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/* Designing a Quarter-Wave Impedance Transformer */
==Designing a Quarter-Wave Impedance Transformer==
[[File:RF11.png|right|thumb|400px480px|The quarter-wave impedance transformer circuit.]]
Quarter-wave impedance transformer are often used for impedance matching between two [[Transmission Lines|transmission lines]] of different characteristic impedances Z<sub>o1</sub> and Z<sub>o2</sub>. In that case, a line segment of length L = 0.25λ<sub>g</sub> with a characteristic impedance of Z<sub>0</sub> = √( Z<sub>o1</sub> . Z<sub>o2</sub> ) is inserted between the two [[Transmission Lines|transmission lines]]. In this part of the tutorial lesson, we design a quarter-wave impedance transformer that matches your 100Ω resistive load to the voltage source with the 50Ω internal resistance.
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This time, the source will see a matched transmission line between Node 2 and the ground at the frequency f = 3GHz. In other words, the input impedance of the T-Line looking to the right at Node 2 is 50 Ohms at 3GHz. The source voltage is equally divided between the source impedance and the input of the T-Line. Therefore, V(2) = 0.5V at 3GHz as can be seen from the figure below. Also, since the generic T-Line is a reciprocal device, the load at the other end of the T-line is impedance-matched at f = 3GHz, too. In other words, the input impedance of the T-Line looking to the left at Node 3 from the point of view of the resistive load is 100 Ohms at 3GHz. As you can see from the figure, this results is much more subdued oscillations of the load voltage over the entire frequency band.
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