Basic Principle of Narrow-band Designs
Devices based upon both lumped components and transmission lines can be purchased or constructed. The simplest example of a transmission line based system is the transformer formed by a quarter wavelength of mismatched transmission line. For example if a quarter wavelength of 75 Ω coaxial cable is linked to a 50 Ω load then the SWR in the 75 Ω quarter wavelength of line can be calculated to be 75 Ω / 50 Ω = 1.5, the quarterwavelength of line transforms this mismatched impedance to 112.5 Ω (75 Ω x 1.5 = 112.5 Ω). For more details please see the Smith chart.
The basic circuit required when lumped capacitances and inductors are used is shown below.
This basic network is able to act as an impedance transformer. If the output has an impedance consisting of Rload and jXload, while the input is to be attached to a source which has an impedance of Rsource and jXsource.
In this example circuit XL and XS can be swapped. All the ATU circuits below serve to create this network which exists between the systems with different impedances.
For instance if the source has a resistive impedance of 50 ohms while the load has a resistive impedance of 1000 ohms then.
If the frequency is 28 MHz then
Read more about this topic: Antenna Tuner
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... By adding another element in series which has a reactive impedance of +j 217.94, the impedance is 50 ohms (resistive). ...
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