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4.5 Discrete vs Distributed elements 191 4.5 Discrete vs Distributed elements When operating in higher frequency bands the parasitic elements of discrete (or lumped) electrical components become very significant thereby greatly influencing the value (and sometime the type!) of their impedance. To avoid such problems, the designer may need to resort to using smaller and higher quality components and this may increase the overall cost of the RF systems in terms of materials purchased and assembly costs. There is however a very viable and widely used alternative to discrete components for capacitors and inductors which comes from two extremely important facts about transmission lines: - Short 32 transmission line segments terminated with low impedances behave like inductors - Short transmission line segments terminated with high impedances behave like capacitors Let us see where these statements come from. Figure 4.5-1 Short section of transmission line and equivalent electrical model Figure 4.5-1 shows a small section of transmission line, of electrical length θ, terminated with a resistance R L , and the electrical model for such a line. Let us assume that R L = 1Ω and that each capacitor has an impedance and each inductor has an impedance of . Now, starting from the load end, let us consider the parallel of R L and C 1 . The modulus of the impedance of C 1 is much higher than that of R L . This means that C 1 is quite small and hence draws a very small current compared to the resistor. We may therefore ignore C 1 and assume that the impedance of the parallel is equal to R L . The impedance seen at point α will therefore be . A similar reasoning may lead us to assume that the capacitor C 2 is also negligible and hence the impedance at point β will be . Now, when calculating the impedance at point γ, since the impedance of C 3 is still much larger than ( ) , we can again neglect the capacitor and assume that . We could carry on repeating this process for a few more inductors but we would eventually come to a point (i.e. to a transmission line length) at which we would need to take into account the impedance of the capacitors. This simple example explains why we may state that short transmission line segments terminated with low impedances behave like inductors. 32 By "short" we mean less than 90ι in electrical length at the frequency of interest. θ C 1 L 1 C 2 L 2 C 3 L 3 C 4 R L Z IN α β γ Conquer Radio Frequency 191 www.cadence.com/go/awr