FXR Radio Transmission Line Calculator

Calculator Input

Frequency

Frequency Unit

Line Length

Length Unit

Velocity Factor

Reference Impedance Z0, Ω

Load Resistance R, Ω

Load Reactance X, Ω

Attenuation, dB per 100 m

Forward Power, W

Target Match Impedance, Ω

Decimal Precision

Formula Used

The calculator treats the line as a distributed radio transmission path.

Wavelength: λ = c × VF / f
Phase constant: β = 2π / λ
Propagation constant: γ = α + jβ
Load reflection coefficient: ΓL = (ZL - Z0) / (ZL + Z0)
Input impedance: Zin = Z0 × (ZL + Z0 tanh(γl)) / (Z0 + ZL tanh(γl))
VSWR: (1 + |Γ|) / (1 - |Γ|)
Return loss: -20 log10(|Γ|)
Mismatch loss: -10 log10(1 - |Γ|²)
Quarter wave transformer: Zt = √(Ztarget × Rload)

How To Use This Calculator

Enter the operating frequency and choose the correct unit.
Enter the physical cable or feed line length.
Add the velocity factor from the cable data sheet.
Enter reference impedance, usually 50 Ω or 75 Ω.
Enter load resistance and reactance from an antenna analyzer.
Add attenuation in dB per 100 meters.
Enter forward power for voltage and power estimates.
Press Calculate and review the result above the form.
Use CSV or PDF export for reports and field records.

Example Data Table

Case	Frequency	Length	VF	Z0	Load	Attenuation	Use
HF dipole feed	14.2 MHz	10 m	0.66	50 Ω	75 + j20 Ω	0.8 dB / 100 m	Check tuner input impedance
VHF coax run	146 MHz	18 m	0.82	50 Ω	42 - j8 Ω	4.5 dB / 100 m	Estimate loss and SWR
Broadcast sample	100 MHz	30 m	0.78	75 Ω	75 + j0 Ω	3 dB / 100 m	Confirm matched line behavior

FXR Radio Transmission Line Guide

A radio line connects a transmitter, tuner, amplifier, or receiver to an antenna system. The calculator studies that line as a distributed circuit. It uses frequency, physical length, velocity factor, attenuation, reference impedance, and complex load impedance. These values describe how voltage and current waves move along the conductor pair.

Why The Result Matters

A small mismatch can still waste power. A large mismatch can raise voltage stress, increase heat, and hide tuning problems. Input impedance is especially useful. It tells you what the transmitter or tuner sees at the near end of the line. The load impedance tells you what the antenna presents at the far end. They are often very different when the line is not an exact half wavelength.

Practical Use Cases

Use the tool before cutting feed line. Compare coax choices by changing velocity factor and loss. Test quarter wave or half wave lengths for a planned band. Estimate SWR and return loss before choosing a matching network. You can also check how extra length rotates the impedance around the Smith chart.

Reading The Outputs

Wavelength shows the distance for one full cycle in the selected line. Electrical length converts the physical length into degrees. Reflection coefficient shows mismatch strength and phase. VSWR gives a familiar radio measure. Return loss expresses the reflected wave in decibels. Input impedance gives the complex resistance and reactance at the equipment end.

Design Notes

The model assumes a uniform line. It also assumes the reference impedance is real. Real installations may include connectors, traps, baluns, moisture, bends, and ground effects. Treat the output as an engineering estimate. Then verify important systems with a calibrated analyzer.

Better Decisions

Start with measured antenna impedance when possible. Enter the operating frequency and the actual installed cable length. Use the maker value for velocity factor. Use published attenuation for the cable at the same frequency. Then compare several lengths. The best length is not always the shortest. It is the one that supports safe voltage, acceptable loss, and an easier match.

Exporting Results

Use the CSV export for spreadsheets. Use the PDF export for field records. Keep the report with antenna notes, weather, and analyzer readings during later checks.

FAQs

What is an FXR radio transmission line calculator?

It is a radio line analysis tool. It estimates wavelength, electrical length, input impedance, reflection coefficient, SWR, return loss, mismatch loss, and power behavior from frequency, line length, cable data, and load impedance.

Why does input impedance differ from load impedance?

A transmission line transforms impedance as waves travel along it. Frequency, length, velocity factor, loss, and load reactance all affect the impedance seen at the transmitter end.

What velocity factor should I enter?

Use the value from the feed line data sheet. Solid polyethylene coax may be near 0.66. Foam dielectric cable may be higher. Open wire line can be higher still.

What does VSWR mean?

VSWR compares maximum and minimum standing wave voltage on the line. A value near 1:1 means a close match. Higher values show stronger mismatch and more reflected energy.

Is return loss better when it is higher?

Yes. Higher return loss means the reflected wave is smaller. For example, 20 dB return loss is better than 10 dB return loss.

Can this replace an antenna analyzer?

No. It is an estimating tool. Use measured impedance from an analyzer for best results. Real systems can include connector faults, nearby objects, ground effects, and weather changes.

Why include attenuation?

Attenuation models cable loss. It affects input reflection, delivered power, and matched line loss. Use a value for the same cable type and operating frequency.

When is a quarter wave transformer useful?

It is useful when matching mostly resistive impedances. The calculator estimates transformer impedance with the square root of target impedance times load resistance.