Input Impedance Calculator for Transmission Lines

Estimate input impedance for practical transmission line design studies. Enter load, length, frequency, and attenuation. Review complex results with ready exports for guided study.

Calculator

Formula used

General lossy line:

Zin = Z0 × (ZL + Z0 tanh(γl)) / (Z0 + ZL tanh(γl))

Propagation constant: γ = α + jβ

Phase constant: β = 2π / λ

Wavelength in line: λ = c × VF / f

Loss conversion: α in Np per meter = dB per meter / 8.686

For a lossless line, set attenuation to zero. Then γl becomes jβl.

How to use this calculator

Choose the load type first. Use custom load when you know the real and imaginary parts of ZL.

Enter characteristic impedance Z0. Most common coax examples use 50 Ω or 75 Ω.

Enter physical length, frequency, and velocity factor. The calculator converts them into electrical length.

Enter attenuation if the line is lossy. Use zero for an ideal lossless line.

Press calculate. The result appears above the form and below the header.

Use the CSV or PDF buttons to save the calculated report.

Example data table

Case Z0 ZL Length Frequency Velocity factor Attenuation
Coax load check 50 + j0 Ω 75 + j25 Ω 2 m 100 MHz 0.66 0 dB/m
Shorted stub 50 + j0 Ω Short 0.25 m 300 MHz 0.8 0.02 dB/m
Open stub 75 + j0 Ω Open 1.5 ft 450 MHz 0.7 0 dB/ft

Why input impedance matters

Input impedance tells what a source sees at a line entrance. It is not always equal to the load. A transmission line transforms impedance when its length is a meaningful part of a wavelength. That is why cable length, frequency, velocity factor, loss, and load values all matter. This calculator handles complex loads. It also supports open, short, and matched cases. Those options help with antennas, filters, stubs, and laboratory lines.

What the calculator evaluates

The tool uses the general lossy transmission line equation. It treats characteristic impedance and load impedance as complex numbers. It converts length to meters. It converts frequency to hertz. It then computes phase constant, wavelength, electrical length, and propagation constant. Attenuation can be entered as decibels per chosen unit. A zero attenuation value gives the common lossless result. The output includes rectangular impedance, polar impedance, normalized impedance, admittance, reflection coefficient, return loss, and VSWR.

Practical interpretation

A small input reflection coefficient means the source sees a better match. A high VSWR means stronger standing waves. A quarter wave section can transform a low load into a high input impedance, or the opposite. A half wave line often repeats the load impedance when loss is small. Loss reduces reflected wave magnitude. This can make input VSWR look better, even when the actual load is poorly matched.

Good data improves results

Use measured cable velocity factor when possible. Manufacturer values are useful, but real cables vary. Use the same reference plane for length and load data. Include connector and fixture length when it is important. Keep units consistent. For radio frequency work, small length errors can move the phase strongly. For audio or low frequency work, the same physical line may be electrically short. In that case, the input impedance may stay close to the load.

Advanced use

Try sweeping length outside this page by exporting several runs. Compare open and short stubs at the same frequency. Use normalized impedance when checking Smith chart values. Use admittance for shunt stub design. Always confirm power limits, insulation ratings, and measurement uncertainty before building hardware. Document each assumption clearly. Reports are easier to review when every input, unit, and option remains visible during later checks.

FAQs

What is input impedance?

Input impedance is the impedance seen at the sending end of a transmission line. It depends on load impedance, line length, frequency, velocity factor, and line loss.

When is input impedance equal to load impedance?

It is equal when the line is matched, very short electrically, or near a half wavelength under low loss. Exact equality depends on phase and loss.

Can I enter a complex load?

Yes. Enter the real part and imaginary part separately. Use a positive imaginary value for inductive reactance. Use a negative value for capacitive reactance.

What does velocity factor mean?

Velocity factor is the signal speed in the line divided by light speed. It changes wavelength inside the line and affects electrical length.

What should I enter for a lossless line?

Enter zero in the attenuation field. The calculator then uses the lossless form through the same general equation.

Why can an open line show low impedance?

A line can transform impedance. An open circuit near a quarter wavelength may look like a short at the input when loss is small.

What is normalized impedance?

Normalized impedance is input impedance divided by characteristic impedance. It is useful for Smith charts and quick matching comparisons.

Is VSWR calculated at the load or input?

This page reports input reflection behavior. Loss can reduce reflected wave magnitude before it reaches the input, so input VSWR may differ from load VSWR.

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