How to Determine Ferrite Bead Circuit Model Parameters

For some modeling tasks, an impedance vs. frequency curve for a ferrite bead is needed to properly estimate or simulate circuit behavior. This applies to SPICE simulations of power supplies or filtering applications involving ferrites. While we generally don't advocate the use of ferrites in ways that have been popularized in the past, it's very important to test and validate any proposed design involving ferrites.

When a SPICE model for a ferrite bead is unavailable, it is possible to determine parameters for an equivalent circuit model. This can be done by hand or with an optimization (regression) algorithm.

This article will briefly explain how to determine these approximate parameters from an impedance curve, providing a rough circuit model for a ferrite bead. While we often advocate for eliminating ferrites in most designs, if you choose to use one, this model can help validate the circuit design in simulation before building a prototype.

Ferrite Bead Circuit Model

A very basic circuit model for a ferrite bead is shown in the schematic below. This schematic uses a parallel RLC circuit with a small series resistance. The goal is to mimic the resonance and impedance of the ferrite bead as shown in its impedance curve from the datasheet. Meanwhile, the series resistance provides current limiting at very high and very low frequencies.

This model assumes there is no saturation in the ferrite material due to current through the component. Therefore, nonlinear effects are not expected to arise, and we can treat the model as a linear time-invariant (LTI) circuit. Accurately capturing saturation requires a much more detailed SPICE model, which is sometimes provided by ferrite bead manufacturers for specific part numbers.

Determining the Resistances

The ferrite bead circuit model has four parameters to determine: two resistances, an inductance, and a capacitance. The resistances are the simplest to calculate, so we will start with these.

At resonance, the bead is purely resistive. Therefore, the parallel resistance can be determined directly:

At DC or very low frequencies, the series resistance can be observed from the impedance curve:

Both points can be seen on a ferrite bead impedance curve. An example curve from the datasheet for part number MH2029-401Y is shown below, with the two resistances indicated on the graph.

Now that these two values have been determined, we can move on to calculating the remaining capacitance and inductance parameters. It is important to note that above DC, the impedance will be much larger than the series resistance, especially near the resonance where the impedance is entirely resistive. Therefore, the series resistance can be ignored in the following calculations.

Determining the Capacitance and Inductance

Once the resistive points are identified, the next step is to determine the resonant frequency in terms of capacitance and inductance. At resonance, the capacitive and inductive reactances negate each other, and the resonant frequency is given by:

Additionally, the bandwidth of the impedance curve can provide another equation for the resonant frequency. The bandwidth in this context is the full-width frequency range of the power in the circuit at 50% of the peak power dissipation at resonance (or about 70.7% of the peak current, denoted FWHM). The relation to the circuit parameters is:

One problem with this is that the peak power dissipation curve is not know from ferrite bead datasheets, so you will have to guess what the FWHM value needs to be. I have found that using the impedance curve's FWHM value is a decent starting point for a guess. We will see how accurate this can be in the example below.

Equations 3 and 4 form a system of equations with two unknowns. Solving these equations completes the parameter extraction process. The result is:

This is the complete set of equations required to determine the impedance model for a ferrite bead.

Comparing to a Measured Ferrite Bead Impedance

How does this model prediction compare to the measured impedance of a real ferrite bead? Below is an example of parameter values determined for part number MH2029-401Y shown above. The impedance graph for the circuit model is shown alongside the actual curve, using the same scale. The parameters are as follows:

• Resonant frequency: 160 MHz
• C = 0.842 pF
• L = 1.18 uH
• R = 450 Ohms
• FWHM = 420 MHz (initial guess based on the FWHM value from the impedance curve)

It is clear that while the graphs differ in some areas, the circuit model adequately captures the overall shape of the curve, the peak resistance, and the resonant frequency. Using my initial guess at the FWHM value from the ferrite bead's impedance curve, it is clear that the model is quite accurate below resonance, which can be seen from the overlapping R, X, and Z curves. Above resonance, the circuit model overestimates the total impedance and the resistance, which highlights limitations in the circuit model's predictive ability. Note that the reactance turns negative above the resonant frequency, so it is not shown on the above graph.

Unfortunately, the curves will never perfectly overlap, even if you take the FWHM from a power dissipation curve. The reason is that the circuit model always overestimates the ferrite bead's reactance, and this is why the Z curve is always wider than the ferrite bead's measured Z curve.

Despite its limitations, the circuit model is helpful for determining a reasonably accurate estimate of circuit behavior when a manufacturer-supplied ferrite bead model is unavailable. By extracting parameters from the impedance curve, designers can validate circuit behavior and make informed decisions before building prototypes.

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