Lecher line

In

Wavelength measurement

A Lecher line is a pair of parallel uninsulated wires or rods held a precise distance apart.

The nodes are much sharper than the antinodes, because the change of voltage with distance along the line is maximum at the nodes, so they are used.[10]^[9]

Finding the nodes

Two methods are employed to find the nodes.

The other method used to find the nodes is to slide the terminating shorting bar up and down the line, and measure the current flowing into the line with an RF ammeter in the feeder line.^[9][11] The current on the Lecher line, like the voltage, forms a standing wave with nodes (points of minimum current) every half wavelength. So the line presents an impedance to the applied power which varies with its length; when a current node is located at the entrance to the line, the current drawn from the source, measured by the ammeter, will be minimum. The shorting bar is slid down the line and the position of two successive current minima is noted, the distance between them is half a wavelength.

With care, Lecher lines can measure frequency to an accuracy of 0.1%.^[9][1][10]

Construction

A major attraction of Lecher lines was they were a way to measure frequency without complicated electronics, and could be improvised from simple materials found in a typical shop. Lecher line wavemeters are usually built on a frame which holds the conductors rigid and horizontal, with a track that the shorting bar or indicator rides on, and a built-in measuring scale so the distance between nodes can be read out.

A simpler design is a U-shaped metal bar, marked with graduations, with a sliding shorting bar.^[1] In operation, the U end acts as a coupling link and is held near the transmitter's tank coil, and the shorting bar is slid out along the arms until the transmitter's plate current dips, indicating the first node has been reached. Then the distance from the end of the link to the shorting bar is a half-wavelength. The shorting bar should always be slid out, away from the link end, not in, to avoid converging on a higher order node by mistake.

In many ways Lecher lines are an electrical version of the

Measuring the speed of light

If the frequency f of the radio waves is independently known, the wavelength λ measured on a Lecher line can be used to calculate the speed of the waves, c, which is approximately equal to the speed of light:

${\displaystyle c=\lambda f\,}$

In 1891, French physicist

Other applications

Short lengths of Lecher line are often used as high

The separation between the Lecher bars does not affect the position of the standing waves on the line, but it does determine the characteristic impedance, which can be important for matching the line to the source of the radio frequency energy for efficient power transfer. For two parallel cylindrical conductors of diameter d and spacing D,

${\displaystyle Z_{0}=276\log \left({\frac {D}{d}}+{\sqrt {\left({\frac {D}{d}}\right)^{2}-1}}\right)=}$ ${\displaystyle {\frac {120}{\sqrt {\epsilon _{r}}}}\cosh ^{-1}\left({\frac {D}{d}}\right)}$

For parallel wires the formula for capacitance (per unit length) C is

${\displaystyle C={\frac {\pi \epsilon _{0}\epsilon _{r}}{\ln {\left({\frac {2D}{d}}\right)}}}\,}$

Hence as

${\displaystyle Z_{0}^{2}={\frac {L}{C}}}$

${\displaystyle {\begin{aligned}c&={\frac {1}{\sqrt {{\frac {L}{C}}\cdot C^{2}}}}\\&={\frac {1}{Z_{0}\cdot \left(\pi \epsilon _{0}\epsilon _{r}\right)\cdot \ln \left({\frac {2D}{d}}\right)}}\end{aligned}}}$

Commercially available 300 and 450

See also

• Transmission line

References