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CHAPTER 4 - Impedance Matching 192 Now let us look at what happens when the terminating impedance is much larger, R L = 1000Ωwhile the parameters of the electrical model for the line remain unchanged. Now the impedance of C 1 and R L are comparable and the currents which they draw will be quite similar. This means that we cannot neglect the capacitor when working out the impedance of this parallel. Also since both the impedance of C 1 and that of R L are quite large, the parallel will draw quite a small current overall. This means that the inductor will have little current flowing through it and hence its impedance may be neglected. Again we can carry on doing this for a few more inductor-capacitor sections until we get to a point where the overall current drawn has increased to a value which means that the inductors can no longer be neglected. We can infer therefore that a short segment of transmission line terminated with high impedance behaves a capacitor. Now let us take things a step further and make some quantitative considerations. The lowest impedance that we can terminate our line with would be a short circuit as shown in Figure 4.5-2. Figure 4.5-2 Short-circuited line In section 2.9, we saw a mathematical expression for the impedance seen at the input of the line (eq.(2.9-1)) which is shown below Since, in the case of a line terminated with a short circuit , equation (4.5-1) becomes Now, for values of which are between 0ι and 90ι, is positive and hence will represent an inductive impedance. We could therefore replace a discrete inductor with its distributed equivalent, which is our short-circuited line of the appropriate length. Notice however that, if we choose an electrical length for our line which is between 90ι and 180ι, would be negative and hence we would have a capacitive impedance. This goes to show the versatility of the distributed approach which allows you to realise both capacitors and inductors with same topology by simply selecting the appropriate electrical length. Now we have seen, how things work when we terminate our line with the lowest possible impedance, but what happens when we terminate it with the highest possible impedance, i.e. we have an open circuit at the end of the line? (4.5-1) Conquer Radio Frequency 192 www.cadence.com/go/awr