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CHAPTER 2 - Conveying Power at Radio Frequency 36 All these lengths give as an indication of how the finite speed of propagation influences the relative phases of the generator and load voltages for a signal of a specific frequency. It is quite clear however that they are all multiples (or fractions) of one another and hence we could just calculate one of them and use its fractions or multiples to get the length associated with any phase difference. It is customary to choose for this purpose and then use fractions of it to represent 90⁰ and 180⁰ shifts. What we called is commonly called wavelength and indicated by the greek letter . It essentially represents the distance that a signal is able to travel over its period . Now there are two things that must be pointed out. Firstly our signal may not always travel at the speed of light. If, for instance, the signal propagates through some dielectric material then its propagation speed will be lower. We should therefore use a generic speed ͳ͵ instead of c in the above formula. Also, bearing in mind that ⁄ , the above formula if often written as This is a nice form to express the wavelength because it intuitively suggests that gives an indication of how fast our signal is travelling ( ) with respect to the rate at which it is changing ( ). If this ratio is high, i.e. the signal travels much faster than it can change, then the range of distances over which phase shifts are unimportant is much larger. On the other hand, if this ratio is low, our signal may be changing very quickly hence small distances may introduce significant phase shifts. In general it is assumed that if the wavelength is much greater than the dimensions of the circuit, the lumped elements approximation may be used for circuit analysis i.e. phase offsets due to a finite speed of propagation may be ignored. As a rule of thumb, the wavelength should be at least 10 times greater than the dimensions of the circuit for this approximation to be valid. If such a condition is not verified, then transmission line theory should be used when designing and analysing the circuit. Transmission line theory and its practical applications will be the subject of the following sections. 13 See Section 2.3 and 2.11 to see how the velocity of propagation for common transmission lines is calculated (2.2-4) (2.2-2) (2.2-3) Conquer Radio Frequency 36 www.cadence.com/go/awr

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