Enter Parallel Impedance Branches
Use rectangular form as R + jX. Use polar form as magnitude and phase angle.
Example Data Table
| Branch | Input | Admittance | Example Result |
|---|---|---|---|
| A | 50 + j25 Ω | 0.016 - j0.008 S | Zeq = 28.442 + j2.785 Ω |
| B | 80 - j35 Ω | 0.010492 + j0.00459 S | |
| C | 120 + j0 Ω | 0.008333 + j0 S |
Formula Used
For parallel impedance, every branch is first converted into admittance.
Y1 = 1 / Z1, Y2 = 1 / Z2, ... Yn = 1 / Zn
Ytotal = Y1 + Y2 + ... + Yn
Zequivalent = 1 / Ytotal
For rectangular impedance, Z = R + jX.
For polar impedance, Z = magnitude × cos(angle) + j × magnitude × sin(angle).
When voltage is entered, I = V / Z. Complex power is estimated with S = V × conjugate(I).
How To Use This Calculator
- Select each branch you want to include.
- Choose rectangular or polar input for that branch.
- Enter resistance and reactance for rectangular form.
- Enter magnitude and phase for polar form.
- Choose the correct impedance unit for each branch.
- Enter source voltage if current and power are needed.
- Press the calculate button.
- Use CSV or PDF export for records.
Understanding Parallel Impedance
Parallel impedance appears when two or more paths share the same voltage. Each path may contain resistance, inductive reactance, capacitive reactance, or a mixed load. Because impedance is complex, the total is not found by simple addition. The calculator converts every branch into admittance first. Admittance is the reciprocal of impedance. After all admittances are added, the reciprocal gives the equivalent impedance.
Why Complex Values Matter
A resistor uses only a real value. Inductors and capacitors add an imaginary value. Positive reactance usually represents inductive behavior. Negative reactance usually represents capacitive behavior. These signs affect both magnitude and phase. Two branches can partly cancel each other. That is why a parallel network may have a lower magnitude and a shifted angle.
Practical Use In Circuits
This tool helps during amplifier matching, filter design, sensor loading, and general circuit checking. It also helps when several loads connect across one source. By entering each branch, you can see branch admittance, total admittance, equivalent impedance, current, and power. The optional voltage field gives a deeper view. It estimates total source current and apparent power from the same result.
Reading The Result
The rectangular result shows real and imaginary parts. The polar result shows magnitude and phase angle. A small magnitude means the circuit draws more current for the same voltage. A phase near zero behaves mostly resistive. A positive phase suggests inductive influence. A negative phase suggests capacitive influence.
Good Input Habits
Use consistent units for every branch, or choose the correct unit beside each row. Avoid entering a zero impedance branch, because its reciprocal is infinite. When using polar form, magnitude must be positive. Phase is entered in degrees. For rectangular form, use resistance for the real part and reactance for the imaginary part.
Design Notes
The exported files are useful for lab reports and design records. They keep inputs and results together. You can repeat a calculation after changing one branch. This makes comparison simple. It also helps find the branch that dominates total impedance. In real hardware, component tolerance, temperature, and frequency can change impedance. Use measured values when accuracy matters most. Save one file per design version to track assumptions and later changes easily and clearly.
FAQs
What is impedance in parallel?
It is the equivalent impedance of two or more impedance branches connected across the same two nodes. Each branch shares the same voltage, while current divides between branches.
Why does the calculator use admittance first?
Parallel impedances are easiest to combine by using reciprocals. The reciprocal of impedance is admittance. Add all branch admittances, then take the reciprocal to get total impedance.
Can I enter capacitive reactance?
Yes. Enter capacitive reactance as a negative imaginary value in rectangular form. For example, a capacitive branch may be written as 20 - j40 ohms.
Can I enter inductive reactance?
Yes. Enter inductive reactance as a positive imaginary value in rectangular form. For example, an inductive branch may be written as 30 + j60 ohms.
What does the phase angle mean?
The phase angle shows how much the equivalent impedance leans toward inductive or capacitive behavior. Positive angles suggest inductive influence. Negative angles suggest capacitive influence.
Why is zero impedance rejected?
A zero impedance branch is a short circuit. Its reciprocal is infinite admittance. That makes normal finite branch calculations invalid for this form.
Do all branches need the same unit?
No. Each branch has its own unit selector. The calculator converts every selected branch to ohms before calculating admittance and equivalent impedance.
What is the source voltage field for?
The voltage field is optional. When entered, the calculator estimates total current, branch currents, and complex power using the equivalent network result.