Impedance to Admittance Calculator
Convert electrical impedance (Z) to admittance (Y) in Siemens (S) using our free calculator. It supports both scalar magnitude only and complex mode with resistance (R) and reactance (X) inputs for AC circuit analysis.
Impedance to Admittance Calculator
How to Use the Impedance to Admittance Calculator
Converting electrical impedance to admittance is simple using our converter tool. Follow these step-by-step instructions:
- 1Select calculation mode: Choose Magnitude Only (for scalar impedance Z) or Complex Impedance (for vector R + jX parameters).
- 2Enter known circuit values: Input either the impedance magnitude or enter resistance and reactance values. Select matching units (Ω, kΩ, or MΩ).
- 3Click Calculate: Press the 'Calculate to Admittance' button to run the reciprocal solver equations and view admittance, conductance, and susceptance.
How to Calculate Impedance to Admittance (Step-by-Step Guide)
In electrical engineering, admittance (Y) is defined as the measure of how easily a circuit or device allows alternating current (AC) to flow. It is the mathematical reciprocal of electrical impedance (Z). Because impedance in AC systems is a complex quantity, admittance is also complex, consisting of conductance (G) as its real part and susceptance (B) as its imaginary part. The formulas and mathematical workflow are presented below.
Scalar Impedance Conversion Formula
For scalar or magnitude-only calculations where phase angles are neglected, admittance is calculated directly using the simple reciprocal formula:
Where:
- Y: Admittance in Siemens (S)
- Z: Impedance magnitude in Ohms (Ω)
Complex Impedance Conversion Formulas
For complex AC circuits where resistance (R) and reactance (X) are given, the impedance is represented as Z = R + jX. The reciprocal relationship Y = 1 / Z is solved as:
Where:
- G: Conductance in Siemens (S), representing the real part
- B: Susceptance in Siemens (S), representing the imaginary part
- R: Resistance in Ohms (Ω)
- X: Reactance in Ohms (Ω)
Note: The sign of susceptance (B) is opposite to the sign of the reactance (X). Inductive reactance (+jX) results in a negative susceptance (−jB), while capacitive reactance (−jX) results in a positive susceptance (+jB).
Real-Life Scenario 1: Scalar Transmission Line (50 Ω Line Impedance)
A telecom designer measures a line impedance magnitude of 50 Ω. Let's calculate its admittance:
- 1Apply Scalar Formula:
Y = 1 ÷ Z
Y = 1 ÷ 50 - 2Solve the Math:
Y = 0.02 S
Final Admittance: 0.02 Siemens.
Real-Life Scenario 2: Parallel Wye Filter Winding (Complex 8 + j6 Ω)
An industrial power designer analyzes a filter winding with a measured resistance of 8 Ω and an inductive reactance of 6 Ω. Let's calculate the complex admittance:
- 1Calculate Denominator (R² + X²):
R² + X² = 8² + 6² = 64 + 36 = 100 - 2Calculate Conductance (G):
G = R ÷ Denominator = 8 ÷ 100 = 0.08 S - 3Calculate Susceptance (B):
B = −X ÷ Denominator = −6 ÷ 100 = −0.06 S
Final Complex Admittance (Y = G + jB): 0.08 − j0.06 Siemens.
Impedance to Admittance Reference Conversion Chart
The table below displays pre-calculated admittance magnitude values in Siemens (S) for various nominal electrical impedance ratings:
| Impedance (Ω) | Admittance (S) |
|---|---|
| 1 Ω | 1.0000 S |
| 2 Ω | 0.5000 S |
| 5 Ω | 0.2000 S |
| 10 Ω | 0.1000 S |
| 20 Ω | 0.0500 S |
| 50 Ω | 0.0200 S |
| 100 Ω | 0.0100 S |
| 200 Ω | 0.0050 S |
| 500 Ω | 0.0020 S |
Impedance to Admittance
The transition from impedance to admittance represents a shift in analytical perspectives. Impedance (Z) measures the opposition to AC current flow, whereas admittance (Y) measures how easily the current is allowed to flow. Mathematically, they are reciprocals of each other, satisfying the equations Y = 1 ÷ Z and Z = 1 ÷ Y.
Impedance to Admittance Conversion
Performing an impedance to admittance conversion is essential when transitioning between series and parallel circuit models. Series circuits are easily analyzed using impedance values (which sum directly), whereas parallel branch circuits are simplified using admittance values (which sum directly in admittance form).
Impedance to Admittance Formula
The complex impedance to admittance formula maps resistance (R) and reactance (X) to conductance (G) and susceptance (B) via vector division:
Y = 1 ÷ (R + jX).
Multiplying by the conjugate yields:
G = R ÷ (R² + X²) and B = −X ÷ (R² + X²), which are measured in Siemens (S).
Impedance to Admittance Smith Chart
An impedance to admittance Smith chart (or Z-Y Smith chart) overlays coordinate grids for both parameters onto a single circular plot. Radio frequency engineers use these charts to design matching impedance networks and analyze reflection coefficients without performing tedious complex matrix multiplications.
Impedance Matrix to Admittance Matrix
In power grid distribution networks, converting the impedance matrix to admittance matrix is critical. The admittance matrix (Ybus matrix) is computed by inverting the network impedance matrix (Zbus):
[Y] = [Z]⁻¹.
This inversion allows engineers to solve load flow and short-circuit fault studies efficiently.
Impedance Admittance Reactance
The interaction of impedance admittance reactance defines AC circuit dynamics. Reactance (X) is the imaginary part of impedance, while susceptance (B) is the imaginary part of admittance. Because susceptance is the imaginary reciprocal, an inductive reactance (+jX) results in a negative susceptance (−jB).
Impedance Admittance Control
In robotics and haptics, impedance admittance control defines the interaction between the manipulator and the environment. Impedance controllers read displacement inputs and command force outputs, while admittance controllers read force sensor inputs and dictate manipulator position adjustments.
Impedance Admittance Conductance Susceptance
Breaking down impedance admittance conductance susceptance reveals the real and imaginary components of circuit parameters. Conductance (G) represents real active current path flow, while susceptance (B) represents reactive energy storage flow. Together they form complex admittance:
Y = G + jB.
Impedance Admittance Susceptance
The imaginary component of admittance, impedance admittance susceptance, determines the reactive behavior of parallel AC lines. Because susceptance (B) sums directly in parallel branches, it is used to design shunt capacitor banks to compensate for inductive line lag in power grids.
Frequently Asked Questions (FAQs)
To convert scalar impedance to admittance, divide one by the impedance value: Y = 1 ÷ Z. To convert complex impedance, divide one by the complex vector: Y = 1 ÷ (R + jX), which resolves to conductance and susceptance components.
The standard complex formula for admittance is: Y = 1 ÷ Z = G + jB, where G is conductance R ÷ (R² + X²) and B is susceptance −X ÷ (R² + X²).
Yes. Admittance is the direct mathematical reciprocal of impedance. A high loop impedance restricting current corresponds to a low admittance, while a low opposition path corresponds to a high admittance.
In AC circuits, calculate admittance by taking the reciprocal of the total complex impedance. For parallel networks, calculate the admittance of each branch separately and sum them directly to find total admittance: Ytotal = Y₁ + Y₂ + Y₃.
The standard International System (SI) unit of admittance is the Siemens (S). It was historically referred to as the "mho" (which is ohm spelled backwards) and represented by the inverted ohm symbol (℧).
To convert complex impedance to conductance (the real part of admittance), use the formula: G = R ÷ (R² + X²). Note that conductance is not simply 1/R unless the circuit reactance (X) is zero.
Impedance measures the opposition to current flow (measured in Ohms, Ω), while admittance measures the ease with which current is allowed to flow (measured in Siemens, S).
The real resistive component of passive impedance is always positive. However, reactance can carry capacitive sign shifts, and active devices (like tunnel diodes) can exhibit dynamic negative resistance locally.
Susceptance (the imaginary part of admittance) is calculated using the formula: B = −X ÷ (R² + X²), where X is reactance and R is resistance. Its sign is opposite to the reactance sign.
The mathematical reciprocal of electrical impedance is admittance (Y), representing the comprehensive AC conductance and susceptance limits of the component.