All components have some parasitics, including inductors, which have parasitic capacitance.
An inductor’s winding capacitance determines its resonant frequency and the limit at which it starts to function like a capacitor.
In addition to self-resonance, winding capacitance is responsible for some conducted EMI problems.
This toroidal inductor has some parasitic capacitance in the windings
As much as we would like to think every component is perfect, this is simply not the case. Every component, whether it’s a resistor or a MOSFET, has some parasitics that will dominate once the component is driven with sufficiently high frequencies. The frequency-dependent behavior of real components requires describing all components in terms of equivalent RLC models to predict electrical behavior in a real circuit.
One component that has some unique behavior due to its parasitics is an inductor. The parasitic capacitance of an inductor not only causes a self-resonance effect, but it also contributes to some conducted EMI problems that are unique in power systems. If you can account for the parasitic capacitance of an inductor in simulations, you can accurately determine the frequency limits of your inductor and when the inductor will start to act like a capacitor.
Parasitic Capacitance of an Inductor
All inductors have three parasitics that influence AC behavior in a real system:
- Equivalent series resistance (ESR): This arises due to the contact resistance on the input leads.
- Equivalent parallel capacitance (EPC): Winding capacitance, which is the primary source of parasitic capacitance.
- Equivalent parallel resistance (EPR): Coil resistance due to the finite conductivity of the inductor coil.
These three parasitics plus the desired inductance give a total of four parameters that are used to describe electrical behavior. Just like any other component that has parasitic resistance, capacitance, or inductance, we can describe the real electrical behavior as an RLC circuit.
The equivalent model used to describe an inductor in terms of its parasitic capacitance is a parallel RLC circuit with lumped elements. We use this model because the winding capacitance is in parallel with the inductor coil, which arises due to the spacing between loops in the coil.
Resonance in a toroidal inductor coil due to its parasitic capacitance. The equivalent parallel RLC circuit and resonant frequency are shown in the image
From the above graph, we can see the self-resonance effect clearly, which produces the peak in the measured impedance data. This self-resonance peak is at ~130 MHz for this example inductor, which is typical of wirewound toroidal inductors mounted on PCBs. Above this frequency, the inductor behaves more like a capacitor, as its impedance decreases with increasing frequency. This is the inverse of what is seen in a capacitor due to its parasitic inductance, where the impedance reaches a minimum at the self-resonant frequency.
The above model is simple enough to derive an impedance equation for the inductor coil. This is shown below in terms of the parasitic elements in the above list and circuit diagram:
The impedance of a parallel RLC circuit for an inductor
The equation, self-resonant frequency, and circuit model above collectively describe all the electrical behavior of an inductor with known parasitics. Similar models can be developed for other components with coils, namely transformers and chokes. This problem with parasitic capacitance is the reason inductors and coiled components can fail to fully suppress EMI.
When Coils Fail
As a result of parasitic capacitance, coils can fail to operate properly as filters in some important situations:
- Noise filtering: When used to filter common-mode or differential noise, coupled coils will become ineffective at filtering high frequency noise. Therefore, if high frequency noise is a concern, the better approach is to add a shunt capacitor to the filter circuit. Be careful that you do not create an additional pole in the coil’s transfer function, as this creates a new resonance for noise.
- Harmonics reduction: In power systems, it is very important to reduce harmonics on the input power lines. This is normally done with a PFC circuit, which is intended to smooth out the current draw. Parasitic capacitance on coils in a PFC circuit limits harmonic suppression above the self-resonance. The physically larger inductors used in high power systems may not provide sufficient filtering, as they have lower self-resonances.
- Power stability for high speed digital ICs: It is sometimes suggested that ferrite beads or inductors be used to smooth out DC power for high speed digital ICs. Inductor coils and ferrite beads exhibit the same behavior, namely a self-resonance and high-pass filtering behavior at high frequencies. This means high frequency ripple on the power bus will still create power fluctuations at the IC, leading to jitter and noisy logic levels.
There are other instances in power electronics, RF systems, and digital electronics where the parasitic capacitance of an inductor will create noise problems. Be mindful of the inductor’s self-resonant frequency when selecting components. As an example, the impedance curves for two power inductors are shown below. We can see that the self-resonance is at approximately 300 kHz, which would limit this component’s use in a system like a high-power switching regulator.
Impedance curves for two high-power common-mode chokes
Simulating Real Inductors
Although parasitics and self-resonance are unwanted effects, they need to be included in a circuit simulation. Typically, if you open up a SPICE simulator and just use generic components, you won’t have any way to account for the parasitics in the above circuit model. To do this, you have three approaches:
- Create a subcircuit model of the parallel RLC circuit + series resistor shown in the above graph.
- Create a phenomenological model using measured data for a real inductor.
- Use the generic inductor, but add in generic resistors and a generic capacitor to model the parasitics.
These approaches are simple to do with circuit simulation software that integrates with PCB layout tools. Taking account of EMI problems due to coupling in real inductors is more complex and requires a 3D field solver to calculate and pinpoint EMI in your design. When you use the PCB design and analysis tools from Cadence, you’ll have everything you need to account for the parasitic capacitance of an inductor in pre-layout and post-layout simulations. You’ll have access to a field solver that integrates with your PCB layout tools and a SPICE simulator in a schematic capture program to help you design and model your inductive circuits.