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4.2 Impedance and Admittance 161 You must be wondering now, what happens when | | is equal to | | Ω Ω In this case the overall impedance of the L-C series is zero and hence it acts like a short circuit! This is true only at the one frequency that we are operating at (1000 MHz). As shown in Figure 4.2-16, current and voltage are in phase, as they would be if no reactive elements were present. Figure 4.2-16 R-L-C at resonance, | | | | This is a very useful property of R-L-C circuits which is called resonance. Resonance occurs when | | | | Now remember that these impedances are dependent on the value of the frequency but also on the values of C and L. So once the values of C and L are fixed, if we sweep the frequency across a wide range starting from DC, our series L-C will appear capacitive ( | | > | | ) up to the resonant frequency √ It will look inductive for frequencies higher than , since | | < | | , and it will be "invisible" (zero impedance) at the resonant frequency. If we consider the resistor in our R-L-C series as the source internal resistance (RS) and we add a load (RL) at the other end of our R-L-C network (Figure 4.2-17), we can see our circuit as a source with internal resistance RS and a load with resistance RL, with an L-C series resonant circuit between them. This resonator turns out to have a "band-pass" effect across the frequency range as shown in Figure 4.2-18. 0 0.5 1 1.5 2 Time (ns) series R_L_C -1 -0.5 0 0.5 1 -20 -10 0 10 20 p2 p1 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 V mA Conquer Radio Frequency 161 www.cadence.com/go/awr

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