CalcAC Impedance Calculator
AC Impedance Calculator. Free online calculator with formula, examples and step-by-step guide.
AC Impedance Calculator: Analyze RLC Circuit Behavior
The AC impedance calculator computes the total opposition to alternating current in a series RLC circuit, combining pure resistance with frequency-dependent inductive and capacitive reactance. Unlike simple DC resistance, impedance varies with frequency, making it essential for designing filters, matching audio components, tuning radio circuits, and analyzing power systems. Whether you are an electronics hobbyist building a crossover network, an engineering student studying circuit theory, or a professional designing power supplies, this calculator helps you understand how your circuit behaves at any frequency.
AC Impedance Formula
Z = √(R² + (XL − XC)²)
XL = 2πfL
XC = 1 / (2πfC)
Where Z is the total impedance in ohms (Ω), R is the resistance in ohms, XL is the inductive reactance, XC is the capacitive reactance, f is the frequency in hertz (Hz), L is the inductance in henries (H), and C is the capacitance in farads (F). The difference between XL and XC is called the net reactance. When XL > XC, the circuit behaves inductively; when XC > XL, it behaves capacitively.
Impedance is a complex quantity with both magnitude and phase angle, but this calculator focuses on the magnitude. The phase angle φ = arctan((XL − XC) / R) determines whether current leads or lags voltage. In a purely resistive circuit, voltage and current are in phase. In an inductive circuit, current lags voltage. In a capacitive circuit, current leads voltage. This phase behavior is critical for power factor calculations in AC power systems.
Worked Examples
Example 1: Series RLC Circuit at 60 Hz
A series circuit contains a 100 Ω resistor, a 0.5 H inductor, and a 20 µF capacitor. The AC source operates at 60 Hz (standard US power frequency).
Step 1 — Inductive Reactance: XL = 2π × 60 × 0.5 = 188.5 Ω
Step 2 — Capacitive Reactance: XC = 1 / (2π × 60 × 20 × 10−6) = 132.6 Ω
Step 3 — Net Reactance: XL − XC = 188.5 − 132.6 = 55.9 Ω
Step 4 — Impedance: Z = √(100² + 55.9²) = √(10000 + 3125) = √13125 = 114.6 Ω
The circuit exhibits net inductive behavior at 60 Hz because XL exceeds XC. The phase angle φ = arctan(55.9 / 100) ≈ 29.2°, meaning current lags voltage by about 29 degrees. The impedance of 114.6 Ω is higher than the resistance alone because the reactance components do not fully cancel.
Example 2: Near-Resonant Circuit at 1 kHz
A circuit has R = 50 Ω, L = 10 mH, C = 2.5 µF. Find the impedance at 1 kHz.
Inductive Reactance: XL = 2π × 1000 × 0.01 = 62.8 Ω
Capacitive Reactance: XC = 1 / (2π × 1000 × 2.5 × 10−6) = 63.7 Ω
Net Reactance: XL − XC = 62.8 − 63.7 = −0.9 Ω
Impedance: Z = √(50² + (−0.9)²) = √(2500 + 0.81) = √2500.81 = 50.01 Ω
At 1 kHz, the reactances nearly cancel (XL ≈ XC), bringing the impedance very close to the pure resistance of 50 Ω. The resonant frequency for this circuit is f = 1 / (2π√(0.01 × 2.5 × 10−6)) = 1,007 Hz. At resonance, Z = R = 50 Ω, and current reaches its maximum. This illustrates why resonant circuits are used for band-pass filtering — they selectively pass frequencies near resonance while attenuating others.
Common Uses
- Designing crossover networks for multi-driver speaker systems that route different frequency bands to woofers, midranges, and tweeters
- Analyzing impedance matching between antennas, transmission lines, and transceivers for maximum power transfer in RF communications
- Calculating power factor correction capacitor values for industrial electrical installations to reduce reactive power charges
- Designing filter circuits including low-pass, high-pass, band-pass, and notch filters for signal processing applications
- Determining the frequency response of sensors, transducers, and electromechanical actuators in measurement and control systems
- Evaluating the equivalent series resistance and impedance of capacitors and inductors at their operating frequencies in power supply designs
Common Mistakes
- Treating impedance as a scalar sum of resistance and reactance instead of using the vector (Pythagorean) sum — Z is not R + X, it is the square root of R² + X²
- Forgetting to convert capacitance from microfarads (µF) to farads (F) or inductance from millihenries (mH) to henries (H) before using the formulas
- Confusing series and parallel impedance calculations — in parallel RLC circuits, the reciprocal formula 1/Z = √((1/R)² + (1/XL − 1/XC)²) is used instead
- Ignoring the phase angle and treating impedance as purely resistive, which leads to incorrect power calculations and component stress estimates
- Assuming impedance is constant across frequency when both inductive and capacitive reactance change dramatically with frequency
Pro Tip
When designing circuits that must operate across a range of frequencies, always check impedance at the extremes of the operating band, not just the center frequency. A capacitor used for power supply decoupling might have an impedance of 0.1 Ω at its rated frequency but resonate with parasitic inductance at higher frequencies, actually increasing impedance and reducing its effectiveness. Always include the equivalent series resistance (ESR) and self-resonant frequency (SRF) specs from the component datasheet in your calculations. For audio crossover design, plot impedance magnitude versus frequency for each driver to ensure the crossover frequency produces the intended 6 dB or 12 dB per octave slope.
Frequently Asked Questions
Resistance opposes direct current and is frequency-independent. Impedance opposes alternating current and includes both resistance and frequency-dependent reactance. Inductive reactance increases with frequency, while capacitive reactance decreases. Impedance has both magnitude and phase angle, making it a complex quantity.
At resonance, XL = XC, so they cancel. Total impedance equals just the resistance Z = R, the minimum in a series circuit, causing current to peak. Resonance occurs at f = 1 / (2π√(LC)). This is fundamental to radio tuners, filters, and oscillators.
Impedance matching maximizes power transfer and minimizes distortion. Speakers typically have 4, 6, or 8 Ω nominal impedance. An amplifier rated for 8 Ω speakers may overheat with 4 Ω speakers at high volume. Impedance also varies with frequency, affecting tonal balance.
Capacitive reactance is inversely proportional to frequency: as frequency rises, XC falls. This is why capacitors block DC (zero frequency, infinite reactance) but pass high-frequency AC easily. At 60 Hz, a 10 µF capacitor has XC ≈ 265 Ω; at 1 MHz, it drops to 0.016 Ω.