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Chapter 17 – Methods of Analysis & Sel Topics
Lecture 23
by Moeen Ghiyas
19/04/23 1
Independent vs Dependent Sources
Source Conversions
Mesh Analysis
Bridge Networks
19/04/23 2
Independent Sources
The term independent specifies that the magnitude of the
source is independent of the network to which it is applied and
that the source displays its terminal characteristics even if
completely isolated.
Dependent (Controlled) Sources
A dependent or controlled source is one whose magnitude is
determined (or controlled) by a current or voltage of the system in
which it appears
Old Symbols
New Symbols
Dependent (Controlled) Sources
Unlike with the independent source, isolation such that V or I = 0
will result in short-circuit or open-circuit equivalent as indicated
Source conversion can be accomplished in much the same
manner as for dc circuits, except now we shall be dealing
with phasors and impedances instead of just real numbers
and resistors
EXAMPLE - Convert the voltage source of fig to a current source
Solution:
EXAMPLE - Convert the current
source of fig to a voltage source
Solution:
For dependent sources, the direct conversion can be
applied if the controlling variable (V or I) is not determined
by a portion of the network to which the conversion is to be
applied
Conversions of the other kind, where V and I are controlled
by a portion of the network to be converted, are covered in
chapter 18 (Not part of syllabus for 2nd semester)
EXAMPLE - Convert the voltage source of fig to a current source
Solution:
Steps
1. Assign a distinct current direction
to each independent, closed loop
2. Indicate the polarities within
each loop for each resistor
(impedance) . Note that the
polarities be placed within each
loop. Thus 4 Ω resistor have two
sets of polarities across it.
Steps
3. Apply Kirchhoff’s voltage law around each closed loop
the total current through the element (impedance) is the assumed
current of the loop plus the assumed currents of the other loops
passing through in the same direction, minus the assumed currents
through in the opposite direction
The polarity of a voltage source is unaffected by the direction of the
assigned loop currents
4. Solve the resulting simultaneous linear equations for the
assumed loop currents
The general approach to mesh includes the same sequence of
steps as for dc except to substitute impedance for resistance and
admittance for conductance in the general procedure with minor
additional changes as mentioned below:
Independent Voltage Sources
Same as dc analysis with impedances and admittance values
Dependent Voltage Sources
Step 3 is modified: Treat each dependent source like an
independent source when KVL is applied. However, once the
equation is written, substitute the equation for the controlling
quantity (i.e an additional eqn is generated for controlling qty)
Independent Current Sources
Treat each current source as an open circuit (recall supermesh
concept), and write mesh equations for remaining paths.
Then relate the chosen mesh currents to the independent
sources to ensure that the unknowns of the final equations are
limited simply to the mesh currents
Dependent Current Sources
The procedure is same as for independent current sources (i.e.
supermesh concept), except now the dependent sources have
to be defined in terms of the chosen mesh currents so that the
final equations have only mesh currents as the unknown qtys.
EXAMPLE - Using the general approach to mesh analysis, find
the current I1 in Fig
Solution
The network is redrawn
Apply KVL,
Loop 1:
+E1 – I1Z1 – I1Z2 + I2Z2 = 0
I1Z1 + I1Z2 - I2Z2 = E1
I1(Z1 + Z2) – I2Z2 = E1 ----- A
Loop 2:
– E2 – I2Z2 + I1Z2 – I2Z3 = 0
– I1Z2 + I2Z2 + I2Z3 = – E2
– I1Z2 + I2(Z2 + Z3) = – E2 ------ B
Solve by determinants
Solve by determinants and then substitute values
I1(Z1 + Z2) – I2Z2 = E1
– I1Z2 + I2(Z2 + Z3) = – E2
EXAMPLE - Write the mesh currents for the network of fig having
a dependent voltage source.
Solution:
EXAMPLE - Write the mesh currents for the network of fig having
a independent current source.
Solution:
Apply supermesh concept
EXAMPLE - Write the mesh currents for the network of fig
having a dependent current source.
Solution:
Problem # 9 – Using mesh analysis, determine the current IL (in
terms of V) for the network of fig
Solution:
Problem # 9 – Using mesh analysis, determine the current IL (in
terms of V) for the network of fig
Solution:
Solving by determinants
Bridge networks with reactive components & ac voltage or current
Maxwell’s Bridge (V source & RC parallel)
From dc we remember, for IZ5 = 0,
the following condition must be met
or
Hay Bridge (I source & RC series)
From dc we remember, for VZ5 = 0,
the following condition must be met
or
or
Hay bridge – when Z5 is replaced by a sensitive galvanometer is
used for measuring the resistance and inductance of coils in
which the resistance is a small fraction of the reactance XL.
Maxwell bridge – when Z5 is replaced by a sensitive galvanometer
is used for inductance measurements when the resistance of the
coil is large enough not to require a Hay bridge.
Another popular bridge is the capacitance comparison bridge
of fig. An unknown capacitance and its associated resistance
can be determined using this bridge.
Independent vs Dependent Sources
Source Conversions
Mesh Analysis
Bridge Networks
19/04/23 28