5.5 Tapped Capacitors and Inductors

Chapter 5.5 Tapped Capacitors and Inductors

Radio Frequency Integrated Circuit Design Second Edition Book
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Radio Frequency Integrated Circuit Design Second Edition Book

  • 112 Impedance MatchingThus, the inverse of the real part of this equation gives Rp: 2 2 222 21(1)sspsssC RRRQC Rωω+==+ (5.9)where Q known as the quality factor is defined as before as |ZIm|/|ZRe| where Zim is the imaginary part of Z, and ZRe is the real part of Z. This definition of Q is con-venient for the series network, while the equivalent definition of Q as |YIm|/|YRe| is more convenient for a parallel network. The parallel capacitance is thus: 22 2 2211spsssCQCCC RQωæö==ç÷++èø (5.10)Similarly for the case of the inductor: 2(1)psRRQ=+ (5.11) 222111pssQLLLQQæöæö+==+ç÷ç÷èøèø (5.12)For large Q, parallel and series L or C are about the same. Also parallel R is large, while series R is small. 5.5  Tapped Capacitors and Inductors Another two common basic circuits are shown in Figure 5.16. The figure shows two reactive elements with a resistance in parallel with one of the reactive elements. In this case, the two inductors or two capacitors act to transform the resistance into a higher equivalent value in parallel with the equivalent series combination of the two reactances. Much as in the previous section the analysis of either Figure 4.16(a) or Figure 4.16(b) begins by finding the equivalent impedance of the network. In the case of Figure 4.16(b) the impedance is given by: 2121 2in2j L R j L RL LZR j Lωωωω+-=+ (5.13)Equivalently the admittance can be found: 22 232121 22in2 224 221221()()j R LLL R j L LYR LLL Lωωωωω+-+=-+- (5.14)