Impedance condition: After resonance, the imaginary parts are equal in sign and opposite in sign. The series impedance is equal to 0, and the parallel impedance is equal to infinity. This means that during resonance, the resonant current of the series circuit is infinite, and the resonant voltage of the parallel circuit is infinite (theoretical value).
In a series circuit of resistors and inductors, the phenomenon of power supply, voltage, and current being in phase is called series resonance (also known as frequency conversion resonance). Its characteristics are: the circuit is purely resistive, the power supply, voltage, and current are in phase, the reactance X is equal to 0, and the impedance Z is equal to the resistance R. At this time, the impedance of the circuit is the smallest and the current is the largest. High voltages that are many times greater than the power supply voltage may be generated on inductors and capacitors. Therefore, series resonance is also known as voltage resonance.
The phenomenon of parallel resonance occurs when the resonant voltage is superimposed with the original voltage, resulting in the circuit terminal voltage and total current being in phase in a parallel circuit of resistors, capacitors, and inductors. Its characteristic is that parallel resonance is a complete compensation, and the power supply does not need to provide reactive power, only the active power required by the resistor. During resonance, the total current of the circuit is minimized, while the branch current is often greater than the total current in the circuit. Therefore, parallel resonance is also known as current resonance.
In a circuit where resistors, capacitors, and inductors are connected in series, the role of the inductive reactance Xl and Xc is directly subtracted. If certain conditions are met, such that Xl=Xc, the reactance of the circuit is equal to zero, and the current and voltage phases in the circuit are the same. There is no reactive power exchange between the resistor, inductor, or capacitor, and this state of the circuit is called series resonance.
The resonance condition of the circuit is Xc=Xl, that is, ω L=1/ω C. The inherent resonance condition of the circuit can be obtained as f0=1/(2 π√ LC).
Impedance condition: After resonance, the imaginary parts are equal and have opposite signs. The series impedance is equal to 0, and the parallel impedance is infinite. This is when resonance occurs. The resonant current of a series circuit is infinite, and the resonant voltage of a parallel circuit is infinite (theoretical value), or in other words: (1) In a series circuit, the imaginary part of the total input impedance is equal to zero (resonance means that the output voltage and current are in phase); (2) In a parallel circuit, the imaginary part of the total input admittance is zero.