This calculator allows you to calculate the impedance of a quarter-wave impedance transformer, as well as the length of a quarter-wave segment of a coaxial cable, knowing the material of the internal insulation.
Schematic representation of a quarter-wave transformer:
The velocity factor of a foam insulated cable depends on the production technology and varies from manufacturer to manufacturer. Therefore, in this case, measurements are indispensable, the calculator shows the average value. For a cable with solid or “air” insulation, the velocity factor is uniquely dependent on the material of the inner insulation, and the wavelength in the cable can be calculated more accurately.
The characteristic impedance of the transformer is determined by the formula:
The reflection coefficient at the transformer input is determined by the following formula:
where θ - electrical length, β - phase constant, l - physical length of transformer, λ - wavelength;
From the formula it is clear that when l = λ / 4, that is, if the physical length of the transformer is equal to a quarter of the wavelength, θ = π / 2 or 90°, tan(90°) = ∞ and the reflection coefficient is zero. When the frequency deviates, the electrical length changes and a reflected wave appears. This formula allows you to calculate the transformer bandwidth if the SWR does not exceed two.The calculation is approximate, since losses in the transformer are not taken into account, and it is assumed that the load is pure resistive. Under these conditions, there are no reflections and VSWR = 1 at the operating frequency. Otherwise, you can use an impedance matching calculator.
