Lecher lines

The Lecher line, or even the Lecher system, after the Austrian physicist Ernst Lecher (1856-1926) is named arrangement of a two-wire line for resonance studies and impedance matching at high frequency electrical signals.

Construction

A Lecher their original type consists of two parallel wires of a certain length, which are connected either open or another at their end. Along this line member are formed from standing waves corresponding to the feeding frequency. With sufficient high-frequency power at the fed end you can detect with current bellies glow lamps with bulbs and voltage bellies.

For adjustment purposes or for determining an unknown wavelength or frequency is on the line if necessary, a short shifter.

Lecher lines can also be used as a band-pass or band-stop - the distributed capacitance of the line inductance forms a resonant circuit with her. Lecher lines can be regarded as a mis-matched finite line to its closed or open-ended held reflection.

Circuits of symmetrical or asymmetrical line pieces are called line circuit. They are an alternative to resonant circuits and filters from discrete components at high frequencies in addition waveguide arrays. See also stripline.

Special lengths

Voltage curve for two-sided short-circuit

Voltage waveform at both sides idle

Once in AC, the line length exceeds about 5 % of the wavelength, and short pieces of wire must not be regarded simply as electrical connections, but as a series of very small ( infinitesimal ) inductors, at their connecting points small capacitors can store charge ( line covering). The calculation must be done with the help of the transmission line theory and the sometimes surprising results lead especially for equipment in the radar range too often peculiar constructions. Of particular importance are the transforming properties of specific lengths. Such arrangements can also be built as a cavity resonator or stripline. If the lines like a " printed circuit " border on an insulating substrate, the reduction factor should be considered.

λ/2-Leitung

A line whose length is exactly equal to half the wavelength λ of the feeding frequency, does not transform, but "transfers " the impedance - regardless of their impedance - from one point to another. This does not change at renewal for a further λ/2-Stücke.

• If one end is "open" and therefore has a very high impedance, one can measure this at the other end. It is this characteristic also shows a half-wave dipole.
• If an end with " mass " is connected ( in printed circuits this is the rear copper area ), and the other end has very low impedance, which is also referred to as series resonant or virtual short circuit. In general always produces a line of the length at the end of that impedance is present at the other end.

λ/4-Leitung

An open line with the length of an odd multiple of a quarter of the wavelength λ is used when the impedance is to be greatly changed.

• One end directly or via a low-inductance capacitor to ground at the other end to measure very high impedance, the line acts as a parallel resonant circuit and insulated at this frequency very well. A λ/4-Leitung is an ideal inductor with vanishingly low DC resistance.
• Is there an end open, the other acts as a virtual zero with lower impedance than ever so good capacitor.

Applications of λ/4-Leitung

The door seal of a microwave oven is a circumferential λ/4-Leitung: Since the built- magnetron emits at the wavelength 12 cm, the seal is exactly 3 cm wide. The inner, the magnetron facing edge acts like a short circuit for 2.45 GHz and prevents the emission of RF energy.

Another application displays the detail screen of the amplifier part of a single LNB. The signal is received by the antenna on the left side, three-stage amplified and then passes through a bandpass filter before its frequency by a mixer diode is reduced (below right outside of the image) to approximately 2 GHz.

In the picture you can see some λ/4-lange, wide traces whose starting points are marked with a red x. There they act as virtual nodes and replace blocking capacitors to ground. The distance between a collector and the emitter of the following transistor in each case has the length of λ / 2

Closed coaxial or waveguide arrays with a micrometer moving shorting plunger serve the wavelength or frequency measurement in the decimeter and centimeter range (see shaft diameter).

The acoustic analogue of the standing electromagnetic wave at the Lecher line are the Kundt's dust figures. Bass reflex enclosure are the analogue of the open λ/4-Leitung: At the resonant frequency of the bass reflex deflection of the speaker membrane is almost zero ( acoustic short circuit the " feed point " ), while at the end of the bass reflex tube prevails the maximum amplitude ( " open end "). This periodic change of behavior can also be measured with the vibrating air column in thin tubes.

Electrical Description

Of the capacitance C 'of a Lecher line with the conductor diameter d, and the distance between the center points of a conductor is

The inductance L 'results according to

And thus the characteristic impedance neglecting the dissipation pad and the resistance coating:

Or in a simplified form:

With the dielectric constant εr of the insulating material.