ELEMENTARY SYNTHESIS PROCEDURES

1. ELEMENTARY SYNTHESIS PROCEDURES 20050130 EE. EUN SUN KIM

2. Network synthesis • System function • Causality & Stability

3. Causality • Response occurs only during or after the time in which the excitation is applied. • A. • B.

4. Paley -Wiener criterion • must possess a Fourier transform • square magnitude function must be integrable

5. Stability • BIBO (Bounded input Bounded output)

6. Poles & Zeros • Zero : makes H(s) zero • Pole : makes H(s) infinite

7. H(s) cannot have poles in the right-half plane. • H(s) cannot have multiple poles in the jw-axis • The degree of the numerator of H(s) cannot exceed the degree of the denominator by more than unity

8. Positive Real Functions • F(s) is real for real s • if then

9. Properties • if F(s) is p.r. the 1/F(s) is also p.r. • The sum of p.r. functions is p.r. • poles and zeros of a p.r. function cannot be in the right half of the s plane • only simple poles with real positive residues can exist on the jw axis. • The ploes and zeros of a p.r. function are real or occur in conjugate pairs.

10. The highest powers of the numerator and denominator polynomials may differ at most by unity. • The lowest powers of the denominator and numerator polynomials may differ by at most unity.

11. Necessary conditions • R(s) must have no poles in the right half plane. • F(s) may have only simple poles on th jw axis with real and positive residues. • Re [F(jw)] is greater of equal to 0 for all w

12. Elementary synthesis procedures • break up a p.r. function Z(s) into a sum of simpler p.r. functions.

14. Positive real functions • cannot have poles in the right-half plane • poles cannot have multiple poles in the jw-axis. and their residues must be real and positive. • for all w

15. Several cases • Pole at s=0 • Pole at s=infinite

16. a pair of conjugate imaginary poles • if is minimum at some point ,

17. .

18. Examples

19. Examples

20. Examples

21. Examples

22. Examples