Description
Classify the signs of real and imaginary into quadrants I-IV, the four named axes or origin.
Complex impedance has real and imaginary components whose signs depend on the adopted convention. A single-frequency circuit-element expression or quadrant label is separate from a measured spectrum and from a fitted electrochemical mechanism.
Classify the signs of real and imaginary into quadrants I-IV, the four named axes or origin.
When to use this tool
Use Impedance Phase Quadrant Token when checking a supplied impedance component or local ideal-element expression.
How to use the tool and how it works
- Enter real, imaginary. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read quadrant, phaseDefined. Inspect phaseDefined before interpreting the associated values.
Classify the signs of real and imaginary into quadrants I-IV, the four named axes or origin. phaseDefined is false only when both components are zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| real | Real | Required. Finite number. |
| imaginary | Imaginary | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| quadrant | Quadrant | Required. Text; maximum UTF-16 length 8192. |
| phaseDefined | Phase Defined | Required. Boolean. |
{
"input": {
"real": -2,
"imaginary": 3
},
"output": {
"quadrant": "II",
"phaseDefined": true
}
}Limitations and assumptions
- Components must use the same impedance unit and the intended imaginary-sign convention. No phase angle, frequency response, circuit fit or uncertainty tolerance is calculated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use appropriate frequency-domain measurement and circuit fitting to test an actual impedance model.
References
Similar or alternative tools
- Impedance Constant Phase One Frequency Term
magnitude = 1/(admittanceCoefficient*angularFrequency^exponent); real = magnitude*cos(pi*exponent/2); imaginary = -magnitude*sin(pi*exponent/2).
- Electrochemical Warburg Real Imaginary Pair
real = coefficient/sqrt(angularFrequency); imaginary is its negative.