134CHAPTER 6. RESONANCE• Resonance can be exploited for its impedance properties: either dramatically increasing ordecreasing impedance for certain frequencies. Circuits designed to screen certain frequenciesout of a mix of diﬀerent frequencies are called ﬁlters.6.5Resonance in series-parallel circuitsIn simple reactive circuits with little or no resistance, the eﬀects of radically altered impedance willmanifest at the resonance frequency predicted by the equation given earlier. In a parallel (tank) LCcircuit, this means inﬁnite impedance at resonance. In a series LC circuit, it means zero impedanceat resonance:fresonant = 2πLC1However, as soon as signiﬁcant levels of resistance are introduced into most LC circuits, thissimple calculation for resonance becomes invalid. We’ll take a look at several LC circuits withadded resistance, using the same values for capacitance and inductance as before: 10 µF and 100mH, respectively. According to our simple equation, the resonant frequency should be 159.155 Hz.Watch, though, where current reaches maximum or minimum in the following SPICE analyses:10011200V11 VC1L1R1100 Ω100 mH10 µFParallel LC with resistance in series with LFigure 6.20: Parallel LC circuit with resistance in series with L.resonant circuitv1 1 0 ac 1 sinc1 1 0 10ur1 1 2 100l1 2 0 100m.ac lin 20 100 200.plot ac i(v1).end