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4.1 Introduction 151 4 Impedance Matching 4.1 Introduction In this section we will take a step back first and revisit the maximum power transfer theorem when passive components characterised by complex (capacitors, inductors) and real (resistors) impedances (section 1.5.3) are present in the circuit. As you may recall from Figure 2.9-4, in the case of resistive circuits, maximum power transfer is achieved when load and source resistances are equal. What happens however when source and load impedances are complex? This case is similar to the resistive one, in that the real part of the source and load impedances must be the same however the sign of their imaginary parts must be opposite. In mathematical terms the load impedance must be the complex conjugate of the source impedance. Let's see why this is. Our aim is to convey as much power to our load as we can. Any reactive elements which the generator sees, will act to store some of the useful energy which could instead be delivered to the load. If the load and source impedances are equal to the conjugate of one another, then the reactive elements will be virtually invisible to the generator and all the useful power will be delivered to the resistive load. This is shown in Figure 4.1-1, where eq. (4.1-1) is satisfied when . Figure 4.1-1 Source impedance driving its complex conjugate and resulting equivalent circuit 29 Often enough the signal generator has a purely resistive impedance which, in many RF and Microwave systems is 50Ω The load to which it is connected however is often characterised by a complex impedance. This could be the input port of a transistor for instance. This is shown in Figure 4.1-2. We may therefore need to add some additional elements between our source and load to ensure that maximum power transfer is achieved. This is called a matching network and its purpose is to make the load impedance "look like" the complex conjugate of the source impedance (Figure 4.1-3). 29 The impedance of reactive components is frequency dependent. Here we are assuming a sinusoidal steady state. Z S jX S R S R L -jX L Z L R S R L (4.1-1) Conquer Radio Frequency 151 www.cadence.com/go/awr

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