# Inductor Parasitic Capacitance Limits Upper Operating Frequencies

### Key Takeaways

• The unwanted capacitance offered by an inductor is called parasitic capacitance.

• In equivalent circuit modeling, the parasitic capacitance of the inductor is parallel to it.

• The parasitic capacitance limits the upper operating frequency of the inductor. Parasitic resistance is in series with the inductor, whereas parasitic capacitance is parallel to the inductor

Passive elements such as resistors, inductors, and capacitors are present in almost all circuit designs. Apart from their self-property, such as resistance, inductance, or capacitance, passive elements exhibit other unwanted properties, which we call parasitic. Parasitic dependencies of passive elements are inevitable and must be considered when developing sensitive circuits or equivalent circuit models for analysis.

Inductors give an inductance property as well as parasitic resistance and parasitic capacitance. In the equivalent model of inductors, parasitic resistance and capacitance are included. The parasitic resistance is in series with the inductor, whereas the parasitic capacitance is parallel to it. The inductor parasitic capacitance is an important parameter to understand, as it puts limitations on the frequency of application of the inductor. In this article, we will discuss the challenges of inductor parasitic capacitance in more depth.

## Non-Idealities Due to Parasitics in Inductors

Inductors can be single-layer or multi-layer. An inductor is basically a coil made by winding an insulated wire around a ferrite core. The air-core inductors, and, in certain special cases, non-magnetic core inductors are also in use. As long as windings are present in an inductor, the parasitic capacitance cannot be eliminated completely.

An ideal inductor is a myth, as real-world inductors have parasitics. The parasitic resistance is the unwanted resistance offered by the inductor and is in series to it. The unwanted capacitance offered by the inductor is called parasitic capacitance and is parallel to the inductor. The parasitic resistance (Rp) and parasitic capacitance (Cp) make the inductor non-ideal. The equivalent circuit of a non-ideal inductor is given in the figure below. Equivalent circuit of a non-ideal inductor

### Single-Layer Inductor Parasitic Capacitance

If you analyze a single-layer inductor piecewise, you can see two sections of wire (two windings) separated by an insulator. There are several capacitors like this between the windings in an inductor. The surface area between the windings and the gap between the windings are factors affecting the value of inductor parasitic capacitance. The potential across the parasitic capacitance varies slightly from two consecutive windings to others because of the winding inductance and resistance.

The parasitic capacitance in the inductor is a distributed parameter. However, parasitic capacitance is represented as a lumped element connected in parallel to the inductor in the equivalent model illustrated above.

### Multi-Layer Inductor Parasitic Capacitance

Compared to single-layer inductors, multi-layer inductors have multiple parasitic capacitances. In multilayer inductors, the total parasitic capacitance is formed by the combination of three different parasitic capacitances. They are:

• Parasitic capacitance between the turns of the same layer.
• Parasitic capacitance between the turns of the adjacent layer.
• Parasitic capacitance between the turn-to-core and turn-to-shield.

## Frequency Dependency of Inductor Parasitic Capacitance

The parasitic capacitance influences the frequency characteristics as well as the performance of the inductor. The parasitic capacitance limits the upper operating frequency of the inductor. The equivalent impedance of the inductor takes into account the self-inductance of the coil, parasitic resistance, and parasitic capacitance.

There is the phenomenon of self-resonance between the combination of inductance and parasitic capacitance. Below the self-resonant frequency, the equivalent impedance of the inductor is inductive in nature. As the frequency increases, the parasitic capacitance dominates the equivalent impedance of the inductor. Above the self-resonant frequency, the equivalent impedance is predominantly capacitive and the inductor no longer behaves like an inductor, but more as a capacitor. Thus, parasitic capacitance limits the operation of the inductor at high frequency.

The inductor parasitic capacitance is a serious issue in common-mode chokes, EMI filters, and transformers working in high frequency. It can become a hindrance in realizing the power converters containing inductors and high-frequency transformers. Cadence software can help designers extract the parasitic capacitance of an inductor by identifying its self-resonance frequency.