FAQ
TL;DR: For 100 Hz resonance, the LC product is ≈2.53×10^-6; “The Resistance at that point does not affect the resonance.” [Elektroda, Mike Burr, post #21661076]
Why it matters: This FAQ helps students and hobbyists quickly size L, C, and R for 100 Hz LC resonance and simulate it correctly.
Quick Facts
- Targeting 100 Hz requires L·C ≈ 2.53×10^-6 (H·F). [Elektroda, Mike Burr, post #21661076]
- Example picks: 10 mH needs about 2.53 µF; 100 mH needs about 25.3 µF. [Elektroda, Mike Burr, post #21661076]
- At resonance, reactive impedances cancel; R acts as series resistance. [Elektroda, Mike Burr, post #21661076]
- Parallel vs series Q differ: Q_parallel = R·√(C/L); Q_series = (1/R)·√(C/L). [Elektroda, Mike Burr, post #21661080]
- Handy tool: ElectroDroid app provides quick reactance calculators. [Elektroda, Kevin Parmenter, post #21661071]
How do I choose L and C to hit 100 Hz exactly?
Use f0 = 1/(2π√(LC)). Rearrange to LC = 1/(2πf0)^2 ≈ 2.53×10^-6 for 100 Hz. Pick one value, solve the other. Example: choose L = 10 mH, then C ≈ 2.53 µF. This keeps resonance on target and avoids overfitting specific parts early. “1/(2π·√(LC)) = resonant frequency.” [Elektroda, Mike Burr, post #21661076]
Do resistor values change the resonant frequency at 100 Hz?
At resonance, the inductor and capacitor impedances cancel, so resistance behaves like series resistance and does not shift the resonant frequency. It still influences losses and peak amplitude, but the frequency stays set by L and C. “The Resistance at that point does not affect the resonance.” [Elektroda, Mike Burr, post #21661076]
Can a mixed LC network show two resonant frequencies?
Yes. Combining sections can produce a band-stop (notch) response with two skirt corners and a dip between them. The shape depends on how LC sections interact and where you probe. Expect lower output between the peaks and tapered edges from the high- and low-pass behavior. [Elektroda, Mike Burr, post #21661078]
What does SQR mean in the Q formulas, and which R should I use?
SQR denotes the square root. Use the resistance in the configuration of interest: the R in the parallel expression for parallel-tuned sections, and the series resistance for series-tuned ones, per the stated formulas with SQR(C/L). [Elektroda, Mike Burr, post #21661080]
What are the Q-factor formulas for series and parallel LC?
For parallel resonance: Q = R·√(C/L). For series resonance: Q = (1/R)·√(C/L). Higher R raises Q in parallel tanks and lowers Q in series tanks. These relations guide bandwidth and attenuation choices around 100 Hz design targets. [Elektroda, Mike Burr, post #21661080]
How do I compute LC if I only know the target frequency?
Start from LC = 1/(2πf0)^2. For f0 = 100 Hz, LC ≈ 2.53×10^-6. Any L and C pair whose product equals this value will resonate at 100 Hz in the ideal model. Then select practical values near those results. [Elektroda, Mike Burr, post #21661076]
If I pick 10 mH at 100 Hz, what capacitor do I need?
C ≈ (2.53×10^-6)/L. With L = 10 mH (0.01 H), C ≈ 2.53×10^-4 F = 2.53 µF. You can similarly scale: L = 100 mH needs ≈25.3 µF, a useful rule of thumb for low-frequency tanks. [Elektroda, Mike Burr, post #21661076]
My simulation changed when I duplicated L and C into two branches—why?
Duplicating L1/L2 and C1/C2 changes the network topology and effective reactances. The circuit no longer behaves like a single LC tank, so the response can split or shift. Model one resonant branch first, then add sections intentionally and re-solve LC per branch. [Elektroda, Kobi Aflalo, post #21661075]
How do I design a simple 100 Hz notch (band-stop) with LC?
Use an LC resonant section to create a notch near 100 Hz, then add gentle high-pass and low-pass shaping if needed. The resonant tank provides the rejection; outer sections taper the skirts. Expect reduced output in the stop band compared with the pass band. [Elektroda, Mike Burr, post #21661078]
Quick 3-step: set 100 Hz resonance in SPICE (OrCAD, LTspice).
- Compute LC = 2.53×10^-6 for 100 Hz; choose L, then C = 2.53×10^-6/L.
- Build a single LC tank and verify the AC sweep peak/dip at ~100 Hz.
- Add R to study Q using Q = R·√(C/L) or Q = (1/R)·√(C/L), per topology. [Elektroda, Mike Burr, post #21661076]
Is there an Android app to speed up reactance and LC math?
Yes. ElectroDroid offers convenient calculators for reactance and many other quick RF/analog utilities. It’s a free, popular choice to explore LC values before you simulate or prototype. [Elektroda, Kevin Parmenter, post #21661071]
Can I round L or C to common values without breaking 100 Hz?
Yes. Pick a nearby standard value and recompute the partner to keep LC ≈ 2.53×10^-6. This aids parts availability and speeds simulation. “Round those values off to real world capacitors you can buy as standards.” [Elektroda, Kevin Parmenter, post #21661071]
Does resistance ever spoil my filter even if f0 stays put?
Yes—edge case to watch. In series tanks, higher R lowers Q and flattens the peak; in parallel tanks, too little R lowers Q and weakens the notch. Use Q = R·√(C/L) or Q = (1/R)·√(C/L) to predict bandwidth and depth. [Elektroda, Mike Burr, post #21661080]
