Description
magnitude = 1/(admittanceCoefficient*angularFrequency^exponent); real = magnitude*cos(pi*exponent/2); imaginary = -magnitude*sin(pi*exponent/2).
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.
magnitude = 1/(admittanceCoefficient*angularFrequency^exponent); real = magnitude*cos(pi*exponent/2); imaginary = -magnitude*sin(pi*exponent/2).
When to use this tool
Use Impedance Constant Phase One Frequency Term when checking a supplied impedance component or local ideal-element expression.
How to use the tool and how it works
- Enter admittanceCoefficient, angularFrequency, exponent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read real, imaginary, magnitude. Use the output convention below.
Require positive admittanceCoefficient and angularFrequency and exponent in [0,1]. magnitude = 1/(admittanceCoefficient*angularFrequency^exponent); real = magnitude*cos(pi*exponent/2); imaginary = -magnitude*sin(pi*exponent/2).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| admittanceCoefficient | Positive constant-phase coefficient, with exponent-dependent units. | Required. Finite number; strictly above 0. |
| angularFrequency | Angular frequency in rad/s when using SI electrical component values, not Hz. | Required. Finite number; strictly above 0. |
| exponent | Dimensionless constant-phase exponent in [0,1]. | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| real | Real | Required. Finite number. |
| imaginary | Imaginary | Required. Finite number. |
| magnitude | Magnitude | Required. Finite number. |
{
"input": {
"admittanceCoefficient": 2,
"angularFrequency": 4,
"exponent": 0
},
"output": {
"real": 0.5,
"imaginary": 0,
"magnitude": 0.5
}
}Limitations and assumptions
- This is the constant-phase-element impedance under the stated negative-imaginary convention. The coefficient's units depend on exponent; it is capacitance only at the ideal exponent-one limit.
- 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 Phase Quadrant Token
Classify the signs of real and imaginary into quadrants I-IV, the four named axes or origin.
- Electrochemical Warburg Real Imaginary Pair
real = coefficient/sqrt(angularFrequency); imaginary is its negative.