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4.2 Impedance and Admittance 153 4.2 Impedance and Admittance 4.2.1 Introduction In section 1.5.4.3 we saw how the behaviour of a set of resistive and reactive elements may be simply defined by its complex impedance. This complex number allows us to work out the ratio of voltage and current amplitudes and also the relative phase of voltage and current for the series connection. When looking at elements connected in parallel however, it is advantageous to use another quantity, the admittance, to simplify circuit analysis. In this section we will be picking up the concepts illustrated in section 1.5.4.3 and 1.5.5 and extending them to more complex passive networks. Before we proceed we must revisit a very important concept which will be used extensively throughout this section, the relative phase of sinusoids in the time domain. When in a sinusoidal steady state, we do not need to express frequency of our signals explicitly, all we need to know is their amplitude and phase. So, much in the same way as we did for impedances, we can use complex numbers to represent the phase and amplitude of our sinusoidal signals by means of one single number. This is shown in Figure 4.2-1. Figure 4.2-1 Phasor representation on the complex plane of sinusoids of different amplitude and phases As we know, we may represent complex numbers as "vectors" in the complex plane. These are usually referred to as phasors. This type of representation helps us work out the phase difference between voltage and current and which of the two leads the other! Phasor representations of voltage and current for resistors, capacitors and inductors are shown on the right- hand-side of Figure 4.2-4, Figure 4.2-5 and Figure 4.2-6. In the time domain, things are a little less clean-cut and I find that students often interpret things the wrong way around. Let us take a look at the curves plotted in Figure 4.2-2. The sinusoids represented in this graph may be described by equations of the type shown below ( ) where for the dashed, blue curve and for the solid red curve. Ȁʹ φ ͳ φ ʹ Conquer Radio Frequency 153 www.cadence.com/go/awr