Step-up and step-down transformers
So far, we've observed simulations of
transformers where the primary and secondary windings were of identical
inductance, giving approximately equal voltage and current levels in
both circuits. Equality of voltage and current between the primary and
secondary sides of a transformer, however, is not the norm for all
transformers. If the inductances of the two windings are not equal,
something interesting happens:
transformer
v1 1 0 ac 10 sin
rbogus1 1 2 1e-12
rbogus2 5 0 9e12
l1 2 0 10000
l2 3 5 100
k l1 l2 0.999
vi1 3 4 ac 0
rload 4 5 1k
.ac lin 1 60 60
.print ac v(2,0) i(v1)
.print ac v(3,5) i(vi1)
.end
freq v(2) i(v1)
6.000E+01 1.000E+01 9.975E-05 Primary winding
freq v(3,5) i(vi1)
6.000E+01 9.962E-01 9.962E-04 Secondary winding
Notice how the secondary voltage is
approximately ten times less than the primary voltage (0.9962 volts
compared to 10 volts), while the secondary current is approximately ten
times greater (0.9962 mA compared to 0.09975 mA). What we have here is a
device that steps voltage down by a factor of ten and current
up by a factor of ten:
This is a very useful device, indeed.
With it, we can easily multiply or divide voltage and current in AC
circuits. Indeed, the transformer has made long-distance transmission of
electric power a practical reality, as AC voltage can be "stepped up"
and current "stepped down" for reduced wire resistance power losses
along power lines connecting generating stations with loads. At either
end (both the generator and at the loads), voltage levels are reduced by
transformers for safer operation and less expensive equipment. A
transformer that increases voltage from primary to secondary (more
secondary winding turns than primary winding turns) is called a
step-up transformer. Conversely, a transformer designed to do just
the opposite is called a step-down transformer.
Let's re-examine a photograph shown in
the previous section:
This is a step-down transformer, as
evidenced by the high turn count of the primary winding and the low turn
count of the secondary. As a step-down unit, this transformer converts
high-voltage, low-current power into low-voltage, high-current power.
The larger-gauge wire used in the secondary winding is necessary due to
the increase in current. The primary winding, which doesn't have to
conduct as much current, may be made of smaller-gauge wire.
In case you were wondering, it is
possible to operate either of these transformer types backwards
(powering the secondary winding with an AC source and letting the
primary winding power a load) to perform the opposite function: a
step-up can function as a step-down and visa-versa. However, as we saw
in the first section of this chapter, efficient operation of a
transformer requires that the individual winding inductances be
engineered for specific operating ranges of voltage and current, so if a
transformer is to be used "backwards" like this it must be employed
within the original design parameters of voltage and current for each
winding, lest it prove to be inefficient (or lest it be damaged
by excessive voltage or current!).
Transformers are often constructed in
such a way that it is not obvious which wires lead to the primary
winding and which lead to the secondary. One convention used in the
electric power industry to help alleviate confusion is the use of "H"
designations for the higher-voltage winding (the primary winding in a
step-down unit; the secondary winding in a step-up) and "X" designations
for the lower-voltage winding. Therefore, a simple power transformer
will have wires labeled "H1", "H2", "X1",
and "X2". There is usually significance to the numbering of
the wires (H1 versus H2, etc.), which we'll
explore a little later in this chapter.
The fact that voltage and current get
"stepped" in opposite directions (one up, the other down) makes perfect
sense when you recall that power is equal to voltage times current, and
realize that transformers cannot produce power, only convert it.
Any device that could output more power than it took in would violate
the Law of Energy Conservation in physics, namely that energy
cannot be created or destroyed, only converted. As with the first
transformer example we looked at, power transfer efficiency is very good
from the primary to the secondary sides of the device.
The practical significance of this is
made more apparent when an alternative is considered: before the advent
of efficient transformers, voltage/current level conversion could only
be achieved through the use of motor/generator sets. A drawing of a
motor/generator set reveals the basic principle involved:
In such a machine, a motor is
mechanically coupled to a generator, the generator designed to produce
the desired levels of voltage and current at the rotating speed of the
motor. While both motors and generators are fairly efficient devices,
the use of both in this fashion compounds their inefficiencies so that
the overall efficiency is in the range of 90% or less. Furthermore,
because motor/generator sets obviously require moving parts, mechanical
wear and balance are factors influencing both service life and
performance. Transformers, on the other hand, are able to convert levels
of AC voltage and current at very high efficiencies with no moving
parts, making possible the widespread distribution and use of electric
power we take for granted.
In all fairness it should be noted that
motor/generator sets have not necessarily been obsoleted by transformers
for all applications. While transformers are clearly superior
over motor/generator sets for AC voltage and current level conversion,
they cannot convert one frequency of AC power to another, or (by
themselves) convert DC to AC or visa-versa. Motor/generator sets can do
all these things with relative simplicity, albeit with the limitations
of efficiency and mechanical factors already described. Motor/generator
sets also have the unique property of kinetic energy storage: that is,
if the motor's power supply is momentarily interrupted for any reason,
its angular momentum (the inertia of that rotating mass) will maintain
rotation of the generator for a short duration, thus isolating any loads
powered by the generator from "glitches" in the main power system.
Looking closely at the numbers in the
SPICE analysis, we should see a correspondence between the transformer's
ratio and the two inductances. Notice how the primary inductor (l1) has
100 times more inductance than the secondary inductor (10000 H versus
100 H), and that the measured voltage step-down ratio was 10 to 1. The
winding with more inductance will have higher voltage and less current
than the other. Since the two inductors are wound around the same core
material in the transformer (for the most efficient magnetic coupling
between the two), the parameters affecting inductance for the two coils
are equal except for the number of turns in each coil. If we take
another look at our inductance formula, we see that inductance is
proportional to the square of the number of coil turns:
So, it should be apparent that our two
inductors in the last SPICE transformer example circuit -- with
inductance ratios of 100:1 -- should have coil turn ratios of 10:1,
because 10 squared equals 100. This works out to be the same ratio we
found between primary and secondary voltages and currents (10:1), so we
can say as a rule that the voltage and current transformation ratio is
equal to the ratio of winding turns between primary and secondary.
The step-up/step-down effect of coil turn
ratios in a transformer is analogous to gear tooth ratios in mechanical
gear systems, transforming values of speed and torque in much the same
way:
Step-up and step-down transformers for
power distribution purposes can be gigantic in proportion to the power
transformers previously shown, some units standing as tall as a home.
The following photograph shows a substation transformer standing about
twelve feet tall:
- REVIEW:
- Transformers "step up" or "step down"
voltage according to the ratios of primary to secondary wire turns.
-
- A transformer designed to increase
voltage from primary to secondary is called a step-up
transformer. A transformer designed to reduce voltage from primary to
secondary is called a step-down transformer.
- The transformation ratio of a
transformer will be equal to the square root of its primary to
secondary inductance (L) ratio.
-
|
