RLC resonance circuit
Calculate the basic RLC resonance circuit
constants:
Parameters
Resistor
R
\(\Omega\)
Inductor
L
\(H\)
Capactor
C
\(F\)
frequency
f
\(Hz\)
Output
angular frequency `omega`
`omega=2 pi f`
Resonance frequance `f_c`
`f_c=1/(2 pi sqrt(LC))`
Reactance `X_L`
`X_L=omega L`
Condensance `X_C`
`X_C=1/(omega C)`
characteristic impedance `Z_0`
`Z_0=sqrt(L/C)`
expected capactor `C_f`
`f=1/(2 pi sqrt(L C_f))`
RLC series Voltage resonance circuit
Impedance Z
`Z(j omega)=R+j(omega L-1/(omega C))`
Quantity fctor Q
`Q=(omega_c L)/R=1/R sqrt(L/C)`
Bandwidth BW
`BW=f_0/Q`
Voltage gain
`G=U_L/U=(omega L)/(abs(Z))`
|Z| vs f
`abs(Z)=sqrt(R^2+(omega L-1/(omega C))^2)`
Gain vs f
`G=(omega L)/(sqrt(R^2+(omega L-1/(omega C))^2))`
RLC parallel current resonance
admittance Y
`Y=1/R+j(omega C-1/(omega L))`
Quality factor Q
`Q=(omega_c C)/G=R sqrt(C/L)`
Bandwidth BW
`BW=f_0/Q`
Impedance R
`Z=1/Y`
|Z| vs f
`Im(Z)=omega C-1/(omega L)`