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4.5 Discrete vs Distributed elements 193 Figure 4.5-3 Open-circuited line In this case, the impedance seen at the input terminal of the line, may be expressed as Now, for values of which are between 0ι and 90ι, is positive and hence will represent a capacitive impedance. We could therefore replace a discrete capacitor with its distributed equivalent, which is our open-circuited line of the appropriate length. Notice however that, if we choose an electrical length for our line which is between 90ι and 180ι, would be negative and hence we would have an inductive impedance. This goes to show yet again the versatility of the distributed approach which allows you to realise both capacitors and inductors with same topology by simply selecting the appropriate electrical length. These short transmission line segments are usually employed as shunt elements which branch out from the main path and are called transmission line stubs. Since we are dealing with shunt elements, it is advantageous to use admittances instead of impedances. The admittance of short-circuited stubs, which may be used as shunt inductors (or capacitors), may be written as Whereas the admittance of open-circuited stubs, which may be used in place of shunt capacitors (or inductors), may be written as Stubs are usually fabricated as open or short circuited microstrip lines since the planar nature of this type of lines makes them ideal for the implementation of this technique. Figure 4.5-4 shows the equivalence between shunt inductors and short circuited stubs. In this figure , ( ) and the electrical length of the stub is lower than 90°. Figure 4.5-4 Equivalence between shunt inductor and short-circuited shunt stub with electrical length < 90ι Conquer Radio Frequency 193 www.cadence.com/go/awr

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