Definitions

# Lecher lines

Lecher lines are a form of parallel conductor that can be used at UHF for creating resonant circuits. They are used at frequencies between HF/VHF where lumped components are used, and UHF/SHF where resonant cavities are more practical. Ernst Lecher of Vienna, 1856 - 1926, created this device bearing his name, probably around 1890.

## Description

For two parallel lines (diameter d, spacing D),

$Z_0 = 276 log_\left\{10\right\} left\left(D/d + sqrt\left\{\left(D/d\right)^2-1\right\} right\right) = \left(120/\left\{sqrt\left\{epsilon_r\right\}\right\}\right) cosh^\left\{-1\right\} \left(D/d\right)$

For parallel wires the formula for capacitance is

l = length C = capacitance per meter

$C = pi epsilon_0 epsilon_r /ln \left\{\left(2D / d \right)\right\},$

Hence as

$Z_0^2 = L/C$

$c = frac 1 \left\{sqrt\left\{\left(L/C\right) cdot C^2\right\}\right\}$
$=frac 1 \left\{Z_0cdotleft\left(piepsilon_0epsilon_rright\right)cdot left\left[ln left\left(\left\{2D/d\right\}right\right)right\right]\right\}$

= 1/{Zo . (π εo εr) / [ln (2D / d)]}

Note: It is possible to purchase a 300 ohm balanced ribbon feeder which is physically the same as a Lecher line.

## Lecher wire system

The Lecher wire system can be used to measure frequency of standing waves. This amounts to a yardstick approach in analyzing the wavelength of radiant energy, being an electronic filter with a high Q. When the measured distance of the weak points (which have narrow locations) in a transmission line (eg., several feet of two wires in a parallel line, at or below a foot apart) an understanding of the standing wave ratio could be obtained.

The Lecher wire system was developed by Ernst Lecher of Vienna circa 1890. The principles behind the Lecher wire system contributed to high-power transmission line and cavity resonator (eg., waveguide) development.

## Applications

### Power amplifier tank circuits

Lecher line circuits can be used for the tank circuits of UHF power amplifiers. For instance, the twin tetrode (QQV03-20) 432 MHz amplifier described by G.R Jessop uses a Lecher line anode tank.

### Frequency measurement

Lecher lines can be used for a crude measurement of frequency. In many ways this is an electrical version of the Kundt's tube experiment which is used to measure the speed of sound in a gas

The technique relies on observing when a Lecher line transmission line with an infinite SWR is a resonant stub. Similar methods can be used to create stub filters using lengths of coaxial cable.

The 'stub filter' method could be used in the following way. If a pair of parallel conductors is used as the anode tank circuit for a modified Valved RF amplifiers stage, then, if the moveable short was to be moved up and down the line, a dip in the anode current would be observed every half wavelength along the line as the amplifier's tank circuit comes to resonance.

Warning' High voltage electronics. This circuit is not for anyone who is not entirely sure of what they are doing. If you are in any doubt as to the hazards of high voltage electronics, then do not attempt to build such a device''

A second method requiring less electronic equipment to be made is to use a SWR meter or an Antenna analyzer in the following system. A source of RF is connected to the SWR meter or Antenna analyzer before the output is connected to a resistive load which is in parallel with the connections to the balanced Lecher line (A balun may be required for making the connection). A moveable short can then be used to search for voltage nodes on the lecher lines. When the short is at a voltage node the line will be an open circuit at this frequency, it will then be possible to measure the distance between voltage nodes. When using either method the distance between the voltage nodes (λ/2) has been measured then as the speed of waves along the line can be calculated the frequency can then be calculated of the waves.

f = v/λ

## Notes

1. G.R. Jessop, VHF UHF manual, RSGB, Potters Bar, 1983, ISBN 0900612924

• Ron Lebar, " The Lecher Line; Used in high frequency electronics, generation & measurement". 14-5-2005.
• "Index to Physics Demonstrations; Lecher wires". Physics Demonstrations, The University of Minnesota. 1997-06-16.
• "E-82. Electromagnetic Radiation; Demonstration Short-wave apparatus". Electricity/Magnetism, Lecture Demonstrations. Purdue University.
• M B Allenson, A R Piercy and K N R Taylor "". 1973 Phys. Educ. 8 47-49. doi 10.1088/0031-9120/8/1/002.
• F. C. Blake and B. H. Jackson, "". The Ohio Journal of Science. *PDF)
• F. C. Blake, "". Physical Lab, Ohio State University. (PDF)

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