About the AC Circuit Analyzer
The AC Circuit Analyzer computes complex impedance (magnitude & phase), resonance frequency (f&sub0; = 1/(2π√LC)), quality factor Q, and bandwidth for series and parallel RLC networks. A live Bode plot renders log-frequency magnitude and phase response across user-selected ranges, with hover readout. Filter-design mode covers first- and second-order low-pass, high-pass, band-pass, and notch topologies.
It is built for electronics engineers prototyping audio crossovers and EMI filters, EE undergrads grinding through circuit-analysis homework, hobbyists building tube preamps and tone stacks, sensor designers tuning anti-aliasing filters, and HAM radio operators picking RLC components for tank circuits at specific resonance frequencies.
All math runs locally in your browser. R, L, C, frequency, and topology inputs never leave your device. The page makes no network call after first load. The Bode plot is rendered locally with Canvas; the underlying transfer function evaluation is all client-side JavaScript.
This is a first-pass analysis tool, not SPICE. It assumes ideal components (no parasitic resistance / inductance / capacitance), linear behavior, steady-state sinusoidal excitation, and infinite source/load impedance. Real circuits introduce DCR in inductors, ESR in capacitors, and self-resonance frequencies that bound usable range; for audio crossovers, driver-impedance compensation and baffle-step correction are also not modeled. Validate any design with SPICE (LTspice, KiCad) or measurement on a network analyzer before committing to PCB.
How to Use the AC Circuit Analyzer
Tap the topology that matches your circuit, then enter R, L, and C with the appropriate unit prefixes. The frequency field controls where impedance and the |H(f)| readout are evaluated; the Bode plot displays the full response across two decades on either side of resonance. Tap Magnitude or Phase to toggle which curve renders.
Impedance, Reactance, Resistance — Three Different Things
Resistance dissipates energy as heat and has no phase. Reactance stores energy —
inductive reactance XL = 2πfL grows with frequency, capacitive
reactance XC = 1/(2πfC) falls with frequency. Impedance combines
them: Z = R + j(XL − XC). Magnitude is what an AC
voltmeter reads in series; phase is the lag (or lead) between current and voltage.
Resonance: Where the Magic Happens
At resonance, XL = XC and the reactive components cancel.
In a series RLC, impedance hits its minimum (|Z| = R), current peaks, and the circuit appears
purely resistive. In a parallel RLC, impedance hits its maximum — a tank
circuit, beloved of radio engineers. Resonant frequency
f0 = 1 / (2π√(LC)) depends only on L and C, never on R.
The Q Factor in Audio, RF, and Control
Q is the ratio of energy stored to energy dissipated per cycle. For a series RLC,
Q = (1/R)√(L/C); for parallel, Q = R√(C/L). High-Q
resonators (Q > 10) are used in radio tuning where selectivity matters; low-Q resonators
(Q < 2) are used in audio crossovers where transient behavior must stay clean. Bandwidth
follows BW = f0 / Q.
First-Order vs. Second-Order Filters
A first-order RC low-pass rolls off at 6 dB per octave with fc =
1/(2πRC). A second-order Sallen-Key adds a sharper 12 dB/octave slope and a
tunable Q that controls the response shape near cutoff (Bessel, Butterworth, or Chebyshev).
Cascading filters multiplies orders — two second-order sections make a 24 dB/octave
fourth-order, the audio crossover standard.
Reading a Bode Plot
The magnitude plot uses dB on the vertical and log frequency on the horizontal so roll-off slopes appear as straight lines. Cutoff is conventionally the −3 dB point. The phase plot shows the lag introduced at each frequency — a first-order low-pass swings from 0° at DC to −90° at high frequency, crossing −45° at the cutoff. Phase margin in control systems is read directly from where the magnitude crosses 0 dB.
Standard Component Series (E12, E24, E96)
Commercial resistors and capacitors are sold in geometrically-spaced “preferred-value” series. E12 has 12 values per decade (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82), E24 doubles that resolution, E96 is for 1% precision parts. Designing on paper produces exotic values like 173 kΩ that you cannot buy — the Pro snap-to-series feature nudges your design to the nearest commercially available part.
For the DC complement, see the Ohm’s Law Calculator. For sanity-checking units, the Unit-Aware Equation Solver. All Math & Science tools.
Frequently Asked Questions
What is impedance in an AC circuit?
Impedance is the AC analog of resistance, combining resistance and reactance from capacitors and inductors. It is a complex number — magnitude in ohms and phase in degrees. At resonance, reactive parts cancel and impedance equals R.
What does the Q factor describe?
Q (quality factor) measures how sharp the resonance is. High Q above 10 means a narrow peak, used for radio tuning. Low Q below 2 means broad response, typical of audio crossovers. Q equals resonant frequency divided by bandwidth.
When do I use a first-order vs. second-order filter?
First-order rolls off at 6 dB per octave with one reactive component, fine for tone shaping. Second-order rolls off at 12 dB per octave with adjustable Q, used in crossovers, anti-aliasing, and band-limiting.
Why does the Bode plot use log frequency?
Human hearing, control-system response, and most filter behaviors scale logarithmically with frequency. Plotting on log axes turns roll-off slopes into straight lines and makes the negative 3 dB cutoff easy to read.
Is this tool useful for audio crossover design?
For preliminary work, yes. Filter design mode covers LP and HP at first and second order. Real audio crossovers also require driver-impedance compensation and baffle-step correction not modeled here.