Calculator and formulas for calculating a parallel resonant circuit from inductor, capacitor and resistor
This function calculates the most important values of a parallel resonant circuit consisting of a resistor, inductor and capacitor.

Parallel resonant circuits are often used as a bandstop filter (trap circuit) to filter out frequencies.
The total resistance of the resonant circuit is called the apparent resistance or impedance Z. Ohm's law applies to the entire circuit. The impedance Z is greatest at the resonance frequency when X_{L } = X_{C }.
The impedance is calculated according to the formula:
\(\displaystyle Z=\sqrt{R^2 + (X_LX_C)^2} \)
At resonance, X_{L } = X_{C }. The phase of the voltage is opposite; the two values cancel each other out and the following applies:
\(\displaystyle Z=R \)
The resonance frequency is given when X_{L } = X_{C }.
\(\displaystyle 2πf·L=\frac{1}{2πf·C} \)
This results in the formula for the resonance frequency
\(\displaystyle f_0=\frac{1}{2π\sqrt{L·C}} \)
In the case of resonance, the phase shift is = 0 °.
The impedance Z is greatest at resonance. It is then only determined by the ohmic resistance R .
\(\displaystyle Z_0=R \)
Tthe current is smallest at resonance. Larger currents can flow through the coil and the capacitor.
\(\displaystyle I_0=\frac{U}{Z_0}=\frac{U}{R} \)
\(\displaystyle I_L=\frac{U}{X_L}=\frac{U}{X_C} \)
Upper cutoff frequency: \(\displaystyle f_H=f_0+\frac{b}{2} \)
Lower cutoff frequency: \(\displaystyle f_L=f_0\frac{b}{2} \)
The quality Q indicates the excess current
\(\displaystyle Q=\frac{I_L}{I}=\frac{X_C}{R}=\frac{X_L}{R} \)
Damping: \(\displaystyle d=\frac{1}{Q} \)
The bandwidth determines the frequency range between the upper and lower cutoff frequency. The higher the quality Q, the narrower the resonant circuit.
Damping: \(\displaystyle b=\frac{f_0}{Q}=f_0 ·d =\frac{f_0 · R}{X_L} \)
