Parallel Circuit

Parallel Circuit

a parallel resonant RLC circuit. It is the ‘dual’ of the series circuit in that the voltage and current exchange roles. This means that the circuit has a current gain rather than a voltage gain and that the impedance is maximised at the resonant frequency rather than minimised. The total impedance in the circuit is given by,

 Ztotal = R ||ZL || ZC

      =     R/ 1 − jR( 1 XC + 1 XL )

        =  R 1 + jR(ωC − 1 ωL )

the magnitude and phase of the impedance of the circuit. Once again the resonant peak comes when XC = −XL and hence the resonant frequency is given by the same relationship,

iC/ i = jωRC /1 + jR(ωC − 1 ωL )

The current gain magnitude is shown in figure 7. At the resonant frequency,

iC/ i = jωRC