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electronics fundamentals
circuits, devices, and applications
THOMAS L. FLOYD
DAVID M. BUCHLA
chapter 6
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Identifying series-parallel relationships
Most practical circuits have
combinations of series and parallel
components.
Components that are connected in
series will share a common path.
Components that are connected in
parallel will be connected across
the same two nodes.
Electronics Fundamentals 8th edition
Floyd/Buchla
1
2
© 2010 Pearson Education, Upper Saddle
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Chapter 6
Combination circuits
Most practical circuits have various combinations of
series and parallel components. You can frequently
simplify analysis by combining series and parallel
components.
An important analysis method is to form an equivalent
circuit. An equivalent circuit is one that has
characteristics that are electrically the same as
another circuit but is generally simpler.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Equivalent circuits
For example:
R1
1.0 k
R2
is equivalent to
R1
2.0 k
1.0 k
There are no electrical measurements that can
distinguish the boxes.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Equivalent circuits
Another example:
is equivalent to
R1
R2
1.0 k 1.0 k
R1,2
500 
There are no electrical measurements that can
distinguish the boxes.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
is equivalent to
R1
1.0 k
R3
R 1,2
R3
R2
4.7 k
3.7 k
4.7 k
2.7 k
is equivalent to
R1,2,3
2.07 k
Electronics Fundamentals 8th edition
Floyd/Buchla
There are no electrical
measurements that can
distinguish between the
three boxes.
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Kirchhoff’s voltage law and Kirchhoff’s current law
can be applied to any circuit, including combination
circuits.
For example,
applying KVL, the
path shown will
have a sum of 0 V.
R2
470 
VS
5.0 V
R11
270 
So will
this path!
R4
100 
R3
330 
R6
Start/Finish
Electronics Fundamentals 8th edition
Floyd/Buchla
Start/Finish
R5
100 
100 
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Kirchhoff’s current law can also be applied to the
same circuit. What are the readings for node A?
I
+
I
-
26.5 mA
+
A
I
VS
5.0 V
+
+
8.0 mA
R2
470 
R4
-
18.5 mA
100 
R1
270 
R3
330 
R6
R5
100 
100 
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Combination circuits
VS +
10 V
R1
270 
R2
330 
R3
470 
Tabulating current, resistance, voltage and power is a
useful way to summarize parameters. Solve for the
unknown quantities in the circuit shown.
I1= 21.6 mA
I2= 12.7 mA
I3= 8.9 mA
IT= 21.6 mA
R1= 270 
R2= 330 
R3= 470 
RT= 464 
Electronics Fundamentals 8th edition
Floyd/Buchla
V1= 5.82 V P1= 126 mW
V2= 4.18 V P2= 53.1 mW
V3= 4.18 V P3= 37.2 mW
VS= 10 V PT= 216 mW
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Kirchhoff’s laws can be applied
as a check on the answer.
R1
270 
VS +
10 V
R2
330 
R3
470 
Notice that the current in R1 is
equal to the sum of the branch currents in R2 and R3.
The sum of the voltages around the outside loop is zero.
I1= 21.6 mA
I2= 12.7 mA
I3= 8.9 mA
IT= 21.6 mA
R1= 270 
R2= 330 
R3= 470 
RT= 464 
Electronics Fundamentals 8th edition
Floyd/Buchla
V1= 5.82 V P1= 126 mW
V2= 4.18 V P2= 53.1 mW
V3= 4.18 V P3= 37.2 mW
VS= 10 V PT= 216 mW
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Loaded voltage divider
The voltage-divider equation
was developed for a series
circuit. Recall that the output
voltage is given by
 R2 
V2   VS
 RT 
+
R1
A
R2
R3
A voltage-divider with a resistive load is a combinational
circuit and the voltage divider is said to be loaded. The
loading reduces the total resistance from node A to ground.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Loaded voltage divider
What is the voltage
across R3?
VS =
+15 V
R1
330 
R2
470 
A
R3
2.2 k
Form an equivalent series circuit by combining R2 and
R3; then apply the voltage-divider formula to the
equivalent circuit: R2,3  R2 R3  470  2.2 k = 387 
V3  V2,3
 R2,3 
387 



VS  

15 V  8.10 V
R R 
 330   387  
2,3 
 1
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Stiff voltage divider
VS
R1
A stiff voltage-divider is one in
R2
RL
which the loaded voltage nearly
the same as the no-load voltage.
To accomplish this, the load
current must be small compared
to the bleeder current (or RL is large compared to the divider resistors).
If R1 = R2 = 1.0 k, what value of RL will make the divider a
stiff voltage divider? What fraction of the unloaded voltage is
the loaded voltage?
RL > 10 R2; RL should be 10 k or greater. For a 10 k load,
 R2 || RL 
0.91 k


This is 95% of the
VL  
V

 S 
VS   0.476 VS
 1.0 k  0.91 k 
unloaded voltage.
 R1  R2 || RL 
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Loading effect of
a voltmeter
VS +
10 V
R1
470 k
+
4.04
10 VV
R2
Assume VS = 10 V, but the
+
4.04 V
47
0
k

meter reads only 4.04 V
when it is across either R1
or R2.
Can you explain what is happening?
All measurements affect the quantity being measured. A
voltmeter has internal resistance, which can change the
resistance of the circuit under test. In this case, a 1 M
internal resistance of the meter accounts for the readings.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Wheatstone bridge
The Wheatstone bridge consists
R3
R1
of a dc voltage source and four VS
Output
resistive arms forming two
voltage dividers. The output is
R2
R4
taken between the dividers.
Frequently, one of the bridge
resistors is adjustable.
When the bridge is balanced, the output voltage is zero,
and the products of resistances in the opposite diagonal
arms are equal.
+
-
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Wheatstone bridge
R1
470 
R2
Balanced Wheatstone:
R1*R4 must be = R2*R3,
so (470)(270) = R2(330).
Or, R2 = (470)(270)/(330)
Electronics Fundamentals 8th edition
Floyd/Buchla
R3
330 
Output
-
VS
12 V
+
Example: What is the
value of R2 if the bridge
is balanced? 384 
R4
270 
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Thevenin’s theorem
Thevenin’s theorem states that any two-terminal,
resistive circuit can be replaced with a simple
equivalent circuit when viewed from two output
terminals. The equivalent circuit is:
RTH
VTH
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Thevenin’s theorem
VTH is defined as the open circuit voltage between the two
output terminals of a circuit.
RTH is defined as the total resistance appearing between
the two output terminals when all sources have been
replaced by their internal resistances.
RTH
VTH
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Thevenin’s theorem
What is the Thevenin voltage for the circuit? 8.76 V
What is the Thevenin resistance for the circuit? 7.30 k
Output terminals
R1
VS
10 k
12 V
R2
27 k
Electronics Fundamentals 8th edition
Floyd/Buchla
RL
68 k
Remember, the
load resistor
has no effect on
the Thevenin
parameters.
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Thevenin’s theorem
Thevenin’s theorem is useful for solving the Wheatstone
bridge. One way to Thevenize the bridge is to create two
Thevenin circuits - from A to ground and from B to ground.
The resistance between point
R1
R2
V
A and ground is R1||R3 and the S +
RL
A
B
resistance from B to ground is
R2||R4. The voltage on each
R3
R4
side of the bridge is found
using the voltage divider rule.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Thevenin’s theorem
For the bridge shown, R1||R3 = 165  and
R2||R4 = 179  . The voltage from A to ground
(with no load) is 7.5 V and from B to ground
(with no load) is 6.87 V .
VS
+15 V
+
-
R1
R2
330 
390 
RL
A
B
150 
R3
R4
330 
330 
The Thevenin circuits for each of the
bridge are shown on the following slide.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Thevenin’s theorem
''
RRTHTH AA RRLL BB RRTH
TH
THTH
I'TH V
=V
6.87V/494Ω
7.5
7.5VV
= 1.391mA
165
165 150
150
 179
179

'
ITHV=TH
TH
7.5V/494
6.87ΩV
= 1.518mA
Putting the load on the Thevenin circuits and
applying the superposition theorem allows you to
calculate the load current. The load current is:
ITH – I'TH = 1.391mA – 1.518mA = 1.27 mA
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Superposition theorem
The superposition theorem is a way to determine currents
and voltages in a linear circuit that has multiple sources by
taking one source at a time and algebraically summing the
results.
R3
R1
+
-
VS2
18 V
R2
6.8 k
-
-
VS1
12 V
6.8 k
I2
+
Electronics Fundamentals 8th edition
Floyd/Buchla
2.7 k
+
What does the
ammeter read for
I2? (See next slide
for the method and
the answer).
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
-
VS1
12 V
6.8 kk
k

6.8
VS2S2
-++1.56 mA
18 V
RR222
6.8 kk
k

6.8
II222
-
Source 1:
Source 2:
2.7

2.7 kkk
+
Set up a table of
pertinent information
and solve for each
quantity listed:
RR333
RR111
++
What does the ammeter
read for I2?
RT(S1)= 6.10 k I1= 1.97 mA I2= 0.98 mA
RT(S2)= 8.73 k I3= 2.06 mA I2= 0.58 mA
Both sources
I2= 1.56 mA
The total current is the algebraic sum.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Maximum power transfer
The maximum power is transferred from a source to a
load when the load resistance is equal to the internal
source resistance.
RS
VS +
RL
The maximum power transfer theorem assumes the
source voltage and resistance are fixed.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Maximum power transfer
What is the power delivered to the matching load?
RS
The voltage to the
load is 5.0 V. The
power delivered is
V 2  5.0 V 
PL 

= 0.5 W
RL
50 
2
Electronics Fundamentals 8th edition
Floyd/Buchla
VS +
10 V
50 
RL
50 
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Troubleshooting
The effective troubleshooter must think logically about
circuit operation.
Understand normal circuit operation and
find out the symptoms of the failure.
Decide on a logical set of steps to find the
fault.
Following the steps in the plan, make
measurements to isolate the problem.
Modify the plan if necessary.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Troubleshooting
VS =
+15 V
R1
330 
A
R2
R3
The output of the voltage470 
2.2 k
divider is 6.0 V. Describe how
you would use analysis and
planning in finding the fault.
From an earlier calculation, V3 should equal 8.10 V. A low
voltage is most likely caused by a low source voltage or
incorrect resistors (possibly R1 and R2 reversed). If the circuit is
new, incorrect components are possible.
Decide on a logical set of steps to locate the fault. You could
decide to 1) check the source voltage, 2) disconnect the load and
check the output voltage, and if it is correct, 3) check the load
resistance. If R3 is correct, check other resistors.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Selected Key Terms
Loading The effect on a circuit when an element that
draws current from the circuit is connected
across the output terminals.
Load current The output current supplied to a load.
Bleeder The current left after the load current is
current subtracted from the total current into the circuit.
Wheatstone A 4-legged type of bridge circuit with which an
bridge unknown resistance can be accurately measured
using the balanced state. Deviations in resistance
can be measured using the unbalanced state.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Selected Key Terms
Thevenin’s A circuit theorem that provides for reducing
theorem any two-terminal resistive circuit to a single
equivalent voltage source in series with an
equivalent resistance.
Superposition A method for analyzing circuits with two or
more sources by examining the effects of each
source by itself and then combining the
effects.
Maximum Power The condition, when the load resistance
Transfer equals the source resistance, under which
maximum power is transferred to the load.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
1. Two circuits that are equivalent have the same
a. number of components
b. response to an electrical stimulus
c. internal power dissipation
d. all of the above
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
2. If a series equivalent circuit is drawn for a complex
circuit, the equivalent circuit can be analyzed with
a. the voltage divider theorem
b. Kirchhoff’s voltage law
c. both of the above
d. none of the above
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
3. For the circuit shown,
a. R1 is in series with R2
-
c. R2 is in series with R3
VS
+
b. R1 is in parallel with R2
R1
R2
R3
d. R2 is in parallel with R3
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
4. For the circuit shown,
R4
a. R1 is in series with R2
R1
b. R4 is in parallel with R1
Electronics Fundamentals 8th edition
Floyd/Buchla
-
d. none of the above
+
c. R2 is in parallel with R3
VS
R2
R3
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
5. A signal generator has an output voltage of 2.0 V with no
load. When a 600  load is connected to it, the output
drops to 1.0 V. The Thevenin resistance of the generator is
a. 300 
b. 600 
c. 900 
d. 1200 .
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
6. For the circuit shown, Kirchhoff's voltage law
a. applies only to the outside loop
b. applies only to the A junction.
c. can be applied to any closed path.
d. does not apply.
VS +
10 V
R1
270 
A
R2
330 
Electronics Fundamentals 8th edition
Floyd/Buchla
R3
470 
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
7. The effect of changing a measured quantity due to
connecting an instrument to a circuit is called
a. loading
b. clipping
c. distortion
d. loss of precision
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
8. An unbalanced Wheatstone bridge has the voltages
shown. The voltage across R4 is
a. 4.0 V
d. 7.0 V
Electronics Fundamentals 8th edition
Floyd/Buchla
-
c. 6.0 V
VS
12 V
+
b. 5.0 V
R1
7.0 V
R2
R3
+ RL 1.0 V
R4
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
9. Assume R2 is adjusted until the Wheatstone bridge is
balanced. At this point, the voltage across R4 is measured
and found to be 5.0 V. The voltage across R1 will be
a. 4.0 V
d. 7.0 V
Electronics Fundamentals 8th edition
Floyd/Buchla
+ RL -
-
c. 6.0 V
VS
12 V
+
b. 5.0 V
R3
R1
R2
R4
5.0 V
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
10. Maximum power is transferred from a fixed source
when
a. the load resistor is ½ the source resistance
b. the load resistor is equal to the source resistance
c. the load resistor is twice the source resistance
d. none of the above
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 6
Quiz
Answers:
Electronics Fundamentals 8th edition
Floyd/Buchla
1. b
6. c
2. c
7. a
3. d
8. a
4. d
9. d
5. b
10. b
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.