BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING Drect Current Crcuts : Methods of Analyss Ismal Mohd Kharuddn, Zulkfl Md Yusof Faculty of Manufacturng Engneerng Unerst Malaysa Pahang
Drect Current Crcut (DC)- Methods of Analyss BFF1303 ELECTRICAL/ELECTRONICS ENGINEERING Contents: Outcomes Nodal Analyss Mesh Analyss Faculty of Manufacturng Unerst Malaysa Pahang Kampus Pekan, Pahang Darul Makmur Tel: +609-44 5800 Fax: +609-445888 BFF1303 Electrcal/Electronc Engneerng
Compute the soluton of crcuts contanng lnear resstors and ndependent and dependent sources by usng node analyss Compute the soluton of crcuts contanng lnear resstors and ndependent and dependent sources by usng mesh analyss BFF1303 Electrcal/Electronc Engneerng 3 3
There s another method to sole for currents and oltages. Easer More methodcal Stll based on Ohm s Law, KVL and KCL The methods are the nodal and mesh analyss. Nodal analyss s based on the KCL. Mesh analyss s based on the KVL. BFF1303 Electrcal/Electronc Engneerng 4 4
WITHOUT VOLTAGE SOURCE Analyze the crcut usng node oltages as the crcut arables. The node oltages s chosen nstead of the elements oltages. To smplfy matters, t s frst assumed that the crcuts do not contan oltage sources. BFF1303 BFF1303 Electrcal/Electronc Engneerng Engneerng 5 5 http://fkp.ump.edu.my/ 5
Steps to determne node oltages:. Select a node as a reference node Ths reference node also called the ground, hae zero potental. BFF1303 Electrcal/Electronc Engneerng 6 6
. The other node (nonreference nodes) wll be assgned as 1,, BFF1303 Electrcal/Electronc Engneerng 7 7
. Apply KCL to each of the nonreference node. At node 1 : I1 I 1 At node : I 3 BFF1303 Electrcal/Electronc Engneerng 8 8
. Apply the Ohm s law to express the unknown current 1, and 3 n terms of node oltages. hgher R lower Note: Current flows from a hgher potental (poste termnal) to a lower potental (negate termnal) n resstor. BFF1303 Electrcal/Electronc Engneerng 9 9
1 0 1 1 R1 R 3 R 3 0 I 0 0 I 1 1 1 1 I R1 R R3 R BFF1303 Electrcal/Electronc Engneerng 10 10
Obtan the node oltages for the followng crcut BFF1303 Electrcal/Electronc Engneerng 11 11
Soluton. Select a node as a reference node. The other node (nonreference nodes) wll be assgned as 1,. Apply KCL to each of the nonreference node. At node 1 : 1 3 1 3 0 At node : 4 1 5 4 1 5 0 BFF1303 Electrcal/Electronc Engneerng 1 1
. Express the currents n term of node oltages. 4 0 1 1 3 5 6 0 5 4 4 6 1 1 1 10 5 Rearrange the equaton 3 0 1 3 5 60 1 BFF1303 Electrcal/Electronc Engneerng 13 13
Then n matrx form By usng Cramer s Rule 3 1 1 0 3 1 3 5 60 15 3 1 3 5 1 0 1 60 5 1 100 60 13.333V 1 3 0 3 60 180 60 0V 1 BFF1303 Electrcal/Electronc Engneerng 14 14
In the gen crcut, obtan the node oltages Answer 6V 1 4V BFF1303 Electrcal/Electronc Engneerng 15 15
For the gen crcut, determne the oltages at the nodes Answer 4.8V.4V.4V 1 3 BFF1303 Electrcal/Electronc Engneerng 16 16
. Select a node as a reference node Ths reference node also called the ground, hae zero potental.. Reew of steps for nodal analyss wthout oltage sources: The other node (nonreference nodes) wll be assgned as 1,,. Apply KCL to each of the nonreference node.. Apply the Ohm s law to express the unknown current 1, and 3 n terms of node oltages. hgher R lower BFF1303 Electrcal/Electronc Engneerng 17 17
WITH VOLTAGE SOURCE Case 1 If a oltage source s connected between the reference node and a nonreference node. The oltage at the nonreference node equal to the oltage source. 1 10V BFF1303 Electrcal/Electronc Engneerng 18 18
Case If the oltage source (dependent or ndependent) s connected between two nonreference nodes, the two nonreference nodes form a generalzed node or supernode. BFF1303 Electrcal/Electronc Engneerng 19 19
A supernode s formed by enclosng a (dependent or ndependent) oltage source connected between two nonreference nodes and any elements connected n parallel wth t. supernode BFF1303 Electrcal/Electronc Engneerng 0 0
A supernode requres the applcatons of both KCL and KVL. A supernode has no oltage of ts own. A supernode can be assumed as one bg node. BFF1303 Electrcal/Electronc Engneerng 1 1
. Select a node as a reference node Ths reference node also called the ground, hae zero potental.. Steps for nodal analyss wth oltage source: Assgn the other nodes (nonreference nodes) as 1,, and dentfy the supernode.. Apply KCL to each of the nonreference node and the supernode. Note: For supernode, apply the KCL around the supernode. Assume the supernode as one bg node BFF1303 Electrcal/Electronc Engneerng
. Express the currents n term of node oltages. hgher R lower. Apply KVL around the supernode. BFF1303 Electrcal/Electronc Engneerng 3 3
Obtan the node oltages for the followng crcut BFF1303 Electrcal/Electronc Engneerng 4 4
Soluton. Select a node as a reference node. Assgn the other node (nonreference nodes) as 1, and dentfy the supernode. Apply KCL to each of the nonreference node and the supernode. At node 1 @1: 1 1 0 A At node @: 70 7A At supernode 7 0 1 7 1 BFF1303 Electrcal/Electronc Engneerng 5 5
. Express the currents n term of node oltages. 1 0 1 0 4 8 8 Rearrange the equaton 1 0 1 4 1 7. Apply KVL around the supernode. 0 1 1 BFF1303 Electrcal/Electronc Engneerng 6 6
Then n matrx form By usng Cramer s Rule 1 1 0 1 1 1 1 3 1 1 1 0 1 1 0 7.333V 3 0 1 4 0 5.333V 3 1 BFF1303 Electrcal/Electronc Engneerng 7 7
Fnd and for the gen crcut Answer 400mV.8A BFF1303 Electrcal/Electronc Engneerng 8 8
Obtan the node oltages for the followng crcut BFF1303 Electrcal/Electronc Engneerng 9 9
Soluton. Select a node as a reference node.. Assgn the other node (nonreference nodes) as 1, and dentfy the supernode Apply KCL to each of the nonreference node and the supernode. At supernode 1-: 3 10 1 0 3 10 1 At supernode 3-4: 1 3 4 5 0 BFF1303 Electrcal/Electronc Engneerng 30 1 3 4 5 30
. Express the currents n term of node oltages. 1 3 1 4 1 0 3 3 6 4 0 1 4 3 5 4 0 3 1 4 1 10 6 3 3 6 1 4 1 4 3 4 3 5 60 1 3 4 4 5 16 0 1 3 4 BFF1303 Electrcal/Electronc Engneerng 31 31
. Apply KVL around the supernode. At loop 1 0 0 1 1 0 At loop 3 0 and 3 x 4 x 1 3 4 1 4 3 0 3 6 0 0 x At loop 3 x 0 1 3 4 3 and x 1 4 6 3 3 BFF1303 Electrcal/Electronc Engneerng 3 3
From loop 1 10 and subs ths Eq. nto 5 60 1 3 4 and 4 5 16 0 1 3 4 61 3 4 80 6 5 16 40 1 3 4 Then n matrx form 3 1 1 0 6 1 80 3 6 5 16 4 40 BFF1303 Electrcal/Electronc Engneerng 33 33
By usng Cramer s Rule 3 1 6 1 18 6 5 16 1 0 1 80 1 40 5 16 480 18 1 6.667 V BFF1303 Electrcal/Electronc Engneerng 34 34
3 4 3 0 6 80 6 40 16 310 173.333V 18 3 1 0 6 1 80 6 5 40 4 840 46.667 V 18 3 1 0 6.667 0 6.667 V BFF1303 Electrcal/Electronc Engneerng 35 35
By usng nodal analyss obtan the node oltages for the followng crcut Answer 7.608 V 17.39 V 1.6305 V 1 3 BFF1303 Electrcal/Electronc Engneerng 36 36
WITHOUT CURRENT SOURCE Mesh analyss use the mesh currents as the crcut arables. Recall: nodal analyss use the node oltages as the crcut arables. Recall: a loop s a closed path wth no node passed more than once. A mesh s a loop that does not contan any other loop wthn t. BFF1303 Electrcal/Electronc Engneerng 37 37
Recall: nodal analyss apples KCL to fnd unknown oltages. Mesh analyss apples KVL to fnd unknown currents. abefa & bcdeb are meshes. abcdefa s not a mesh. BFF1303 Electrcal/Electronc Engneerng 38 38
The current through a mesh s known as mesh current. Frst, the analyss wll concentrate on crcut wth no current source. Steps to determne mesh currents:. Assgn mesh currents 1,,, n to the n meshes. The flow of the mesh. currents s conentonally assume n clockwse drecton. Determne the polarty & the drecton of current flow through each element.. Apply KCL for each node n term of mesh current.. Apply KVL to each of the n meshes. Use Ohm s law to express the oltages n terms of the mesh currents. BFF1303 Electrcal/Electronc Engneerng 39 39
. Assgn the mesh currents: 1 and. Determne the polarty & the drecton of current. Note: let the drecton of current at the outsde branch = drecton of the mesh current BFF1303 Electrcal/Electronc Engneerng 40 40
. Apply KCL. I I I 3 1 snce I I 1 1 I 3 1 Note: I for branch current, for mesh current. Apply KVL to each mesh. 15 5 10 10 0 Mesh 1 1 1 1 3 1 1 BFF1303 Electrcal/Electronc Engneerng 41 41
6 4 10 10 0 Mesh 1 1 1 Then n matrx form 3 1 1 1 1 By usng Cramer s Rule 3 6 4 1 1 1 1 1A 4 1 3 1 1 1 31 1A 3 BFF1303 Electrcal/Electronc Engneerng 4 4
Calculate the mesh current 1 and for the followng crcut Answer.5A 0A 1 BFF1303 Electrcal/Electronc Engneerng 43 43
Use mesh analyss to fnd I o for the followng crcut BFF1303 Electrcal/Electronc Engneerng 44 44
. Assgn the mesh currents: 1 and.. Determne the polarty & the drecton of current.. Apply KCL. I o 1. Apply KVL to each mesh. Mesh 1 4 10 1 0 1 3 1 1 3 11 5 6 1 1 BFF1303 Electrcal/Electronc Engneerng 45 45
Mesh 4 4 10 0 3 1 5 19 0 1 3 Mesh 3 4 1 4 0 1 3 1 3 0 3 1 3 Then n matrx form BFF1303 Electrcal/Electronc Engneerng 46 46
11 5 6 1 1 5 19 0 1 1 3 0 By usng Cramer s Rule 19 1 43 19 1.5A 144 19 0.75A Thus, I 1 1.5 A o 3 88 1.5A 19 3 BFF1303 Electrcal/Electronc Engneerng 47 47
By usng mesh analyss fnd I o n the followng crcut Answer I 4A o BFF1303 Electrcal/Electronc Engneerng 48 48
WITH CURRENT SOURCE Case 1 When the current source exst only n one mesh Set the alue of = 5 A and wrte a mesh equaton for the other mesh n the usual way. 10 4 6 0 A 1 1 1 BFF1303 Electrcal/Electronc Engneerng 49 49
Case When the current source exst between two meshes. need to create a supermesh by excludng the current source and any elements connected n seres wth t. BFF1303 Electrcal/Electronc Engneerng 50 50
NOTE: A supermesh results when two meshes hae a (dependent or ndependent) current source n common. Applyng KVL to the supermesh 0 6 10 4 0 1 1 6 14 0 1 BFF1303 Electrcal/Electronc Engneerng 51 51
Applyng KCL to the crcut 1 6 Then sole the Eq. (1) and () 1 3.A.8A BFF1303 Electrcal/Electronc Engneerng 5 5
The current source n the supermesh prodes the constrant equaton necessary to sole for the mesh currents. A supermesh has no current of ts own. A supermesh requres the applcaton of both KVL and KCL. BFF1303 Electrcal/Electronc Engneerng 53 53
By usng mesh analyss fnd 1, and 3 n the followng crcut BFF1303 Electrcal/Electronc Engneerng 54 54
. Assgn the mesh currents: 1, and 3... Determne the polarty & the drecton of current. Applyng KCL to supermesh. 4 1 1 Notce that meshes (1) and () form a supermesh snce they hae ndependent current source n common BFF1303 Electrcal/Electronc Engneerng 55 55
. Apply KVL to supermesh. 8 4 8 0 1 3 1 3 3 1 6 8 Applyng KVL n Mesh 3 4 0 3 3 3 1 1 3 4 8 0 3 Then n matrx form BFF1303 Electrcal/Electronc Engneerng 56 56
1 1 0 1 4 1 6 8 4 8 3 0 By usng Cramer s Rule 76 1 35 76 1 4.3516 A 48 76 0.6316 A 3 3 11 1.4737 A 76 BFF1303 Electrcal/Electronc Engneerng 57 57
By usng mesh analyss fnd 1, to 4 n the followng crcut 7.5 A.5 A 3.93A.143A Answer 1 3 BFF1303 Electrcal/Electronc Engneerng 58 58