Electronics Guide

Capacitor High-Frequency Behavior

Real capacitors contain parasitic elements that modify their behavior as frequency increases. Equivalent series inductance (ESL) arises from the leads, internal connections, and electrode geometry. Equivalent series resistance (ESR) represents losses in the electrodes, dielectric, and connections. These parasitic elements create a series resonance where capacitor impedance reaches a minimum, above which the component becomes inductive.

The self-resonant frequency (SRF) varies widely among capacitor types and sizes. Large electrolytic capacitors may resonate below 100 kHz, while small ceramic capacitors can maintain capacitive behavior beyond 100 MHz. Selecting capacitors with self-resonant frequencies appropriate to the filtering requirement ensures the component functions as intended.

Above self-resonance, capacitor impedance increases with frequency at the rate determined by the ESL. A capacitor intended to provide bypassing at 100 MHz may offer little attenuation if its self-resonant frequency is 30 MHz. Using multiple capacitors of different values and types provides low impedance across a wider frequency range, with each capacitor effective in its capacitive region.

Ceramic capacitors in small packages (0402, 0201) offer the lowest ESL and highest self-resonant frequencies. Surface-mount construction eliminates lead inductance, and the small physical size minimizes internal inductance. However, small ceramic capacitors have limited capacitance values, requiring parallel combinations or acceptance of higher impedance at lower frequencies.

Inductor High-Frequency Behavior

Inductors exhibit parasitic capacitance between windings and between the winding and core. This distributed capacitance creates a parallel resonance where inductor impedance reaches a maximum, above which the component becomes capacitive and provides decreasing impedance with frequency.

The self-resonant frequency of inductors depends on winding geometry and construction technique. Multi-layer windings have higher inter-winding capacitance and lower self-resonant frequencies than single-layer windings. Toroidal inductors typically achieve higher self-resonant frequencies than bobbin-wound inductors due to their more uniform winding distribution.

Core permeability typically decreases with increasing frequency, causing inductance to fall even below self-resonance. Ferrite materials are characterized by a complex permeability with real (inductive) and imaginary (lossy) components. At high frequencies, the lossy component dominates, providing attenuation through energy dissipation rather than reactive impedance. This lossy behavior can be advantageous for EMI filtering, where dissipating noise energy is acceptable.

Ferrite beads are specifically designed to exploit high-frequency losses. At low frequencies, a ferrite bead presents low impedance, allowing signal or power current to pass. As frequency increases, the impedance rises due to increasing core losses, attenuating high-frequency noise through dissipation. The impedance versus frequency characteristic of ferrite beads should be matched to the frequency range of the noise to be filtered.

Common-Mode Choke Behavior

Common-mode chokes exhibit complex high-frequency behavior due to the interaction of multiple parasitic elements. Inter-winding capacitance between the two windings provides a high-frequency bypass path that limits common-mode attenuation. Capacitance from the windings to the core can create additional coupling paths.

The common-mode inductance typically falls with increasing frequency due to decreasing core permeability, while the inter-winding capacitance becomes increasingly significant. Together, these effects create a frequency response that rises to a maximum impedance and then falls at higher frequencies.

Multi-section winding techniques can improve high-frequency common-mode choke performance by reducing inter-winding capacitance. Physically separating the windings or using bifilar winding in a specific pattern minimizes the capacitive coupling while maintaining magnetic coupling for common-mode rejection.

Trace Inductance

PCB traces have inductance of approximately 1 nH per millimeter length for typical geometries. While this seems negligible, 10 mm of trace (10 nH) has an impedance of 6 ohms at 100 MHz, significant compared to the milliohm impedance of a good bypass capacitor. This trace inductance adds to the ESL of connected capacitors, reducing their effectiveness at high frequencies.

Minimizing trace length to filter components, particularly ground connections of bypass capacitors, is essential for high-frequency performance. Wide traces reduce inductance compared to narrow traces of the same length. Multiple vias in parallel provide lower inductance connections to ground planes than single vias.

Ground Plane Considerations

Ground planes provide low-impedance return paths for high-frequency currents. However, slots, gaps, or voids in the ground plane can dramatically increase the impedance of return paths that must cross these discontinuities. The return current must flow around the discontinuity, increasing the effective path length and creating opportunities for coupling to other circuits.

Ground plane resonances occur when the ground plane dimensions approach electrical wavelengths. A ground plane can support standing waves, with voltage maxima and minima at specific locations. Filter effectiveness can vary depending on position relative to these resonances. Distributed bypassing and careful placement of filter components away from voltage maxima mitigate these effects.

Filter Input-Output Isolation

Capacitive and inductive coupling between filter input and output traces can bypass the filter, limiting achievable attenuation regardless of component performance. At high frequencies, even small coupling capacitances (tenths of picofarads) provide significant bypass paths.

Physical separation between input and output is the most effective isolation technique. Routing input and output traces on opposite sides of the PCB with ground planes between provides shielding. For very high isolation requirements, placing input and output connections on opposite ends of the filter, with the filter structure providing physical separation, may be necessary.

Ground plane partitioning can prevent high-frequency currents from coupling around filters. Separate ground regions for unfiltered and filtered circuits, connected only through the filter ground, ensure that return currents flow through the intended path.

Distributed Filtering

Rather than concentrating filtering at a single location, distributing filter elements along the signal path provides broader frequency coverage. Multiple smaller filters, each effective over a portion of the frequency range, together achieve wider bandwidth than a single filter attempting to cover the entire range.

For power distribution, placing bypass capacitors at multiple locations throughout the circuit provides local high-frequency bypassing near noise sources and sensitive circuits. Different capacitor values optimize performance at different frequencies, with larger capacitors near power entry points and smaller capacitors near high-frequency circuits.

Feed-Through Capacitors

Feed-through capacitors are constructed specifically for high-frequency filtering. The signal conductor passes through the center of the capacitor, with capacitance distributed around the conductor connecting to a surrounding ground shell. This coaxial construction minimizes parasitic inductance and provides effective bypassing to frequencies above 1 GHz.

Three-terminal feed-through capacitors separate the input and output ground connections, preventing ground coupling that could bypass the filter. The capacitor connects between the center conductor and a ground shell, with the shell mounted to a bulkhead or enclosure wall that provides the ground reference.

Feed-through capacitor filters are commonly used at enclosure entry points for both power and signal lines. They are particularly effective for maintaining shielding effectiveness of enclosures by preventing high-frequency currents from entering on conductor surfaces.

Pi Filters with Feed-Through Construction

For higher attenuation requirements, pi filter configurations using feed-through construction provide excellent high-frequency performance. The center inductor element is surrounded by input and output capacitor sections, all in a single feed-through housing. This construction maintains low parasitic coupling while providing multi-element filter response.

C-L-C, L-C-L, and higher-order configurations are available in feed-through housings. Selection depends on the source and load impedances and the required attenuation characteristic. The feed-through housing mounts to the enclosure bulkhead, providing both filtering and a defined entry point for the conductor.

Ferrite Absorption

At very high frequencies, absorptive filtering using ferrites may be more effective than reflective filtering using capacitors and inductors. Ferrite beads, tubes, and plates dissipate high-frequency energy as heat rather than reflecting it back to the source.

Cable ferrites (split or solid) provide simple, effective high-frequency filtering by clamping around cables without requiring electrical connection. The ferrite increases the common-mode impedance of the cable, attenuating high-frequency common-mode currents. Proper ferrite selection matches the impedance peak to the frequency range of concern.

The absorptive nature of ferrite filtering avoids the resonance issues that can occur with reactive filters. Ferrite impedance increases monotonically with frequency up to a peak, then gradually decreases, without the sharp nulls that can occur when reflective filter elements resonate.

Impedance Transformation

Transmission lines transform impedance between their ends according to line length and characteristic impedance. A quarter-wavelength line transforms a short circuit to an open circuit and vice versa. This transformation can cause filter components to appear to have very different impedance than expected based on their nominal values.

For filter connections shorter than a tenth wavelength, transmission line effects can usually be ignored. As connections approach a quarter wavelength, impedance transformation becomes significant and must be considered in filter design. Keeping connections short avoids these effects in most practical filters.

Standing Waves

Reflections between filter components and their connections create standing waves with voltage and current maxima at specific locations. Filter effectiveness varies with position relative to these maxima. At a current maximum, series filter elements are most effective; at a voltage maximum, shunt elements are most effective.

Standing wave effects can cause filter attenuation to vary significantly across small frequency changes as the electrical length changes. These variations can create pass-through peaks at specific frequencies where the standing wave pattern allows noise to bypass filter elements.

Filter Mounting

Filters at enclosure entry points should mount directly to the enclosure wall with minimum lead length on both input and output. This placement keeps unfiltered conductors outside the enclosure and ensures high-frequency ground connections through the enclosure wall.

The mounting method should provide a low-impedance ground connection across the frequency range of interest. Direct bolting or soldering to a conductive enclosure surface provides the best high-frequency grounding. Mounting feet, brackets, or standoffs can add inductance that degrades high-frequency performance.

Cable Entry Treatment

Cables penetrating shielded enclosures represent potential entry points for high-frequency interference. Even with filtered conductors, the cable shield or outer surface can carry high-frequency currents into the enclosure if not properly terminated.

Peripheral bonding of cable shields to the enclosure at the entry point prevents shield currents from entering the enclosure. EMI backshells, circular grounding clamps, and conductive glands provide 360-degree contact between the shield and enclosure. This termination should occur at the enclosure boundary, with the filter treating the internal conductors.