## The Nonideal Inductor

In general, inductors are more problematic than capacitors. The circuit model for a real inductor is shown in Figure 7.5. The parasitic elements are: 1) resistance within the leads and the wire of the inductor, 2) the capacitance between the leads and between the loops of wire, and 3) the equivalent resistance corresponding to core losses (if the inductor uses a ferromagnetic core). The parasitic capacitance forms a resonant circuit with the inductance, with a resonant frequency at fo = 1/V (LC ). Above this frequency, the impedance of the inductor decreases with frequency; in other words, the component acts like a

Figure 7.4 A) Frequency response of a 0.1 mF surface-mount, size 0805 (0.08" x 0.05") capacitor (Lead = 0.73nH). B) Frequency response of a 0.015 mF surface-mount, size 0805 (0.08" x 0.05") capacitor (Lead = 0.88nH). Above the self-resonant frequency (SRF) of ~40MHz, the device acts like a 0.88nH inductor. C) Frequency response of a 0.001 mF surface-mount, size 0805 (0.08" x 0.05") capacitor (Lead = 0.77nH). Above the self-resonant frequency (SRF) of ~200MHz, the device acts like a 0.77nH inductor. Plots were created with muRata's MCSIL software (http://www.murata.com/).

Impedance

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Apparent Capacitance

Apparent Inductance

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capacitor above the resonant point. Again, there are two options to increase the resonant frequency: 1) reduce the parasitic capacitance or 2) use a smaller value of inductance. Large values of inductance, thus, are not practical at high frequencies.

If the inductor contains a ferromagnetic core, the core losses will also limit frequency response. The core losses arise from hysteresis losses and from eddy currents within the core. The situation is compli-

Figure 7.4 Continued.

Impedance

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Apparent Capacitance

Apparent Inductance

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Impedance

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Apparent Capacitance

Apparent Inductance

Figure 7.5 Hidden schematic of a real-world inductor includes lead resistance (R/eod), core loss (Rcore), and parasitic capacitance (Cp) resulting from the leads and windings. Core losses are typically frequency dependent.

Figure 7.5 Hidden schematic of a real-world inductor includes lead resistance (R/eod), core loss (Rcore), and parasitic capacitance (Cp) resulting from the leads and windings. Core losses are typically frequency dependent. cated by the fact that hysteresis losses are nonlinear and that eddy current losses increase with frequency. Figure 7.6 plots the frequency response of two non-ideal inductors.

All real inductors are limited as to how much current they can carry. This limitation stems from the resistance of the conductors that make up the inductor and its leads. Inductors with ferromagnetic cores are further limited in that the current must be kept below the saturation level for the device to operate properly. 