how to generate barcode in ssrs report Fig. 13-19 KVL gives V1 5I1 2I2 and V2 I1 2I2 in Software

Maker QR in Software Fig. 13-19 KVL gives V1 5I1 2I2 and V2 I1 2I2

Fig. 13-19 KVL gives V1 5I1 2I2 and V2 I1 2I2
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The above equations are identical with the terminal characteristics obtained for the network of Fig. 13-18. Thus, the two networks are equivalent.
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Find the Y-parameters of Fig. 13-19 using its Z-parameters.
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From Problem 13.4, Z11 5; Z12 2; Z21 1; Z22 2
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TWO-PORT NETWORKS
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[CHAP. 13
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Since DZZ Z11 Z22 Z12 Z21 5 2 2 1 12, Y11 Z22 2 1 DZZ 12 6 Y12 Z12 2 1 12 6 DZZ Y21 Z21 1 12 DZZ Y22 Z11 5 DZZ 12
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Find the Y-parameters of the two-port network in Fig. 13-20 and thus show that the networks of Figs. 13-19 and 13-20 are equivalent.
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Fig. 13-20 Apply KCL at the ports to obtain the terminal characteristics and Y-parameters. Input port: Output port: and Y11 1 6 Y12 V1 V2 6 6 V2 V1 I2 2:4 12 1 1 Y21 6 12 I1 Thus,
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1 5 2:4 12
which are identical with the Y-parameters obtained in Problem 3.5 for Fig. 13-19. Thus, the two networks are equivalent.
Apply the short-circuit equations (10) to nd the Y-parameters of the two-port network in Fig. 13-21.
Fig. 13-21  1 1 1 V or Y11 12 12 1 6   V2 V2 1 1 1 V or Y12 4 12 2 6 4 12 V1 1 or Y21 12 12   V2 V2 1 1 5 or Y22 V 3 12 2 12 3 12 
I1 Y11 V1 jV2 0 I1 Y12 V2 jV1 0 I2 Y21 V1 jV2 0 I2 Y22 V2 jV1 0
CHAP. 13]
TWO-PORT NETWORKS
Apply KCL at the nodes of the network in Fig. 13-21 to obtain its terminal characteristics and Yparameters. Show that two-port networks of Figs. 13-18 to 13-21 are all equivalent.
Input node: Output node: V1 V1 V2 V2 12 12 4 V2 V2 V1 I2 3 12 1 1 1 5 I2 V1 V2 I1 V 1 V 2 6 6 12 12 I1
The Y-parameters observed from the above characteristic equations are identical with the Y-parameters of the circuits in Figs. 13-18, 13-19, and 13-20. Therefore, the four circuits are equivalent.
Z-parameters of the two-port network N in Fig. 13-22(a) are Z11 4s, Z12 Z21 3s, and Z22 9s. (a) Replace N by its T-equivalent. (b) Use part (a) to nd input current i1 for vs cos 1000t (V).
(a) The network is reciprocal. Therefore, its T-equivalent exists. shown in the circuit of Fig. 13-22(b). Its elements are found from (6) and
Fig. 13-22
TWO-PORT NETWORKS
[CHAP. 13
Za Z11 Z12 4s 3s s Zb Z22 Z21 9s 3s 6s Zc Z12 Z21 3s (b) We repeatedly combine the series and parallel elements of Fig. 13-22(b), with resistors being in k
and s in krad/s, to nd Zin in k
as shown in the following. Zin s Vs =I1 s 3s 6 6s 12 3s 4 9s 18 (mA). or Zin j 3j 4 5 36:98 k
and i1 0:2 cos 1000t 36:98
13.10 Two two-port networks a and b, with open-circuit impedances Za and Zb , are connected in series (see Fig. 13-12). Derive the Z-parameters equations (31a).
From network a we have V1a Z11;a I1a Z12;a I2a V2a Z21;a I1a Z22;a I2a From network b we have V1b Z11;b I1b Z12;b I2b V2b Z21;b I1b Z22;b I2b From connection between a and b we have I1 I1a I1b I2 I2a I2b Therefore, V1 Z11;a Z11;b I1 Z12;a Z12;b I2 V2 Z21;a Z21;b I1 Z22;a Z22;b I2 from which the Z-parameters (31a) are derived. V1 V1a V1b V2 V2a V2b
13.11 Two two-port networks a and b, with short-circuit admittances Ya and Yb , are connected in parallel (see Fig. 13-13). Derive the Y-parameters equations (32a).
From network a we have I1a Y11;a V1a Y12;a V2a I2a Y21;a V1a Y22;a V2a and from network b we have I1b Y11;b V1b Y12;b V2b I2b Y21;b V1b Y22;b V2b From connection between a and b we have V1 V1a V1b V2 V2a V2b Therefore, I1 Y11;a Y11;b V1 Y12;a Y12;b V2 I2 Y21;a Y21;b V1 Y22;a Y22;b V2 from which the Y-parameters of (32a) result. I1 I1a I1b I2 I2a I2b
CHAP. 13]
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