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CHAPTER 1 - Fundamentals of Electrical Circuits 24 1.5.4.3 Impedance of electrical networks We have seen how reactive and non-reactive components may be represented individually but how do we represent a combination of them? Let us consider a simple network, comprising of a resistor and a capacitor. Figure 1.5-10 Individual components and overall impedance of an RC combination As shown in Figure 1.5-10, the total impedance of this network is simply the sum of the individual impedances. This impedance is more easily expressed in polar form as | | | | √ ( ) ( ) Equation (1.5-14) shows that, as more elements are added in series, the expression for the overall impedance becomes more complex. Also, when elements are added in parallel, the maths complicates matters further. This is why, at high frequency, we use a special graphical tool called Smith chart which allows us to calculate the impedance of complex networks in a clever graphical manner (section 3.6 and 4.4). So, we have seen how impedance gives an indication of the relative values of voltage and current and also of the phase difference between them. As you may recall, in sections 1.3 and 1.4, we saw how voltage and current are a simplification of Electric and Magnetic fields and how the values of R, C and L also give a relationship between the moduli of such fields. The impedance goes a step further and, in addition to showing a relationship between the moduli of E and H, it gives us an indication of the phase difference between them. We will clarify what we mean by phase difference in this context in due course but, for now, you may think of such a difference as an indication of how long it takes one field to respond to changes in the other field. The Impedance also helps us describe how the frequency of excitation affects the magnitudes and phases of electric and magnetic field. (1.5-14) Conquer Radio Frequency 24 www.cadence.com/go/awr