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Keysight Technologies
Impedance Measurement Handbook
A guide to measurement technology and techniques
4th Edition
Application Note
i | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
Table of Contents
1.0 Impedance Measurement Basics
1.1 Impedance ........................................................................................................................ 1-01
1.2 Measuring impedance ..................................................................................................... 1-03
1.3 Parasitics: There are no pure R, C, and L components .................................................. 1-03
1.4 Ideal, real, and measured values ..................................................................................... 1-04
1.5 Component dependency factors ..................................................................................... 1-05
1.5.1 Frequency .............................................................................................................. 1-05
1.5.2 Test signal level ..................................................................................................... 1-07
1.5.3 DC bias................................................................................................................... 1-07
1.5.4 Temperature........................................................................................................... 1-08
1.5.5 Other dependency factors....................................................................................... 1-08
1.6 Equivalent circuit models of components........................................................................ 1-08
1.7 Measurement circuit modes ............................................................................................. 1-10
1.8 Three-element equivalent circuit and sophisticated component models ...................... 1-13
1.9 Reactance chart................................................................................................................ 1-15
2.0 Impedance Measurement Instruments
2.1 Measurement methods .................................................................................................... 2-01
2.2 Operating theory of practical instruments ...................................................................... 2-04
LF impedance measurement
2.3 Theory of auto balancing bridge method ....................................................................... 2-04
2.3.1 Signal source section ............................................................................................ 2-06
2.3.2 Auto-balancing bridge section ............................................................................. 2-07
2.3.3 Vector ratio detector section................................................................................. 2-08
2.4 Key measurement functions ............................................................................................ 2-09
2.4.1 Oscillator (OSC) level ............................................................................................ 2-09
2.4.2 DC bias .................................................................................................................. 2-10
2.4.3 Ranging function .................................................................................................. 2-11
2.4.4 Level monitor function .......................................................................................... 2-12
2.4.5 Measurement time and averaging ....................................................................... 2-12
2.4.6 Compensation function ........................................................................................ 2-13
2.4.7 Guarding ............................................................................................................... 2-14
2.4.8 Grounded device measurement capability .......................................................... 2-15
RF impedance measurement
2.5 Theory of RF I-V measurement method ......................................................................... 2-16
2.6 Difference between RF I-V and network analysis measurement methods ...................... 2-17
2.7 Key measurement functions ............................................................................................ 2-19
2.7.1 OSC level ............................................................................................................... 2-19
2.7.2 Test port ................................................................................................................ 2-19
2.7.3 Calibration ............................................................................................................ 2-20
2.7.4 Compensation ....................................................................................................... 2-20
2.7.5 Measurement range ............................................................................................. 2-20
2.7.6 DC bias .................................................................................................................. 2-20
ii | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
3.0 Fixturing and Cabling
LF impedance measurement
3.1 Terminal configuration ..................................................................................................... 3-01
3.1.1 Two-terminal configuration ................................................................................... 3-02
3.1.2 Three-terminal configuration ................................................................................ 3-02
3.1.3 Four-terminal configuration .................................................................................. 3-04
3.1.4 Five-terminal configuration ................................................................................... 3-05
3.1.5 Four-terminal pair configuration ........................................................................... 3-06
3.2 Test fixtures ...................................................................................................................... 3-07
3.2.1 Keysight-supplied test fixtures.............................................................................. 3-07
3.2.2 User-fabricated test fixtures.................................................................................. 3-08
3.2.3 User test fixture example....................................................................................... 3-09
3.3 Test cables ....................................................................................................................... 3-10
3.3.1 Keysight supplied test cables ............................................................................... 3-10
3.3.2 User fabricated test cables .................................................................................. 3-11
3.3.3 Test cable extension ............................................................................................. 3-11
3.4 Practical guarding techniques ........................................................................................ 3-15
3.4.1 Measurement error due to stray capacitances ..................................................... 3-15
3.4.2 Guarding techniques to remove stray capacitances ............................................ 3-16
RF impedance measurement
3.5 Terminal configuration in RF region ................................................................................ 3-16
3.6 RF test fixtures ................................................................................................................. 3-17
3.6.1 Keysight-supplied test fixtures ............................................................................. 3-18
3.7 Test port extension in RF region....................................................................................... 3-19
4.0 Measurement Error and Compensation
Basic concepts and LF impedance measurement
4.1 Measurement error .......................................................................................................... 4-01
4.2 Calibration ........................................................................................................................ 4-01
4.3 Compensation .................................................................................................................. 4-03
4.3.1 Offset compensation ............................................................................................ 4-03
4.3.2 Open and short compensations ........................................................................... 4-04
4.3.3 Open/short/load compensation .......................................................................... 4-06
4.3.4 What should be used as the load? ...................................................................... 4-07
4.3.5 Application limit for open, short, and load compensations ................................ 4-09
4.4 Measurement error caused by contact resistance ......................................................... 4-09
4.5 Measurement error induced by cable extension ............................................................ 4-11
4.5.1 Error induced by four-terminal pair (4TP) cable extension .................................. 4-11
4.5.2 Cable extension without termination .................................................................... 4-13
4.5.3 Cable extension with termination ......................................................................... 4-13
4.5.4 Error induced by shielded 2T or shielded 4T cable extension ............................. 4-13
4.6 Practical compensation examples .................................................................................. 4-14
4.6.1 Keysight test fixture (direct attachment type) ...................................................... 4-14
4.6.2 Keysight test cables and Keysight test fixture ...................................................... 4-14
4.6.3 Keysight test cables and user-fabricated test fixture (or scanner) ...................... 4-14
4.6.4 Non-Keysight test cable and user-fabricated test fixture .................................... 4-14
iii | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
RF impedance measurement
4.7 Calibration and compensation in RF region .................................................................. 4-16
4.7.1 Calibration ........................................................................................................... 4-16
4.7.2 Error source model .............................................................................................. 4-17
4.7.3 Compensation method ....................................................................................... 4-18
4.7.4 Precautions for open and short measurements in RF region ............................ 4-18
4.7.5 Consideration for short compensation ............................................................... 4-19
4.7.6 Calibrating load device ....................................................................................... 4-20
4.7.7 Electrical length compensation .......................................................................... 4-21
4.7.8 Practical compensation technique ..................................................................... 4-22
4.8 Measurement correlation and repeatability .................................................................. 4-22
4.8.1 Variance in residual parameter value ................................................................. 4-22
4.8.2 A difference in contact condition ........................................................................ 4-23
4.8.3 A difference in open/short compensation conditions ........................................ 4-24
4.8.4 Electromagnetic coupling with a conductor near the DUT ............................... 4-24
4.8.5 Variance in environmental temperature .............................................................. 4-25
5.0 Impedance Measurement Applications and Enhancements
5.1 Capacitor measurement ................................................................................................ 5-01
5.1.1 Parasitics of a capacitor ....................................................................................... 5-02
5.1.2 Measurement techniques for high/low capacitance .......................................... 5-04
5.1.3 Causes of negative D problem ............................................................................. 5-06
5.2 Inductor measurement ................................................................................................... 5-08
5.2.1 Parasitics of an inductor ...................................................................................... 5-08
5.2.2 Causes of measurement discrepancies for inductors ......................................... 5-10
5.3 Transformer measurement ............................................................................................. 5-14
5.3.1 Primary inductance (L1) and secondary inductance (L2) ................................... 5-14
5.3.2 Inter-winding capacitance (C) ............................................................................. 5-15
5.3.3 Mutual inductance (M) ......................................................................................... 5-15
5.3.4 Turns ratio (N)....................................................................................................... 5-16
5.4 Diode measurement ....................................................................................................... 5-18
5.5 MOS FET measurement ................................................................................................. 5-19
5.6 Silicon wafer C-V measurement .................................................................................... 5-20
5.7 High-frequency impedance measurement using the probe ......................................... 5-23
5.8 Resonator measurement ................................................................................................ 5-24
5.9 Cable measurements ..................................................................................................... 5-27
5.9.1 Balanced cable measurement ............................................................................. 5-28
5.10 Balanced device measurement ..................................................................................... 5-29
5.11 Battery measurement ..................................................................................................... 5-31
5.12 Test signal voltage enhancement .................................................................................. 5-32
5.13 DC bias voltage enhancement ...................................................................................... 5-34
5.13.1 External DC voltage bias protection in 4TP configuration ................................ 5-35
5.14 DC bias current enhancement ....................................................................................... 5-36
5.14.1 External current bias circuit in 4TP configuration ............................................. 5-37
5.15 Equivalent circuit analysis function and its application ................................................ 5-38
iv | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
Appendix A: The Concept of a Test Fixture's Additional Error ....... A-01
A.1 System configuration for impedance measurement ...................................................... A-01
A.2 Measurement system accuracy........................................................................................ A-01
A.2.1 Proportional error .................................................................................................. A-02
A.2.2 Short offset error ................................................................................................... A-02
A.2.3 Open offset error................................................................................................... A-03
A.3 New market trends and the additional error for test fixtures ........................................... A-03
A.3.1 New devices ........................................................................................................... A-03
A.3.2 DUT connection configuration .............................................................................. A-04
A.3.3 Test fixture's adaptability for a particular measurement ...................................... A-05
Appendix B: Open and Short Compensation ......................................... B-01
Appendix C: Open, Short, and Load Compensation ............................. C-01
Appendix D: Electrical Length Compensation ....................................... D-01
Appendix E: Q Measurement Accuracy Calculation ............................. E-01
1-01 | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
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|_ . Figure 1-1 also shows the mathematical relationship
between R, X, |Z|, and . 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 (), 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
1-02 | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
Reactance takes two forms: inductive (XL) and capacitive (Xc). By definition, XL = 2fL and Xc = 1/(2fC), where f is
the frequency of interest, L is inductance, and C is capacitance. 2f can be substituted for by the angular frequency
(: omega) to represent XL = L and Xc =1/(C). 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 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 , the angle
shown in Figure 1-4 (d).
Figure 1-4. Relationships between impedance and admittance parameters
1-03 | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
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|, , |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.
1-04 | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
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
1-05 | Keysight | Impedance Measurement Handbook, A guide to measurement technology and techniques, 4th Edition - Application Note
1.5 Component 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.
Ls C R s Ls: Lead inductance
Rs: Equivalent series resistance (ESR)
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