Impedance Amplitude

Fit sine/cosine components with a DC intercept to simultaneous voltage/current samples at a supplied injection frequency and derive complex impedance magnitude/phase; no FFT leakage assumption is needed.

Description

Impedance at one sinusoidal frequency compares fitted voltage and current amplitudes and phases.

Impedance at one sinusoidal frequency compares fitted voltage and current amplitudes and phases. Fitting sine, cosine and an offset accommodates a constant baseline.

The tool returns voltageAmplitudeMv (voltage amplitude mv); currentAmplitudeNa (current amplitude na); impedanceMagnitudeMohm (impedance magnitude mohm); phaseDegrees (phase degrees). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Impedance Amplitude

Use Impedance Amplitude when you already have timesSeconds, voltageMv, currentNa, frequencyHz and want voltageAmplitudeMv, currentAmplitudeNa, impedanceMagnitudeMohm, phaseDegrees. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Impedance Amplitude and understand its results

Enter timesSeconds, voltageMv, currentNa, frequencyHz using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read voltageAmplitudeMv, currentAmplitudeNa, impedanceMagnitudeMohm, phaseDegrees. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
timesSeconds	Times seconds	list of number	Required
voltageMv	Voltage mv	list of number	Required
currentNa	Current na	list of number	Required
frequencyHz	Frequency hz	number	Required

Fit both traces by centered two-component least squares at the supplied positive frequency. Require at least four samples and a nonsingular design; wrap phase into [−180,180) degrees.

Z magnitude[MΩ] = voltageAmplitude[mV]/currentAmplitude[nA]; phase = voltagePhase−currentPhase

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "timesSeconds": [
      0,
      0.25,
      0.5,
      0.75
    ],
    "voltageMv": [
      0,
      2,
      0,
      -2
    ],
    "currentNa": [
      0,
      1,
      0,
      -1
    ],
    "frequencyHz": 1
  },
  "output": {
    "voltageAmplitudeMv": 2,
    "currentAmplitudeNa": 1,
    "impedanceMagnitudeMohm": 2,
    "phaseDegrees": 0
  }
}

Limitations and assumptions

No frequency sweep or artifact correction occurs. Insufficient phase coverage and zero amplitudes are rejected.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Resonance Frequency: Find the unique sampled impedance maximum and distinguish an interior resonance candidate from an edge maximum; ratio references the lowest measured frequency, not extrapolated DC. Subthreshold Oscillation Frequency: Estimate subthreshold oscillation frequency from interpolated upward reference crossings; spikes and drift must be removed beforehand and cadence must resolve the waveform.

Methodological background: Least squares estimation.^[1]

References

Least squares estimation — NIST/SEMATECH

Similar or alternative tools

Resonance Frequency
Find the unique sampled impedance maximum and distinguish an interior resonance candidate from an edge maximum; ratio references the lowest measured frequency, not extrapolated DC.
Subthreshold Oscillation Frequency
Estimate subthreshold oscillation frequency from interpolated upward reference crossings; spikes and drift must be removed beforehand and cadence must resolve the waveform.