Scribd
Upload
7 views2 pages

Ns 7

The document discusses network synthesis using Foster's II and Cauer's I forms, providing examples and solutions for synthesizing specific functions. It includes mathematical formulations and conditions for determining positive real functions (p.r.f.). Figures are referenced to illustrate the synthesized networks.

Uploaded by

rampratap
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
7 views2 pages

Ns 7

The document discusses network synthesis using Foster's II and Cauer's I forms, providing examples and solutions for synthesizing specific functions. It includes mathematical formulations and conditions for determining positive real functions (p.r.f.). Figures are referenced to illustrate the synthesized networks.

Uploaded by

rampratap
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

Network Synthesis 349

?+ 2s s 48 +3 |1 Z,
s² + 2s
2s + 3 s + 2s Y
1
2s +3 (4> 23
28
1 1
X
Therefore, the synethesized network is shown in figure 8.24.
12 42
Z(9)-’
Fig. 8.24.
EXAMPLE 8.34 Synthesize
(s +5)
Zs) = in Foster's II form. (U.P.T.U, 2001)
(s +1)(s +6)
Solution :
8+5
Z(s) =
(s+ 1)(s + 6)
(s+1) (s+6)
Ys) =
(s+5)
8+5)8 + 7s + 6 |s + 2
g2 + 5s
2s + 6
2s + 10
-4
-4
Y(8) = 8+2+
s+5
Y(s) g +7s +6 5
s+58 4
Zs)’ 1F
6
g + 5sy s + 7s + 6 |1 4
25
+ 5s
28 + 6 Fig. 8.25.
Synthesis
Network Analysia and
348
2r-6
A,(x) 3
A, Ay No. of Sign Changes
Ao
0
8) 2
Now
Therefore, A(o) 0 for
all o
not a p.r.f.
Hence, given function is
g+6s +5 (8+1)(8+5)
+9s +14
(s+2)(8 +7)
(ü)
N(s) = 9s
Condition (1): M(s) = g + 14;
9s
14) 9s 14
9s
Therefore, Dls) is Hurmitz polynomial.
Condtion (2): doesnot exist.
Condition (3): M, (s) =g²+ 5,Mals) =² + 14
N,(s) = 6s, Ngls) = 9s
M,M, -N, N, 20
(s2 + 5) (s² + 14) -(6s) (9s) 20
s + 19s2+ 70 - 54 s² 0
s-35s+ 70 20
A(o) = a+35 w + 70 >0
Since allcoefficients of A(o?) are positive therefore, A(@²) >0for all o.
Hence given function is a p.r.f.
EXAMPLE 8.33. Synthesize
(s +1) (s +3)
Zs) = in Cauer'sI form. (U.P.T.U,, 2001, 2003/C.0.)
s (s+2)
Solution: Z(s) =
s+4s +3
s+2s

You might also like