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CHAPTER 4 - Impedance Matching 170 4.2.7 'Q' – Quality Factor and Series to Parallel Conversions So far we have looked at the unloaded Q of reactive components based on the value of the component reactance and of the respective parasitic resistance. However when our reactive element is connected to an external resistive one, the Q is no longer determined by the parasitic element internal to the reactive component, which is usually quite small, but by the external resistive element connected to it. In this section we will therefore define Q for networks of resistive and reactive elements. Let us now look at a few illustrative examples to clarify this. For the R-C network shown in Figure 4.2-8, and repeated below in Figure 4.2-31 for the reader's convenience, Figure 4.2-31 Series R-C in MWO the Q factor is defined as For the series R-L circuit shown in Figure 4.2-11, and repeated below in Figure 4.2-32, the Q factor is calculated in an identical fashion and has the same value, Figure 4.2-32 Series R-L in MWO For parallel circuits, it is easier to use the real part (conductance, G) and imaginary part (susceptance, B) of the admittance to calculate the Q. For the parallel R-C of Figure 4.2-19 and repeated in Figure 4.2-33 Figure 4.2-33 Parallel R-C in MWO we may write ACVS ID=V1 Mag=1 V Ang=0 Deg Offset=0 V DCVal=0 V RES ID=R1 R=50 Ohm CAP ID=C1 C=5.6 pF M_PROBE ID=VP1 ACVS ID=V1 Mag=1 V Ang=0 Deg Offset=0 V DCVal=0 V RES ID=R1 R=50 Ohm M_PROBE ID=VP1 IND ID=L1 L=4.5 nH 0 0.5 1 1.5 2 Time (ns) parallel_R_C -1 -0.5 0 0.5 1 -60 -30 0 30 60 p2 p1 1.257 ns 0.999 V 1.079 ns 40.5 mA 0.5 ns 0 V 0.3323 ns 0 mA Vtime(M_PROBE.VP1,1)[*] (L, V) parallel_R_C Itime(ACVS.V1,1)[*] (R, mA) parallel_R_C p1: Freq = 1000 MHz p2: Freq = 1000 MHz Freq = 1000 MHz Conquer Radio Frequency 170 www.cadence.com/go/awr

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