# Impedance Measurement Handbook

Application Notes

Impedance measurement data helps engineers design circuits and systems that require specific resistance, capacitance, and inductance values to perform optimally. To maximize power transfer and minimize reflections in radio frequency (RF) devices, engineers must impedance match each component in the RF chain.

What is electrical impedance?

Engineers use impedance measurements to characterize electronic circuits, components, and materials. In RF applications, engineers generally define impedance (Z), represented as a complex quantity in the vector plane, as the total opposition a device or circuit offers to the flow of an alternating current (AC) at a given frequency. Engineers select a particular impedance measurement technique according to the required test frequency, impedance parameter, and preferred display parameters.

This application note shows reference solutions that include currently available products and discontinued and/or obsolete products to leverage Keysight’s impedance measurement expertise for specific application requirements. Whatever application or industry you work in—from circuit design and signal integrity to manufacturing or biomedical applications—Keysight offers excellent performance and high reliability to give you confidence when making impedance measurements.

Starting with impedance measurement basics, this paper begins by defining impedance and impedance parameters, the fundamentals of impedance measurements, and passive component theoretical and natural behavior—including parasitics and ideal, real, and measured values.

An impedance vector consists of a real part (resistance, R) and an imaginary part (reactance, X). We express impedance using the rectangular-coordinate form R + jX or the polar form as a magnitude and phase angle: |Z|_ θ. In some cases, using the reciprocal of impedance proves mathematically expedient.  Thus, 1/Z = 1/(R + jX) = Y = G + jB, where Y represents admittance, G conductance, and B susceptance. Impedance measurements use the unit of ohms (Ω), while admittance uses Siemens (S). Impedance proves especially useful for representing a series connection of resistance and reactance as a simple sum of R and X. Admittance better represents parallel connections.

Reactance takes two forms: inductive (XL) and capacitive (Xc). By definition, XL = 2πfL and Xc = 1/(2πfC), where f represents the frequency of interest, L indicates inductance and C capacitance. Substitute 2πf for by the angular frequency (ω: omega) to represent XL = ωL and Xc =1/(ωC). A similar reciprocal relationship applies to susceptance and admittance.

From these definitions, the application note expands on component dependency factors (such as test, test signal level, DC bias, and temperature) and equivalent circuit models for common components like capacitors and inductors.

How do you measure impedance?

After defining the terminology and relationships between impedance parameters, this document covers impedance measurement fundamentals. To find the impedance, we need to measure at least two values, given the impedance’s complex nature. 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.

This paper details impedance measurement circuit modes, test instruments, three-element equivalent circuits and sophisticated component models, and common measurement methods, including:

• bridge impedance measurements
• resonant impedance measurements
• I-V impedance measurements
• RF I-V impedance measurements
• network analysis measurements
• auto-balancing bridge impedance measurements

The bridge impedance measurement method, common in standard labs, offers high accuracy at a low cost. However, bridge impedance measurements need manual balancing and only offer narrow frequency coverage with a single instrument.

Resonant impedance measurements provide good Q accuracy up to high Q but require tuning to resonance. The resonant impedance measurement method also suffers from low impedance measurement accuracy.

I-V impedance measurements enable grounded device measurement and compatibility with probe-type test needs. As such, developers working with grounded devices prefer this method. However, using the I-V impedance measurement method, the probe transformer limits the operating frequency range.

RF I-V, network analysis, and auto-balancing bridge impedance measurement methods best serve engineers working on RF component characterization. RF I-V impedance measurements deliver high accuracy and a broad impedance range (mΩ to MΩ) at high frequencies. Like the I-V impedance measurement method, though, the transformer used in the test head limits the operating frequency range.

The network analysis impedance measurement method covers a frequency range from low-frequency (LF) to RF, along with good accuracy when the unknown impedance appears close to the characteristic impedance. Unfortunately, network analyzers require recalibration after altering the measurement frequency and only allow for a narrow impedance measurement range.

Auto-balancing bridge impedance measurements offer wide frequency coverage from LF to high frequency (HF) while maintaining exceptionally high accuracy over a wide impedance measurement range (mΩ to the order of 100 MΩ). They also enable grounded device measurement like the I-V method but lack support for high-frequency range testing.

What instrument is used to measure impedance?

Further in the paper, we delve into the theory behind RF I-V impedance measurements, network analysis, and auto-balancing bridge impedance measurements in particular, given their relevance to the various Keysight solutions, including capacitance meters, LCR meters, impedance analyzers, and network analyzers.

LCR meters and impedance analyzers differ primarily by display properties. An LCR meter displays numeric data, while an impedance analyzer displays data in either numeric or graphic formats. Alternatively, standard VNAs offer the function to calculate impedance from measured S-parameter data, though Keysight ENA series network analyzers support various applications for impedance and network analysis on a single platform.

Our discussion of impedance measurement solutions includes reactance charts, the operating theory of practical instruments, key measurement functions, fixturing and cabling, and measurement error compensation.

What is a system configuration for impedance measurement?

Frequently, the system configured for impedance measurements uses the following components:

1. impedance measurement instrument
3. test fixture

Finally, this application note concludes with recommendations for impedance measurement enhancements for various applications, including:

• capacitors
• inductors
• transformers
• diodes
• MOSFETs
• batteries

Read this handbook to find the best measurement methodology and instruments for your impedance measurement needs.

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