5.12 Transmission Lines 1255.12 Transmission Lines When designing circuits on-chip, often transmission line effects can be ignored, but at chip boundaries they are very important. Transmission lines have effects that must be considered at these interfaces in order to match the input or output of an RFIC. As already discussed, transmission lines have a characteristic impedance, and when they are loaded with an impedance different from this characteristic imped-ance, they cause the impedance looking into the transmission line to change with distance. If the transmission line, such as shown in Figure 5.32, is considered loss-less, then the input impedance at any distance d from the load is given by  in2tan( )2tanLoooLZjZdZ dZZjZdπλπλéùæö+ç÷êúèøêú=æöêú+ç÷êúèøëû (5.40)where l is one wavelength of an EM wave at the frequency of interest in the trans-mission line. A brief review of how to calculate l will be given in Chapter 6. Thus, Figure 5.31 The reflection coefficient of a device matched from 3–5 GHz.Figure 5.32 Impedance seen moving down a transmission line.