Special transformers and applications
Because transformers can step voltage and
current to different levels, and because power is transferred
equivalently between primary and secondary windings, they can be used to
"convert" the impedance of a load to a different level. That last phrase
deserves some explanation, so let's investigate what it means.
The purpose of a load (usually) is to do
something productive with the power it dissipates. In the case of a
resistive heating element, the practical purpose for the power
dissipated is to heat something up. Loads are engineered to safely
dissipate a certain maximum amount of power, but two loads of equal
power rating are not necessarily identical. Consider these two 1000 watt
resistive heating elements:
Both heaters dissipate exactly 1000 watts
of power, but they do so at different voltage and current levels (either
250 volts and 4 amps, or 125 volts and 8 amps). Using Ohm's Law to
determine the necessary resistance of these heating elements (R=E/I), we
arrive at figures of 62.5 Ω and 15.625 Ω, respectively. If these are AC
loads, we might refer to their opposition to current in terms of
impedance rather than plain resistance, although in this case that's all
they're composed of (no reactance). The 250 volt heater would be said to
be a higher impedance load than the 125 volt heater.
If we desired to operate the 250 volt
heater element directly on a 125 volt power system, we would end up
being disappointed. With 62.5 Ω of impedance (resistance), the current
would only be 2 amps (I=E/R; 125/62.5), and the power dissipation would
only be 250 watts (P=IE; 125 x 2), or one-quarter of its rated power.
The impedance of the heater and the voltage of our source would be
mismatched, and we couldn't obtain the full rated power dissipation from
the heater.
All hope is not lost, though. With a
step-up transformer, we could operate the 250 volt heater element on the
125 volt power system like this:
The ratio of the transformer's windings
provides the voltage step-up and current step-down we need for
the otherwise mismatched load to operate properly on this system. Take a
close look at the primary circuit figures: 125 volts at 8 amps. As far
as the power supply "knows," it's powering a 15.625 Ω (R=E/I) load at
125 volts, not a 62.5 Ω load! The voltage and current figures for the
primary winding are indicative of 15.625 Ω load impedance, not the
actual 62.5 Ω of the load itself. In other words, not only has our
step-up transformer transformed voltage and current, but it has
transformed impedance as well.
The transformation ratio of impedance is
the square of the voltage/current transformation ratio, the same as the
winding inductance ratio:
This concurs with our example of the 2:1
step-up transformer and the impedance ratio of 62.5 Ω to 15.625 Ω (a 4:1
ratio, which is 2:1 squared). Impedance transformation is a highly
useful ability of transformers, for it allows a load to dissipate its
full rated power even if the power system is not at the proper voltage
to directly do so.
Recall from our study of network analysis
the Maximum Power Transfer Theorem, which states that the maximum
amount of power will be dissipated by a load resistance when that load
resistance is equal to the Thevenin/Norton resistance of the network
supplying the power. Substitute the word "impedance" for "resistance" in
that definition and you have the AC version of that Theorem. If we're
trying to obtain theoretical maximum power dissipation from a load, we
must be able to properly match the load impedance and source (Thevenin/Norton)
impedance together. This is generally more of a concern in specialized
electric circuits such as radio transmitter/antenna and audio
amplifier/speaker systems. Let's take an audio amplifier system and see
how it works:
With an internal impedance of 500 Ω, the
amplifier can only deliver full power to a load (speaker) also having
500 Ω of impedance. Such a load would drop higher voltage and draw less
current than an 8 Ω speaker dissipating the same amount of power. If an
8 Ω speaker were connected directly to the 500 Ω amplifier as shown, the
impedance mismatch would result in very poor (low peak power)
performance. Additionally, the amplifier would tend to dissipate more
than its fair share of power in the form of heat trying to drive the low
impedance speaker.
To make this system work better, we can
use a transformer to match these mismatched impedances. Since we're
going from a high impedance (high voltage, low current) supply to a low
impedance (low voltage, high current) load, we'll need to use a
step-down transformer:
To obtain an impedance transformation
ratio of 500:8, we would need a winding ratio equal to the square root
of 500:8 (the square root of 62.5:1, or 7.906:1). With such a
transformer in place, the speaker will load the amplifier to just the
right degree, drawing power at the correct voltage and current levels to
satisfy the Maximum Power Transfer Theorem and make for the most
efficient power delivery to the load. The use of a transformer in this
capacity is called impedance matching.
Anyone who has ridden a multi-speed
bicycle can intuitively understand the principle of impedance matching.
A human's legs will produce maximum power when spinning the bicycle
crank at a particular speed (about 60 to 90 revolution per minute).
Above or below that rotational speed, human leg muscles are less
efficient at generating power. The purpose of the bicycle's "gears" is
to impedance-match the rider's legs to the riding conditions so that
they always spin the crank at the optimum speed.
If the rider attempts to start moving
while the bicycle is shifted into its "top" gear, he or she will find it
very difficult to get moving. Is it because the rider is weak? No, it's
because the high step-up ratio of the bicycle's chain and sprockets in
that top gear presents a mismatch between the conditions (lots of
inertia to overcome) and their legs (needing to spin at 60-90 RPM for
maximum power output). On the other hand, selecting a gear that is too
low will enable the rider to get moving immediately, but limit the top
speed they will be able to attain. Again, is the lack of speed an
indication of weakness in the bicyclist's legs? No, it's because the
lower speed ratio of the selected gear creates another type of mismatch
between the conditions (low load) and the rider's legs (losing power if
spinning faster than 90 RPM). It is much the same with electric power
sources and loads: there must be an impedance match for maximum system
efficiency. In AC circuits, transformers perform the same matching
function as the sprockets and chain ("gears") on a bicycle to match
otherwise mismatched sources and loads.
Impedance matching transformers are not
fundamentally different from any other type of transformer in
construction or appearance. A small impedance-matching transformer
(about two centimeters in width) for audio-frequency applications is
shown in the following photograph:
Another impedance-matching transformer
can be seen on this printed circuit board, in the upper right corner, to
the immediate left of resistors R2 and R1. It is
labeled "T1":
Transformers can also be used in
electrical instrumentation systems. Due to transformers' ability to step
up or step down voltage and current, and the electrical isolation they
provide, they can serve as a way of connecting electrical
instrumentation to high-voltage, high current power systems. Suppose we
wanted to accurately measure the voltage of a 13.8 kV power system (a
very common power distribution voltage in American industry):
Designing, installing, and maintaining a
voltmeter capable of directly measuring 13,800 volts AC would be no easy
task. The safety hazard alone of bringing 13.8 kV conductors into an
instrument panel would be severe, not to mention the design of the
voltmeter itself. However, by using a precision step-down transformer,
we can reduce the 13.8 kV down to a safe level of voltage at a constant
ratio, and isolate it from the instrument connections, adding an
additional level of safety to the metering system:
Now the voltmeter reads a precise
fraction, or ratio, of the actual system voltage, its scale set to read
as though it were measuring the voltage directly. The transformer keeps
the instrument voltage at a safe level and electrically isolates it from
the power system, so there is no direct connection between the power
lines and the instrument or instrument wiring. When used in this
capacity, the transformer is called a Potential Transformer, or
simply PT.
Potential transformers are designed to
provide as accurate a voltage step-down ratio as possible. To aid in
precise voltage regulation, loading is kept to a minimum: the voltmeter
is made to have high input impedance so as to draw as little current
from the PT as possible. As you can see, a fuse has been connected in
series with the PTs primary winding, for safety and ease of
disconnecting the PT from the circuit.
A standard secondary voltage for a PT is
120 volts AC, for full-rated power line voltage. The standard voltmeter
range to accompany a PT is 150 volts, full-scale. PTs with custom
winding ratios can be manufactured to suit any application. This lends
itself well to industry standardization of the actual voltmeter
instruments themselves, since the PT will be sized to step the system
voltage down to this standard instrument level.
Following the same line of thinking, we
can use a transformer to step down current through a power line so that
we are able to safely and easily measure high system currents with
inexpensive ammeters. Of course, such a transformer would be connected
in series with the power line, like this:
Note that while the PT is a step-down
device, the Current Transformer (or CT) is a step-up
device (with respect to voltage), which is what is needed to step
down the power line current. Quite often, CTs are built as
donut-shaped devices through which the power line conductor is run, the
power line itself acting as a single-turn primary winding:
Some CTs are made to hinge open, allowing
insertion around a power conductor without disturbing the conductor at
all. The industry standard secondary current for a CT is a range of 0 to
5 amps AC. Like PTs, CTs can be made with custom winding ratios to fit
almost any application. Because their "full load" secondary current is 5
amps, CT ratios are usually described in terms of full-load primary amps
to 5 amps, like this:
The "donut" CT shown in the photograph
has a ratio of 50:5. That is, when the conductor through the center of
the torus is carrying 50 amps of current (AC), there will be 5 amps of
current induced in the CT's winding.
Because CTs are designed to be powering
ammeters, which are low-impedance loads, and they are wound as voltage
step-up transformers, they should never, ever be operated with an
open-circuited secondary winding. Failure to heed this warning will
result in the CT producing extremely high secondary voltages, dangerous
to equipment and personnel alike. To facilitate maintenance of ammeter
instrumentation, short-circuiting switches are often installed in
parallel with the CT's secondary winding, to be closed whenever the
ammeter is removed for service:
Though it may seem strange to
intentionally short-circuit a power system component, it is
perfectly proper and quite necessary when working with current
transformers.
Another kind of special transformer, seen
often in radio-frequency circuits, is the air core transformer.
True to its name, an air core transformer has its windings wrapped
around a nonmagnetic form, usually a hollow tube of some material. The
degree of coupling (mutual inductance) between windings in such a
transformer is many times less than that of an equivalent iron-core
transformer, but the undesirable characteristics of a ferromagnetic core
(eddy current losses, hysteresis, saturation, etc.) are completely
eliminated. It is in high-frequency applications that these effects of
iron cores are most problematic.
One notable example of air-core
transformer is the Tesla Coil, named after the Serbian electrical
genius Nikola Tesla, who was also the inventor of the rotating magnetic
field AC motor, polyphase AC power systems, and many elements of radio
technology. The Tesla Coil is a resonant, high-frequency step-up
transformer used to produce high voltages that are relatively harmless
to human beings (the "skin effect" of high-frequency alternating current
precluding electric shock, although capable of producing skin burns).
One of Tesla's dreams was to employ his coil technology to distribute
electric power without the need for wires, simply broadcasting it in the
form of radio waves which could be received and conducted to loads by
means of antennas. The basic schematic for a Tesla Coil looks like this:
The capacitor in parallel with the
transformer's primary winding forms the tank circuit needed for
resonance. The secondary winding is wound in close proximity to the
primary, usually around the same nonmagnetic form. Several options exist
for "exciting" the primary circuit, the simplest being a high-voltage,
low-frequency AC source and spark gap:
With each cycle peak of the high-voltage
AC source, the current will jump across the spark gap, briefly
energizing the tank circuit. The tank circuit, tuned for a resonant
frequency far in excess of the AC source, will oscillate for many cycles
before the next cycle peak of the source, when it will receive another
"kick" to keep the oscillations going. The secondary of the Tesla Coil
will output a fairly constant high voltage at very high frequencies,
usually producing a spark discharge into the surrounding air at the
discharge terminal.
Tesla Coils find application primarily as
novelty devices, showing up in high school science fairs, basement
workshops, and the occasional low budget science-fiction movie.
So far, we've explored the transformer as
a device for converting different levels of voltage, current, and even
impedance from one circuit to another. Now we'll take a look at it as a
completely different kind of device: one that allows a small electrical
signal to exert control over a much larger quantity of electrical
power. In this mode, a transformer acts as an amplifier.
The device I'm referring to is called a
saturable-core reactor, or simply saturable reactor.
Actually, it is not really a transformer at all, but rather a special
kind of inductor whose inductance can be varied by the application of a
DC current through a second winding wound around the same iron core.
Like the ferroresonant transformer, the saturable reactor relies on the
principle of magnetic saturation. When a material such as iron is
completely saturated (that is, all its magnetic domains are lined up
with the applied magnetizing force), additional increases in current
through the magnetizing winding will not result in further increases of
magnetic flux.
Now, inductance is the measure of how
well an inductor opposes changes in current by developing a voltage in
an opposing direction. The ability of an inductor to generate this
opposing voltage is directly connected with the change in magnetic flux
inside the inductor resulting from the change in current, and the number
of winding turns in the inductor. If an inductor has a saturated core,
no further magnetic flux will result from further increases in current,
and so there will be no voltage induced in opposition to the change in
current. In other words, an inductor loses its inductance (ability to
oppose changes in current) when its core becomes magnetically saturated.
If an inductor's inductance changes, then
its reactance (and impedance) to AC current changes as well. In a
circuit with a constant voltage source, this will result in a change in
current:
A saturable reactor capitalizes on this
effect by forcing the core into a state of saturation with a strong
magnetic field generated by current through another winding. The
reactor's "power" winding is the one carrying the AC load current, and
the "control" winding is one carrying a DC current strong enough to
drive the core into saturation:
The strange-looking transformer symbol
shown in the above schematic represents a saturable-core reactor, the
upper winding being the DC control winding and the lower being the
"power" winding through which the controlled AC current goes. Increased
DC control current produces more magnetic flux in the reactor core,
driving it closer to a condition of saturation, thus decreasing the
power winding's inductance, decreasing its impedance, and increasing
current to the load. Thus, the DC control current is able to exert
control over the AC current delivered to the load.
The circuit shown would work, but it
would not work very well. The first problem is the natural transformer
action of the saturable reactor: AC current through the power winding
will induce a voltage in the control winding, which may cause trouble
for the DC power source. Also, saturable reactors tend to regulate AC
power only in one direction: in one half of the AC cycle, the mmf's from
both windings add; in the other half, they subtract. Thus, the core will
have more flux in it during one half of the AC cycle than the other, and
will saturate first in that cycle half, passing load current more easily
in one direction than the other. Fortunately, both problems can be
overcome with a little ingenuity:
Notice the placement of the phasing dots
on the two reactors: the power windings are "in phase" while the control
windings are "out of phase." If both reactors are identical, any voltage
induced in the control windings by load current through the power
windings will cancel out to zero at the battery terminals, thus
eliminating the first problem mentioned. Furthermore, since the DC
control current through both reactors produces magnetic fluxes in
different directions through the reactor cores, one reactor will
saturate more in one cycle of the AC power while the other reactor will
saturate more in the other, thus equalizing the control action through
each half-cycle so that the AC power is "throttled" symmetrically. This
phasing of control windings can be accomplished with two separate
reactors as shown, or in a single reactor design with intelligent layout
of the windings and core.
Saturable reactor technology has even
been miniaturized to the circuit-board level in compact packages more
generally known as magnetic amplifiers. I personally find this to
be fascinating: the effect of amplification (one electrical signal
controlling another), normally requiring the use of physically fragile
vacuum tubes or electrically "fragile" semiconductor devices, can be
realized in a device both physically and electrically rugged. Magnetic
amplifiers do have disadvantages over their more fragile counterparts,
namely size, weight, nonlinearity, and bandwidth (frequency response),
but their utter simplicity still commands a certain degree of
appreciation, if not practical application.
Saturable-core reactors are less commonly
known as "saturable-core inductors" or transductors.
- REVIEW:
- Transformers can be used to transform
impedance as well as voltage and current. When this is done to improve
power transfer to a load, it is called impedance matching.
- A Potential Transformer (PT) is
a special instrument transformer designed to provide a precise voltage
step-down ratio for voltmeters measuring high power system voltages.
- A Current Transformer (CT) is
another special instrument transformer designed to step down the
current through a power line to a safe level for an ammeter to
measure.
- An air-core transformer is one
lacking a ferromagnetic core.
- A Tesla Coil is a resonant,
air-core, step-up transformer designed to produce very high AC
voltages at high frequency.
- A saturable reactor is a
special type of inductor, the inductance of which can be controlled by
the DC current through a second winding around the same core. With
enough DC current, the magnetic core can be saturated, decreasing the
inductance of the power winding in a controlled fashion.
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