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The paper introduces the concept of hyperbolic reflections in order to complement the hyperbolic rotation matrices used in the lossy coupling matrix filter synthesis. A complex transversal coupling matrix representing a lossy filter is chosen and it is seen how by applying a succession of similarity transformations based also on hyperbolic reflections one obtains different results than by using hyperbolic...
The paper presents in premiere a simple mapping property of the sum of the reflection and transmission parameters of reciprocal two port networks. It is proved that although the reflection and transmission parameter may have very complicated paths on the Smith chart, their sum will be always moving on the unit circle if the circuit is symmetric and lossless. Further once symmetrical losses at the...
Unilateral transducer constant power gain circles play an essential role in the design of radio-frequency amplifiers and active modulators, as they help to determine optimal impedance matching conditions to meet gain and stability specifications. It is shown that these gain circles are a subfamily of Apollonius circles. For better visualisation, unilateral transducer constant gain power circles have...
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