Specifications

5-8
5.2 Inductor measurement
5.2.1 Paracitics of an inductor
An inductor consists of wire wound around a core and is characterized by the core material used.
Air is the simplest core material for making inductors, but for volumetric efficiency of the inductor,
magnetic materials such as iron, permalloy, and ferrites are commonly used. A typical equivalent
circuit for an inductor is shown in Figure 5-9 (a). In this figure, Rp represents the magnetic loss
(which is called iron loss) of the inductor core, and Rs represents the copper loss (resistance) of the
wire. C is the distributed capacitance between the turns of wire. For small inductors the equivalent
circuit shown in Figure 5-9 (b) can be used. This is because the value of L is small and the stray
capacitance between the lead wires (or between the electrodes) becomes a significant factor.
Figure 5-9. Inductor equivalent circuit
Generally, inductors have many parasitics resulting from the complexity of the structure (coil) and
the property of the magnetic core materials. Since a complex equivalent circuit is required for repre-
senting the characteristics, which include the effects of many parasitics, a simplified model for
approximation is used for practical applications. In this section, we discuss the frequency response
of a low-value inductor, which is represented by equivalent circuit model shown in Figure 5-9 (b).
This model will fit for many SMD (chip) type RF inductors.
When the inductor circuit shown in Figure 5-10 is measured using the Ls-Rs mode, the measured
Ls value is expressed by the equation shown in Figure 5-11. The measured Ls value is equal to the
L value only when the inductor has low Rs value (Rs << wL) and low C value (1/wC >> wL). Typical
frequency characteristics of impedance (|Z|_ q) for a low-value inductor are shown in Figure 5-12 (a).
Since the reactance (wL) decreases at lower frequencies, the minimum impedance is determined by
the resistance (Rs) of winding. The stray capacitance Cp is the prime cause of the inductor frequen-
cy response at high frequencies. The existence of Cp can be recognized from the resonance point,
SRF, in the higher frequency region. At the SRF, the inductor exhibits maximum impedance because
of parallel resonance (wL = 1/wCp) due to the Cp. After the resonance frequency, the phase angle of
impedance is a negative value around –90° because the capacitive reactance of Cp is dominant. The