LC Resonance & Filter Analyzer

Commercial-grade RLC simulator. Calculates resonant frequency ($f_r$), Q-factor, and Bandwidth with parasitic resistance modeling. Features Bode Plots (Frequency Domain) and Step Response (Time Domain) to visualize transient ringing.

Quick Load Presets:

Topology

Inductance ($L$)

Capacitance ($C$)

Series Res ($R_s$/DCR)

Parallel Load ($R_p$)

Simulation Results

Circuit Parameters

Parameter	Value	Unit
Resonant Freq ($f_0$)	0.00	MHz
Natural Freq ($f_n$)	0.00	MHz
Angular Freq ($\omega_0$)	0.00	rad/s
Characteristic Imp ($Z_0$)	0.00	Î©
Q-Factor (Loaded)	0.00	-
Bandwidth (-3dB)	0.00	kHz
Damping Ratio ($\zeta$)	0.00	-
Resonant Impedance	0.00	Î©

Critically Damped

Frequency Response (Impedance)

Step Response (Time Domain)

Mathematical Derivation

Calculations utilize full parasitic model including series DCR and parallel load resistance.

Resonance Mechanics

Energy "Sloshing" Dynamics

Resonance in an RLC circuit is the periodic exchange of energy between the Magnetic Field of the inductor and the Electric Field of the capacitor. At the resonant frequency ($f_0$), these energy transfers perfectly synchronize, allowing the circuit to oscillate with minimal external drive.

Textbook models describe this as a lossless exchange, but in industrial reality, energy is continually bled off by the parasitic resistance ($R$) of the copper windings, leading to the "damping" of the resonant peak.

Quality Analysis

The Q-Factor & Selectivity

The Quality Factor (Q) represents the efficiency of the resonator. A high Q ($Q > 10$) indicates very low energy loss and a extremely sharp frequency response, whereas a low Q ($Q < 1$) suggests rapid energy dissipation and a "mushy" selectivity.

In radio applications, High Selectivity is required to reject adjacent channels. Conversely, in digital signal snubbing, a Low Q is preferred to prevent high-frequency "ringing" that can corrupt data bits.

Impedance Topology

Series vs. Parallel Nuance

The circuit topology fundamentally changes the "job" of resonance. Series RLC acts as an Acceptor, where impedance drops to its minimum ($R_s$) at resonance. Parallel RLC acts as a Rejector (Tank), where impedance rises to its maximum ($Z_p$) at resonance.

This "opposing" behavior makes Series circuits ideal for Harmonic Filters and Parallel circuits ideal for Wave Traps and oscillator feedback loops.

Real-World Parasitics

The Limit of Ideal Models

Professional engineering requires modeling of Parasitics. Inductors possess DC resistance (DCR) and inter-winding capacitance ($C_p$). Capacitors possess Equivalent Series Resistance (ESR) and leakage ($R_p$). These "hidden" components create the Self-Resonant Frequency (SRF).

When an inductor reaches its SRF, it technically becomes a capacitor, rendering it useless for filtering at higher frequencies. This tool accounts for these parasitics to provide "Industrial-Grade" accuracy.

Industrial Resonance FAQ

1. Why is High Q vital for Radio Selectivity?

Selectivity is the ability of a receiver to separate the desired signal from noise. A High-Q resonant circuit acts like a narrow gate; it only allows a tiny sliver of the frequency spectrum through. Without high Q, radio stations would "bleed" into each other, creating a wall of unlistenable noise.

2. What is the danger of "Voltage Magnification"?

In Series resonance, the voltage across L and C can be Q times higher than the input. If your input is 230V and your Q is 10, the capacitor sees 2,300V! This frequently leads to insulation failure and explosions in high-power industrial filter banks.

3. How does Damping Ratio ($\zeta$) affect ringing?

The damping ratio ($\zeta$) determines the transient "ring-down" time. Underdamped ($\zeta < 1$) circuits oscillate before settling. Critical Damping ($\zeta = 1$) returns to zero in the shortest possible time without crossing the axis, which is the "Gold Standard" for sensor and instrument design.

4. What is "Self-Resonant Frequency" (SRF)?

Every inductor has internal parasitic capacitance. The SRF is the frequency where the inductor resonates with its own internal parasitics. Beyond this point, the inductor acts like a capacitor. For high-speed digital clocks, choosing components with an SRF higher than the clock speed is mandatory.

5. Why use Parallel Resonance for Wave Traps?

Parallel resonance creates a Maximum Impedance point. In power systems, "Wave Traps" are parallel LC filters tuned to block high-frequency communication signals from entering a substation while allowing the low-frequency (50/60Hz) power to pass through with zero resistance.

6. How does "Skin Effect" impact the Q-Factor?

At high frequencies, current only flows on the outer shell (skin) of a conductor. This increases the effective AC resistance ($R_{ac}$), which directly lowers the Q-factor. This is why high-performance RF inductors are often plated in silver or utilize Litz wire.

7. Do temperature shifts change Resonant Frequency?

Yes. Most capacitors and Ferrite cores have a Temperature Coefficient. As heat increases, the physical dimensions or permittivity change, shifting the resonance. In high-precision timing, NPO/C0G grade capacitors are used because they maintain stability across temperature swings.

8. When is Ferrite Shielding necessary?

Resonant loops act as efficient antennas. They broadcast EMI which can interfere with nearby electronics. Proper shielding or using "Closed-Core" toroidal inductors is necessary to contain the magnetic flux and fulfill EMC compliance (like FCC or CE) for commercial products.