Filters and Signals
Model class: Exact relationship
Bode magnitude and phase explorer
Evaluate a first-order pole and optional zero at a selected frequency with exact magnitude and phase.
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.
Assumptions to check
- One real pole and at most one real zero.
- Stable linear small-signal behavior.
- Gain and corner frequencies are known.
Magnitude and phase change together
A pole rolls off amplitude and adds lag. A zero does the opposite. At one selected frequency, this engine evaluates the exact first-order response rather than an asymptotic sketch, making the -3 dB and -45° behavior at a pole easy to inspect.
Use it to build intuition and check a simple stage. Cascaded poles, complex poles, sampling, saturation, and stability margins need the full response and the selected circuit model.
Use frequency as a decision variable
A response that is acceptable at a low-frequency marker can become unusable near a pole. Compare the operating band with the relevant corners, then use the next engine or a complete sweep before making a bandwidth or stability decision.
Interpret the marker in the context of a response
A frequency marker is valuable when it answers a specific question, such as whether a sensor signal is attenuated, whether a measurement path loads a node, or whether a control-loop feature is near the intended crossover. Enter the pole and optional zero from a clearly stated transfer function, then compare the selected frequency with the corner frequencies. Magnitude alone is not enough when phase margin, timing, or waveform shape is the practical risk.
This page intentionally evaluates one first-order pole and optional zero. Cascaded filters, op-amp response, parasitic poles, sample-and-hold behavior, transmission-line effects, and nonlinear components can add behavior not visible here. Use a sweep, selected-part data, simulation, or measurement when the operating band approaches another corner or when the output drives a stability, compliance, or timing decision.
Common mistakes
- Confusing amplitude dB with power dB.
- Ignoring phase while checking magnitude.
- Applying a first-order model to a multi-pole stage.
Model limit and handoff
Use a full frequency sweep, selected part data, simulation, and measurement when additional poles, zeros, or stability matter.
FAQs
Why is the response -3 dB at a pole?
A first-order pole reduces magnitude to 1 divided by square root of two at its corner frequency.