Engineering
RLC Circuit formulas: Resonant Frequency, Reactance (XL, XC), Impedance Z & Q-Factor
Calculate series RLC resonant frequency f0 = 1 / (2*PI()*SQRT(L*C)), total AC impedance Z = SQRT(R^2 + (XL - XC)^2), and circuit Quality Factor Q.
Analyze AC filter tuning, reactance cancellation, and impedance Z in spreadsheets!
For an ideal series RLC circuit in sinusoidal steady state, inductive voltage leads current by 90 degrees and capacitive voltage lags current by 90 degrees. Reactance magnitudes are XL=2*pi*f*L and XC=1/(2*pi*f*C); net reactance is XL-XC.
Total AC impedance magnitude is Z = SQRT(R^2 + (XL - XC)^2), and at exact resonant frequency f0 = 1 / (2 * PI() * SQRT(L * C)), XL equals XC so reactive terms cancel completely and Z drops to pure resistance R!
Assume ideal lumped components with constant values and R including all modeled series losses. Real parasitics and frequency-dependent losses shift behavior. This example requires positive R, L, C and frequency; it does not evaluate the DC or lossless limiting cases.
| Circuit Element / Metric | Cell | Series RLC Filter | AC Value |
|---|---|---|---|
| Resistance R (Ohms) | B2 | 50 Ohms | Minimum Z at resonance |
| Inductance L & Capacitance C | B3 = 0.001 H, B4 = 1E-6 F | 1 mH & 1 uF | Resonant f0 = 5,032.92 Hz |
| Operating Frequency f | B5 | 1,000 Hz | XL = 6.28 Ohms | XC = 159.15 Ohms |
| Impedance Z & Q-Factor | PI() & SQRT | Z = 160.84 Ohms | Q = 0.6325 | At f = f0 -> Z = 50.00 Ohms! |
LC Resonant Frequency f0 = 1 / (2 * PI() * SQRT(L * C)) (Hz)
Enter L in Henries (1 mH = 0.001) and C in Farads (1 uF = 0.000001).
=IF(OR(COUNT(B2:B5)<>4,MIN(B2:B5)<=0),"Invalid inputs",ROUND(1 / (2 * PI() * SQRT(B3 * B4)), 2))Total Series RLC Impedance Z = SQRT(R^2 + (XL - XC)^2) (Ohms)
LET computes XL and XC cleanly before combining resistive and net reactive legs in quadrature.
=IF(OR(COUNT(B2:B5)<>4,MIN(B2:B5)<=0),"Invalid inputs",LET(xl, 2 * PI() * B5 * B3, xc, 1 / (2 * PI() * B5 * B4), ROUND(SQRT(B2 ^ 2 + (xl - xc) ^ 2), 2)))Try the example
Use the original values or change them to test your understanding.