© The Institution of Engineering and Technology
In this study, a boundary analysis is carried out for the derivative of driving point impedance (DPI) functions, which is mainly used for the synthesis of networks containing resistorinductor, resistor–capacitor and resistor–inductor–capacitor circuits. It is known that DPI function, , is an analytic function defined on the right half of the splane. In this study, the authors present four theorems using the modulus of the derivative of DPI function, , by assuming the function is also analytic at the boundary point on the imaginary axis and finally, the sharpness of the inequalities obtained in the presented theorems are proved. It is also shown that simple inductor–capacitor tank circuits and higherorder filters are synthesised using the unique DPI functions obtained in each theorem.
References


1)

1. Reza, F.M.: ‘A bound for the derivative of positive real functions’, SIAM Rev., 1962, 4, (1), pp. 40–42.

2)

2. Saleh Tavazoei, M.: ‘Passively realizable impedance functions by using two fractional elements and some resistors’, IET Circuits Devices Syst., 2017, 12, (3), pp. 280–285, .

3)

3. Sharma, A., Soni1, T.: ‘A review on passive network synthesis using Cauer form’, World J. Wirel. Devices Eng., 2017, 1, (1), pp. 39–46.

4)

4. Mukhtar, F., Kuznetsov, Y., Russer, P.: ‘Network modelling with Brune's synthesis’, Adv. Radio Sci., 2011, 9, pp. 91–94.

5)

5. Hu, J.S., Tsai, M.C.: ‘Robustness analysis of a practical impedance control system’, IFAC Proc. Volumes, 2004, 37, (11), pp. 725–730.

6)

6. Khilari, S.S.: ‘Transfer function and impulse response synthesis using classical techniques’. , University of Massachusetts, Amherst, 2007.

7)

7. Ochoa, A.: ‘Driving point impedance and signal flow graph basics: a systematic approach to circuit analysis’, in ‘Feedback in analog circuits’ (Springer International Publishing, Switzerland, 2016), pp. 13–34.

8)

8. Şengül, M.: ‘Foster impedance data modeling via singly terminated LC ladder networks’, Turkish J. Electr. Eng. Comput. Sci., 2013, 21, (3), pp. 785–792.

9)

9. Wunsch, A.D., Hu, S.P.: ‘A closedform expression for the drivingpoint impedance of the small inverted L antenna’, IEEE Trans. Antennas Propag., 1996, 44, (2), pp. 236–242.

10)

10. Hazony, D.: ‘Elements of network synthesis’ (Reinhold Pub. Corp., New York, USA, 1963).

11)

11. Van Der Pol, B.: ‘A new theorem on electrical networks’, Physica, 1937, 4, (7), pp. 585–589.

12)

12. Krueger, R.J., Brown, D.P.: ‘Positive real derivatives of driving point functions’, J. Franklin Inst., 1969, 287, (1), pp. 51–60.

13)

13. Reza, F.M.: ‘On the Schlicht behavior of certain impedance functions’, IRE Trans. Circuit Theory, 1962, 9, (3), pp. 231–232.

14)

14. Richards, P.I.: ‘A special class of functions with positive real part in a halfplane’, Duke Math. J., 1947, 14, (3), pp. 777–789.

15)

15. Reza, F.M.: ‘Schwarz Lemma for nports’, J. Franklin Inst., 1984, 317, (2), pp. 57–71.

16)

16. Reza, F.M.: ‘Schwarz's Lemma and linear passive systems’, Proc. IRE, 1961, 49, (2), pp. 17–23.

17)

17. Huang, T.: ‘Some mapping properties of RC and RL drivingpoint impedance functions’, IEEE Trans. Circuit Theory, 1965, 12, (2), pp. 257–259.

18)

18. Golusin, G.M.: ‘Geometric theory of functions of complex variable [in Russian]’ (Moscow, Moscow, Russia, 1966, 2nd edn.). .

19)

19. Osserman, R.: ‘A sharp Schwarz inequality on the boundary’, Proc. Am. Math. Soc., 2000, 128, (12), pp. 3513–3517.

20)

20. Dubinin, V.N.: ‘The Schwarz inequality on the boundary for functions regular in the disc’, J. Math. Sci., 2004, 122, (6), pp. 3623–3629.

21)

21. Aliyev Azeroğlu, T., Örnek, B.N.: ‘A refined Schwarz inequality on the boundary’, Complex Variables and Elliptic Equations, 2013, 58, (4), pp. 571–577.

22)

22. Örnek, B.N.: ‘Sharpened forms of the Schwarz lemma on the boundary’, Bull. Korean Math. Soc., 2013, 50, (6), pp. 2053–2059.

23)

23. Boas, H.P.: ‘Julius and Julia: mastering the art of the Schwarz lemma’, Am. Math. Mon., 2010, 117, (9), pp. 770–785.
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