Filters and Signals
Model class: Exact ideal relationship
State-variable filter designer
Check the ideal unity-normalized low-pass, high-pass, and band-pass magnitude checkpoint at the natural frequency.
Interactive engine
Start with the stated conditions.
Values stay in this browser. Choose a representative scenario, then calculate deliberately.
Example ready
Calculate to inspect the result.
The result will identify the direct answer, assumptions, and any warning that changes the next decision.
How much does each input matter?
Each row holds every other input fixed at its current value and moves one input by ±10%, using the same model as the main result. It identifies which input is the binding lever, not a full tolerance stack.
Assumptions to check
- The entered state-variable-filter values represent the stated operating condition.
- This exact ideal relationship is evaluated in the declared lumped or first-pass model.
- A state-variable-filter calculation is not a component qualification or safety approval.
What this state-variable-filter calculation establishes
Check the ideal unity-normalized low-pass, high-pass, and band-pass magnitude checkpoint at the natural frequency. The useful result is the stated electrical quantity and the decision it supports, not an unstated claim about a finished product. This engine keeps the governing relationship visible so an input, unit, condition, or model boundary can be reviewed before a value becomes a component or layout choice.
Under unity normalization, a state-variable filter produces simultaneous low-pass, high-pass, and band-pass outputs that each reach unity magnitude at the natural frequency. Treat the number as a first-pass result for the declared operating point. When a source, load, temperature, frequency, waveform, component tolerance, or measurement condition changes, repeat the calculation at the relevant corner rather than assuming the nominal answer persists.
Worked decision context
For a Q = 1 normalized state-variable filter, low-pass and high-pass magnitudes are 1 at f0 while band-pass magnitude is also 1 under unity normalization. That example verifies the equation and illustrates the scale of the result, but it does not select a part by itself. Compare the result with available values, ratings, tolerance bands, and the receiving circuit or physical environment before implementation.
Use the primary output to identify the binding constraint. If it leaves little margin, document which input dominates and use selected-part data, a higher-fidelity model, simulation, or measurement. This is especially important when a small numerical difference changes a thermal, timing, noise, or reliability decision.
Limits and validation handoff
It is an ideal normalized checkpoint. The synthesized integrator and summer resistor ratios must be verified independently to reach this response in a real implementation. The calculation does not silently include omitted parasitics, installation conditions, manufacturing variation, or product policy. Those conditions can be decisive even when the arithmetic is exact for the selected model.
Record inputs, units, model assumptions, and the intended decision with the result. Verify the leading risk against the selected component data sheet and a representative measurement when the circuit has consequential energy, high voltage, safety, compliance, or reliability requirements.
Common mistakes
- Treating the state-variable-filter result as a guaranteed operating limit rather than a first-pass exact ideal relationship estimate.
- Mixing a data-sheet value measured under one condition with this state-variable-filter calculation performed at another.
- Selecting a component before checking the boundary this calculation names: it is an ideal normalized checkpoint. The synthesized integrator and summer resistor ratios must be verified independently to reach this response in a real implementation.
Model limit and handoff
Keep the entered state-variable-filter conditions with the calculation, then validate the binding limit using the selected component, physical implementation, and representative operating corner.
FAQs
Is this state-variable-filter result sufficient to approve a design?
No. It applies exact ideal relationship reasoning to the entered state-variable-filter values and names the checks that still need selected-part data, a higher-fidelity model, or measurement. It is an ideal normalized checkpoint. The synthesized integrator and summer resistor ratios must be verified independently to reach this response in a real implementation.
What does this state-variable-filter calculator assume that could make the result wrong?
Under unity normalization, a state-variable filter produces simultaneous low-pass, high-pass, and band-pass outputs that each reach unity magnitude at the natural frequency. If the entered values do not match the real operating condition, the result no longer describes the actual circuit.
Where should this state-variable-filter result go next?
Compare this state-variable-filter result with Selecting an op-amp from the signal envelope, then use the stated next decision below the calculator to move from this first-pass number toward an implementation.