सीएसआईआर-राष्ट्रीय भौतिक प्रयोगशाला

CSIR-National Physical Laboratory

## LF, HF Impedance and DC Metrology

###### Measurement Capabilities and Traceability

**Primary / National Standards**

LF, HF Impedance and DC Metrology sub-division is part of the electrical and electronics metrology division, which provides calibration services for a large number of electrical parameters, standards and instruments. The laboratory is responsible for maintaining national and reference standards of impedance parameters upto radio frequencies, precise ac voltage ratio, dc voltage, dc current, and dc resistance and dc high voltage up to 100 kV.

The metrological traceability to SI units are derived from Josephson Voltage Standard (JVS) and Quantum Hall Resistance (QHR) standard, which are being maintained at CSIR-NPL. The primary standard of current (ampere) is derived from JVS and QHR through the Ohm’s law of electrical conductivity. A brief description of the latest revision of the SI units; this assumes importance particularly as the ampere is being defined using the fundamental constant of electron charge (e).

**Traceability Chart for Impedance Metrology**

The fused-silica capacitor standards of 10 pF and 100 pF are driving the traceability of impedance standards and the scaling of capacitance was performed through the four-terminal capacitance bridge and capacitance bridge from General Radio. The quadrature bridge is used to assign the resistance standard in terms of capacitance standards and Kelvin double-arm bridge used for scaling the resistance from 1 Ω to 1 MΩ. Thereafter, the inductor standards are defined in terms of resistance and capacitance standards through Maxwell-Wein Bridge. CSIR-NPL utilizes the high value capacitance bridge for 10 μF to 10 mF values while low value inductance-bridge is used to measure inductance values equal to below 10 μH.

**Measurement Capabilities Related to Impedance Parameters**

The mandate of the LF, HF Impedance Metrology is to maintain and disseminate the unit’s related capacitance, inductance, AC resistance, Inductive-voltage-divider (IVD), ratio transformers, LCR meter, impedance analyzer and capacitance bridge. All these quantities are linked to the respective primary / National standards through an unbroken chain of traceability. With a total number of 8 CMCs (listed on the BIPM portal), this section is internationally competent in almost all quantities related to impedance parameters.

**Measurement Capabilities**

- Fused Silica capacitor (10 pF, 100 pF) @ 1 kHz
- Air Capacitor (10 pF, 100 pF & 1000 pF) @ 1 kHz
- Mica Capacitor (0.1 µF, 0.01 µF, 0.001 µF & 1 µF) @ 1 kHz
- AC Resistance (1 Ω to 1 MΩ) @ 1 kHz
- AC Voltage Ratio (using Inductive Voltage Divider) at 1 kHz
- Standard Inductors: 100 µH to 10 H @ 1 kHz
- Low value Inductor from 0.1 µH to 10 µH @ 1 kHz
- Precision LCR meter and Capacitance Bridge

Traceability of impedance parameters are maintained through coaxial bridges which are at par with international standards.

**Table 3** Measurement Capabilities of LF, HF Impedance Metrology laboratory at CSIR-NPL

**Table 4** Calibration and measurement capabilities registered at BIPM (KCDB database)

###### Measurement Facility

**Transformer-based coaxial bridges**

- Quadrature Bridge
- Kelvin double arm AC resistance Bridge
- Maxwell-Wein Bridge
- Absolute calibration of IVD

**Capacitance Bridges**

- 1. Ultra precision capacitance bridge
- Model AH2700
- Frequency Range: 20 Hz to 20 kHz
- Make: Andeen Hagerling

- 2. Capacitance bridge
- Model 1615 (1620 capacitance assembly)
- Frequency Range: 50 Hz to 10 kHz
- Make: General Radio

- 3. Capacitance bridge
- Model 1616 (1621 capacitance assembly)
- Frequency Range: 50 Hz to 10 kHz
- Make: General Radio

**LCR Meters**

- 1. LCR Meter
- Model E4980A
- Frequency Range: 20 Hz to 2 MHz
- Make: Agilent’s Technologies

- 2. High frequency LCR Meter
- Model 4285A
- Frequency Range: 75 kHz – 30 MHz
- Make: Agilent’s Technologies

- 3. RF Impedance / Material Analyzer
- Model E4991A
- Frequency Range: 1 MHz – 3 GHz
- Make: Agilent’s Technologies

###### AC Impedance Standards upto Radio Frequency

**Coaxial Airlines**

Low value capacitance standards (2 pF -20 pF) upto 100 MHz, Coaxial Airline GR 900, LZ Series Four-terminal air pair (4TP) capacitance Standards (1 pF – 1000 pF) upto 30 MHz, Agilent’s Model 16380A

Four-terminal pair capacitance standards (10 nF – 1 μF) upto 1 MHz, IET Labs, SCA Series

Four-terminal pair resistance standards upto 1 MHz, Agilent’s Model 16074A

A set of seven GR900 Type LZ series coaxial air-liness has been realized as reference standard of low value capacitance. The dimensions of coaxial air-lines; the outer diameter of inner conductor (a), inner diameter of outer conductor (b) and geometrical length of air-line (l_g) have been measured precisely and are traceable to the primary standard of length being maintained at CSIR-NPL. The transfer or reference standards of capacitance include coaxial capacitance standards and four-terminal-pair (4TP) air capacitance standards. These reference standards are used in turn to calibrate high precision LCR meters and impedance analysers.

**Four-Terminal Pair Air Capacitance Standards**

Four-terminal-pair air capacitance standards from 1 pF to 1000 pF have been evaluated using electrical equivalent circuit model (EECM) as shown in the figure. The approach used for the evaluation is based on the determination of capacitive and inductive residual components of EECM.

The frequency characteristics of 4TP capacitance standard involves the use of the relation between S and Z given as

Z_{4TP}= Z_{0} * [U-S]^{-1} * [U+S]

Where U is unit matrix [4 X 4] and Z_{0} is the characteristic impedance, 50 Ω. The procedure used for the evaluation of 4TP capacitance standards is given below:

- Measurem