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Chapter 17



Voltage / Current source conversions
Mesh and Nodal analysis in an AC circuit
Balance conditions and what elements are needed
in a bridge network
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

Magnitude is independent of
the network
Displays terminal
characteristics even if
completely isolated
FIG. 17.1 Independent sources.
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

Magnitude determined by the circuit it appears in
Used in AC analysis of Bipolar Junction Transistors
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FIG. 17.5 Source
Conversion.
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FIG. 17.6 Example
17.1.
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FIG. 17.7 Example
17.2.
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
Used to find currents when multiple circuit
loops with sources exist
◦ Accounts for contributions from other sources
◦ Matrix used to solve (Appendix C, pg. 1160)
◦ Calculator preferred method (Experiment 1)
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Assign loops, all one
arbitrary direction
2. Combine series elements
3. Convert I sources to E
sources
4. Write out formula for each
loop
1.
1.Far right – total sources in loop
2.Use 0 as place holder as needed
1( 1 + 2)
− 2( 2)
= 1
− 1( 2)
+ 2( 2 + 3) = − 2
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5.
Form a matrix to solve each
loop
a) Substitute sources for that
loop’s values
b) Base matrix without sources
c) Only enter impedances into
matrix
=
=
6.
1
− 2
− 2( 2)
+ 2( 2 + 3)
1( 1 + 2)
− 2( 2)
− 1( 2)
+ 2( 2 + 3)
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Values are
det(MatIx)/det(Matbase)
=
1
− 2
1+ 2
− 2
− 2
2
− 2
2+ 3
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
Treat source as
open
◦ Forms one large I1
loop

Second equation
is − + = 0
◦ Becomes -1 1 0 in
matrix
FIG. 17.13 Applying mesh analysis
to a network with an independent
current source.
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Find I1
FIG. 17.10 Example
17.5.
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
Find I2
FIG. 17.15 Example
17.9.
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Form equations to find
current through R3
FIG. 17.18 Example
17.10.
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1.
2.
Combine all series impedances
Determine the number of nodes and label
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3.
4.
Convert any voltage sources to current
sources (in schematic or equations)
Form equations for each node, using 0 to
fill spaces as needed (Y=1/Z)
1
1
1
+ )
− 2( )
1
2
2
1
1
1
2→
− 1( )
+ 2( + )
2
2
3
1(
1→
=− 1
= 2
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Form a matrix to solve each node
a) Substitute sources for that loop’s values
b) Base matrix without sources
c) Only enter impedances into matrix
6.
Values are det(MatIx)/det(Matbase)
1
−( 2)
1
1
2 ( 2 + 3)
1
1
1
( 1 + 2)
−( 2)
1
1
1
−( 2)
( 2 + 3)
−1
=
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
Find V1
FIG. 17.22 Example
17.12.

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Find Nodal Analysis
formulas
FIG. 17.32 Example 17.17.
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

No matrix needed
Short IES
◦ Form one supernode
◦ V1 and V2 become the
same node


Solve equation for V1
Solve for V2 using IES
1
1
1
+
1
2
= 1− 2
2= 1+ 1

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With components
parallel to IES
◦ Same initial process
◦ Additional current source
◦ 1
+
=− 1− 2−
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


Find voltage drop across
the capacitor
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Very common circuit
used in sensing systems
Two circuits in parallel
with common source
◦ Adjustable point across
from sensor for calibration
◦ Can use resistors,
capacitors, or inductors

Output measured as
difference between arms
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
Balanced state critical
◦ Allows for zeroing output with no input
◦ Improves accuracy, dynamic range

Output changes reflect sensor input
=
or
=
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Very common sensing circuit
◦ Two stabilizing resistors, equal value
◦ Nulling potentiometer
◦ Sensor (temp, pressure, etc)

Potentiometer used to calibrate
◦ Known input used on sensor
◦ Potentiometer adjusted till zeroed
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 Used to measure unknown coil inductance
 R1 used to null output
 Adjustment amount reflects inductor value

Q<10
Maxwell Bridge

Q>10
Hay Bridge
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This bridge is balanced.
Find the value of Lx
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
Effective voltage at 70.7% of amplitude
◦ More time near peak, better efficiency of energy
delivered

Voltage Ripple (VR)
◦ Percent of travel waveform amplitude translates
though between peak and average
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Single phase
◦ 100% VR

Three phase
◦
◦
◦
◦

Six pulses per cycle
More consistent voltage
Voltage never drops to zero
14 % VR
High Frequency
◦ Most efficient
◦ <1% VR
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Delta-WYE HV secondary used
◦ Delta provides 30 degree phase shift


Pair of FWRs output to same circuit
4% voltage ripple
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
Convert Δ to Y
◦ Eq. 17.18 – 17.20

Convert Y to Δ
◦ Eq. 17.21 – 17.23

If all Z match
◦ Eq. 17.24
◦ ALL PHASES MUST
MATCH
FIG. 17.45 Δ-Y
configuration.
Mirrored over Zc for
Delta pointing up
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FIG. 17.47 Converting the upper Δ of a bridge configuration
to a Y.
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FIG. 17.48 The network in Fig.
17.47 following the substitution of
the Y configuration.
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Convert to Y-Y configuration
FIG. 17.49 Example 17.21.
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FIG. 17.50 Converting a Δ configuration to a Y
configuration.
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FIG. 17.51 Substituting the Y configuration in Fig. 17.50 into
the network in Fig. 17.49.
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FIG. 17.52 Converting the Y configuration in Fig. 17.49
to a Δ.
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FIG. 17.53 Substituting the Δ configuration in Fig. 17.54
into the network in Fig. 17.49.
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
READ THE QUESTION
◦ Some only require equations
◦ Some only ask for value across an element
◦ Ensure you look at the correct element
 Ex - Resistor vs Inductor

Q 30
◦ The bridge is balanced. Prove that the current
through the capacitor is zero by finding the loop
currents that pass through it.
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