A quater wave line may be considered as an impendence inverter because it can transform a low impendence in to a high impendence and vice versa.

**IMPEDANCE MATCHING: QUARTER WAVE TRANSFORMER.**

A quater wave line may be considered as an impendence
inverter because it can transform a low impendence in to a high impendence and
vice versa.

Quarter-Wave Transformer

The input impedance of a transmission line of
length L with characteristic impedance Z0 and connected to a load with
impedance ZA:

An interesting thing happens when the length of
the line is a quarter of a wavelength:

The above equation is important: it states that
by using a quarter-wavelength of transmission line, the impedance of the load
(ZA) can be transformed via the above equation. The utility of this operation
can be seen via an example.

Example. Match a load with impedance ZA=100
Ohms to be 50 Ohms using a quarter-wave transformer, as shown below.

Solution: The problem is to determine Z0 (the
characteristic impedance of our quarter-wavelength transmission line) such that
the 100 Ohm load is matched to 50 Ohms. By applying the above equation, the
problem is simple:

Hence, by using a transmission line with a characteristic
impedance of 70.71 Ohms, the 100 Ohm load is matched to 50 Ohms. Hence, if a
transmitter has an impedance of 50 Ohms and is trying to deliver power to the
load (antenna), no power will be reflected back to the transmitter.

In general, impedance matching is very
important in RF/microwave circuit design. It is relatively simple at a single
frequency, but becomes very difficult if wideband impedance matching is
desired.

This technique is commonly employed with patch
antennas. Circuits are printed as shown in the following figure. A 50 Ohm
microstrip transmission line is matched to a patch antenna (impedance typically
200 Ohms or more) via a quarter-wavelength microstrip transmission line with
the characteristic impedance chosen to match the load

Because the quarter-wavelength transmission
line is only a quarter-wavelength at a single frequency, this is a narrow-band
matching technique

An important application of the quarter wave
matching section is to a couple a transmission line to a resistive load such as
an antenna .The quarter –wave matching section then must be designed to have a
characteristic impendence Ro so chosen that the antenna resistance Ra is
transformed to a value equal to the characteristic impendence Ra of the
transmission line

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Transmission Lines and Waveguides : Impedance Matching in High Frequency Lines : Impedance Matching: Quarter Wave Transformer |

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