Lecture #13 Power supplies, dependent
sources, summary of ideal components
Reading:
Malvino chapter 3, 4.1-4.4
Next: 4.10, 5.1, 5.8
Then transistors (chapter 6 and 14)
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Topics
Today:
• Inductors and transformers
• Power supplies
• A new type of ideal device, the dependent
source.
• Summary of ideal devices
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Inductors
• Any coil of wire will produce a magnetic field
when current flows through it
• The magnetic field holds energy.
• If the current is changed, the magnetic field will
change, and therefore the energy stored will
change.
• Since the power must come from the circuit, this
creates a voltage:
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dI
V L
dt
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Symbol for and ideal inductor
• The symbol for an inductor is similar to
that of a resistor, but with loops
dI
V L
dt
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Transformers
• A transformer is a couple of coils of wire
which transfer power from one to the other
by a changing magnetic field.
• By having different numbers of windings,
or turns of wire, a transformer can step up
or step down an AC voltage.
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Transformers
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Transformer symbols
• The symbol for a transformer is a pair of the
same loopy lines used for inductors, but close
together. If the inductor has a core of a
magnetic material, it is shown as a couple of
lines between the coils.
The number of turns in the coils will
Be written nearby.
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Ideal transformer
• The voltage across the secondary of the
transformer (the output windings) is:
N2
V2 
V1
N1
• But this only works for changes in the
voltage—and therefore for AC only
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Ideal transformer
• The transfer of power can increase or
decrease the voltage, and the current
changes as well.
• Remember:
P  I1V1
so P  I1V1  I 2V2 if it is ideal (lossless))
V1 N1

V2 N 2
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Half-wave rectifier
• A single diode can be used to take an
alternating current, and allow only the
positive voltage swing to be applied to the
load
~
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An AC input is sinusoidal
1.5
1
0.5
0
0
5
10
15
20
-0.5
-1
-1.5
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The diode blocks the negative
voltages
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
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Full-wave rectifier
• If we add an additional diode, it does not pass current at
the same time as the first diode, but the load is now
disconnected during the negative half cycle.
• What if we could flip the connection and use the negative
half wave?
~
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Full-wave rectifier
• The result is called a full wave rectifier
~
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Full-wave rectified voltage
1.2
1
0.8
0.6
0.4
0.2
0
0
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Filtering
• A transformer and a full wave rectifier will
produce a voltage which is always
positive, but varies with time
• In order to power electronic devices, we
need to smooth out the variations with
time.
• Another way to look at this is that we need
to store energy temporarily while the input
voltage changes sign.
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Power supply filter capacitor
• If we add a capacitor in parallel with the load, it will
charge up when power is available from the voltage
source, and then it will slowly discharge through the load
when the diodes are off.
~
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Full wave rectified, with filtering
1.2
1
0.8
0.6
0.4
0.2
0
0
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Ripple
The result is a DC voltage, with some residual variations at twice the
frequency of the AC power. The variation is called ripple.
1.2
1
0.8
0.6
0.4
0.2
0
0
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Regulated power supply
• In order to produce a power supply without
ripple, we will need to use an active device
called a regulator
~
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Constant voltage
power supply
to load
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Ideal devices
Wire:
Current in =current out
No voltage differences
Resistor
V  IR
dV
I  C
dt
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Ideal devices 2
Inductor:
dI
V L
dt
Ideal diode:
Reversed bias  no current, open circuit
Forward bias  no voltage drop, just like a wire
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Ideal devices 3
+
+
Transformer
V1
V2
-
-
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V1 N1

V2 N 2
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Ideal devices 4
V (t )
I (t )
~
Voltage source:
Voltage given, current can be anything
Note: the voltage could be given as
A function of time
Current source
Current given, voltage can be anything
Note: the current could be given as
A function of time
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Ideal devices 5
+
V1
-
+
~
V2
-
+
V1
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I (t )
Dependent Voltage source:
Voltage given as a multiple of another
Voltage or a current, current can be anything
V2  KV1
Dependent Current source
Current given as a multiple of a different
current or voltage, voltage can be anything
I 2  GV1
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