Download The Voltage Source

The Voltage Source
The voltage source is the principal type of energy source in electronic applications so
it is important to understand its characteristics. The voltage source ideally provides
constant voltage to a load even when the load resistance varies. After completing this
section, you should be able to:
Describe the characteristics of a voltage source
Compare a practical voltage source to an ideal source
Discuss the effect of loading on a practical voltage source
The graphs of an ideal voltage source and a practical voltage source are shown below.
Output
Voltage
‘ideal’ voltage source
practical voltage source
Load Current
Figure 1
Figure 2(a) is the familiar symbol for an ideal dc voltage source. The voltage across
terminals A and B remains fixed regardless of the value of load resistance that ma
connected across its output. Figure 2(b) shows a load resistor, RL, connected. All of
source voltage, VS, is dropped across RL. Ideally, RL can be changed to any value ex
zero, and the voltage will remain fixed. The ideal voltage source has an internal
resistance of zero.
FIGURE 1
Ideal dc voltage source.
A
A
Vs
Vs
(a) Unloaded
B
RL
(b) Loaded
B
In reality, no voltage source is ideal. That is, all have some inherent internal resistance
as a result of their physical and/or chemical makeup, which can be represented
resistor in series with an ideal source, as shown in Figure 3(a). RS is the internal so
resistance and VS is the source voltage. With no load, the output voltage (voltage from
A to B) is VS. This voltage is sometimes called the open circuit voltage.
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FIGURE 3 Practical voltage source.
RS
A
RS
Vs
Vs
A
RS
B
(a) Unloaded
(b) Loaded
Loading of the Voltage Source
When a load resistor is connected across the output terminals, as shown in Figure 3 all
of the source voltage does not appear across R L. Some of the voltage is dropped
across RS because of the current through RS to the load, RL.
If RS is very small compared to RL, the source approaches ideal because almost all of
the source voltage, VS, appears across the larger resistance, RL. Very little voltage is
dropped across the internal resistance, RS. If RL changes, most of the source voltage
remains across the output as long as RL is much larger than RS. As a result, very little
change occurs in the output voltage. The larger R L is compared to RS, the less change
there is in the output voltage. As a rule, before it can be neglected, R L should be at
least ten times RS (RL  10RS).
Example 1 illustrates the effect of changes in RL on the output voltage when RL is
much greater than RS. Example 2 shows the effect of smaller load resistances.
Calculate the voltage output of the source in Figure 4 for the following values of R L:
100, 560, and 1k.
Example 1
FIGURE 4
10 
Vs
A
Vout
RL
2
Solution For RL = 100,
VOUT = RLVS = 100 x 100 = 90.9V
RL+ RS
110
For RL = 560 
VOUT = RLVS = 560 x 100 = 98.2V
RL+ RS 570
For RL = 1 k,
VOUT = RLVS = 100 x 100 = 99V
RL+ RS
110
Notice that the output voltage is within 10% of the source voltage, VS, for all three
values of RL, because RL is at least ten times RS.
Exercise 1 Determine VOUT in Figure 4 if RS = 50  and RL = 10 k.
Example 2
Determine VOUT for RL = 10  and for RL = 1  in Figure 4.
Solution For RL = 10,
For RL = 10 
VOUT = RLVS = 10 x 100 = 50V
RL+ RS 20
For RL = 1 ,
VOUT = RLVS = 1 x 100 = 9.09V
RL+ RS 11
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Exercise 2 What is VOUT with no load resistor in Figure 4?
Notice in Example 2 that the output voltage decreases significantly, as R L is smaller
compared to RS. This example illustrates the requirement that RL must be larger than
RS in order to maintain the output voltage near its open circuit value.
The Current Source
The current source is another type of energy source that ideally provides a constant
current to a load even when the resistance of the load varies. The concept of a current
source is important in certain types of transistor circuits. After completion this
section, you should be able to:
Describe the characteristics of a current source
Compare a practical current source to an ideal source
Discuss the effect of loading on a practical current source
Figure 5 Shows the graphs of an ideal current source and a practical current source.
practical current
source
Output
Voltage
‘ideal’ constant
current source
Load Current
Figure 6(a) shows a symbol for the ideal current source. The arrow indicates direction
of current, and IS is the value of the source current. An ideal current source produces a
fixed or constant value of current through a load, regardless of the value load. This
concept is illustrated in Figure 6(b), where a load resistor is connected current source
between terminals A and B. The ideal current source has an infinitely internal
resistance.
FIGURE 6
Ideal current source.
A
IS
A
IS
RL
B
(a) Unloaded
B
(b) Loaded
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Transistors act basically as current sources, and for this reason, knowledge of the
current source concept is important. You will find that the equivalent model of a
transistor does contain a current source.
Although the ideal current source can be used in most analysis work, no device is
ideal. A practical current source representation is shown in Figure 7. The internal
resistance appears in parallel with the ideal current source.
If the internal source resistance, RS, is much larger than a load resistor, the practical
source approaches ideal. The reason is illustrated in the practical current source shown
Figure 7. Part of the current Is flows through RS, and part through RL. RS and RL acts
as a current divider.
FIGURE 7
Current source
Practical current source with load.
A
IS
RS
RL
If RS is much larger than RL, most of the current will flow through RL and very little
will flow through RS. As long as RL remains much smaller than RS, the current
through it will stay almost constant, no matter how much RL changes.
If we have a constant-current source, we normally assume that RS is so much larger
than the load that RS can be neglected. This simplifies the source to ideal, making the
analysis easier.
Example 3 illustrates the effect of changes in RL on the load current when RL is much
smaller than RS. Generally, RL should be at least ten times smaller (10RL  RS).
Calculate the load current in Figure 8 for the following values of RL: 100 , 560 ,
and 1 k.
FIGURE 8
A
IS
1A
RS
10 k
RL
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Solution For RL = 100,
IL =
RS x IS = 10k x 1 = 990mA
RS + R L
10.1k
For RL= 560,
IL =
RS x IS = 10k x 1 = 947 mA
RS + R L
10.56 k
For RL= 1k,
IL =
RS x IS = 10k x 1 = 909 mA
RS + R L
11 k
Notice that the load current, IL, is within 10% of the source current for each value of
RL because RL is at least ten times smaller than RS.
Exercise 3 At what value of RL in Figure 8 will the load current equal 750 mA?
Source Conversions
In circuit analysis, it is sometimes useful to convert a voltage source to an equivalent
current source', or vice versa. After completing this section, you should be able to:
Perform source conversions
Convert a voltage source to a current source
Convert a current source to a voltage source
Define terminal equivalency
Converting a Voltage Source into a Current Source
The source voltage, VS, divided by the source resistance, RS, gives the value of the
equivalent source current.
IS = VS
RS
The value of RS is the same for both the voltage and current sources. As illustrated in
Figure 9, the directional arrow for the current points from minus to plus. The
equivalent current source is in parallel with RS.
FIGURE 9
Conversion of voltage source to equivalent current source.
RS
A
A
Vs
IS
RS
RL
B
B
(a) Voltage source
(b) Current source
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Equivalency of two sources means that for any given load resistance connected to the
two sources, the same load voltage and load current are produced by both sources.
This concept is called terminal equivalency.
We can show that the voltage source and the current source in Figure 9 equivalent by
connecting a load resistor to each, as shown in Figure 10, and then calculating the
load current as follows: For the voltage source,
IL =
RS
VS
RS + RL
A
A
VS
RL
IL =
VS
Rs+RL
IS
RS
IL = VS
RS+RL
RL
B
B
(a) Loaded voltage source
(b) Loaded current source
FIGURE 10 Equivalent sources with loads.
For the current source,
IL = RSVs
RS+RL
= Vs
RS+RL
As you see, both expressions for IL are the same. These equations prove that the
sources are equivalent as far as the load or terminals AB are concerned.
Convert the voltage source in Figure 11 to an equivalent current source.
FIGURE 11
Rs
Solution
A
50 
IS =VS = l00 = 2A
RS 50
RS = 50
VS
100V
B
The equivalent current source is shown in Figure 12
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FIGURE 12
A
IS
2A
RS
50
B
Exercise 3 Determine IS and RS of a current source equivalent to a voltage source with
VS = 12V and RS= l0.
Converting a Current Source into a Voltage Source
The source current, IS multiplied by the source resistance, RS, gives the value of the
equivalent source voltage.
VS = ISRS
Again, RS remains the same. The polarity of the voltage source is minus to plus in the
direction of the current. The equivalent voltage source is the voltage in series with RS,
as illustrated in Figure 13.
FIGURE 13 Conversion of current source to equivalent voltage source.
A
IS
RS
ISRS
RS
B
B
(a) Current source
A
(b) Voltage source
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EXAMPLE 5 Convert the current source in Figure 14 to an equivalent voltage
source.
A
10 mA
1 k
B
FIGURE 14
Solution
VS = ISRS = 10 x 10-3 x 1000 = 10 V
RS = 1 k
The equivalent voltage source is shown in Figure 15
FIGURE 15
RS = 1k
A
10 V
B
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Exercise 6
Determine VS and RS of a voltage source equivalent to a current source with IS = 500
mA and RS = 600.
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