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4.2 Impedance and Admittance 173 4.2.8 Q of series and parallel L-C resonators Let us now talk about the Q factor of the series RLC (Figure 4.2-38) and parallel RLC (Figure 4.2-37) networks which we examined in sections 4.2.3 and 4.2.5. Although in both of these cases we have two reactive elements, their reactance or susceptance will be the same at the resonant frequency! For the series resonant circuit shown in Figure 4.2-37 Figure 4.2-37 Series RLC resonator We may therefore write Where is the series resistance, is the reactance of the series inductor and is the reactance of the series capacitor (Figure 4.2-37). For the parallel circuit shown in Figure 4.2-38 Figure 4.2-38 Parallel RLC Resonator we may write where is the parallel resistance, is the reactance of the parallel inductor and is the reactance of the parallel capacitor. Or, equivalently Remember that, although the reactance of the inductor and the capacitor cancel each other out at resonance, there is still current flowing between them! This means that you still get losses in the resistor which allow you to define the resonant Q of the circuit! This is true for both parallel and series connections. 0 0.5 1 Time (ns) series R_L_C -1 -0.5 0 0.5 1 Vtime(M_PROBE.VP1,1)[*] (L, V) series R_L_C Itime(ACVS.V1,1)[*] (R, mA) series R_L_C p1: Freq = 1000 MHz p2: Freq = 1000 MHz Freq = 1000 MHz 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 IND ID=Ls L=4.5 nH 0 0.5 1 Time (ns) parallel_R_L_C -1 -0.5 0 0.5 1 Vtime(M_PROBE.VP1,1)[*] (L, V) parallel_R_L_C Itime(ACVS.V1,1)[*] (R, mA) parallel_R_L_C p1: Freq = 1000 MHz p2: Freq = 1000 MHz Freq = 1000 MHz Conquer Radio Frequency 173 www.cadence.com/go/awr

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