# Impedance Measurement Handbook

Application Notes

Introduction

In this document, not only currently available products but also discontinued and/or obsolete products will be shown as reference solutions to leverage Keysight’s impedance measurement expertise for specific application requirements. For whatever application or industry you work in, Keysight offers excellent performance and high reliability to give you confidence when making impedance measurements. The table below shows the product status of instruments, accessories, and fixtures listed in this document. Please note that the status is subject to change without notice.

1.0 Impedance Measurement Basics

1.1 Impedance

Impedance is an important parameter used to characterize electronic circuits, components, and the materials used to make components. Impedance (Z) is generally defined as the total opposition a device or circuit offers to the flow of an alternating current (AC) at a given frequency and is represented as a complex quantity that is graphically shown on a vector plane. An impedance vector consists of a real part (resistance, R) and an imaginary part (reactance, X) as shown in Figure 1-1. Impedance can be expressed using the rectangular-coordinate form R + jX or in the polar form as a magnitude and phase angle: |Z|_ θ. Figure 1-1 also shows the mathematical relationship between R, X, |Z|, and θ . In some cases, using the reciprocal of impedance is mathematically expedient. In which case 1/Z = 1/(R + jX) = Y = G + jB, where Y represents admittance, G conductance, and B susceptance. The unit of impedance is the ohm (Ω), and admittance is the siemen (S). Impedance is a commonly used parameter and is especially useful for representing a series connection of resistance and reactance, because it can be expressed simply as a sum, R and X. For a parallel connection, it is better to use admittance (see Figure 1-2.).

Reactance takes two forms: inductive (XL) and capacitive (Xc). By definition, XL =2πfL and Xc = 1/(2πfC), where f is the frequency of interest, L is inductance, and C is capacitance. 2πf can be substituted for by the angular frequency (ω: omega) to represent XL = ωL and Xc =1/(ωC). Refer to Figure 1-3.

A similar reciprocal relationship applies to susceptance and admittance. Figure 1-4 shows a typical representation for a resistance and a reactance connected in series or in parallel.

The quality factor (Q) serves as a measure of a reactance’s purity (how close it is to be a pure reactance, no resistance), and is defined as the ratio of the energy stored in a component to the energy dissipated by the component. Q is a dimensionless unit and is expressed as Q = X/R = B/G. From Figure 1-4, you can see that Q is the tangent of the angle θ. Q is commonly applied to inductors; for capacitors the term more often used to express purity is dissipation factor (D). This quantity is simply the reciprocal of Q, it is the tangent of the complementary angle of θ, the angle δ shown in Figure 1-4 (d).

1.2 Measuring impedance

To find the impedance, we need to measure at least two values because impedance is a complex quantity. Many modern impedance measuring instruments measure the real and the imaginary parts of an impedance vector and then convert them into the desired parameters such as |Z|, θ, |Y|, R, X, G, B, C, and L. It is only necessary to connect the unknown component, circuit, or material to the instrument. Measurement ranges and accuracy for a variety of impedance parameters are determined from those specified for impedance measurement. Automated measurement instruments allow you to make a measurement by merely connecting the unknown component, circuit, or material to the instrument. However, sometimes the instrument will display an unexpected result (too high or too low.) One possible cause of this problem is incorrect measurement technique, or the natural behavior of the unknown device. In this section, we will focus on the traditional passive components and discuss their natural behavior in the real world as compared to their ideal behavior.

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