Technology / Technical guide
LC Filter Resonance: Natural Frequency and Damping
Inductance and capacitance can exchange stored energy. That interaction gives an ideal LC model a natural frequency, but an actual filter is connected to a source, load and losses. Its useful frequency response cannot be inferred from one formula alone.
Separate natural oscillation from driven filter response.
The familiar LC frequency describes an ideal two-element model; topology, loading and damping shape a real response.
01 / Stored energy
Two elements store energy in different forms.
An ideal capacitor stores electric-field energy, while an ideal inductor stores magnetic-field energy.
An ideal capacitor stores electric-field energy, while an ideal inductor stores magnetic-field energy. When an isolated ideal LC circuit is excited, capacitor voltage and inductor current can exchange energy rather than each remaining constant.
For capacitance C and inductance L, the stored energies are ½Cv² and ½Li². The total remains constant in the ideal lossless model. OpenStax develops this oscillation model; real losses and an external source change the energy balance.
02 / Natural frequency
State the ideal model behind the LC formula.
For a single ideal inductor and capacitor forming a lossless oscillator, angular natural frequency is ω0 = 1/√(LC), in rad/s.
For a single ideal inductor and capacitor forming a lossless oscillator, angular natural frequency is ω0 = 1/√(LC), in rad/s. The corresponding frequency is f0 = 1/(2π√(LC)), in hertz.
As a purely mathematical comparison, doubling L while keeping C fixed lowers f0 by a factor of √2. This follows from the model’s square-root relationship. It is not a component-selection recommendation or a description of an installed MARSTON filter.
03 / Damping
Loss changes the persistence of an oscillation.
Damping dissipates energy that would otherwise continue to exchange between the two storage elements.
Damping dissipates energy that would otherwise continue to exchange between the two storage elements. Depending on the circuit and damping strength, a disturbance can produce decaying oscillation or a nonoscillatory return toward equilibrium.
Resistance and other losses can contribute damping, but where they occur matters. TI’s public LC-filter description highlights resonance and the need to account for damping. It does not establish one damping arrangement for every converter or installation.
04 / Driven response
A connected filter has more than an isolated LC pair.
A converter filter receives a driven waveform and connects to source and load impedances.
A converter filter receives a driven waveform and connects to source and load impedances. Its voltage or current response depends on those boundaries, element arrangement and losses. An unloaded ideal oscillator is therefore not a complete transfer model.
A resonant peak, a natural frequency and a defined attenuation point are different concepts. They may be related within a specified model, but the ideal f0 formula cannot be labelled a universal −3 dB cutoff for arbitrary LC networks.
05 / Frequency content
Attenuation depends on the frequencies present.
A switching waveform can contain a fundamental, switching-related components and other spectral content.
A switching waveform can contain a fundamental, switching-related components and other spectral content. A filter acts differently at different frequencies. The PWM frequency guide distinguishes the waveform quantities before a filter response is discussed.
More than one reactive stage can introduce additional modes. Parasitic capacitance, lead inductance and frequency-dependent losses can also matter outside a simple lumped-element approximation. A model should retain the frequency range over which its assumptions are useful.
06 / Model boundaries
Use resonance as an explanation, not a setting.
The purpose of this model is to explain why reactive elements can amplify some disturbances while attenuating others.
The purpose of this model is to explain why reactive elements can amplify some disturbances while attenuating others. It does not provide L/C values, damping-component choices, gain adjustments or protective limits for equipment.
No MARSTON LC topology, component values or measured filter response is confirmed here. The ideal relationship and qualitative loading effects remain distinct from an actual converter design, laboratory result or compliance claim.
Continue the review with PWM Switching Frequency, Carrier & Fundamental.
Continue the review with DC Capacitor Ripple Current, ESR & Frequency Dependence.
Continue the review with Common-Mode & Differential-Mode Electrical Noise.
Extend the filter-component review with filter-capacitor reactive power and stored energy.
Review LCL network states and boundary conditions as a separate filter-network topic, retaining its stated connections and boundary conditions.
General background: OpenStax: ideal LC energy exchange and natural frequency · Texas Instruments: public description of LC-filter resonance and damping. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Capacitor energy | ½Cv² in J | Ideal lumped capacitance. |
| Inductor energy | ½Li² in J | Ideal linear inductance. |
| Natural frequency | 1/(2π√(LC)) in Hz | Single ideal lossless LC oscillator. |
| Damping | Energy dissipated over time | Loss location and connected circuit matter. |
| Filter response | Gain versus frequency | Defined topology, source, load and measurement quantity. |
Engineering questions.
Is f0 a universal LC filter cutoff?
No. It is the natural frequency of the stated ideal oscillator model.
Does doubling L halve f0?
No. With C unchanged, the ideal frequency decreases by a factor of √2.
Can an LC network increase a signal at some frequencies?
A driven network can show a resonant peak under applicable loading and damping conditions.
Is damping identical to removing all ripple?
No. Damping and frequency-selective attenuation describe different effects.
Do several reactive stages share one simple resonance?
Not generally; additional elements can introduce additional modes.
Does this provide filter component or gain settings?
No. It explains the model and its boundaries without operational adjustments.
Technical enquiry
Discuss the technical question.
Inductance and capacitance can exchange stored energy. Share the model and applicable operating or design information for an engineering discussion.