Modelling ferrite beads

Created: Nov. 2022


Ferrite beads provide wideband, multi-octave choking, in RF & microwave circuits. So, beads are a subset of the larger inductor family. While there is an abundance of tutorials on modelling inductors [1 - 3], but ferrite beads are rarely covered.


Up to VHF, a conventional inductor is typically modelled using 3 elements [4]. However, compared to the inductor, the bead's impedance Z spans over a much wider bandwidth. Another unique characteristic is the broad reactance X peak; i.e. X is flat over a wide bandwidth (fig. 1). Due to the aforementioned characteristics, the bead's model is necessarily more complex than the conventional inductor's. 

Fig. 1 The ferrite bead has Z, R & X parameters that span over large range of frequencies, hence complicating the model

Previously, 2-element [5], 4-element [6 - 7] and 8-element [8] models have been proposed (fig. 2), but their accuracy have not been demonstrated. Moreover, it is doubtful that the simpler 2-element and 4-element models can predict the Z,R & X parameters over a wide frequency range.

Fig. 2 Prior arts that have proposed for modelling the ferrite bead, but none has been validated against wideband measurement

To address the need for an accurate ferrite bead model, we propose one formed from a cascade of two parallel RLC sections (fig. 3). The model comprises 6 elements. This model was previously proposed, but not validated [9]. This work provides the experimental validation for this model.

Fig. 3 Proposed model to account for the ferrite bead's unique characteristics

Results


Murata BLM18RK102 is a ferrite bead in the 0603 SMD format [10]. The proposed model is shown as an inset in fig. 4. The model parameters are empirically adjusted to fit the datasheet's curves. The simulated Z, R & X traces have good agreement with the datasheet over much of the simulated frequency range. The predicted Z & R have some error over 20-50 MHz, but these are inconsequential for most applications.

Fig. 4 The modeled result agrees almost perfectly with the datasheet. Simulated traces are in pink, while datasheet traces are black

Conclusion


The 6-element ferrite bead model is reasonably accurate over LF - UHF.

 

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“I am never content until I have constructed a mechanical model of the subject I am studying. If I succeed in making one, I understand, otherwise I do not.” "Can you make a model of it? If not, your theory is apt to be based more upon imagination than upon knowledge." - Lord Kelvin, English physicist.

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References


[1] I. Bahl, "Inductors" in Lumped elements for RF & microwave circuits, MA : Artech, 2003, ch. 2.

[2] P. L. D. Abrie, "Radio frequency components" in Design of RF & microwave amplifiers & oscillators, MA : Artech, 2000, section 3.3 "Inductors".

[3] "Self-resonant Frequency of an Inductor", Available: www.cliftonlaboratories.com/self-resonant_frequency_of_inductors.htm

[4] R. W. Rhea, “A multimode high-frequency inductor model”, Applied Microwave & Wireless, Nov. 1997. 

[5] M. F. DeMaw, “Beads, sleeves & pot cores” in Ferromagnetic core design & application handbook, New Jersey : Prentice-Hall, 1981, ch. 4.  

[6] Application note, “AN 583: Designing Power Isolation Filters with Ferrite Beads for Altera FPGAs”, Jul. 2009. Available: https://www.eeweb.com/wp-content/uploads/articles-app-notes-files-designing-power-isolation-filters-with-ferrite-beads-for-altera-fpgas.pdf

[7] J. Zhang, et al, "Ferrite bead model extraction & its application in high-performance ASIC analog power filtering", 2011 IEEE Intl. Symp. Electromagnetic

[8] "BLM Series SPICE-DATA Ferrite Bead Inductor", Ver 6.7, Murata, Jan. 2005.

[9] C. L. Lim, "Cut Loss in Low-Voltage, Wideband PIN Attenuators", Microwaves & RF, Apr. 2008.

[10] Datasheet, "BLM18RK102", Available: https://www.murata.com/en-eu/api/pdfdownloadapi?cate=cgsubChipFerriBead&partno=BLM18RK102SN1%23