Această analiză are la bază răspunsurile primite de la antreprenorii și oamenii de afaceri care au participat la conferința Business-2more-Business organizată de Doingbusiness.ro la Brașov în data de 10 martie 2016. La conferință au participat 150 de companii cu cifra de afaceri între 250 mii euro și peste 500 milioane euro. Pe lângă top management, au fost prezenți directori financiari, directori de achiziții, directori de vânzări, marketing, etc. Barometrul “Business-2more-business” este o analiză care și-a propus să afle răspunsul oamenilor de afaceri din 10 orașe mari din România în legătură cu nivelul de încredere în evoluția pozitivă a economiei. Cercetarea se va derula pe parcursul anului 2016. Datele demografice sunt detaliate la finalul acestui raport. Vă invităm să descoperiți care sunt rezultatele acestui sondaj, dar mai ales care sunt tendințele identificate de acesta.
Circuits with current sources
On the perimeter of meshes
Summary of Steps
For Mesh Analysis
Circuits with current sources
In between meshes
Supermesh
Example with Supermesh
Home Work Problems
The difference between mesh and nodal analysis is that nodal analysis is an application of Kirchhoff's current law, which is used for calculating the voltages at each node in an equation. While mesh analysis is an application of Kirchhoff's voltage law which is used for calculating the current.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
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2. Basic Circuits
Mesh Analysis: Basic Concepts:
In formulating mesh analysis we assign a mesh
current to each mesh.
Mesh currents are sort of fictitious in that a particular
mesh current does not define the current in each branch
of the mesh to which it is assigned.
I 1 I 2 I 3
3. Basic Circuits
Mesh Analysis: Basic Concepts:
R 1
R x
R 2
+
_ I 1 I 2
+
_V A V B
+ +
+
_
_
_V 1
V L 1
V 2
Figure 7.2: A circuit for illustrating mesh analysis.
( )
AXX
XL
AL
VIRIRRso
RIIVRIVwhere
VVV
=−+
−==
=+
211
211111
11
)(,
;
Eq 7.1
Around mesh 1:
4. Basic Circuits
Mesh Analysis: Basic Concepts:
R 1
R x
R 2
+
_ I 1 I 2
+
_V A V B
+ +
+
_
_
_V 1
V L 1
V 2
BVIRXRIXRor
BVIRXRIXR
givesinEqngSubstituti
RIVXRIILVwith
BVVLV
havewemeshAround
−=++−
=+−
=−−=
=−
2)2(1
2)2(1
,2.73.7
222;)12(1;
21
2
Eq 7.2
Eq 7.3
Eq 7.4
5. Basic Circuits
Mesh Analysis: Basic Concepts:
We are left with 2 equations: From (7.1) and (7.4)
we have,
AXX VIRIRR =−+ 211 )(
BXX VIRRIR −=++− 221 )(
Eq 7.5
Eq 7.6
We can easily solve these equations for I1 and I2.
6. Basic Circuits
Mesh Analysis: Basic Concepts:
The previous equations can be written in matrix form as:
−
+−
−+
=
−
=
+−
−+
−
B
A
XX
XX
B
A
XX
XX
V
V
RRR
RRR
I
I
or
V
V
I
I
RRR
RRR
1
2
1
2
1
2
1
2
1
(
)(
(
)(
Eq (7.7)
Eq (7.8)
7. Basic Circuits
Mesh Analysis: Example 7.1.
Write the mesh equations and solve for the currents I1, and I2.
+
_
1 0 V
4 Ω 2 Ω
6 Ω
7 Ω
2 V 2 0 V
I 1 I 2
+
+
_
_
Figure 7.2: Circuit for Example 7.1.
Mesh 1 4I1 + 6(I1 – I2) = 10 - 2
Mesh 2 6(I2 – I1) + 2I2 + 7I2 = 2 + 20
Eq (7.9)
Eq (7.10)
8. Basic Circuits
Mesh Analysis: Example 7.1, continued.
Simplifying Eq (7.9) and (7.10) gives,
10I1 – 6I2 = 8
-6I1 + 15I2 = 22
Eq (7.11)
Eq (7.12)
» % A MATLAB Solution
»
» R = [10 -6;-6 15];
»
» V = [8;22];
»
» I = inv(R)*V
I =
2.2105
2.3509
I1 = 2.2105
I2 = 2.3509
9. Basic Circuits
Mesh Analysis: Example 7.2
Solve for the mesh currents in the circuit below.
+
_
6 Ω
1 0 Ω
9 Ω
1 1 Ω
3 Ω
4 Ω
2 0 V 1 0 V
8 V
1 2 V
I 1 I 2
I 3
+
+
__
_
_
+
+
_
Figure 7.3: Circuit for Example 7.2.
The plan: Write KVL, clockwise, for each mesh. Look for a
pattern in the final equations.
11. Basic Circuits
Mesh Analysis: Example 7.2
Clearing Equations (7.13), (7.14) and (7.15) gives,
20I1 – 4I2 – 10I3 = 30
-4I1 + 18I2 – 11I3 = -18
-10I1 – 11I2 + 30I3 = 20
In matrix form:
−=
−−
−−
−−
20
18
30
3
2
1
301110
11184
10420
I
I
I
WE NOW MAKE AN IMPORTANT
OBSERVATION!!
Standard Equation form
12. Basic Circuits
Mesh Analysis: Standard form for mesh equations
Consider the following:
R11 =
∑
∑ of resistance around mesh 1, common to mesh 1 current I1.
R22 = of resistance around mesh 2, common to mesh 2 current I2.
R33 = ∑ of resistance around mesh 3, common to mesh 3 current I3.
∑
∑
∑
=
)3(
)2(
)1(
3
2
1
333231
232221
131211
emfs
emfs
emfs
I
I
I
RRR
RRR
RRR
13. Basic Circuits
Mesh Analysis: Standard form for mesh equations
R12 = R21 = - resistance common between mesh 1 and 2
when I1 and I2 are opposite through R1,R2.
R13 = R31 = - resistance common between mesh 1 and 3
when I1 and I3 are opposite through R1,R3.
R23 = R32 = - resistance common between mesh 2 and 3
when I2 and I3 are opposite through R2,R3.
)1(emfs∑ = sum of emf around mesh 1 in the direction of I1.
)2(emfs∑ = sum of emf around mesh 2 in the direction of I2.
)3(emfs∑ = sum of emf around mesh 3 in the direction of I3.
14. Basic Circuits
Mesh Analysis: Example 7.3 - Direct method.
2 0 V
1 0 V
1 5 V
3 0 V
2 0 Ω
1 0 Ω
3 0 Ω
1 0 Ω
1 2 Ω
8 Ω
+
_
I 1 I 2 I 3
+
+
+
_
_
_
Use the direct method to write the mesh equations for the following.
Figure 7.4: Circuit diagram for Example 7.3.
=
−
−−
−
15
25
10
3
2
1
30100
105010
01030
I
I
I
Eq (7.13)
15. Basic Circuits
Mesh Analysis: With current sources in the circuit
Example 7.4: Consider the following:
1 0 V
2 0 V
4 A
1 0 Ω
5 Ω
2 0 Ω
2 Ω
+
_
1 5 Ω
+
_
I 1 I 2
I 3
Figure 7.5: Circuit diagram for Example 7.4.
Use the direct method to write the mesh equations.
16. 1 0 V
2 0 V
4 A
1 0 Ω
5 Ω
2 0 Ω
2 Ω
+
_
1 5 Ω
+
_
I 1 I 2
I 3
Basic Circuits
Mesh Analysis: With current sources in the circuit
This case is explained by using an example.
Example 7.4: Find the three mesh currents in the circuit below.
Figure 7.5: Circuit for Example 7.4.
When a current source is present, it will be directly related to
one or more of the mesh current. In this case I2 = -4A.
17. Basic Circuits
Mesh Analysis: With current sources in the circuit
Example 7.4: Continued. An easy way to handle this case is to
remove the current source as shown below. Next, write the mesh
equations for the remaining meshes.
Note that I2 is retained for writing the equations through the
5 Ω and 20 Ω resistors.
1 0 V
2 0 V
1 0 Ω
5 Ω
2 0 Ω
2 Ω
+
_
1 5 Ω
+
_
I 1 I 2
I 3
18. Basic Circuits
Mesh Analysis: With current sources in the circuit
Example 7.4: Continued.
1 0 V
2 0 V
1 0 Ω
5 Ω
2 0 Ω
2 Ω
+
_
1 5 Ω
+
_
I 1 I 2
I 3 Equation for mesh 1:
10I1 + (I1-I2)5 = 10
or
15I1 – 5I2 = 10
Equations for mesh 2:
2I3 + (I3-I2)20 = 20
or
- 20I2 + 22I3 = 20
Constraint Equation
I2 = - 4A
19. Basic Circuits
Mesh Analysis: With current sources in the circuit
Example 7.4: Continued. Express the previous equations in
Matrix form:
1
2
3
15 5 0 10
0 20 22 20
0 1 0 4
I
I
I
−
− =
−
I1 = -0.667 A
I2 = - 4 A
I3 = - 2.73 A