This chapter details the key SI primary and secondary standards of capacitance, resis tance and inductance for applications covering the frequency range DC to 100 MHz. These standards include the Thompson-Lampard calculable cross-capacitor, Gibbings quadrifilar resistor, Campbell mutual inductance standard as well as the latest standard of impedance derived from the quantum Hall effect (QHE). Impedance measurements span one of the widest ranges of any physical quantity, from nano-ohms to tera-ohms (i.e. a ratio of 10). This chapter also discusses the limitations of the standards and their evolution to meet the contemporary scientific and industrial needs.

Chapter Contents:

• 6.1 The history of impedance standards
• 6.2 The Thompson-Lampard theorem
• 6.3 Primary standards of phase angle
• 6.4 Impedance components in general
• 6.4.1 Capacitors
• 6.4.2 Parallel-plate capacitance standard
• 6.4.3 Two-terminal capacitors
• 6.4.4 Three-terminal capacitors
• 6.4.5 Two- and four-terminal-pair capacitors
• 6.4.6 The mechanical construction and properties of various types of capacitors
• 6.4.7 Capacitance standards of greater than 1 μF
• 6.4.8 Voltage dependence of capacitors
• 6.4.9 Resistors
• 6.4.10 T-networks
• 6.4.11 Adding auxiliary components to resistors to reduce their reactive component
• 6.4.12 Mutual inductors: Campbell's calculable mutual inductance standard
• 6.4.13 Self-inductors
• 6.5 Resistors, capacitors and inductors of calculable frequency dependence
• 6.5.1 Resistance standards
• 6.5.2 Haddad coaxial resistance standard
• 6.5.3 A nearly ideal HF calculable coaxial resistance standard
• 6.5.4 A bifilar resistance standard
• 6.5.5 Gibbings quadrifilar resistance standard
• 6.5.6 Boháček and Wood octofilar resistance standard
• 6.5.7 HF secondary resistance standards
• 6.5.8 HF parallel-plate capacitance standard
• 6.5.9 HF calculable coaxial capacitance standard
• 6.5.10 HF calculable coaxial inductance standard
• 6.5.11 A frequency-independent standard of impedance
• 6.5.12 An ideal standard of impedance of calculable frequency dependence
• 6.6 Quantum Hall resistance
• 6.6.1 Properties of the quantum Hall effect (QHE) and its use as a DC resistance standard
• 6.6.2 The properties and the equivalent circuit of a quantum Hall device
• 6.6.3 Device handling
• 6.7 QHE measured with AC
• 6.7.1 Multiple-series connection scheme
• 6.7.2 A device holder and coaxial leads
• 6.7.3 Active equalisers
• 6.7.4 Capacitive model of ungated and split-gated quantum Hall devices
• 6.7.5 Ungated quantum Hall devices
• 6.7.6 Split-gated quantum Hall devices
• 6.7.7 Double-shielded device
• References

Inspec keywords: electric impedance measurement; resistors; quantum Hall effect; capacitors; measurement standards

Other keywords: impedance standard; Gibbings quadrifilar resistor standard; SI primary standard; QHE; impedance measurement; Thompson-Lampard calculable cross-capacitor standard; quantum Hall effect; SI secondary standard; Campbell mutual inductance standard

Subjects: Impedance and admittance measurement