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Unformatted text preview: Mesh Current Technique Of Circuit Analysis DePiero EE 201 Learning Objec@ves • Analyze circuits containing both independent and dependent sources using mesh current analysis. • Notes: – Mesh analysis most convenient for circuits containing voltage sources. – Voltage sources will be addressed before current sources – Dependent sources will not be addresses ini=ally Mesh Current Method is Systema@c • Yields a set of simultaneous equa@ons from which unknown current and voltages may be found. • Should work for any circuit… – Pathological cases may exist. (No worries). • Simultaneous equa@ons may be solved via Cramer’s Rule, or directly on a calculator. – See Appendix A for Cramer’s Rule. Mesh Current Analysis
Ini=al Version • 1) Deﬁne the currents around each mesh in the same direc@on (clockwise). • 2) Apply KVL around each mesh. Express each KVL voltage, Vn, in terms of one or more mesh currents. Use the passive sign conven@on. • 3) Solve KVL equa@ons simultaneously. Example 1
• Find power (delivered or absorbed) by the 8 V source. • 1) Deﬁne mesh currents • 2) KVL for meshes – Assign V polarity to resistors – Sum Vn = 0 • 3) Solve for mesh currents • Find power for 8 V source Left mesh current (CW) = 4A
Right mesh current (CW) = 1/3A Branches Sharing Mesh Currents
Require Special A]en@on
• Consider the net current (downward) for the 8V source • Net current is I1 – I2 I1 I2 Branches Sharing Mesh Currents
Require Special A]en@on…
• Suppose the upper terminal of the 1
Ohm resistor is (+). • What mesh currents would result in given polarity for the 1
Ohm resistor? • Mesh currents: I1 – I2 I1 I2 Mesh Current Analysis – Full Version • 1) Deﬁne the currents around each mesh in the same direc@on (clockwise). • 2) If a current source is present – Deﬁne Vx as the voltage across it. The polarity for Vx is arbitrary, but should remain unchanged in all KVL equa@ons. – Use KCL to create another equa@on, rela@ng mesh currents to current of the current source. • 3) Apply KVL around each mesh. Express each KVL voltage, Vn, in terms of one or more mesh currents. Use the passive sign conven@on. • 4) If dependent sources are present, add another equa@on based on the deﬁni@on of the dependent source. • 5) Solve KVL equa@ons simultaneously. ...
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 Spring '08
 ARAKAKI

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