Parallel Square Conductor Transmission Line Calculator

Estimate transmission line behavior using square conductor geometry and dielectric inputs. Compare spacing effects instantly. Save tables, charts, and clean reports for analysis today.

Calculator Inputs

The center spacing must be larger than twice the equivalent radius. The model uses an equal-area round-conductor approximation for square bars.

Formula Used

This calculator models two identical square conductors as an equivalent round pair. The equivalent radius is req = a / √π, where a is the square side.

The geometric term is u = acosh(D / (2req)). Here D is the center spacing. This term drives impedance, capacitance, and inductance estimates.

Inductance per meter is L′ = (μ / π)u. Capacitance per meter is C′ = (π ε) / u. Characteristic impedance is Z0 = √(L′ / C′).

Wave velocity is v = 1 / √(L′C′). Delay is length divided by velocity. Wavelength is velocity divided by frequency.

For conductor loss, skin depth is δ = √[1 / (πfμσ)]. AC resistance uses the smaller of full square area and skin-depth area 4aδ. Total attenuation is approximated by conductor and dielectric low-loss terms.

How to Use This Calculator

Enter the square side length, conductor spacing, and total line length. Choose matching units for each dimension so the geometry is interpreted correctly.

Set the dielectric constant for the medium surrounding the conductors. Use 1 for air. Increase the value for plastics, laminates, or other insulating materials.

Enter frequency, conductivity, and loss tangent. Conductivity affects resistance. Loss tangent estimates dielectric dissipation. Relative permeability usually remains 1 for nonmagnetic materials.

Press the calculate button. The result block appears under the header and above the form. Use the export buttons to save current outputs.

Review the graph to see how spacing changes impedance. Wider spacing raises impedance for the same conductor size and dielectric condition.

Example Data Table

Case Side Spacing Length εr Frequency Impedance Delay Total loss
Air-spaced copper pair 8.000 mm 25.000 mm 10.000 m 1.000 100.000 MHz 201.159 ohm 33.356 ns 0.044307 dB
Low-loss dielectric pair 10.000 mm 30.000 mm 25.000 m 2.100 50.000 MHz 135.179 ohm 120.845 ns 0.107063 dB
Higher permittivity pair 12.000 mm 40.000 mm 5.000 m 4.300 10.000 MHz 100.991 ohm 34.585 ns 0.018952 dB

Frequently Asked Questions

1. Why does spacing change impedance?

Greater spacing weakens electric coupling between conductors. That lowers capacitance and raises the geometric term. The result is a higher characteristic impedance.

2. Why use an equivalent round radius?

Closed-form square-bar formulas are less convenient for a compact calculator. The equivalent round model gives practical quasi-static estimates with clear assumptions.

3. What dielectric constant should I enter?

Use 1 for air. Use the material’s relative permittivity when the conductors are embedded or closely surrounded by a dielectric.

4. Does this tool handle loss?

Yes. It estimates conductor loss from skin depth and dielectric loss from loss tangent. These are low-loss approximations, not a full field-solver result.

5. What happens at zero frequency?

Wave properties still exist in theory, but wavelength and skin-depth behavior become less meaningful. The calculator mainly targets AC and transmission applications.

6. Is the result valid for very close conductors?

Accuracy drops when the spacing approaches the equivalent diameter. Very tight geometries often need numerical electromagnetic analysis for stronger confidence.

7. Why include conductivity and loss tangent?

Conductivity controls metal resistance, especially at higher frequency. Loss tangent captures dielectric heating and energy dissipation in insulating material.

8. Can I use this for design comparisons?

Yes. It is useful for screening conductor sizes, spacings, and dielectrics. Final designs should still be verified against measurements or detailed simulation.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.