5.4 Conversions Between Series and Parallel RL and RC Circuits 1115.4 Conversions Between Series and Parallel Resistor-Inductor and Resistor-Capacitor CircuitsSeries and parallel resistor-capacitor (RC) and resistor-inductor (RL) networks are widely used basic building blocks of matching networks [1, 2]. In this section, conversions between series and parallel forms of these networks will be discussed. All real inductors and capacitors have resistors (either parasitic or intentional) in parallel or series with them. For the purposes of analysis, it is often desirable to replace these elements with equivalent parallel or series resistors as shown in Figure 5.15. To convert between series and parallel RC circuits, we first note that the imped-ance is 1ssZ Rj Cω=+ (5.7)Converting to an admittance 2 22 2 21sssssj CC RYC Rωωω+=+ (5.8)Figure 5.15 Narrowband equivalent models for: (a) a capacitor and series resistor and (b) an induc-tor and series resistor.Figure 5.14 Calculation of impact of impedance matching on base shot noise.