Series resonant circuit

Series resonant circuit

Figure 2 shows a series resonant RLC circuit. The total impedance in the circuit is given by,

Ztotal = R + ZL + ZC

= R + j(XL + XC )

Figure 3 shows how the total impedance changes with frequency Figure 1 shows that the absolute reactances of a capacitor and inductor will approach each other and cross as frequency increases. If we now recall that XC is actually negative then it is clear that XL + XC must head towards zero in this frequency range. At the specific frequency where XL = −XC , the imaginary components of the impedance exactly cancel each other out (equation 4 shows this most clearly). At this frequency the impedance of the circuit has its smallest magnitude and a phase

angle of zero (remember only imaginary components can move phase angles away from zero). This is called the resonant frequency of the circuit, f0. It is always the frequency which causes XL and XC to cancel each other out,

XL + XC = 0

⇒ XL = −XC ⇒ ω0L                           = 1/ ω0C

⇒ ω ² 0 = 1 /LC

where ω0 = 2πf0, the resonant angular frequency.