Impedance
Transformation with Quarter-Wave Lines
The input
impedance of a line an odd multiple of λ/4
long is
where Zi is the
input impedance and ZL is the load impedance. If ZL is a pure
resistance, Zi will also be a pure resistance. Rearranging this equation
gives
This means that
if we have two values of impedance that we wish to �match,� we can do so
if we connect them together by a λ/4
transmission line having a characteristic impedance equal to the square
root of their product. A λ
/4 line is, in effect, a transformer, and in fact is
often
referred to as a
quarter-wave
transformer.
It is frequently used as such in antenna work when it is desired, for
example, to transform the impedance of an antenna to a new value that
will match a given transmission line.
You can easily construct your own transmission lines with a suitable
impedance to be used in a Quarter-wave transformer. This page tells you
how to construct your own transmission line with the impedance you want:
Construction of air insulated
transmission lines
When constructing a quarter-wave impedance transformer it is
important to know the velocity factor of the transmission line to get
the lenght of the quarter-wave impedance transformer right.
To calculate the quarter wave length of a certain transmission line
with a known velocity factor and frequency you may use this
calculator. |
