5.7 Matching Using Transformers

Chapter 5.7 Matching Using Transformers

Radio Frequency Integrated Circuit Design Second Edition Book
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Radio Frequency Integrated Circuit Design Second Edition Book

  • 116 Impedance MatchingWe can solve for the impedance by 2 ()VZj L MIω==+ Thus since Z = jwLeq, we can solve for Leq: eq22LLM=+ In the second case for the circuit on the right in Figure 5.20, the dots are placed in such a way that the flux is reduced. We repeat the analysis: 2Vj LI j MIωω=- 2 ()VZj L MIω==- eq22LLM=- Thus, in the first case the inductance reinforces itself, but in the second case it is decreased. 5.7  Matching Using TransformersTransformers as shown in Figure 5.17 can transform one resistance into another re-sistance depending on the ratio of the inductance of the primary and the secondary. Assuming that the transformer is ideal (that is, the coupling coefficient k is equal to 1, which means that the coupling of magnetic energy is perfect) and lossless and psLNL= (5.23)then it can be shown from elementary physics that psspVINVI== (5.24)Figure 5.20  Circuits to find the equivalent impedance.