Slide 6.1CE164 - 2024 F. Sepulveda - CSEE - Essex University
Foundations of Electronics – II
Lecture 6 (Week 21)
 Transformers
 AC/DC Power Supplies
Francisco Sepulveda
E-mail: f.sepulveda
CE164
moodle.essex.ac.uk/course/view.php?id=3644
Slide 6.2CE164 - 2024 F. Sepulveda - CSEE - Essex University
Transformers
Reading:
Chapter 14 in T. Floyd (2007edition) - on Moodle
(the latest version of the book has a different topic on chp.14)
Slide 6.3CE164 - 2024 F. Sepulveda - CSEE - Essex University
When two coils are placed close to each other, a changing flux in one
coil will cause an induced voltage in the second coil. The coils are
said to have mutual inductance (LM), which can either add or subtract
from the total inductance depending on whether the fields are aiding or
opposing.
LM
k
The coupling coefficient (k) is
a measure of how well the
coils are linked; it is a number
between 0 and 1.
1 2L L
Mutual Inductance
Primary: on the voltage source side
Secondary: on the load side
Slide 6.4CE164 - 2024 F. Sepulveda - CSEE - Essex University
The formula for mutual inductance is:
LM
k
1 2ML k L L
k = the coupling coefficient (dimensionless)
L1, L2 = inductance of each coil (H)
The coefficient of coupling
depends on factors such as
the orientation of the coils to
each other, their proximity,
and whether they are on a
common core.
1 2L L
Mutual Inductance
Slide 6.5CE164 - 2024 F. Sepulveda - CSEE - Essex University
The basic transformer is formed from two coils that are
usually wound on a common core to provide a path for the
magnetic field lines. Schematic symbols indicate the type of
core.
Air core Ferrite core Iron core
Small power transformer
Basic Transformers
Slide 6.6CE164 - 2024 F. Sepulveda - CSEE - Essex University
A useful parameter for ideal transformers is the turns ratio
defined* as:
sec
pri
N
n
N

Nsec = number of secondary windings
Npri = number of primary windings
* Based on the IEEE dictionary definition for power transformers.
Turns ratio
Primary: on the voltage source side
Secondary: on the load side
Npri Nsec1ry 2ry
Slide 6.7CE164 - 2024 F. Sepulveda - CSEE - Essex University
The direction of the windings determines the polarity of
the voltage across the secondary winding with respect
to the voltage across the primary. Phase dots are
sometimes used to indicate polarities.
In phase Out of phase
Direction of windings
effect on phase
the dot system
Slide 6.8CE164 - 2024 F. Sepulveda - CSEE - Essex University
120 Vrms
Vpri
In a step-up transformer, the secondary voltage is greater
than the primary voltage and n > 1.
In a step-down transformer, the secondary voltage is less
than the primary voltage and n < 1.
What is the secondary voltage?
4:1
?30 Vrms
What is the turns ratio? 0.25
Step-up and step-down transformers
=



 Vsec = n Vpri
Slide 6.9CE164 - 2024 F. Sepulveda - CSEE - Essex University
A special transformer with a turns ratio of 1 is called an isolation
transformer. Because the turns ratio is 1, the secondary voltage is the same
as the primary voltage, hence AC is passed from one circuit to another.
Also, the average DC component is blocked by the transformer, because magnetic
flux does not change with constant DC voltage (Faraday’s law!)
 DC offset is removed from 1ry to 2ry sides.
Application: DCoffset Removal
AC + DCoffset
AC only!
primary secondary
Slide 6.10CE164 - 2024 F. Sepulveda - CSEE - Essex University
Amplifier
stage 1
Amplifier
stage 2ac + dc
voltage
ac
voltage
only
Coupling transformer
Primary resonant circuit Secondary resonant circuit
Coupling transformers are used to pass a higher frequency signal
from one stage to another. Because they are high frequency
transformers, they typically are configured with a resonant circuit on
the primary and the secondary. Some specialty isolation amplifiers use
transformer coupling to isolate power.
Application: Coupling transformers
Slide 6.11CE164 - 2024 F. Sepulveda - CSEE - Essex University
Transformers cannot increase the applied power.
If the secondary voltage is higher than the primary
voltage, then the secondary current must be lower
than the primary current and vice-versa.
pri
sec
I
n
I

The ideal transformer turns ratio equation for
current is
Notice that the primary
current is in the numerator.
Power Conservation &
Current
Slide 6.12CE164 - 2024 F. Sepulveda - CSEE - Essex University
The ideal transformer does not dissipate power.
Power delivered from the source is passed on to the
load by the transformer. This important idea can be
summarized as:
pri sec
pri pri sec sec
prisec
pri sec
P P
V I V I
IV
V I


 These last ratios are, of
course, the turns ratio, n.
Power
Slide 6.13CE164 - 2024 F. Sepulveda - CSEE - Essex University
A transformer changes both the voltage and
current on the primary side to different values
on the secondary side. This makes a load
resistance (RL) appear to have a different
value (Rpri) on the primary side.
RL
If you “look” into the primary side of the circuit, you see an
effective load that is changed by the reciprocal of the turns
ratio squared.
You see the primary
side resistance, so the
load resistance is
effectively changed.
RL
Reflected resistance
Slide 6.14CE164 - 2024 F. Sepulveda - CSEE - Essex University
From Ohm’s law,
Reflected resistance
and
pri sec
pri L
pri sec
V V
R R
I I
 
Taking the ratio of Rpri to RL,
2
1 1 1
=
pri pri sec
L sec pri
R V I
R V I n n n
                 
RL
Rpri
The resistance “seen” on the primary side is called the reflected resistance:
2
1
pri LR R
n
   
 
Slide 6.15CE164 - 2024 F. Sepulveda - CSEE - Essex University
To match a load resistance to the internal source resistance
(and hence transfer maximum power to the load), a special
impedance matching transformer is used so that*
Impedance matching
RL
Rint
Vs
Impedance matching
transformers are designed
for a wider range of
frequencies than power
transformers, and hence
tend to be non-ideal. Impedance
matching
transformer
* Caution: Rint is not usually the same as Rpri but their values
will be the same when the impedances are matched
Rint = Rpri
primary internal
resistance
Slide 6.16CE164 - 2024 F. Sepulveda - CSEE - Essex University
Centre tap (CT)
nA = n/2
nB = n/2
Slide 6.17CE164 - 2024 F. Sepulveda - CSEE - Essex University
An ideal transformer has no power loss; all power applied to the primary is
all delivered to the load. Actual transformers depart from this ideal model.
Some loss mechanisms are:
Winding resistance causing power to be dissipated in the windings.
Hysteresis loss due to the continuous reversal of the magnetic field.
Core losses due to circulating current in the core (eddy currents).
Flux leakage from the primary that does not link to the secondary
Winding capacitance that has a bypassing effect for the windings.
Core saturation: maximum magnetic flow is reached.
Non-ideal transformers
1:1
Slide 6.18CE164 - 2024 F. Sepulveda - CSEE - Essex University
Transformer efficiency
100%out
in
P
P

 
  
 
The efficiency of a transformer is the ratio of power delivered to the
load (Pout) to the power delivered to the primary (Pin), i.e.:
What is the efficiency of the transformer below?
120 Vrms
Vpri RL
100 W15 Vrms
20 mA
100%out
in
P
P

 
  
        
2
215 V
100 100% 100% 94%
120 V 0.020 A
L
L
pri pri
V
R
V I
     W           
Slide 6.19CE164 - 2024 F. Sepulveda - CSEE - Essex University
AC/DC
Power Supplies
Reading:
Continue Ch. 15, Floyd & Buchla (2014, 8th ed.)
Slide 6.20CE164 - 2024 F. Sepulveda - CSEE - Essex University
The model you will use depends on your requirements.
Diode models (from CE163)
The ideal model assumes the diode is
either an open or closed switch.
VR VF
IF
IR
Reverse
bias
Forward
bias
0.7 V
The practical model includes the
barrier voltage in the approximation.
VR VF
IF
IR
Reverse
bias
Forward
bias
0.7 V
The complete model includes the
forward and reverse resistances
VR VF
IF
IR
Reverse
bias
Forward
bias
0.7 V
used for rough estimates, and in circuits with
large voltages (e.g., > 60V) and medium and
large resistances (e.g., > 500 Ohm)
used in circuits with small to medium voltages
(e.g., < 60V) and medium and large resistances
used in circuits with small to medium voltages (e.g.,
< 60V) and low resistances (e.g., <500 Ohm)
Slide 6.21CE164 - 2024 F. Sepulveda - CSEE - Essex University
Rectifiers are circuits that convert AC to DC. Special diodes, called
rectifier diodes, are designed to handle the higher current
requirements in these circuits.
Half-wave (or half-cycle) Rectifier
Vp(out) = Vp(in) – 0.7V
Overall
output
The half-wave rectifier
converts AC to
pulsating DC by acting
as a closed switch
during the positive
alteration.
D
R
L
+ -
Forward bias
V
in
V
out
The diode acts as an
open switch during the
negative alteration.
D
R
L
- +
Reverse bias
V
in
V
outX
Slide 6.22CE164 - 2024 F. Sepulveda - CSEE - Essex University
The full-wave rectifier allows unidirectional current on
both alterations of the input. The center-tapped full-wave
rectifier uses two diodes and a center-tapped transformer.
F D1
D2
R
L
V
sec
2
V
sec
2
V on each side of the center-tap is ½ of the total
secondary voltage. Only one diode will be forward biased
at a time as the two CT branches are 180o out of phase.
Full-wave Rectifier
V
out
(across RL)
Slide 6.23CE164 - 2024 F. Sepulveda - CSEE - Essex University
The bridge rectifier is a type of full-wave circuit that uses
four diodes. The bridge rectifier does not require a
center-tapped transformer.
F
D1
D2
R
L
At any instant, two of the diodes are conducting and
two are off.
D3
D4
Bridge Rectifier
V
out
(across RL)
Slide 6.24CE164 - 2024 F. Sepulveda - CSEE - Essex University
Power supplies
Basic DC power supply
Regulator: a circuit that maintains a constant DC voltage even
under variations on the input voltage or in the load.
Slide 6.25CE164 - 2024 F. Sepulveda - CSEE - Essex University
Vin
Vout
Slide 6.26CE164 - 2024 F. Sepulveda - CSEE - Essex University
Power supplies: Filtering
Vin
Vout
Vout
Slide 6.27CE164 - 2024 F. Sepulveda - CSEE - Essex University
Power supplies: post-filter ripple
Fig 16.42 & 16.43
Ripple factor r = (Vr / VDC ) 100%
Slide 6.28CE164 - 2024 F. Sepulveda - CSEE - Essex University
By adding a filter and regulator to the basic rectifier, a basic power
supply is formed.
Typically, a large electrolytic capacitor is used as a filter before
the regulator, with a smaller one following the regulator to
complete filtering action.
Power supplies: Voltage regulation
ideal
regulation
V regulation
Slide 6.29CE164 - 2024 F. Sepulveda - CSEE - Essex University
AC/DC Power Supply Lab
Basic DC power supply
Weeks 21 & 22 Weeks 23 & 24