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Agilent
Impedance Measurement
Handbook
A guide to measurement
technology and techniques
4th Edition
Table of Contents

1.0 Impedance Measurement Basics
1.1 Impedance............................................................................................................. 1-1
1.2 Measuring impedance ........................................................................................ 1-3
1.3 Parasitics: There are no pure R, C, and L components ................................. 1-3
1.4 Ideal, real, and measured values ...................................................................... 1-4
1.5 Component dependency factors ....................................................................... 1-5
1.5.1 Frequency .................................................................................................... 1-5
1.5.2 Test signal level........................................................................................... 1-7
1.5.3 DC bias ......................................................................................................... 1-7
1.5.4 Temperature................................................................................................ 1-8
1.5.5 Other dependency factors ......................................................................... 1-8
1.6 Equivalent circuit models of components........................................................ 1-8
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 ....................................................................................... 2-1
2.2 Operating theory of practical instruments ..................................................... 2-4
LF impedance measurement
2.3 Theory of auto balancing bridge method ......................................................... 2-4
2.3.1 Signal source section................................................................................. 2-6
2.3.2 Auto-balancing bridge section ................................................................. 2-7
2.3.3 Vector ratio detector section.................................................................... 2-8
2.4 Key measurement functions .............................................................................. 2-9
2.4.1 Oscillator (OSC) level ............................................................................... 2-9
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

i
3.0 Fixturing and Cabling
LF impedance measurement
3.1 Terminal configuration ...................................................................................... 3-1
3.1.1 Two-terminal configuration ..................................................................... 3-2
3.1.2 Three-terminal configuration................................................................... 3-2
3.1.3 Four-terminal configuration .................................................................... 3-4
3.1.4 Five-terminal configuration ..................................................................... 3-5
3.1.5 Four-terminal pair configuration ............................................................ 3-6
3.2 Test fixtures ......................................................................................................... 3-7
3.2.1 Agilent-supplied test fixtures .................................................................. 3-7
3.2.2 User-fabricated test fixtures .................................................................... 3-8
3.2.3 User test fixture example ......................................................................... 3-9
3.3 Test cables ............................................................................................................ 3-10
3.3.1 Agilent 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 Agilent-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 ............................................................................................. 4-1
4.2 Calibration ........................................................................................................... 4-1
4.3 Compensation ...................................................................................................... 4-3
4.3.1 Offset compensation ................................................................................. 4-3
4.3.2 Open and short compensations .............................................................. 4-4
4.3.3 Open/short/load compensation .............................................................. 4-6
4.3.4 What should be used as the load? .......................................................... 4-7
4.3.5 Application limit for open, short, and load compensations .............. 4-9
4.4 Measurement error caused by contact resistance ......................................... 4-9
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 Agilent test fixture (direct attachment type) ........................................ 4-14
4.6.2 Agilent test cables and Agilent test fixture............................................ 4-14
4.6.3 Agilent test cables and user-fabricated test fixture (or scanner)....... 4-14
4.6.4 Non-Agilent test cable and user-fabricated test fixture....................... 4-14

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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 ................................................................................... 5-1
5.1.1 Parasitics of a capacitor .......................................................................... 5-2
5.1.2 Measurement techniques for high/low capacitance............................ 5-4
5.1.3 Causes of negative D problem ................................................................ 5-6
5.2 Inductor measurement ..................................................................................... 5-8
5.2.1 Parasitics of an inductor ......................................................................... 5-8
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

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Appendix A: The Concept of a Test Fixture's Additional Error ............. A-1

A.1 System configuration for impedance measurement ...................................... A-1
A.2 Measurement system accuracy .......................................................................... A-1
A.2.1 Proportional error ..................................................................................... A-2
A.2.2 Short offset error ....................................................................................... A-2
A.2.3 Open offset error........................................................................................ A-3
A.3 New market trends and the additional error for test fixtures ...................... A-3
A.3.1 New devices ................................................................................................ A-3
A.3.2 DUT connection configuration................................................................. A-4
A.3.3 Test fixture's adaptability for a particular measurement ................... A-5

Appendix B: Open and Short Compensation ......................................................... B-1

Appendix C: Open, Short, and Load Compensation ......................................... C-1

Appendix D: Electrical Length Compensation ...................................................... D-1

Appendix E: Q Measurement Accuracy Calculation ...................................... E-1

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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 repre-
sented 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 sus-
ceptance. 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

1-1
Reactance takes two forms: inductive (X L) and capacitive (Xc). By definition, X L = 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 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 . Q is commonly applied to induc-
tors; for capacitors the term more often used to express purity is dissipation factor (D). This quanti-
ty 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

1-2
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 deter-
mined 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 incor-
rect 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 cir-
cuit components are neither purely resistive, nor purely reactive. They involve both of these imped-
ance elements. This means that all real-world devices have parasitics--unwanted inductance in resis-
tors, 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.

1-3
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 para-
sitics 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.