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CHAPTER 1 - Fundamentals of Electrical Circuits 16 1.5.3 Complex Numbers and Impedance Equation (1.4-1)(a) shows that a resistor, which is a non-reactive component, introduces a voltage drop in a circuit which is equal to current times resistance. However there is no phase difference between the voltage across it and the current through it. We have also seen how capacitors and inductors, which are reactive components, do not introduce any loss (in their idealised from) but they do introduce a phase offset between the current through them and voltage across their terminals (eq.(1.5-3)). In most passive circuits, you will get both reactive and non- reactive elements so how can we express the voltage drop and the V-I phase difference for a complex electrical network without using two different quantities?? The answer is, by using complex numbers and introducing the complex quantity Z, called impedance. 1.5.3.1 Complex Numbers and their properties A complex number effectively allows you to represent two values ( and ) with one entity and comprises of a real part and an imaginary part , as shown below The letter represents the imaginary constant 6 which is equal to √ . Because is multiplied by the imaginary constant , there is no way to mix it with , which is the beauty of complex numbers. The number may be plotted on a Cartesian graph where the abscissa represents real values and the ordinate represents imaginary values as shown in Figure 1.5-5. Figure 1.5-5 Cartesian representation of a complex number Equivalently, may be represented in polar form by means of its modulus and angle as shown in Figure 1.5-6. Figure 1.5-6 Polar representation of a complex number 6 is sometimes called √ Conquer Radio Frequency 16 www.cadence.com/go/awr

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