Calculate impedance, resonant frequency, Q-factor, and phase angle for RLC series/parallel circuits in real time. Visualize Bode plot and phasor diagram to intuitively understand AC circuit behavior.
Circuit Parameters
Logarithmic scale: 10¹〜10⁸ Hz
|Z| Impedance
—Ω
Phase Angle φ
—°
Resonant Frequency f₀
—Hz
Q Factor / Bandwidth
—
Bode
Phase
Phasor
Theory & Key Formulas
$Z = R + j\!\left(\omega L - \dfrac{1}{\omega C}\right)$
Parallel RLC:
$\dfrac{1}{Z} = \dfrac{1}{R} + j\!\left(\omega C - \dfrac{1}{\omega L}\right)$
💬 Impedance and Resonance — The Heart of AC Circuits
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For DC, we can use Ohm's law V=IR, but for AC, when coils and capacitors are involved, it gets complicated, right?
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For AC, Ohm's law still applies as V = Z·I, but Z becomes a complex number. The reactance of a coil is XL = jωL (imaginary, proportional to frequency), a capacitor is XC = 1/(jωC) (imaginary, inversely proportional to frequency), and a resistor is R (real). Adding these gives the series impedance. By using complex numbers, we can calculate both amplitude and phase simultaneously—this is the power of phasor representation.
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What is the resonant frequency? When I press the 'Match resonant frequency' button in the simulator, |Z| suddenly drops.
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That's the characteristic of series resonance. At the frequency where the coil's reactance ωL and the capacitor's reciprocal 1/(ωC) are exactly equal, they cancel each other out, and the impedance becomes minimal (= R only). The current becomes maximum, so radio tuning circuits use this to 'select' a specific frequency. Try the AM radio preset—you should see a sharp peak around f₀ ≈ 540 kHz.
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What is the Q factor? What changes between 'high Q' and 'low Q'?
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Q = ω₀L/R represents the 'sharpness of resonance'. A higher Q means a sharper resonance peak (narrower bandwidth). For example, radio tuning circuits have Q ≈ 50–200 to avoid interference from adjacent stations. On the other hand, audio filters use Q ≈ 1–3 for a gradual passband change. In filter design, Q is one of the most important parameters.
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How is a parallel RLC different from a series RLC?
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In series resonance, current is maximum; in parallel resonance, impedance is maximum and current is minimum. This is called a 'tank circuit' and is used in transmitter antenna circuits and high-frequency filters. The key point is that voltage, not current, peaks at resonance. The parallel impedance formula is 1/Z = 1/R + jωC + 1/(jωL), and it's easier to work with admittance (Y = 1/Z).
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How is impedance calculation used in CAE/EMC design?
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In EMC (electromagnetic compatibility) design, LC filters are designed to remove unwanted noise on power lines. Inverter circuits and PWM-driven motors generate switching noise, so resonant filters are optimized using impedance calculations to attenuate it. Also, the combination of PCB trace inductance and mounted capacitors can cause unintended resonance—this is a tricky issue in decoupling capacitor design. It's common to use such lumped-element models for rough analysis as a pre-processing step before FEM electromagnetic field simulation.
Frequently Asked Questions
What is the difference between impedance and reactance?
Impedance Z = R + jX is the complex sum of resistance (real part) and reactance (imaginary part). Reactance X refers only to the imaginary part, including inductive reactance XL = ωL (inductive) and capacitive reactance XC = -1/(ωC) (capacitive). The magnitude |Z| = √(R² + X²) is the actual quantity that limits current, and the phase angle φ = arctan(X/R) is the phase difference between voltage and current.
What is the voltage amplification phenomenon in series resonance?
At series resonance, the voltage across the coil is VL = Q × Vin, and across the capacitor is VC = Q × Vin (amplified by Q times). They are opposite in phase and cancel each other, so the voltage across R equals Vin. With Q = 100, a 1V input produces 100V across the coil and capacitor. This is not energy loss but energy oscillating between L and C. Be careful of capacitor damage due to overvoltage.
How do I read a Bode plot?
The horizontal axis is frequency (log scale), and the vertical axis is |Z| or phase. For a series RLC, |Z| decreases (capacitive) for f < f₀, is minimum (= R) at f = f₀, and increases (inductive) for f > f₀. In the phase plot, the phase is -90° (current leading) below f₀, +90° (current lagging) above f₀, and changes sharply to 0° near f₀. The sharpness of this change corresponds to the Q factor.
What parasitic components are problematic in real components?
Real capacitors have equivalent series resistance (ESR) and equivalent series inductance (ESL). Due to ESL, capacitors have a self-resonant frequency; above that frequency, they behave as inductive components. Coils also have parasitic capacitance between windings, causing self-resonance. In PCB design, it's important to check the self-resonant frequency of mounted components to ensure proper operation in the target frequency band.
What is the difference between LC filters and RC filters?
RC filters (resistor + capacitor) have a first-order roll-off of -20 dB/decade and involve power loss. LC filters (coil + capacitor) ideally have zero loss and a steeper cutoff of -40 dB/decade. However, LC filters can cause voltage peaks (ringing) due to resonance, requiring proper damping (Q factor adjustment). LC filters are common in power circuits carrying large currents.
What is AC Circuit Impedance?
AC Circuit Impedance is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind AC Circuit Impedance Simulator. Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind AC Circuit Impedance Simulator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.