Please enter all required numeric values.
Formulas & Mathematical Logic
Step 1: Convert Cs from fF to F: Cs = Cs × 10^-15. This converts motional capacitance into SI units.
Step 2: Convert Cp from pF to F: Cp = Cp × 10^-12. This converts static capacitance into farads.
Step 3: Convert Ls from mH to H: Ls = Ls × 10^-3. This converts motional inductance into henries.
Step 4: Series resonant frequency: Fs = 1 / (2 × π × sqrt(Ls × Cs)). This is the crystal motional branch resonance.
Step 5: Parallel capacitance combination: Cmix = (Cs × Cp) / (Cs + Cp). This combines motional and static capacitance effects.
Step 6: Parallel resonant frequency: Fp = 1 / (2 × π × sqrt(Ls × Cmix)). This estimates anti-resonance or parallel resonance.
Step 7: Crystal Q factor: Q = 1 / (2 × π × Fs × Rs × Cs). Higher Q means sharper resonance and lower loss.
Step 8: Pulling factor: Pulling Factor = Cp / Cs. This gives a simple ratio for frequency pulling sensitivity.
Step-by-Step Example
Example values: Rs = 50 Ω, Cs = 25 fF, Cp = 3 pF, Ls = 40 mH.
Convert units: Cs = 25 × 10^-15 F, Cp = 3 × 10^-12 F, Ls = 40 × 10^-3 H.
Series frequency: Fs = 1 / (2 × π × sqrt(0.04 × 25e-15)) = about 5032921 Hz.
Parallel capacitance mix: Cmix = (25e-15 × 3e-12) / (25e-15 + 3e-12).
Q factor: Q = 1 / (2 × π × Fs × 50 × 25e-15), showing resonance sharpness.
Practical meaning: the crystal works near its series frequency, while Cp shifts the parallel resonant point slightly higher.
About This Calculator
Understand a quartz crystal like a real resonator, not just a two-pin part.
This CalcBoy calculator estimates series resonance, parallel resonance, Q factor and pulling factor from crystal equivalent circuit values.
A quartz crystal resonator is widely used as a stable frequency reference in oscillators, RF systems, microcontroller clocks, communication equipment and timing circuits. Although the component looks simple from the outside, the electrical behavior is usually described with an equivalent circuit. That model includes motional resistance, motional inductance and motional capacitance in series, plus a static capacitance across the terminals.
Best UseQuartz oscillator design, RF reference planning, crystal filter analysis and frequency stability checks.
Key OutputsSeries frequency, parallel frequency, Q factor and crystal pulling factor.
Design BenefitCompare equivalent circuit values before choosing a crystal for oscillator or filter design.
Practical ReminderReal frequency also depends on load capacitance, drive level, PCB layout, temperature and aging.
The series resonant frequency is mainly determined by the motional inductance and motional capacitance. At this point, the motional branch impedance becomes very low. The parallel resonant frequency is affected by static capacitance, so it appears slightly different from the series resonance. The Q factor gives an idea of how sharp and low-loss the resonance is. A high-Q quartz crystal has a narrow resonance bandwidth and is often desirable for stable oscillator and RF frequency reference applications.
Quick tip: for oscillator design, always compare the calculator result with the crystal datasheet load capacitance, ESR limit, drive level and circuit startup margin.
The pulling factor is useful when studying how capacitance around the crystal may shift the oscillation frequency. In practical Pierce oscillator circuits, microcontroller clock circuits, TCXO modules and RF reference oscillators, small capacitance changes can slightly move the operating frequency. This calculator gives a fast engineering estimate, but final production design should still be verified with measurement, temperature testing and the crystal manufacturer’s equivalent circuit data.
Frequently Asked Questions
What is series resonant frequency in a quartz crystal?
It is the frequency where the motional inductance and motional capacitance resonate and the motional branch impedance becomes very low.
What is parallel resonant frequency?
Parallel resonance includes the effect of the crystal static capacitance, so it is usually slightly different from the series resonance.
What does crystal Q factor mean?
Q factor indicates resonance sharpness and loss. A higher Q usually means lower loss and narrower resonance bandwidth.
What is pulling factor?
Pulling factor is a simple capacitance ratio that helps describe how sensitive the crystal frequency may be to capacitance changes.
Can I use this for oscillator design?
Yes, it is useful for oscillator estimation, but final design should also check load capacitance, ESR, drive level and startup margin.
Why are Cs and Cp in different units?
Motional capacitance Cs is usually very small and often given in femtofarads, while static capacitance Cp is normally in picofarads.
Does this include temperature drift?
No. Temperature drift, aging and load capacitance tolerance should be checked from the crystal datasheet and measured circuit behavior.