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CHAPTER 4 - Impedance Matching 184 4.4 Matching any two complex impedances - Smith Chart Matching 4.4.1 Introduction – The Impedance Smith Chart Let us first have a little recap on the concepts which form the basis of Smith Chart plots. We have seen how, when a generator is connected to a load through a transmission line, depending on the value of the load impedance (Z L ) some of the signal may be reflected. We may quantify the proportion of the incident signal that gets reflect through the reflection coefficient . This is shown in Figure 4.4-1. Figure 4.4-1 Reflection coefficient at the input of a transmission line in series with a load impedance Z L Usually the internal resistance of the voltage source V S and the characteristic impedance of the line Z 0 , are chosen to be the same value. This is done because in order to achieve maximum power transfer we must have R S =Z 0 =Z L (section 2.9). The first part of this equality, R S =Z 0 , may be easily achieved by utilising transmission lines throughout the RF system with identical characteristic impedance to R S . In most microwave systems R S and Z 0 are chosen to be 50Ω for the reasons explained in section 2.12. The load impedance Z L however, may be any value and hence, to satisfy the condition for maximum power transfer, we may need to carry out some impedance matching. Now, although the reflection coefficient is a very useful quantity, we would ideally like to work with impedances since they are more easily relatable to our physical circuit. To this end we may use (3.5-3) which gives us a direct correspondence between ( ) and ( ). This in turn simplifies the formulation of the condition for maximum power transfer which becomes R S = (Figure 4.4-2). ( ) ( ) ( ) ( ) ( ) ( ) Figure 4.4-2 Impedance seen at the input of a transmission line in series with a load impedance Z L l,θ l,θ (l) (4.4-1) Conquer Radio Frequency 184 www.cadence.com/go/awr

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