AWR eBooks

4.3 Matching two unequal resistive impedances 177 Secondly, resonance and hence a perfect match will only occur at the one frequency at which the capacitive and inductive reactances, and cancel each other out. At 100 MHz for instance, the values of and yield C P = 4.78pF and L S =477nH. To summarise: - The shunt component of the L-section acts to reduce the impedance seen by the generator to one whose real part is equal to the real part of the source impedance - The series component of the L-section acts as to resonate out the reactive component introduced by the shunt component (and possibly parasitics) A general procedure may be given to work out the elements of the L-section matching network shown in Figure 4.3-6. Figure 4.3-6 The general case for L-section matching X S and X P must be of different types 1) Calculate Q P and Q S , which have the same value, by means of the formula below √ 2) Calculate the reactances and as shown below 3) Decide which reactance is going to represent a capacitor and which an inductor. You may chose either but they must not be the same! 4) Work out the values of capacitor and inductor at the frequency of interest I know that you may feel that this whole algebraic procedure looks cumbersome and error prone but do not despair! We will soon see how we can use the Smith Chart (section 4.4) to make the design of L-section matching networks a great deal easier! Note how the network which we devised earlier to achieve a match at 100MHz (Figure 4.3-7(a)) could be replaced with another L-network where the places of capacitor and inductor have been swapped (Figure 4.3-7(b)). X P V SOURCE R S R LP X S Q S =X S /R S Q P =R P /X P (4.3-2) R P Conquer Radio Frequency 17 7 www.cadence.com/go/awr

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