Transmission Lines: QuarterWave Transformer
We are now aware of the fundamental properties of transmission lines, which are very important in electronics and antenna theory for microwave frequencies (anything above 600 MHz). On this page, we'll look at using the properties of a transmission line to our advantage. The first application is in impedance matching, with the quarterwave transformer.
QuarterWave Transformer
Recall our formula for 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 quarterwavelength 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.
Solution: The problem is to determine Z0 (the characteristic impedance of our quarterwavelength 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 quarterwavelength microstrip transmission line with the characteristic impedance chosen to match the load.
Because the quarterwavelength transmission line is only a quarterwavelength at a single frequency, this is a narrowband matching technique. In the next section, we'll look at more uses of transmission lines.

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