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RF Electronics Chapter4: Transmission Line Transformers and Hybrids Page 64 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Chapter 4 Transmission Line Transformers and Hybrids Introduction At RF and microwave frequencies, lines connecting devices can be an appreciable fraction of a wavelength. As a result, transmission lines models should be used, to connect all devices. Those transmission lines can also be used to change impedances, just like the transformers in chapter 3. In addition, by connecting transmission lines in special ways, circuits like hybrids, power splitters, power combiners and couplers can be made. Their design is described in this chapter. Since this chapter deals with transmission lines and their use in transformers, hybrids and couplers, a brief review of properties of transmission lines will be given. Zs ZL Z0 l Figure 4.1. Transmission line parameters. For a transmission line of characteristic impedance Z 0 and length l, the sending end impedance is given by [1 - 3]: ) tan( ) tan( 0 0 0 l jZ Z l jZ Z Z Z L L S Eqn. 4.1 If the transmission line is close to one quarter wavelength long then tan(l) >>1 so that: L L S Z Z l jZ l jZ Z Z 2 0 0 0 ) tan( ) tan( Eqn. 4.2 so that: Z S Z L = Z 0 2 or Z S = Z 0 2 / Z L Eqn. 4.3 The impedance transformation ratio R is given by: 0 0 Z Z Z Z R L S or R Z Z S 0 and 0 RZ Z L Eqn. 4.4 In figure 4.1, if a voltage waveform travels along the transmission line with an impedance Z 0 , when that arrives at the load Z L , that voltage is reflected and the amplitude of the reflected waveform is changed by a factor of the reflection coefficient , where: ൌ ௓ ಽ ି௓ బ ௓ ಽ ା௓ బ Eqn. 4.5 If Z L = Z 0 , the system is matched. = 0 and there is no reflected wave. If the transmitted wave is a single sinewave, then the reflected wave will reinforce the incident wave at some points and oppose it at other points along the transmission line. The ratio between RF Electronics: Design and Simulation 64 www.cadence.com/go/awr

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