5. Calibration of the phase shifter PS

To calibrate the phase shifter PS, the VV measures three signals of the calibration circuit R3-C1:


Complex of these signals is described by proper system of equations. Solution of this system (formula (29)) gets the accurate deviation δ<sup>p</sup> of the phase shifter PS transfer coefficient from its nominal value "j":

$$
\delta\_p = \delta\_{p\mu} \left( \mathbf{1} + \delta\_{k\mu} \right) \tag{29}
$$

where:

$$\delta\_{\mu\nu} \approx \frac{\delta\_{\mu\upsilon}}{2} \frac{j\mathcal{U}\_{p3}}{\mathcal{U}\_{p2} - \mathcal{U}\_{p1}} - \frac{\delta\_i}{2} \frac{1}{1 + \delta\_i} \text{ and }$$

$$\delta\_{k\mu\iota} \approx \frac{\delta\_{\mu\upsilon}}{2} \frac{j\mathcal{U}\_{p3} - \mathcal{U}\_{p1}}{\mathcal{U}\_{p2} - \mathcal{U}\_{p1}} - \frac{\delta\_i}{2} \frac{1}{1 + \delta\_i}$$

δpa and δpka are the approximate values of the transfer coefficients of the inverter PS and calibration circuit, respectively.

After the calibration procedure, we know the real value of the phase shifter transfer coefficient with an uncertainty better than 1–3 ppm. μC makes this calibration procedure automatically at least every hour.

4. Calibration of the inverter I

; δkia ≈ <sup>δ</sup>iv 2 Ui3�Ui<sup>1</sup> Ui2�Ui<sup>1</sup>

of the inverter I and calibration circuit R1-R2.

5. Calibration of the phase shifter PS

between input and output of the phase shifter;

<sup>δ</sup>pa <sup>≈</sup> <sup>δ</sup>pv 2

<sup>δ</sup>kpa <sup>≈</sup> <sup>δ</sup>pv 2

value "1."

44 Metrology

where.

δia ≈ <sup>δ</sup>iv 2 Ui3þUi<sup>1</sup> Ui2�Ui<sup>1</sup>

nominal value "j":

tion circuit, respectively.

where:

• The initial output signal of the calibration circuit Ui1;

input and output of the inverter I by the switchers S1 and S2.

To calibrate the inverter, the VV measures three signals of the calibration circuit R1–R2:

• The signal Ui2 after the variation of the inverter transfer coefficient on the value δiv;

• The signal Ui3 after the inversion of the connection of the calibration circuit between the

Complex of these signals is described by proper system of equations. Solution of this system (formula 38) gets the accurate deviation δ<sup>i</sup> of the inverter transfer coefficient from its nominal

To calibrate the phase shifter PS, the VV measures three signals of the calibration circuit R3-C1: • The initial output signal Up1 of the calibration circuit, when calibration circuit is connected

• The signal Up2 after the variation of the phase shifter PS transfer coefficient in the value δpv;

• The signal Up3 after the inversion of the calibration circuit and connection of this circuit between the input of the inverter I and output of the phase shifter PS by the switchers S1 and S2.

Complex of these signals is described by proper system of equations. Solution of this system (formula (29)) gets the accurate deviation δ<sup>p</sup> of the phase shifter PS transfer coefficient from its

δ<sup>p</sup> ¼ δpa 1 þ δkpa

� δi 2

> � δi 2

1 1 þ δ<sup>i</sup>

> 1 1 þ δ<sup>i</sup>

and

jUp<sup>3</sup> þ Up<sup>1</sup> Up<sup>2</sup> � Up<sup>1</sup>

jUp<sup>3</sup> � Up<sup>1</sup> Up<sup>2</sup> � Up<sup>1</sup>

δpa and δpka are the approximate values of the transfer coefficients of the inverter PS and calibra-

δ<sup>i</sup> ¼ δiað Þ 1 þ δkia (28)

(29)

; δia and δkia are the approximate values of the transfer coefficients

Figure 10. Some results of experimental investigations.

## 5.1. Experimental results

All results of the theoretical investigations shown earlier were used to develop the comparator PICS.

6. Conclusion

than 10<sup>7</sup>

equipment.

–10<sup>8</sup>

Acknowledgements

Author details

Michael Surdu

References

part of their life realizing variational ideas.

Address all correspondence to: michaelsurdu1941@gmail.com

[5] Grinevich FB. Automatic bridges – Novosibirsk. 216 pp. 1964

Ukrainian Academy of Metrology, Kiev, Ukraine

History\_of\_Z\_Measurement.pdf

Variational calibration sharply increases the accuracy of measurement. In case of variation correction, for precision measurements, we can use simple and cheap measuring circuits with rather high uncertainty. Variational calibration diminishes the uncertainty of such circuits on thousands or even more times. It does not need too accurate variational standards. Time and space clustering in significant measure overcomes disadvantages of this calibration—increasing the time of measurement. Experimental investigations of the comparator PICS have shown that uncertainty of measurement on main ranges is lower than 10<sup>6</sup> and sensitivity is better

The author is grateful to Dr. H. Bachmair, Dr. J. Melcher and Dr. M. Klonz (PTB), to Dr. A. Koffman, Dr. J. Kinnard and Dr. Y. Wang (NIST), to Dr. A. Tarlowski (GUM) for their constant support and very useful advice during the project development, to Dr. H. Hall for his very helpful criticism and advice during paper consideration. I would like to specially acknowledge my teacher F. B. Grinevich and colleagues A. Lameko and D. Surdu, who have spent a great

[1] Hall HP. A History of Z Measurement. 64 pp. www.ietlabs.com/pdf/GenRad\_History/A\_

[2] Ornatsky PP. Automatic Measurements and Instrumentation. Kiev: High School; 1986. p. 310

[3] Kibble BP, Rayner GH. Coaxial AC Bridges. Bristol: Adam Hilger Ltd; 1984. p. 203

[4] Hague B. Alternating Current Bridge Methods. 6th ed. Pitman Publishing; 1971. p. 602

. Variational calibration also decreases the weight and cost of the accurate

Variational Calibration

47

http://dx.doi.org/10.5772/intechopen.74220

PICS very short specification is given as follows.

Short PICS Specification.

PICS operates on frequencies 1.00 and 1.59 kHz.

Frequency set discreteness 5 <sup>10</sup><sup>5</sup> .

Capacitance range of measurement (F) 10<sup>19</sup>–10<sup>3</sup> .

Resistance range of measurement (R) 10<sup>7</sup> –108 .

Inductance range of measurement (H) 10<sup>12</sup>–103 .

Dissipation factor tgδ (tgφ) 10<sup>6</sup> –1.0.

Main uncertainty (ppm) 1.0.

Sensitivity (ppm) 0.02–0.05

Weight (kg) 5

PICS was tested in USA (NIST) and Russia (VNIIM), in Germany (PTB) and Poland (GUM), in Ukraine (Ukrmetrteststandard) and Byalorussia (Center of metrology).

Some results of these tests are shown in Figure 10.

Appearance of the PICS, together with intermediary thermostated standards, is shown in Figure 11.

Figure 11. Appearance of the PICS.
