E6D: Inductors and Piezoelectricity

E6D covers the magnetic and mechanical properties of inductors and transformers, and the piezoelectric phenomenon that underlies quartz crystal oscillators and filters. Topics include permeability as the property that determines inductance, ferrite versus powdered iron core characteristics, eddy current loss reduction through lamination, toroidal core field confinement, VHF parasitic suppression with ferrite beads, inductor saturation, and the piezoelectric effect in both directions — including the equivalent circuit of a quartz crystal.

The Extra exam draws one question from E6D. Questions require knowing which material property controls inductance, the trade-offs between core types, why toroidal geometry is preferred, and the physics of piezoelectricity.

Permeability and Inductance

The inductance of a coil depends on the core material's permeability — a measure of how readily the material supports a magnetic field. Higher permeability means a stronger magnetic field for a given current, which means more inductance per turn of wire.

Some core materials actually reduce inductance relative to air. Brass is a diamagnetic material that, when inserted into a coil, decreases the effective permeability and therefore decreases inductance. This effect is used in trimmer coils where a brass slug provides a fine inductance adjustment downward.

Core Materials: Ferrite vs. Powdered Iron

Both ferrite and powdered iron are common inductor core materials, but they have different characteristics that make each better suited for specific applications.

Ferrite cores generally require fewer turns to produce a given inductance value because of their higher permeability. Powdered iron has the highest temperature stability of common magnetic core materials, making it the preferred choice when inductance must remain constant as temperature changes.

Laminated Cores and Eddy Currents

In solid metal cores, changing magnetic fields induce circulating currents (eddy currents) within the core itself. These eddy currents dissipate power as heat and reduce the efficiency of inductors and transformers. The solution is to construct the core from thin layers separated by insulating material (laminations).

Lamination restricts eddy currents to flow within each thin layer rather than circulating through the full cross-section. Since power loss is proportional to the square of the eddy current path length, thinner laminations dramatically reduce eddy current losses.

Toroidal Cores

A toroidal (donut-shaped) core has a major advantage over a solenoid (straight cylinder) core: toroidal cores confine most of the magnetic field within the core material. Because the core forms a closed loop, the magnetic flux has a continuous high-permeability path and does not need to cross air gaps or emerge from the ends of the core.

This field confinement means toroidal inductors have:

• Lower stray field radiation — less interference with nearby components
• Higher efficiency — less flux escapes to induce losses in surrounding metal
• Less susceptibility to external fields — the enclosed geometry provides natural shielding

Ferrite Beads as Parasitic Suppressors

At VHF and UHF frequencies, transistor amplifiers can oscillate at unexpected frequencies due to stray inductance and capacitance in the circuit creating parasitic resonances. Ferrite beads placed on the input and output leads of transistor HF amplifiers suppress these VHF/UHF parasitic oscillations by adding resistive losses at high frequencies without significantly affecting the intended HF operating frequencies.

Inductor Saturation

Ferromagnetic core materials can only support a limited magnetic flux density before the magnetic domains are all aligned and no additional flux can be sustained. This condition is called saturation. The cause of inductor saturation is operation at excessive magnetic flux, which occurs when the current through the inductor exceeds the core's capability.

When a core saturates, its effective permeability drops dramatically, causing the inductance to collapse. This can allow large current spikes to flow, potentially damaging circuit components. Avoiding saturation requires selecting a core with sufficient cross-sectional area and permeability for the expected peak current.

Piezoelectricity and Quartz Crystals

Piezoelectricity is a property of certain crystalline materials — particularly quartz — where mechanical stress generates an electrical voltage, and conversely, an applied electrical voltage produces mechanical deformation. Both directions of the effect are part of the piezoelectric phenomenon.

Quartz Crystal Equivalent Circuit

A quartz crystal resonator has an extremely precise mechanical resonant frequency determined by its physical dimensions. The electrical equivalent circuit is a series RLC circuit (representing the mechanical resonance) in parallel with a shunt capacitance C that represents the electrode capacitance and stray capacitance of the crystal package.

This equivalent circuit means a crystal has two resonant frequencies: a series resonance (where the series RLC branch is at resonance, presenting very low impedance) and a parallel resonance (where the series branch resonates with the shunt capacitance, presenting very high impedance). The extremely high Q of the mechanical resonance (often 10,000 to 1,000,000) gives crystals their exceptional frequency stability.

E6D Practice Questions