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Unformatted text preview: SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Recall: Ch 4. MeshCurrent Method
EE 203 Circuit Analysis 2
Lecture 08
Chapter 9.9
MeshCurrent Method
Kwang W. Oh, Ph.D., Assistant Professor
SMALL (Nanobio Sensors & MicroActuators Learning Lab)
Department of Electrical Engineering
University at Buffalo, The State University of New York
215E Bonner Hall, SUNYBuffalo, Buffalo, NY 142601920
Tel: (716) 6453115 Ext. 1149, Fax: (716) 6453656
kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  1/12 Step
Step 1: Assign a current in each
mesh in an arbitrary direction
Step 2: Show polarities according to
the assigned direction of current in
each
each mesh
Step 3: Apply KVL around each
Step
closed mesh M1 : − v1 + ia R1 + (ia − ib ) R3 = 0
M1 : v2 + (ib − ia ) R3 + ib R2 = 0 Step 4: Solve the resulting equations
for the mesh currents
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  2/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.12
EE 203 Circuit Analysis 2
Lecture 08
Chapter 9.10
Transformer Mesh 1: KVL
Mesh 2: KVL Kwang W. Oh, Ph.D., Assistant Professor
SMALL (Nanobio Sensors & MicroActuators Learning Lab)
Department of Electrical Engineering
University at Buffalo, The State University of New York
215E Bonner Hall, SUNYBuffalo, Buffalo, NY 142601920
Tel: (716) 6453115 Ext. 1149, Fax: (716) 6453656
kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  3/12 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  4/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Transformer Linear Transformer Transformer: A device that is based on magnetic coupling
Linear Transformer
found primarily in communication circuits
in communication to match impedances and eliminate
DC signals from portions of the system
Ideal Transformer
used to model the ferromagnetic transformer found in
power circuits
in power circuits to establish ac voltage levels that
facilitate the transmission, distribution, and consumption of
electrical power
When
When analyzing circuits containing mutual inductance
use the mesh or loopcurrent method for writing circuit
equations.
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo VS = the internal
voltage of the
sinusoidal source
ZS = the internal
impedance of the
source
ZL = the load
connected to the
secondary winding of
the transformer
I1 = the primary
phasor current
I2 = the secondary
phasor current
Lecture 08  Chapter 09  6/7  5/12 M = k L1 L2 , k : coefficient of coupling
li EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  6/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Linear Transformer Linear Transformer
Vs/I1( Meshcurrent equations Zint) Let
Selfimpedance of the mesh containing the primary winding
Selfimpedance of the mesh containing the secondary winding the impedance seen looking into the primary terminals of the transformer
Zab= Zint Zs Then, EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Impedance at the terminals (ab) of the source Lecture 08  Chapter 09  6/7  7/12 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  8/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.13 (1) Reflected Impedance
Reflected Impedance Zr M = k L1 L2 the impedance of
the primary winding Reflected Impedance (Zr)
The equivalent impedance of the secondary coil and load impedance transmitted,
or reflected, to the primary side of the transformer
Due solely to the existence of mutual inductance (if M 0, then Zr 0) j ωM c
R2 R1
L1
Z11 The linear transformer reflects the conjugate of the selfimpedance of the
secondary
secondary circuits (Z22*) into the primary winding by (ωM/Z22)2
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  9/12 L2 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Z22 d Lecture 08  Chapter 09  6/7  10/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.13 (2) Example 9.13 (2) b) the selfimpedance of the primary circuits is f)
f) the impedance seen looking into the primary terminals of the transformer
= the impedance of the primary winding + the reflected impedance
= (R1 + jωL1) + (Zr) c) the selfimpedance of the secondary circuits is g) The Thévenin voltage will equal the open circuit value of Vcd. The open circuit
value of Vcd will equal j1200 times the open circuit value of I1. The open circuit
cd
value of I1 is d) the impedance reflected into the primary winding is The Thévenin impedance will be Equal to the impedance of the secondary
winding plus the impedance reflected from the primary when the voltage source
is replaced by a shortcircuit. Thus e) the scaling factor for the reflected impedance
The scaling factor by which Z*22 is reflected is 8/9 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  11/12 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 08  Chapter 09  6/7  12/12 ...
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