Special cases of the quarter wavelength conversion


Above seen method is used to convert different impedances together without affecting standing wave reflections.
The resolution of convert impedances Z1 and Z3 is a piece of  line which impedance is Z2. The length of the line must be equal a quarter wavelength.

Special cases of the impedance conversion method

Metallic insulator

This paradoxal case is when there is a quarter wavelength wire which is grounded on the other end, so short circuited. The case is present for example when transmission line is mounted on ground by quarter wavelength metal rods.

Does it not mean short cicuit? Contrary no, it means insulation. Lets solve the equation Z1 = Z22  / Z3. When Z3 is shorted its impedance is zero and Z1 becomes infinite, so-called insulator. This not only a theory but very practical use.

How an insulator becomes to short circuit

Contrary but also a paradoxal case is when a quarter wavelength wire is left open on the other end.

Then the impedance of Z3 is infinite or insulator. Lets solve the equation Z1 = Z22  / Z3 and we'll found that Z1 becomes zero or it means short circuit.
We can note that it is not a good practice to leave some lateral brances to a transmission line. It is same as leave short circuits here and there.

The open dipole antenna is an application of this. The branches of it are usually quarter wave length. And one point of a good antenna is that it is eating all the singnal from antenna cable and not reflecting any part of it back.

Martti Palomäki