EE 529 Circuit and Systems Analysis Lecture 5

Mathematical Model of a Dependent Source A. Voltage Controlled Voltage Source a c 1

Mathematical Model of a Dependent Source B. Current Controlled Voltage Source a c 1

Mathematical Model of a Dependent Source A. Voltage Controlled Current Source a c 1

Mathematical Model of a Dependent Source A. Current Controlled Current Source a c 1

Circuit Analysis A-Branch Voltages Method: Consider the following circuit. Find v and i

Circuit Analysis • Draw the circuit graph 5 6 4 1 2 3 7

Circuit Analysis Select a proper tree: (n-1=4 branches) Ø Place voltage sources in tree

Circuit Analysis • Write the fundamental cut-set equations for the tree branches which do

Circuit Analysis • Write the currents in terms of voltages using terminal equations. 5

Circuit Analysis • Substitute the currents into fundamental cut-set equation. • v 2, and

Circuit Analysis • Subst. Eq. (2) into (1) yields

Chord Currents Method n Consider the circuit. Find v using chord currents method.

Chord Currents Method n Draw the circuit graph. a 5 4 3 b c

Chord Currents Method n Select a proper tree a 5 4 3 b c

Chord Currents Method n Write the fundamental circuit equations for the chords which are

Chord Currents Method n Write all resistor voltages in terms of terminal currents using

Chord Currents Method n Substitute the terminal equations to fundamental circuit equations a 5

Chord Currents Method n Write fundamental cut-set equations for i 3 and i 6.

Chord Currents Method n Substitute the fundamental cut-set equations to fundamental circuit equations a

Chord Currents Method n Using Eqns. (1) and (2), i 2 and i 4

Chord Currents Method n Consider the following circuit. Find v 0.

Slides: 25

Download presentation

EE 529 Circuit and Systems Analysis Lecture 5 EASTERN MEDITERRANEAN UNIVERSITY

Mathematical Model of a Dependent Source A. Voltage Controlled Voltage Source a c 1 2 b d

Mathematical Model of a Dependent Source B. Current Controlled Voltage Source a c 1 2 b d

Mathematical Model of a Dependent Source A. Voltage Controlled Current Source a c 1 2 b d

Mathematical Model of a Dependent Source A. Current Controlled Current Source a c 1 2 b d

Circuit Analysis A-Branch Voltages Method: Consider the following circuit. Find v and i

Circuit Analysis • Draw the circuit graph 5 6 4 1 2 3 7

Circuit Analysis Select a proper tree: (n-1=4 branches) Ø Place voltage sources in tree Ø Place the voltages controlling the dependent sources in tree Ø Place current sources in co-tree Ø Complete the tree from the resistors 5 6 4 1 2 3 7

Circuit Analysis • Write the fundamental cut-set equations for the tree branches which do not correspond to voltage sources. 5 6 4 1 2 3 7

Circuit Analysis • Write the currents in terms of voltages using terminal equations. 5 6 4 1 2 3 7

Circuit Analysis • Substitute the currents into fundamental cut-set equation. • v 2, and v 6 must be expressed in terms of branch voltages using fundamental circuit equations.

Circuit Analysis 5 6 4 3 2 1 7

Circuit Analysis • Therefore and

Circuit Analysis • Subst. Eq. (2) into (1) yields

Chord Currents Method n Consider the circuit. Find v using chord currents method.

Chord Currents Method n Draw the circuit graph. a 5 4 3 b c 6 2 1 7 d n v = v 3

Chord Currents Method n Select a proper tree a 5 4 3 b c 6 2 1 7 d

Chord Currents Method n Write the fundamental circuit equations for the chords which are not current sources. a 5 4 3 b c 6 2 7 1 d

Chord Currents Method n Write all resistor voltages in terms of terminal currents using terminal equations. a 5 4 3 b c 6 2 7 1 d

Chord Currents Method n Substitute the terminal equations to fundamental circuit equations a 5 4 3 b c 6 2 7 1 d

Chord Currents Method n Write fundamental cut-set equations for i 3 and i 6. a 5 4 3 b c 6 2 1 7 d

Chord Currents Method n Substitute the fundamental cut-set equations to fundamental circuit equations a 5 4 3 b c 6 2 7 1 d

Chord Currents Method n Using Eqns. (1) and (2), i 2 and i 4 can be calculated as