How do I simulate a crystal oscillator?

Open this page and use the live Pole–Zero Response tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a crystal oscillator from your own measurements.

Use case · powered by Pole–Zero Response

Pole–Zero Response for a crystal oscillator

Simulate a crystal oscillator live in your browser. This runs the real Pole–Zero Response solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

Pole–Zero & Frequency ResponseLive

poles peak, zeros notch

Controls

Presets

Pole radius

Pole angle (°)

Zero angle (°)

A digital filter is defined by its poles and zeros in the z-plane. A pole near the unit circle creates a resonant peak at its angle; a zero on the circle carves a notch. Move them and watch the frequency response reshape. Educational tool.

▶ Run in Python

Data Inspector

Pole radius0.85

Resonance at45° (ω)

Stabilitystable ✓

Governing equation

H (z) = \frac{( z - e ^{j 12 0^{\circ}} ) ( z - e ^{- j 12 0^{\circ}} )}{( z - 0.85 e ^{j 4 5^{\circ}} ) ( z - 0.85 e ^{- j 4 5^{\circ}} )}, stable ⟺ ∣ p ∣ = 0.85 < 1

Reading this result: A pole at r=0.85, 45° gives a resonant peak while the zero at 120° carves a separate notch — a classic two-feature filter.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

About this simulation

The full Pole–Zero Response tool models a crystal oscillator with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

More you can do with Pole–Zero Response

Pole–Zero Response for an RLC circuit Pole–Zero Response for a power supply Pole–Zero Response for a transformer Pole–Zero Response for a DC motor Pole–Zero Response for an op-amp filter Pole–Zero Response for an antenna Pole–Zero Response for a transmission line Pole–Zero Response for a PCB trace

Other ways to simulate a crystal oscillator

Fourier Transform for a crystal oscillator Bode Plot for a crystal oscillator Filter Designer for a crystal oscillator PID Controller for a crystal oscillator Transmission Line for a crystal oscillator Op-Amp Circuits for a crystal oscillator

Frequently asked questions

How do I simulate a crystal oscillator?: Open this page and use the live Pole–Zero Response tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a crystal oscillator from your own measurements.