是德科技建议您使用《是德科技阻抗测量手册》，该手册包括与阻抗基础知识相关的基本信息。该手册主题包括：阻抗测量；测量方式；夹具和电缆；误差测量及补救措施 A guide to measurement technology and techniques 6th Edition

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 product status of instruments, accessories, and fixtures listed in this document. Please note that the status is subject to change without notice. 推荐阅读：

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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 which 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|_ q. Figure 1-1 also shows the mathematical relationship between R, X, |Z|, and q. 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.)

Figure 1-1. Impedance (Z) consists of a real part (R) and an imaginary part (X)

Figure 1-2. Expression of series and parallel combination of real and imaginary components

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 (w: omega) to represent XL = wL and Xc =1/(wC). Refer to Figure 1-3.

Figure 1-3. Reactance in two forms: inductive (XL) and capacitive (Xc)
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 being a pure reactance, no resist- ance), 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 q. 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 q, the angle d shown in Figure 1-4 (d).

Figure 1-4. Relationships between impedance and admittance parameters

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|, q, |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.1.3 Parasitics: There are no pure R, C, and L components

The principal attributes of L, C, and R components are generally represented by the nominal values of capacitance, inductance, or resistance at specified or standardized conditions. However, all circuit components are neither purely resistive, nor purely reactive. They involve both of these impedance elements. This means that all real-world devices have parasitics—unwanted inductance in resistors, unwanted resistance in capacitors, unwanted capacitance in inductors, etc. Different materials and manufacturing technologies produce varying amounts of parasitics. In fact, many parasitics reside in components, affecting both a component's usefulness and the accuracy with which you can determine its resistance, capacitance, or inductance. With the combination of the component's primary element and parasitics, a component will be like a complex circuit, if it is represented by an equivalent circuit model as shown in Figure 1-5.

Figure 1-5. Component (capacitor) with parasitics represented by an electrical equivalent circuit
Since the parasitics affect the characteristics of components, the C, L, R, D, Q, and other inherent impedance parameter values vary depending on the operating conditions of the components. Typical dependence on the operating conditions is described in Section 1.5.1.4 Ideal, real, and measured values

When you determine an impedance parameter value for a circuit component (resistor, inductor, or capacitor), it is important to thoroughly understand what the value indicates in reality. The parasitics of the component and the measurement error sources, such as the test fixture's residual impedance, affect the value of impedance.
Conceptually, there are three sorts of values: ideal, real, and measured. These values are fundamental to comprehending the impedance value obtained through measurement. In this section, we learn the concepts of ideal, real, and measured values, as well as their significance to practical component measurements.
— An ideal value is the value of a circuit component (resistor, inductor, or capacitor) that excludes the effects of its parasitics. The model of an ideal component assumes a purely resistive or reactive element that has no frequency dependence. In many cases, the ideal value can be defined by a mathematical relationship involving the component's physical composition (Figure 1-6 (a).) In the real world, ideal values are only of academic interest.
— The real value takes into consideration the effects of a component's parasitics (Figure 1-6 (b).) The real value represents effective impedance, which a real-world component exhibits. The real value is the algebraic sum of the circuit component’s resistive and reactive vectors, which come from the principal element (deemed as a pure element) and the parasitics. Since the parasitics yield a different impedance vector for a different frequency, the real value is frequency dependent.
— The measured value is the value obtained with, and displayed by, the measurement instrument; it reflects the instrument's inherent residuals and inaccuracies (Figure 1-6 (c).) Measured values always contain errors when compared to real values. They also vary intrinsically from one measurement to another; their differences depend on a multitude of considerations in regard to measurement uncertainties. We can judge the quality of measurements by comparing how closely a measured value agrees with the real value under a defined set of measurement conditions. The measured value is what we want to know, and the goal of measurement is to have the measured value be as close as possible to the real value.

Figure 1-6. Ideal, real, and measured values

1.5 Components dependency factors
The measured impedance value of a component depends on several measurement conditions, such as test frequency, and test signal level. Effects of these component dependency factors are different for different types of materials used in the component, and by the manufacturing process used. The following are typical dependency factors that affect the impedance values of measured components.1.5.1 Frequency
Frequency dependency is common to all real-world components because of the existence of parasitics. Not all para- sitics affect the measurement, but some prominent parasitics determine the component's frequency characteristics. The prominent parasitics will be different when the impedance value of the primary element is not the same. Figures 1-7 through 1-9 show the typical frequency response for real-world capacitors, inductors, and resistors.

Figure 1-7. Capacitor frequency response

Figure 1-8. Inductor frequency response

Figure 1-9. Resistor frequency response
As for capacitors, parasitic inductance is the prime cause of the frequency response as shown in Figure 1-7. At low frequencies, the phase angle (q) of impedance is around –90°, so the reactance is capacitive. The capacitor frequency response has a minimum impedance point at a self-resonant frequency (SRF), which is determined from the capacitance and parasitic inductance (Ls) of a series equivalent circuit model for the capacitor. At the self-resonant frequency, the capacitive and inductive reactance values are equal (1/(wC) = wLs.) As a result, the phase angle is 0° and the device is resistive. After the resonant frequency, the phase angle changes to a positive value around +90° and, thus, the inductive reactance due to the parasitic inductance is dominant.
Capacitors behave as inductive devices at frequencies above the SRF and, as a result, cannot be used as a capacitor. Likewise, regarding inductors, parasitic capacitance causes a typical frequency response as shown in Figure 1-8. Due to the parasitic capacitance (Cp), the inductor has a maximum impedance point at the SRF (where wL = 1/(wCp).) In the low frequency region below the SRF, the reactance is inductive. After the resonant frequency, the capacitive reactance due to the parasitic capacitance is dominant. The SRF determines the maximum usable frequency of capacitors and inductors.1.5.2 Test signal level
The test signal (AC) applied may affect the measurement result for some components. For example, ceramic capacitors are test-signal-voltage dependent as shown in Figure 1-10 (a). This dependency varies depending on the dielectric constant (K) of the material used to make the ceramic capacitor.
Cored-inductors are test-signal-current dependent due to the electromagnetic hysteresis of the core material. Typical AC current characteristics are shown in Figure 1-10 (b).

Figure 1-10. Test signal level (AC) dependencies of ceramic capacitors and cored-inductors1.5.3 DC bias
DC bias dependency is very common in semiconductor components such as diodes and transistors. Some passive components are also DC bias dependent. The capacitance of a high-K type dielectric ceramic capacitor will vary depending on the DC bias voltage applied, as shown in Figure 1-11 (a).
In the case of cored-inductors, the inductance varies according to the DC bias current flowing through the coil. This is due to the magnetic flux saturation characteristics of the core material. Refer to Figure 1-11 (b).

Figure 1-11. DC bias dependencies of ceramic capacitors and cored-inductors1.5.4 Temperature
Most types of components are temperature dependent. The temperature coefficient is an important specification for resistors, inductors, and capacitors. Figure 1-12 shows some typical temperature dependencies that affect ceramic capacitors with different dielectrics.
1.5.5 Other dependency factors
Other physical and electrical environments, e.g., humidity, magnetic fields, light, atmosphere, vibration, and time, may change the impedance value. For example, the capacitance of a high-K type dielectric ceramic capacitor decreases with age as shown in Figure 1-13.

Figure 1-12. Temperature dependency of ceramic capacitors

Figure 1-13. Aging dependency of ceramic capacitors1.6 Equivalent circuit models of components
Even if an equivalent circuit of a device involving parasitics is complex, it can be lumped as the simplest series or parallel circuit model, which represents the real and imaginary (resistive and reactive) parts of total equivalent circuit impedance. For instance, Figure 1-14 (a) shows a complex equivalent circuit of a capacitor. In fact, capacitors have small amounts of parasitic elements that behave as series resistance (Rs), series inductance (Ls), and parallel resistance (Rp or 1/G.) In a sufficiently low frequency region, compared with the SRF, parasitic inductance (Ls) can be ignored. When the capacitor exhibits a high reactance (1/(wC)), parallel resistance (Rp) is the prime determinative, relative to series resistance (Rs), for the real part of the capacitor’s impedance. Accordingly, a parallel equivalent circuit consisting of C and Rp (or G) is a rational approximation to the complex circuit model. When the reactance of a capacitor is low, Rs is a more significant determinative than Rp. Thus, a series equivalent circuit comes to the approximate model. As for a complex equivalent circuit of an inductor such as that shown in Figure 1-14 (b), stray capacitance (Cp) can be ignored in the low frequency region. When the inductor has a low reactance, (wL), a series equivalent circuit model consisting of L and Rs can be deemed as a good approximation. The resistance, Rs, of a series equivalent circuit is usually called equivalent series resistance (ESR).

Figure 1-14. Equivalent circuit models of (a) a capacitor and (b) an inductor
Note: Generally, the following criteria can be used to roughly discriminate between low, middle, and high impedances (Figure 1-15.) The medium Z range may be covered with an extension of either the low Z or high Z range. These criteria differ somewhat, depending on the frequency and component type.

Figure 1-15. High and low impedance criteria
In the frequency region where the primary capacitance or inductance of a component exhibits almost a flat frequency response, either a series or parallel equivalent circuit can be applied as a suitable model to express the real impedance characteristic. Practically, the simplest series and parallel models are effective in most cases when representing characteristics of general capacitor, inductor, and resistor components.

1.7 Measurement circuit modes

As we learned in Section 1.2, measurement instruments basically measure the real and imaginary parts of impedance and calculate from them a variety of impedance parameters such as R, X, G, B, C, and L. You can choose from series and parallel measurement circuit modes to obtain the measured parameter values for the desired equivalent circuit model (series or parallel) of a component as shown in Table 1-1.

Table 1-1. Measurement circuit modes

Though impedance parameters of a component can be expressed by whichever circuit mode (series or parallel) is used, either mode is suited to characterize the component at your desired frequencies. Selecting an appropriate measurement circuit mode is often vital for accurate analysis of the relationships between parasitics and the component’s physical composition or material properties. One of the reasons is that the calculated values of C, L, R, and other parameters are different depending on the measurement circuit mode as described later. Of course, defining the series or parallel equivalent circuit model of a component is fundamental to determining which measurement circuit mode (series or parallel) should be used when measuring C, L, R, and other impedance parameters of components. The criteria shown in Figure 1-15 can also be used as a guideline for selecting the measurement circuit mode suitable for a component.
Table 1-2 shows the definitions of impedance measurement parameters for the series and parallel modes. For the parallel mode, admittance parameters are used to facilitate parameter calculations.

Table 1-2. Definitions of impedance parameters for series and parallel modes
Though series and parallel mode impedance values are identical, the reactance (Xs), is not equal to reciprocal of par- allel susceptance (Bp), except when Rs = 0 and Gp = 0. Also, the series resistance (Rs), is not equal to parallel resist- ance (Rp) (or reciprocal of Gp) except when Xs = 0 and Bp = 0. From the definition of Y = 1/Z, the series and parallel mode parameters, Rs, Gp (1/Rp), Xs, and Bp are related with each other by the following equations:

Table 1-3 shows the relationships between the series and parallel mode values for capacitance, inductance, and resistance, which are derived from the above equations.

Table 1-3. Relationships between series and parallel mode CLR values

Cs, Ls, and Rs values of a series equivalent circuit are different from the Cp, Lp, and Rp values of a parallel equivalent circuit. For this reason, the selection of the measurement circuit mode can become a cause of measurement discrepancies. Fortunately, the series and parallel mode measurement values are interrelated by using simple equations that are a function of the dissipation factor (D.) In a broad sense, the series mode values can be converted into parallel mode values and vice versa.

Figure 1-16 shows the Cp/Cs and Cs/Cp ratios calculated for dissipation factors from 0.01 to 1.0. As for inductance, the Lp/Ls ratio is same as Cs/Cp and the Ls/Lp ratio equals Cp/Cs.

Figure 1-16. Relationships of series and parallel capacitance values
For high D (low Q) devices, either the series or parallel model is a better approximation of the real impedance equivalent circuit than the other one. Low D (high Q) devices do not yield a significant difference in measured C or L values due to the measurement circuit mode. Since the relationships between the series and parallel mode measurement values are a function of D2, when D is below 0.03, the difference between Cs and Cp values (also between Ls and Lp values) is less than 0.1 percent. D and Q values do not depend on the measurement circuit modes.
Figure 1-17 shows the relationship between series and parallel mode resistances. For high D (low Q) components, the measured Rs and Rp values are almost equal because the impedance is nearly pure resistance. Since the difference between Rs and Rp values increases in proportion to 1/D2, defining the measurement circuit mode is vital for measurement of capacitive or inductive components with low D (high Q.)

Figure 1-17. Relationships of series and parallel resistance values

1.8 Three-element equivalent circuit and sophisticated component models

The series and parallel equivalent circuit models cannot serve to accurately depict impedance characteristics of components over a broad frequency range because various parasitics in the components exercise different influence on impedance depending on the frequency. For example, capacitors exhibit typical frequency response due to parasitic inductance, as shown in Figure 1-18. Capacitance rapidly increases as frequency approaches the resonance point. The capacitance goes down to zero at the SRF because impedance is purely resistive. After the resonant frequency, the measured capacitance exhibits a negative value, which is calculated from inductive reactance. In the aspect of the series Cs-Rs equivalent circuit model, the frequency response is attributed to a change in effective capacitance. The effect of parasitic inductance is unrecognizable unless separated out from the compound reactance. In this case, introducing series inductance (Ls) into the equivalent circuit model enables the real impedance characteristic to be properly expressed with three-element (Ls-Cs-Rs) equivalent circuit parameters.

When the measurement frequency is lower than approximately 1/30 resonant frequency, the series Cs-Rs measurement circuit mode (with no series inductance) can be applied because the parasitic inductance scarcely affects measurements.

Figure 1-18. Influence of parasitic inductance on capacitor
When both series and parallel resistances have a considerable amount of influence on the impedance of a reactive device, neither the series nor parallel equivalent circuit models may serve to accurately represent the real C, L, or R value of the device. In the case of the capacitive device shown in Figure 1-19, both series and parallel mode capacitance (Cs and Cp) measurement values at 1 MHz are different from the real capacitance of the device. The correct capacitance value can be determined by deriving three-element (C-Rp-Rs) equivalent circuit parameters from the measured impedance characteristic. In practice, C-V characteristics measurement for an ultra-thin CMOS gate capacitance often requires a three-element (C-Rs-Rp) equivalent circuit model to be used for deriving real capacitance without being affected by Rs and Rp.

Figure 1-19. Example of capacitive device affected by both Rs and Rp
By measuring impedance at a frequency you can acquire a set of the equivalent resistance and reactance values, but it is not enough to determine more than two equivalent circuit elements. In order to derive the values of more than two equivalent circuit elements for a sophisticated model, a component needs to be measured at least at two frequencies. The Keysight Technologies, Inc. impedance analyzers have the equivalent circuit analysis function that automatically calculates the equivalent circuit elements for three- or four-element models from a result of a swept frequency measurement. The details of selectable three-/four-element equivalent circuit models and the equivalent circuit analysis function are described in Section 5.15.

1.9 Reactance chart
The reactance chart shows the impedance and admittance values of pure capacitance or inductance at arbitrary frequencies. Impedance values at desired frequencies can be indicated on the chart without need of calculating 1/(wC) or wL values when discussing an equivalent circuit model for a component and also when estimating the influence of parasitics. To cite an example, impedance (reactance) of a 1 nF capacitor, which is shown with an oblique bold line in Figure 1-20, exhibits 160 kΩ at 1 kHz and 16 Ω at 10 MHz. Though a parasitic series resistance of 0.1 Ω can be ignored at 1 kHz, it yields a dissipation factor of 0.0063 (ratio of 0.1 Ω to 16 Ω) at 10 MHz. Likewise, though a parasitic inductance of 10 nH can be ignored at 1 kHz, its reactive impedance goes up to 0.63 Ω at 10 MHz and increases measured capacitance by +4 percent (this increment is calculated as 1/(1 – XL/XC) = 1/(1 – 0.63/16).) At the intersection of 1 nF line (bold line) and the 10 nH line at 50.3 MHz, the parasitic inductance has the same magnitude (but opposing vector) of reactive impedance as that of primary capacitance and causes a resonance (SRF). As for an inductor, the influence of parasitics can be estimated in the same way by reading impedance (reactance) of the inductor and that of a parasitic capacitance or a resistance from the chart.

Figure 1-20. Reactance chart

Most of the modern impedance measuring instruments basically measure vector impedance (R + jX) or vector admittance (G + jB) and convert them, by computation, into various parameters, Cs, Cp, Ls, Lp, D, Q, |Z|, |Y|, q, etc. Since measurement range and accuracy are specified for the impedance and admittance, both the range and accuracy for the capacitance and inductance vary depending on frequency. The reactance chart is also useful when estimating measurement accuracy for capacitance and inductance at your desired frequencies. You can plot the nominal value of a DUT on the chart and find the measurement accuracy denoted for the zone where the DUT value is enclosed. Figure 1-21 shows an example of measurement accuracy given in the form of a reactance chart. The intersection of arrows in the chart indicates that the inductance accuracy for 1 µH at 1 MHz is ±0.3 percent. D accuracy comes to ±0.003 (= 0.3/100.) Since the reactance is 6.28 Ω, Rs accuracy is calculated as ±(6.28 x 0.003) =±0.019 Ω. Note that a strict accuracy specification applied to various measurement conditions is given by the accuracy equation.

Figure 1-21. Example of measurement accuracy indicated on a reactance chart

(未完待续）第二章 Impedance Measurement Instruments

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