − Cseries)
- Solve C1: C1 = Cseries × C2 ÷ (C2 − Cseries)
- Feedback fraction: β = C1 ÷ (C1 + C2)
- Loop gain estimate: Aloop = amplifier gain × β
- Quality factor estimate: Q = XL ÷ ESR
- Frequency offset: ppm = ((fcalc − fcrystal) ÷ fcrystal) × 1,000,000
These formulas give a practical design estimate. Final values should be verified on the real circuit.
How to Use This Calculator
- Select the calculation mode.
- Enter C1, C2, inductance, and frequency values.
- Add estimated stray capacitance from layout and device pins.
- Enter the crystal target load capacitance.
- Add ESR or expected tank loss.
- Enter available amplifier gain.
- Press Calculate.
- Review frequency, load capacitance, gain margin, Q, and ppm shift.
- Download CSV or PDF for your design record.
Design Article
Why This Calculator Matters
A Colpitts crystal oscillator uses a resonator, an inductor, and two capacitors. The capacitors form a divider. That divider returns a small part of the output signal to the active device. The crystal controls the final frequency. The LC network still matters, because it sets the load seen by the crystal.
This calculator helps during early design. It combines C1 and C2 into one effective capacitance. It also adds stray capacitance. Then it uses the tank formula to estimate frequency. You can reverse the same formula to find an inductor. You can also solve either divider capacitor for a chosen target frequency.
Design Notes
Crystal circuits need more than one number. A frequency can look correct while the feedback is weak. For that reason, the tool reports feedback fraction, required gain, loop gain, and start margin. A margin above one suggests oscillation may begin. A higher margin is usually safer. Very high gain can increase distortion and unwanted modes.
Stray capacitance is important. Socket pads, traces, transistor input capacitance, and probe loading all add capacitance. Small values can shift a high frequency oscillator. Enter realistic stray capacitance before choosing final parts. Use short traces. Keep the resonator area clean. Place the capacitors close to the active device.
Practical Checks
ESR affects quality factor. A lower ESR can improve starting behavior. A high ESR can reduce margin. The calculator estimates Q from inductive reactance and ESR. This is a simple guide. Real circuits also depend on bias, device noise, crystal motional data, and layout.
The result table is useful for documentation. You can export the calculated values as CSV. You can also save a simple PDF report. Use these files when comparing parts, recording test conditions, or sharing a design note with another engineer.
Start with known crystal frequency. Enter the target load capacitance from the crystal data sheet. Choose C1 and C2 values that create a matching effective capacitance. Add estimated stray capacitance. Then review the predicted frequency shift. After that, check the gain margin. Build the circuit on a clean layout. Measure it with a light probe. Update the stray value if measured frequency differs from the estimate. Repeat the check after changing bias, board material, or shield placement. Document each revision carefully.
FAQs
What does this calculator estimate?
It estimates Colpitts tank frequency, effective capacitance, load capacitance, gain margin, Q, and crystal frequency offset. It can also solve inductance, C1, or C2 for a target frequency.
Is this suitable for final production design?
Use it for planning and comparison. Final designs need bench testing. Crystal motional values, board layout, bias current, temperature, and device parasitics can change real performance.
Why is stray capacitance included?
Stray capacitance comes from traces, packages, sockets, transistor input nodes, and test probes. It adds to the effective load capacitance and can shift the oscillator frequency.
What is feedback fraction beta?
Beta is the estimated feedback fraction from the capacitive divider. A larger beta gives more feedback. The active device still needs enough gain to overcome losses.
What start margin should I target?
A margin above one suggests possible startup. A value near one is risky. Many designers prefer extra margin, while avoiding excessive gain that may cause distortion.
Why compare target load capacitance?
Crystal data sheets specify a load capacitance. If your circuit load differs, the oscillation frequency can pull away from the nominal crystal frequency.
What does Q mean here?
Q is estimated from inductive reactance and ESR. Higher Q usually means lower loss and cleaner resonance. This calculator gives a simplified estimate only.
Can I download the results?
Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a simple report containing the displayed result table.