Radio Antenna Engineering is a free introductory textbook on radio antennas and their applications. See the editorial for more information.... 
Home Impedancematching Networks Generalized Case of Impedance Transformation  
Search the VIAS Library  Index  
Generalized Case of Impedance TransformationAuthor: Edmund A. Laport
Any fourterminal network whose output power is equal to its input power must be composed of pure reactances. This was the basis of reasoning in all the preceding problem solutions.
Let us transform a low value Z_{0} = R_{0}  jX_{0} to a large value
with random phase shift (Fig. 5.43). We start from the load as before and set up a vector statement of the problem at that point. We do the same for the input impedance, including phase angle between input and output potentials or currents, as shown in Fig. 5.44. The original problem is written vectorially in solid lines. The unknown current is I_{1} (Fig. 5.43), which must connect I_{0} with Iin. We draw this immediately. But when it comes to determining V_{1} and V_{3}, we find an infinite number of choices.
Let us select a point P at random, anywhere in the entire plane of the diagram. Completing the diagram through P, we obtain where V_{1} leads I_{0} less than 90 degrees,
where I_{1} leads V_{2} more than 90 degrees, and
where V_{3} leads I_{in} less than 90 degrees.


Home Impedancematching Networks Generalized Case of Impedance Transformation 