n 2.2.54 to produce inductive and capacitive reactances: (2.2.57) Zin = - jZo cot 2 (2.2.56) At first glance Equation 2.2.57 may not seem to be very useful but if you refer back to Figure 2.2-7, you will see Equation 2.2.56 follows a cotangent curve and will that the characteristic impedance (Zo) of microstrip therefore also produce positive and negative impedances. transmission lines can be easily changed by changing its Adjustment of Z and line length will set the required width (w); therefore, impedance matching is a very reactance. practical proposition. Example 2.2.14 Example 2.2.15 A 75 S line is left unterminated with an open circuit at A transmission line has a characteristic impedance (Zo) of one end. Its electrical length is 1/5. Calculate its input 90 Q. Its electrical length is 2/4 and it is terminated by impedance at the other end. a load impedance (ZL) of 20 Q. Calculate the input im- pedance (Zin) presented by the line. Solution Given: Z = = = 2/4 Using Equation 2.2.56 Required: Zin Solution = -j75 x 0.325 = -j24.4 Q Using Equation 2.2.57 Zin = (90) 2/20 = 405 0 2.2.13.4 Transmission lines as transformers 2.2.14 Transmission line couplers An interesting case arises when l = 2/2. In this case Equation 2.2.54 becomes Transmission lines can be arranged in special configura- tions to divide an input signal at the input port into two separate signals at the output ports. Such an arrangement is often called a signal splitter. Since the splitter is bi- directional, the same arrangement can also be used to What this means is that the transmission line acts as a 1:1 combine two separate signals into one. These splitter/ transformer which is very useful for transferring the combiners are often called couplers. electrical loading effect of a termination which cannot be The advantages of couplers are that they are very ef- placed in a particular physical position. For example, a re- ficient (low loss), provide good matching on all ports, and sistor dissipating a lot of heat adjacent to a transistor can offer r