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Elliott Sound Products Beginners' Guide to Transformers - Part 2
Transformers - The Basics (Section 2)
Copyright 2001 - Rod Elliott (ESP)Page Updated April 2015
Articles IndexMain Index
Contents - Section 2Section 1Introduction8. Windings in Series
and Parallel
8.1 Series Connections8.2 Parallel Connections
9. Valve Output Transformer Example10. Compromises11. Losses
11.1 Iron Losses11.2 Copper Losses
11.2.1 Current Density11.2.2 Skin & Proximity Effect
11.3 Regulation11.4 Other Losses11.5 Temperature Classes11.6
Voltage & Frequency
12. Sample Measurements12.1 Magnetising Current Waveforms12.2
Inrush Current12.3 Inductance
13. Core Styles13.1 Air Gaps
14 Core Materials15 Distortion16 Reusing Transformers17 Current
Transformers18 DC In Transformer Windings19
AutotransformersReferencesUnitsMagnetic TerminologySection 3
IntroductionFor those brave souls who have ploughed their way
through the first section - I commend you! As you have discovered,
transformers are not simple after all, but they areprobably far
more versatile than you ever imagined. They are, however, real
world devices, and as such are prey to the failings of all real
components - they areimperfect.This section will concentrate a
little more on the losses and calculations involved in transformer
design, as well as explain in more detail where different core
styles are tobe preferred over others. Again, it is impossible to
cover all the possibilities, but the information here will get you
well on your way to a full understanding of the subject.The first
topic may seem obvious, but based on the e-mails I get, this is not
the case. Transformers can have multiple windings, and these can be
on the primary orsecondary. Windings can be interconnected to do
exciting and different things, but from a safety perspective it is
imperative that primary and secondary windings arekept
segregated.There are several references to 'shorted turns' within
this article. If any two turns of a winding short to each other,
the current flow is limited only by the DC resistance ofthe shorted
section of the winding. The current flow can be enormous, and with
even one shorted turn, the transformer is no longer serviceable and
must be discarded orrewound. No shield or other conductive material
may be wrapped around the winding and joined, as this creates a
shorted turn capable of possibly hundreds of amperes.The exception
to this is the magnetic shield sometimes used with E-I laminated
transformers, but this is wrapped around the entire transformer
(outside the core), and isnot considered as a 'turn' as it is not
in the winding window with the primary and secondary.It is also
worth noting that a transformer behaves quite differently depending
upon whether it is driven from a voltage source (i.e. very low
impedance, such as a transistoramp or the mains) or a current
source or intermediate impedance. This will be covered in a little
more detail further on in this article.Three things that you need
to keep in mind - always ...
Core flux is at maximum when a transformer has no load. [See
Note]1. A transformer wound for 50Hz operation can safely be used
at 60Hz (with the correct or even slightly higher voltage).2. A
60Hz transformer will draw excessive magnetising current at 50Hz,
and may fail due to overheating.3. Note: This is the practical
case, assuming normal usage of the transformer. A theoretical
'ideal' transformer having zero winding resistance will have
constant flux, regardlessof load - provided the input voltage is
constant. Since the real world has real-world transformers, the
flux decreases slightly with load due to the voltage lost across
thetransformer's primary winding. This is explained in more detail
below.
Before reusing any transformer - especially if designed for a
different purpose, voltage or frequency - you need to check that it
will not draw excessive magnetisingcurrent. Worst case is with no
load, and the current should be measured and the temperature
monitored for long enough to be certain that the transformer does
not get sohot that it's uncomfortable to hold. If the idle
temperature rise is more than about 25C the transformer should not
be used. Bear in mind that some small transformers runrather hot
all the time, so on occasion you may have to make a value judgement
based on experience.
8. Windings in Series and ParallelMany transformers are supplied
with two (or more) secondaries. In many cases, the data sheet will
indicate that the windings may be connected in parallel or series.
Forexample, a toroidal transformer may be rated at 2 x 25V at 5A
(250VA). With the windings in parallel, the available current is
10A, but only for a single voltage of 25V AC.
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Connect the windings in series, and you get 50V at 5A, or by
referencing the centre tap to earth, the familiar 25-0-25
designation.
Figure 8.1 - Windings in Series and ParallelThere are some rules
that apply to winding interconnections - if you break them, you may
break your transformer as well. Note the dots on the windings -
this is thetraditional way to identify the start of a winding, so
that the phase may be determined.Autotransformers are covered in
Section 19 below. These are a special case of windings in series,
and are commonly used to obtain a reduced voltage with the
highestpossible efficiency and lowest cost.Antiphase wiring will
not harm a transformer when wired in series (although the zero
volts output for equal windings is somewhat limited in usefulness).
Parallel antiphaseconnection will destroy the transformer unless
the fuse blows - which it will do mightily. Always use a fuse when
testing, as a simple mistake can be rather costly withoutsome form
of protection for the transformer and house wiring!
8.1 Series ConnectionsWindings may be connected in series
regardless of voltage. The maximum current available is the rating
specified for the lowest current winding. Windings may beconnected
so as to increase or decrease the final voltage. For example, dual
25V windings may be connected so as to produce 50V or zero volts -
although the latter isnot generally useful :-)When windings are
connected in phase the voltages add together, and if connected out
of phase, they subtract. A 50V, 1 amp winding and a 10V 5 amp
winding maytherefore be connected to provide any of the following
...
10V @ 5A - The 10V winding by itself50V @ 1A - The 50V winding
by itself60V @ 1A - Both 50V and 10V windings, connected in series
and in phase40V @ 1A - Both 50V and 10V windings, connected in
series and out of phase
The above example was used purely for the sake of example (such
a transformer would not be useful for most of us), but the
principle applies for all voltages andcurrents. Series connections
are sometimes used in the primaries as well, mainly for equipment
destined for the world market. There are several common mains
supplyvoltages, and primary windings are connected in various
combinations of series and parallel to accommodate all the
variants.
8.2 Parallel ConnectionsParallel connection of transformer
windings is permitted in one case only - the windings must have
exactly the same voltage output, and must be connected in
phase.Different current capacities are not a problem, but it is
rare to find a transformer with two windings of the same voltage
but different current ratings.Even a 1V difference between winding
voltages will cause big problems. A typical winding resistance for
a 5A winding might be 0.25 ohm. Should two such windings
beconnected in parallel, having a voltage difference of 1V, there
will be a circulating current limited only by the resistances of
the windings. For our example, the totalwinding resistance is 0.5
ohm, so a circulating current of 2A will flow between the windings,
and this is completely wasted power. The transformer will get
unexpectedlyhot, and the maximum current available is reduced by
the value of the circulating current.Should the windings be
connected out of phase, the circulating current will be possibly
100A or more, until the transformer melts or the fuse blows. The
latter is generallyto be preferred.The transformer manufacturer's
specifications will indicate if parallel operation is permitted. If
you are unsure, measure the voltages carefully, and avoid
parallelconnection if the voltages differ by more than a couple of
hundred millivolts. There will always be a difference, and only the
manufacturer's winding tolerances can predictwhat it will be. With
toroidal transformers, the windings are often bifilar, meaning that
the two windings are wound onto the transformer core
simultaneously. The toleranceof such windings is normally very
good, and should cause no problems.
9. Valve Output Transformer Example CalculationIn Section 1, I
described a very basic push-pull valve output stage. Now it is time
to examine this a little more closely. We shall use the same
voltages as were obtained inthe basic description of Section 1 - an
RMS voltage of 707V. It must be said that the following is not
intended to be an accurate representation of valves, as the losses
inreal life are somewhat higher than indicated here. This is for
example only. We shall also take the (typical) losses as 10%, and
adjust the secondary impedanceaccordingly.A valve (tube) amplifier
is required to drive an 8 ohm loudspeaker. The primary impedance
(called the Plate-Plate impedance for a push-pull amplifier) is
6,000 Ohms, andthe supply voltage is 600V. Allowing for losses of
100V across each valve, the maximum voltage swing on the plates
(anodes) of the valves is 1kV p-p (or effectively 2kVpeak to peak
on the transformer primary). What is the output power?Secondary
impedance will be 7.2 ohms, based on the 10% loss ...
Zs = 8 / 1.1 = 7.2 ohmsThe impedance ratio is calculated first
...
Z = 6,000 / 7.2 = 833The turns ratio may now be determined
N = 833 = 28.8 (29:1)The voltage ratio is the same as the turns
ratio, so the peak to peak voltage to the speaker is
Vs (p-p) = Vp / N = 2,000 / 29 = 69VTo convert this to RMS
...
Vp = 1/2 Vp-p = 34.5VRMS = peak * 0.707 = 24VPower is therefore
24 / 8 = 72W
Notice that at each calculation, the figures were rounded to the
closest (or next lowest) whole number. This was for convenience,
but the way I did it also gives aconservative rating that is more
likely to be met in practice.
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Ouch! Sorry, that was a bit nasty for this time of day .A bit
nasty or not, it is a reasonable representation of the reality of
an output transformer design, but naturally real (as opposed to my
"invented" figures) will besubstituted. Typically the losses across
the output valves will often be far greater than indicated here.
but that depends on the valves used (and the topology -
triodesbehave very differently from pentodes or tetrodes).Just to
complete this section and to put the above into perspective, I have
included a few figures (taken from the 1972 Miniwatt Technical Data
manual) for the EL34/6CA7 power pentode - quite possibly the
world's all-time favourite output valve.Class Mode * Plate
VoltsPlateCurrent
ScreenVolts
ScreenCurrent
GridBias
LoadImpedance
PowerOutput
Comments
Class-A S-E 250 100 265 15 -13V 2,000 11W Plate supply = 265V,
THD** 10%Class-AB P-P 375 2 x 75 ##
2 x 95365 2 x 11.5
2 x 22.5-19V 3,400 (p-p) # 35W Cathode bias resistor 130 ohms,
common screen resistor, 470 ohms, THD 5%
Class-B P-P 775 2 x 252 x 91
400 2 x 3.02 x 19
-39V 11,000 (p-p) 100W Plate supply, 800V, THD 5%
Class-A(Triode)
S-E 375 70 - - -25V 3,000 6W Cathode bias resistor 370 ohms,
Screen tied to plate, 400V plate supply, THD 8%
Class-AB(Triode)
P-P 400 2 x 652 x 71
- - -28V 5,000 (p-p) 16W Screen tied to plate, Cathode bias
resistor 220 ohms, THD 3%Table 9.1 - Abbreviated Data For EL34
Power Pentode
* S-E: Single Ended, P-P: Push-Pull** THD - Total Harmonic
Distortion (this is for the valves only, and does not include
transformer distortion)# p-p: Plate to Plate impedance## First
figure is no load, second figure is full power
As can be seen quite readily, the distortion of the S-E
configurations is much worse than the push-pull versions. Not only
that, but (to maintain relevance :-) thetransformers are larger and
harder to design, and even then will be worse than their push-pull
counterparts. In the maximum efficiency configuration, power output
is100W, and distortion is still lower than for either of the single
ended configurations. The losses across the output valve in this
mode are about 58V, but are considerablyhigher for any of the
cathode biased versions - as one might expect.This will be
revisited in another article on the design of valve amplifiers.
10. CompromisesIt is very important that the core does not
saturate (see below), since there will be no continuous sinusoidal
variation of flux, greatly reduced back EMF, and excessivecurrent
will be drawn - especially at no load. The final design of any
transformer is a huge compromise, and there is a fine line between
a transformer that will giveacceptable regulation and one that gets
too hot to touch at no load.Somewhat surprisingly, the flux density
in the core actually decreases with increased load current drawn
from the secondary. Even though the primary is drawing morecurrent,
this is transferred to the secondary and thence the load - it does
not cause the flux density to increase. The flux density decreases
largely due to primaryresistance, which causes the effective
primary voltage to decrease. Any voltage lost to resistance
(remember Ohm's law?) is voltage that is "lost" to the transformer,
andserves no function in the transformation process. It does cause
the transformer to get hot (or hotter) than at no load. See the
next section for more details on this.Also, the normal variation of
mains voltage must be allowed for. A transformer running at the
very limit of saturation at nominal supply voltage will overheat if
the mains isat the upper (normal) limit. A transformer that is
designed to run at the limit will have superior regulation compared
to a more conservative design, but this is of littleconsequence if
it fails in normal use due to overheating.For audio transformers,
there are even more compromises.
11. LossesAs discussed earlier, a transformer is a real
component, and therefore has losses. These are divided into two
primary types, but there are other "hidden" losses as well.All
losses reduce efficiency, and affect frequency response. The low
frequency limit is determined by the primary inductance, and this
is proportional to the area (andconsequent mass) of the transformer
core. High frequency losses are caused by eddy currents in the core
(see below), and by leakage inductance and windingcapacitances.None
of these can be eliminated, but by careful selection of core
material, winding style and operational limits, they can be reduced
to the point where the transformer iscapable of doing the job
required of it.
11.1 Iron (Core) LossesCore losses are partly the result of the
magnetising current, which must keep forcing the magnetic field in
the core to reverse in sympathy with the applied signal.Because the
direction of flux is constantly changing, the transformer core is
subject to a phenomenon called hysteresis, shown in Figure 11.1
Figure 11.1 - The Hysteresis LoopWhen the magnetomotive force is
reversed in a magnetic material, the residual magnetism (remanence
- also known as remnance in some cases) in the core tries toremain
in its previous state until the applied flux is too great
(coercivity). It will then reverse, and the same situation will
occur twice for each cycle of applied AC. Thepower required to
force the flux to change direction is the hysteresis loss, which
although usually small, is still significant. I am not about to go
into great detail on this, buta Web search will no doubt reveal
more information than you will ever need.
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Figure 11.2 - B-H CurveAs can be seen from the two magnetic
field drawings, the flux density (B) is dependent upon the applied
magnetic field strength (H). For the example shown, the "knee"
ofthe curve coincides with the point where permeability starts to
fall. Above this, a progressively larger change in the magnetic
field is required to increase the flux density.This is saturation,
and most transformers will be designed to operate at or below the
knee. Above the knee is dangerous, as a small increase in applied
voltage will notproduce the required increase in back EMF, and the
primary current will increase disproportionately to the rise in
voltage. In other words, the transformer will be toosensitive to
applied voltage, and will possibly self destruct if the mains
voltage were even slightly higher than normal. If such a
transformer is wound for 60Hz but used at50Hz, failure is
inevitable.
Figure 11.3 - Cutaway View of a TransformerThe transformer shown
is a "split bobbin" type, having separate sections on the former
for the primary and secondary windings. This reduces the
capacitance betweenwindings, and also provides a safety barrier
between the primary and secondary. For some applications, this is
the only winding method that meets safety standards. It isalso very
simple to add an electrostatic shield between the windings - a flat
plate of thin metal is cut so that it can be slipped over the
bobbin, and the ends are insulatedso that it does not create a
shorted turn. This is connected to earth, and prevents noise from
being capacitively coupled between windings. The shield would
logically beplaced on the secondary side of the bobbin divider for
safety.In addition, there are so-called "eddy current" losses.
These are small circulating currents within the magnetic core, as
shown (exaggerated) in Figure 11.4, and thesecause the core
material itself to get hot. Each of these eddy current loops acts
as a tiny shorted turn to the transformer, and to reduce the
effect, the core is laminated -i.e. made from thin sheets of steel,
insulated from each other. The thinner the laminations, the smaller
are the eddy current losses, but they will never be eliminated.
Eddycurrent losses increase with frequency, requiring different
techniques for high frequency operation, and are the major
contributor to the iron losses in any transformer.
Figure 11.4 - Eddy Currents in LaminationsThe eddy currents are
shown for three lamination thicknesses. Although not shown (for the
sake of clarity), the current loops are constantly overlapping, and
areeffectively infinite in number. The thick laminations allow the
loops to be larger, and therefore the lamination section is cut by
more magnetic "lines" of force, so thecurrents (and losses) are
larger. For high frequencies (above 10kHz), it is generally not
possible to make laminations thin enough to prevent the losses from
becomingexcessive, and ferrite materials are preferred. These
effectively have a huge number of incredibly small magnetic
particles, all insulated from each other, and eddy currentloops are
very small indeed. Even so, ferrite materials are normally
specified up to a few hundred kilo-Hertz for power applications
before the losses become too greatagain.Iron losses of both types
are the primary source of losses in any transformer that is
operating at no load or only light loading. At no load, the core
flux density is at itsmaximum value for any given applied voltage /
frequency combination. Power transformers are usually designed to
operate below the knee of the saturation curve (this isessential
with toroidal types), with sufficient safety margin to ensure that
the core can never saturate.Saturation involves a dramatic loss of
permeability (and therefore inductance), and causes the primary
current to rise disproportionately to an increase of voltage.
Whereone would hope for a nice sinusoidal current waveform with low
distortion, significant current waveform distortion occurs once the
core starts to saturate.As a load is drawn from the secondary, the
primary must supply more current, and this means that the
resistance of the primary winding becomes significant. Any
voltage'lost' to winding resistance is effectively no longer part
of the applied voltage, so core flux is reduced.For example, if the
primary resistance is 5 ohms and the loaded primary current is 2A
at 230V, 10V is lost across the winding resistance, so the
effective primary voltageis reduced to 220V. This reduces the
magnetising current, but the effect is not linear. It depends a lot
on how close to saturation the core operates with no load, and
thedifference may be anything from minimal to significant,
depending on the design.
11.2 Copper LossesFollowing on from the previous point, the
voltage lost to winding resistance is copper loss, and all such
losses must be dissipated as heat. Consider the same transformeras
above at idle, with 230V on the primary. The primary resistance may
be in the order of 5 ohms (a transformer of around 300VA), and the
idle current perhaps 20mA.
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The loss is determined by the normal power formula, and in this
case is ...P = I * R = 0.02 * 5 = 2mWV = R * I = 5 * 0.02 =
100mV
For all intents and purposes, the full 230V is applied to the
primary. When the transformer is loaded, this changes. Let's assume
2A primary current and look at the figuresagain ...
P = I * R = 2.00 * 5 = 20WV = R * I = 5 * 1.00 = 10V
Now, the effective primary voltage is only 220V, because 10V is
'lost' due to winding resistance. Naturally, if the voltage is
lower, the flux density must also be lower. Thepower lost in the
primary must be dissipated as heat, so the transformer will start
to get hot. Remember that there will be additional losses in the
secondary that add to theheat that must be dissipated.Minimising
copper loss in both primary and secondary is essential, but there
are limits to what can be achieved. These are imposed by the
available space for thewinding, and just how much copper the
manufacturer can get into that space. Allowance must still be made
for insulation and manufacturing tolerances.You may see that in
Figure 11.3 the windings are shown stacked directly on top of each
other. Surely a more efficient winding can be made by making use of
the "valleys",minimising the winding height and allowing heavier
windings. Ah, if only life were that simple! The windings are
traditionally made from left to right, then right to left, so
theturns in each layer are at a slight angle relative to the layer
below or above. It is therefore not possible to utilise the
inter-turn winding valleys properly, and if you were towind a
transformer based on the erroneous assumption that this would work,
the finished winding would not fit into the window.For the normal
layered construction (i.e. primary closest to the core, and
secondary over the top), we also have to allow for insulation
between primary and secondary,and in some cases additional
insulation is used between layers of larger transformers because of
the large voltage difference between the outer limits of each
winding.These are another set of compromises that must be made, all
of which mean that the windings must be thinner than we might like,
and thus the losses are increased.Because any length of wire has
resistance, there will always be winding resistance. The greater
the resistance for a given current, the more power is dissipated as
heat -this is a complete loss. At no load (provided saturation is
avoided), there is virtually no loss, since the currents are low,
but as secondary current increases, so too do thecopper
losses.11.2.1 Current DensityThe current density allowable for the
copper windings is a somewhat variable figure. Current density
refers to the current in Amps per unit of wire area, for
example2.565A/mm (a reference standard used in Australia and
presumably elsewhere as well). Increasing the current density has a
major effect - it causes the wire to get hotterfor a given current.
Side forces caused by the magnetic fields generated between each
turn need to be considered in large power distribution
transformers, especiallyunder short-circuit conditions where the
forces can be destructive. There is no such thing as a "typical"
current density, because different manufacturers use
differentdesign criteria. In general, it's better to keep current
density below 3.0A/mm and 2.5A/mm is even better. Naturally, a
lower current density means that the transformer islarger and
heavier than one operated at a high density, and ultimately it's
all a trade-off against temperature rise and cost.For many
transformers used in audio, the current density can often be
expected to be somewhat higher than one might prefer. This is
because exceptionally highefficiency is not needed, and the demand
from normal music programme material has a rather low average
value. As a result, transformers for power amplifiers (forexample)
are rarely operated at continuous full load - they are more likely
to be run with short term overloads, but at perhaps 50% full load
on a long-term average basiswhen operated at the onset of clipping
with "typical" programme material.I took a few measurements on
transformers I have to hand, and found that with toroidals in
particular, there is a common trend. The current density of the
primary iscomparatively low, averaging around 2.1A/ mm, while the
secondaries all used a much higher current density - around 4.8A/
mm. This makes sense, because thesecondary is on the outside and
has the advantage of better cooling than the primary. The primary
winding can only get rid of heat through the secondary winding,
whichstands between the winding and cooling air. This may be less
of a problem with E-I cores, because the core itself acts as a
heatsink (although not a very efficient one).Small transformers are
likely to be operated at higher current densities than larger ones,
and this is reflected in that fact that they get hotter and (almost
always) haveworse regulation. A current density of up to 3.5A/ mm
is typical of some smaller transformers. One reason for this is
that it becomes extremely difficult to fit the number ofturns
needed into the space allowed. The main reason is that the
insulation requirements don't change, so insulation takes a larger
percentage of the winding space withsmall transformers than with
larger examples.Guitar amplifiers (and any other that is regularly
operated into heavy distortion) should have a transformer rated for
at least double the nominal 10% THD output power.Thus a nominal
100W amp needs a 200VA transformer as the bare minimum. This is
especially important for valve amplifiers, because they are already
operating in ahotter than normal ambient due to the heat from the
valves themselves. Regrettably, this is regularly ignored, with the
result that some amps have a reputation for burningout mains
transformers.Note that skin effect can be ignored for mains
frequency transformers (50/ 60Hz), but is a significant problem
with high frequency switching transformers. These are notcovered
here - the information in this article is based almost exclusively
on transformers used at low frequencies where skin effect has
little or no impact.Copper loss is the primary source of loss at
any appreciable power from a transformer. Conventional rectifiers
as used in semiconductor amplifier power supplies causethe
resistance to be more significant than would otherwise be the case.
See Linear Power Supply Design for more details on these losses,
which cause regulation to bemuch worse than expected.Ultimately,
copper losses limit the power available from a transformer. Since
all copper loss results in heat, this becomes a limiting factor, so
once you reach the pointwhere the temperature rise cannot be
limited to a safe value, the size of the core must be increased.
This allows the manufacturer to use fewer turns per Volt, and
thelarger core has more space for the windings. The wire size can
therefore be increased, so copper losses are brought back to the
point where overheating is no longer aproblem. This process
continues from the smallest transformers to the largest - each size
is determined by the VA rating and allowable temperature
rise.Keeping a transformer as cool as possible is always a good
idea. At elevated temperatures the life of the insulation is
reduced, and the resistance also increases furtherbecause copper
has a positive temperature coefficient of resistance. As the
transformer gets hot, its resistance increases, increasing losses.
This (naturally) leads togreater losses that cause the transformer
to get hotter. There is a real risk of drastically reduced
operational life (or even localised "hot-spot" thermal runaway) if
anytransformer is pushed too far - especially if there is
inadequate (or blocked) cooling.It is generally accepted that any
transformer will have one part of the winding that (for a variety
of reasons) is hotter than the rest. It's also a rule of thumb that
the lifeexpectancy of insulation (amongst other things) is halved
for every 10C (some claim as low as 7C) temperature increase. When
these two factors are combined, it isapparent that any transformer
operated at a consistently high temperature will eventually fail
due to insulation breakdown. The likelihood of this happening with
a homesystem is small, but it's a constant risk for power
distribution transformers. Despite all this, mains frequency iron
cored transformers typically outlast the product they arepowering,
and even recycled transformers can easily outlast their second or
third incarnation. Once a transformer is over 50 years old I
suggest that the chassis beearthed, as the insulation can no longer
be trusted at that age.Fan cooling can increase the effective VA
rating of a transformer significantly, but does not improve
regulation. Large power distribution transformers are almost always
oilcooled, and they are now starting to use vegetable oils because
they are less inclined to catch on fire, and pose minimal
environmental impact should there be a coolantleak or other major
fault.11.2.2 Skin & Proximity EffectThe skin effect is well
known (and exploited by snake-oil cable makers), but has little or
no relevance for audio frequencies. With switchmode power supply
transformers itis a real problem, and the most common way to
minimise the influence is to use multiple small (insulated) wires
in parallel - typically bundled and twisted into a singlerope-like
strand. This is commonly referred to as Litz wire, and its use
reduces skin effect losses because the wire bundle has a
comparatively large surface (or 'skin')area.You don't normally hear
much (if anything) of the so-called proximity effect, but it refers
to the (often chaotic) disturbance of the current flow in a
conductor when thatconductor is immersed in an intense magnetic
field. For small transformers (below perhaps 2kVA), there is little
evidence that it causes any problems, but in larger
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transformers it can cause localised heating because the current
is forced to use far less of the wire's cross section than
expected. Use of Litz wire again reduces theproximity effect, and
may be crucial to prevent failure. Proximity effect may reduce
current carrying ability far more dramatically than does skin
effect, and at much lowerfrequencies.The proximity effect therefore
has the potential to cause localised "hot spot" thermal problems,
that degrade the insulation and cause eventual failure. It is
especiallyproblematical when the transformer current is highly
distorted, and this is invariably the case when a transformer is
used with a bridge rectifier and filter capacitors.Despite the
above, it's almost certain that there will be identifiable minor
localised heating, but as noted it is unlikely to cause reduced
life of any transformer used foraudio or other applications that
are of interest to hobbyists or typical commercial products. Given
the legendary reliability of transformers - most of which will
outlast theproduct - the proximity effect never seems to have
caused premature failure. Most transformer failures are the result
of much more mundane abuse, such as consistentlong-term
overload.However, the proximity effect does cause failures in large
distribution transformers, and is also said to lead to motor
failures. These failures are almost always attributableto a highly
distorted mains current waveform, and may be localised to a single
industrial installation. I suggest that the reader not stress about
it - you didn't even knowabout it until now.
11.3 RegulationCopper loss is responsible for a transformer's
regulation - the ratio of voltage at no load versus full load.
Regulation is almost always specified into a resistive load,
whichconsidering the way nearly everyone uses transformers, is
virtually useless. It is rare that any transformer is operated into
a purely resistive load - the vast majority will beused with a
rectifier and filter capacitors, and the manufacturer's figure is
worthless. Actually, it is worse than worthless, as it misleads the
uninitiated to expect morevoltage than they will obtain under load,
and causes people grief as they try to work out why their amplifier
(for example) gives less power than expected.Naturally, there are
some to whom any measurement is sacrilege, so none of this applies
to them The output voltage is (nearly) always specified at full
load into a resistance. So a 50V, 5A transformer will give an
output of 50V at a sinewave output current of 5A. If theregulation
of this transformer were 4%, what is the no-load voltage?The answer
is 52V. Regulation is determined quite simply from the formula
...
Reg% = ( VN - VL) / VL * 100 / 1Where VN is no-load volts, and
VL is loaded volts.As determined earlier, this assumes a sinusoidal
output current, and this just does not happen with a rectifier /
filter load. It may be found that this same transformer hasan
apparent regulation of 8 to 10% when supplying such a load. See
Linear Power Supply Design for more information on this topic
(there is little point in doing the articletwice :-)The regulation
with rectifier loads is a complex topic, but you will need to know
the ramifications before you start construction of your latest
masterpiece, rather than findout later that all your work has
resulted in much lower output power than you expected. Not that you
can change it for any given transformer, but at least you will
knowwhat to expect.To gain a full understanding of regulation
requires a lot more information than I can provide in a simple web
page, but a crucial factor is getting the balance of
windingresistances right. If you are making your own transformer
you'll do this as a matter of course, but will a manufacturer (in
the "far-East") go to the trouble? I'm not about todebate that
point. If we determine from the specification that regulation is
(say) 6% for a reasonable sized transformer (around 500VA), we can
work out everything weneed to know.Knowing the regulation and
voltage, we can calculate the effective winding resistance. A 50V
transformer with 6% regulation will give us 53V at no load, and
500VA at50V means 10A - all very straightforward. We lose 3V at
full current, so the total effective winding resistance must be
...
Rw = V / I = 3 / 10 = 0.3 OhmsHalf of this resistance is in the
secondary, and the other half is reflected from the primary, based
on the impedance ratio. As you will recall, this is the square of
the voltageratio. If we assume a primary voltage of 230V, output
voltage of 50V at 10A, we already know that the unloaded output
voltage is 53V. The turns and impedance ratios(TR and ZR
respectively) are therefore ...
TR = VIN / VOUT = 230 / 53 = 4.34:1ZR = TR = 4.34 = 18.83:1
Knowing this, we can determine the optimum winding resistance
for each winding. Since half of the resistance is that reflected
from the primary (Rp), the secondaryresistance (Rs) is 0.15 ohms,
being half of the total. Primary resistance must be ...
Rp = Rs * ZR = 0.15 * 18.83 = 2.82 OhmsBased on all that, it is
now possible for the designer to determine the appropriate wire
gauge for the number of turns needed for the core size. The ideal
case is that theresistive (copper) losses should be as close as
possible to identical for both windings, and this is why we worked
out the resistance. At full load, dissipation (copper loss)is 15W
for each winding (almost exactly) at full load. Total dissipation
is therefore 30W, and the transformer efficiency is 94.3% ...
Eff (%) = POut / Ptot * 100 / 1 = 500 / 530 * 100 / 1 = 94.34%It
may not be immediately obvious, but there is a very good reason for
keeping the primary and secondary copper losses equal. Any core
only has a limited space for thewindings, and this space must be
used as efficiently as possible. It follows that if one winding is
thicker than necessary, the other has to be thinner so it will fit
in the spaceallowed. This invariably leads to total losses that are
greater than would be the case if the resistance is optimised as
described. In the case of toroidal transformers, thereis good
reason to keep primary losses lower than secondary losses, because
the primary winding is trapped inside the secondary winding and
heat can only escapethrough the outer layers. The toroidal core
doesn't act as a heatsink either, because it's inside all the
windings.
VA Reg % Rp - 230V Rp - 120V Diameter Height Mass (kg)15 18 195
- 228 53 - 62 60 31 0.3030 16 89 - 105 24 - 28 70 32 0.4650 14 48 -
57 13 - 15 80 33 0.6580 13 29 - 34 7.8 - 9.2 93 38 0.90120 10 15 -
18 4.3 - 5.0 98 46 1.20160 9 10 - 13 2.9 - 3.4 105 42 1.50225 8 6.9
- 8.1 1.9 - 2.2 112 47 1.90300 7 4.6 - 5.4 1.3 - 1.5 115 58 2.25500
6 2.4 - 2.8 0.65 - 0.77 136 60 3.50625 5 1.6 - 1.9 0.44 - 0.52 142
68 4.30800 5 1.3 - 1.5 0.35 - 0.41 162 60 5.101000 5 1.0 - 1.2 0.28
- 0.33 165 70 6.50
Table 11.1 - Typical Toroidal Transformer SpecificationsThe
primary resistance for all of the examples in the above table was
calculated using the method shown - this figure is rarely given by
manufacturers. Resistance isshown for both 230V and 120V primary
windings. Knowing the basics at this level is often very handy -
you can determine the approximate VA rating of a transformer justby
knowing its weight and primary resistance. The secondary resistance
can be calculated from the primary resistance and the turns ratio.
The result obtained by using
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nominal turns ratio (based on the stated primary and secondary
voltages) is accurate enough for most purposes. As shown by the
range provided, the primary windingresistance could be up to 15%
lower than calculated to reduce the current density in the primary.
(See Reusing Transformers for another table covering a wider range
ofVA ratings.)Taking the 500VA example again, and assuming a 230V
primary and a dual 50V secondary winding (100V total), the total
secondary resistance is ...
TR = Vp / Vs = 230 / 100 = 2.3ZR = TR = 5.29
If the primary resistance is 2.8 ohms (from the table), then the
secondary resistance must be approximately ...Rs = Rp / ZR = 2.8 /
5.29 = 0.53 Ohm
The resistance of each half of the secondary winding is
naturally half of the total.Note: Because of the common practice of
using different current densities for the inner (primary) and outer
(secondary) wire, this will skew the figures shown hereslightly.
The figures determined above are based on a theoretical "ideal"
case, but this will rarely translate into reality due to the
inevitable "fudge factors" that are appliedto real world parts.
Basic tests I've run indicate that the above figures are more than
satisfactory for a quick check of the expected resistances. As a
very basic rule,expect the primary resistance to be a little less
than calculated, and the secondary resistance will be a little
higher.
11.4 Other LossesSince the transformer is not an ideal device,
it has unwanted properties apart from the losses described so far.
The other losses are relatively insignificant for a
powertransformer, but become difficult to manage for transformers
intended for wide bandwidth, such as microphone transformers and
valve output transformers.The standard equivalent circuit does not
include frequency dependent disruptions such as skin or proximity
effect. Nor does it include any means to simulate thenon-linear
magnetising current in a power transformer. As such, it is limited
to general simulations of small signal transformers, valve
amplifier output transformers (butonly at low levels and/or higher
frequencies) and similar. While it can still be used with a power
transformer, the results are generally not at all useful. Power
transformersgenerally require measurements to confirm the overall
performance, and we are only interested in low frequencies - 50Hz
and 60Hz.
Figure 11.5 - Transformer Simplified Equivalent CircuitThe
equivalent circuit shown in Figure 11.5 is greatly simplified, but
serves to illustrate the points. Since the windings are usually
layered, there must be capacitance (C1and C2) between each layer
and indeed, each turn. This causes phase shifts at high
frequencies, and at some frequency, the transformer will be "self
resonant". This isnot a problem with power transformers, but does
cause grief when a wide bandwidth audio transformer is needed.In
addition, there is some amount of the magnetic field that fails to
remain in the core itself. This creates a "leakage" inductance (LL)
that is effectively in series with thetransformer. Although small,
it tends to affect the high frequencies in particular, and is
especially troublesome for audio output transformers. This is
typically measuredwith an inductance meter, with the output winding
short circuited. Any inductance that appears is the direct result
of leakage flux.Lp is the primary inductance, and as you can see,
there is a resistor in parallel (Rp). This represents the actual
impedance (at no load) presented to the input voltagesource, and
simulates the iron losses. The series resistance (Rw) is simply the
winding resistance, and is representative of the copper losses as
described above.Cp-s is the inter-winding capacitance, and for
power transformers can be a major contributor to noise at the
output. This is especially irksome when the transformer issupplying
a hi-fi system, and mains borne noise gets through and makes horrid
clicks, electronic "farts", electric motor whine, and various other
undesirable noises in themusic. Toroidal transformers are very much
worse than conventional (E-I) transformers in this respect, because
of the large area of each winding. An electrostatic shieldwill all
but eliminate such noises, but these are expensive and uncommon
with toroids (pity).This problem always exists when the capacitance
between primary and secondary is high - electrical noise on the
primary is capacitively coupled from the primary to thesecondary.
As noted above, this can lead to mains noise getting through the
entire power supply and into the amplifier in extreme cases. The
electrostatic shield is veryeffective, and this is connected to
earth. Note that the shield cannot be joined in a complete circle
around the winding, as this would create a shorted turn that would
drawa tremendous current and burn out the transformer.There is a
technique that is used for valve output transformers, shown in
Figure 11.6 - you will not find this method used in power
transformers, as it is completelyunnecessary and increases the
primary-secondary capacitance dramatically.
Figure 11.6 - Interleaved Winding for Extended HF ResponseThe
trick to winding transformers to minimise the winding leakage
inductance and self capacitance is called "interleaving", but this
results in much greater inter-windingcapacitance. The most common
way an interleaved winding is done is to use a multi-segmented
winding, as shown in the sectional drawing of Figure 11.6. This
type ofwinding is (or was) quite common for high quality valve
output transformers, and the extension of frequency on the top end
of the audio spectrum is very noticeable.The capacitance between
the primary and secondary can become troublesome with this
technique, and although possible, an electrostatic shield
(actually, a number ofelectrostatic shields may be needed) adds
considerably to the cost, but creates a minimal overall benefit.
This winding method is not used (or needed) with low frequencypower
transformers, and would lead to greatly reduced electrical safety
because of the difficulty of insulating each section from the next.
The same problem also existswith an output transformer, but is
easier to control because one side of the secondary is earthed and
the internal DC is already isolated from the mains.
11.5 Temperature ClassesAll the losses add together to increase
the temperature of a transformer. Insulation materials (wire
enamel, inter-layer insulation, formers and/or bobbins, tape
overwinds,
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etc.) all have limits to the maximum safe temperature. It should
come as no surprise that the high temperature materials are
considerably more expensive than lowertemperature grades, and as
always there is a trade-off (compromise) between minimising losses
for cool running or reducing the size and weight at the expense
ofgreater losses and higher temperature operation.There are several
internationally recognised temperature grades, as well as one that
is recognised by the authorities, but the class designation is not
universallyaccepted. Temperature is specified as either an absolute
maximum figure, temperature rise, or both. The standard classes are
...
Class Max. Temp. Temp Rise A 105 C 60 C E 120 C 75 C B 130 C 80
C F 155 C 100 C H 180 - 200 C 125 C C (not global *) 220 C 160
C
Table 11.2 - Insulation Temperature Classes* Class-C is not a
globally recognised class, but 220C is accepted under several
different world standards.It's inevitable that transformers in use
will get hot, and it is up to the equipment designer to ensure that
the insulation class is adequate for reliable operation over the
lifeof the equipment. Unless stated otherwise, you can expect that
nearly all commercial off-the-shelf transformers intended for DIY
applications will be Class-A (105Cmaximum temperature). Higher
temperatures are not recommended anyway, for the simple reason that
having a transformer at (say) 100C will transfer its heat
totransistors, electrolytic capacitors and all other components in
the chassis. For this reason alone, specifying a larger than
necessary transformer not only reducestemperatures, but improves
regulation as well.
11.6 Voltage & FrequencyAll power transformers are rated for
either a specific input voltage and frequency, or for a limited
range. Often, dual primaries are used that allow the user to
connect thewindings in series or parallel as shown in Figure 8.1,
but on the primary instead of the secondary. The most common
configuration is to have two windings, each rated for120V. For 120V
mains, these are wired in parallel, and wired in series for
230/240V.Sometimes, the primary windings will be rated for 115V
each. This has long been a problem in the US, with no-one quite
certain for many years whether the voltage is110, 115, 117 or 120.
According to US standards, the nominal mains voltage in the US and
Canada is 120V, but like everywhere else it varies from one place
to anotherand with time of day. All power transformers must be
wound to take this inevitable variation into account. (Note that
the US also uses a 'two-phase' system, providing240V at 60Hz - this
is not the same as using two phases of a 3-phase connection, where
the voltage is 208V at 60Hz.)While just two windings are common
now, it used to be the case that transformers had multiple taps on
the primary winding, or used several windings that could
beconnected in often mysterious ways using a complex switching
system. These still exist, but mainly as salvage items. The range
of voltages offered was intended to coveranywhere in the world, but
also could lead to a wrong assumption and blown fuses (or a burnt
out transformer).Ultimately though, the claimed voltage of a
transformer is the easiest to verify - the nameplate rating is
always correct. I have never seen a transformer that claimed to
be230V (or some other voltage) that didn't work properly at that
voltage. Of more concern is the frequency rating. While usually
stated, it is sometimes confusing to theuninitiated.A transformer
rated for 50Hz can be used anywhere in the world - it will work
perfectly at 60Hz. However, the converse is not true. A transformer
designed specifically for60Hz will overheat at 50Hz, even if the
voltage is correct! This is not well understood, and leads to an
enormous amount of traffic on Usenet and in forum pageseverywhere.
The answer is quite simple - 60Hz is 20% greater than 50Hz, so the
core and turns per volt can both be reduced by up to 20% compared
to a 50Hztransformer of the same rating.Therefore, a transformer
that was designed for 60Hz at 220/230V (The Philippines, South
Korea and a few others use this combination [Ref]) has a smaller
core andfewer turns than an otherwise identically rated 50Hz
transformer. As a result, it will most likely fail with 220V at
50Hz. Operating a 60Hz power transformer at 50Hz isexactly the same
as operating the transformer at its rated frequency, but with a 20%
voltage increase. If you absolutely must run a 60Hz transformer at
50Hz, you mustreduce the mains voltage from the rated value (say
230V) by 20% (184V). This is a large drop, and exceeds the normal
mains variation allowances that are provided forin properly
designed circuits.Failure to reduce the voltage will cause the
transformer to be heavily into saturation, and it may easily
consume half its rated VA (or more) at idle, due to
excessivemagnetising current caused by core saturation. Needless to
say, the secondary voltage will also be reduced by the same
percentage. For evidence of the current increasedue to core
saturation, see the next section (specifically Figure
12.1.1).Operating a 60Hz transformer at 50Hz is effectively the
same as a 20% increase in mains voltage, but note that this does
not mean that the secondary voltage isincreased. For a 230V
transformer that's the same as running at 60Hz, but at a supply
voltage of 276V. The core will be seriously saturated, and the
magnetising currentwill be increased dramatically.Should the power
transformer be for a valve amplifier, care is needed, because the
valve heaters will be operating from a lower than normal voltage
(6.3V will only be 5V)and may not reach the proper operating
temperature. Output power is also reduced, and a 20% reduction of
voltage will reduce the maximum power to fall from (say)100W to
64W, a drop of just under 2dB. It also means that all unregulated
preamp supplies will be 20% lower. With regulated supplies, the
drop might be enough to causethe regulator ICs to allow rectified
mains buzz through to the signal circuits.For information about how
you can reduce the supply voltage (in this case by 46V), see the
article Bucking Transformers. While the methods described certainly
do work,the other compromises you have to make will almost
certainly mean that the transformer will have to be replaced to
maintain original performance.Should you have a transformer rated
for 240V at 50Hz and wish to use it at a lower voltage and/or 60Hz,
then there is no problem. If used at 120V 60Hz, the transformerwill
operate with an exceptionally low magnetising current, but the
secondary voltages will obviously be halved. While the maximum
current rating remains the same,regulation will be worse than a
transformer wound for 120V mains because the winding resistance is
higher.In short, you can operate a ...
50Hz transformer at 60Hz with no loss of performance, provided
voltage is correct50Hz transformer at 60Hz at a supply voltage up
to 20% higher than the nameplate ratingtransformer at any voltage
below the nameplate rating. There is no limit other than that
imposed by common sense60Hz transformer at 50Hz, provided the
supply voltage is 20% lower than the rated voltage
Likewise, you cannot operate a ...60Hz transformer at 50Hz at
full rated voltagetransformer at any voltage above the nameplate
rating, unless rigorous testing shows that it will be safe
(unlikely)
Note that I have simply assumed 20% in both directions (50Hz to
60Hz and 60Hz to 50Hz), although it is clear that a reduction from
60Hz to 50Hz is actually 17%. Feelfree to think of the extra 3% as
a safety margin.
12. Sample MeasurementsI measured the characteristics of a small
selection of transformers to give some comparative data. I excluded
regulation from this, as it is difficult to make a suitablevariable
load, and loads tend to get rather hot even with short usage. Most
manufacturers will provide this information in their
specifications, but be warned that this refersto a resistive load,
and regulation will be much worse when supplying a conventional
rectifier and filter capacitor (see above, and the Power Supply
Design article formore details). It is also worth noting that an
inductance meter is often of little use with large iron cored
transformers, unless it operates with a sinusoidal waveform at
(or
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near) the design frequency of the transformer. The inductances
shown are calculated, since the measured values with my meter were
a long way off.Bear in mind that the inductance value shown is
nominal, based on the magnetising current (which is actually
distorted for most transformers), and is much lower than thereal
value. It is included only as a guide - the actual value will be
much higher, but only with a lower primary voltage that ensures
that the core is nowhere near saturation.Manufacturers don't
provide this figure, because it's meaningless in the real
world.
Type Rating Inductance Resistance Turns/Volt Magnetising Core
Loss Reactance Mass (kg)Toroidal 500VA 34.7 H 2R4 2 22mA 5.28W
10.91k ohms 5.0Toroidal 300VA 63 H 5R1 3 12mA 2.88W 20k ohms 2.7E-I
200VA 4.36 H 6R6 2 175mA 42W 1.37k ohms 3.2
Table 12.1 - Measured Characteristics of Some TransformersThe
toroidals are clear winners in terms of core loss in particular,
but it must be said that the E-I transformer tested is not really
representative of the majority. This is oneof a few left that I had
specially made to my design, and they were deliberately designed to
push the saturation limits of the core. These transformers run
quite hot at noload, but give much better regulation than a more
conservative design - the vast majority of such transformers. They
were actually designed to run just above the "knee"of the B-H curve
for the laminations used, and although somewhat risky, none has
failed (to my knowledge) since they were made about 20 years ago. I
use a pair ofthem in my hi-fi system, which has been in daily use
for 10 years now. I originally got the idea of designing
transformers like this long ago, when I used to make my
owntransformers for guitar and bass amps. I ran some tests at the
time, and found that by pushing the core a little harder, I could
make a transformer that had far betterregulation than anything I
could buy from any of the existing manufacturers. I never had a
transformer failure.It is also worth noting that the mass is lower
than for a more "traditional" transformer design - a conventional
design of the same power rating would be expected to weighin at
about 5kg.
Figure 12.1 - Current vs. Voltage for the E-I TransformerTo take
my measurements to the logical limit, I measured the magnetising
current of my sample E-I transformer. Look closely at the graph in
Figure 12.1, and you will seea typical BH curve (as shown in Figure
11.2 but with the axes reversed). As you can see, at 240V input,
the transformer is operating at the knee of the curve, and is
wellon the way to saturation. There was no point doing this for the
toroidals, as they are operated well below saturation level and I
would be unable to (conveniently) measurethem.Toroids usually have
a more pronounced knee, and a correspondingly steeper rise in
current once the saturation limit has been reached. This is
primarily because of thefully enclosed magnetic path, which has no
air gaps at all. E-I laminated transformers have a small but
significant gap where the 'E' and 'I' laminations meet. This
isunavoidable in any practical transformer, but has little effect
on performance in real life.
12.1 Magnetising Current WaveformsFor these measurements, I used
a 300VA toroidal transformer, but not the same one as was used for
the data in Table 12.1. There seems to be very little on the Net
thatdiscusses or shows actual (as opposed to theoretical or
imagined) magnetising current. The true value of this varies more
or less linearly up to the point where the coreapproaches
saturation, but it is very common that power transformers are
designed so that they are already into the non-linear part of the
BH curve for normal operation.While this region is usually well
below true saturation, the current waveform is already quite
distorted, because the mains voltage peaks cause the flux to rise
to itsmaximum value, so additional current is drawn at the peak of
the AC waveform, displaced by 90. This is shown below, for a 240V,
300VA toroidal transformer, operatedat four different voltages ...
the first (A) is well below saturation at 120V, the second (B) at
nominal input voltage (240V), the third (C) at a voltage that is
somewhat greater(280V) and the last (D) at an excessive mains
voltage (290V). The transformer was designed for nominal 240V
operation.
Figure 12.1.1 - Magnetising Current Vs. Input VoltageThe
magnetising current is a nice friendly 7.3mA at 120V input, and at
240V is showing signs of saturation, but the current is still only
42mA. When the voltage isincreased further, saturation is clearly
well advanced - at 280V the transformer draws 443mA, but just a
small further increase to 290V causes the current to soar to 1.6A
-exceeding the transformer's continuous VA rating with no load. If
you look carefully at Figure 12.1.1.A, you will notice that the
waveform is slightly asymmetrical. Thisindicates that there is
probably some remanent flux in the core from the last time the
transformer was used.The volt-amps dissipated in the transformer
primary winding is determined by VA = V * I, so at 240V the
transformer draws only 10VA, climbing to 124VA at 280V and arather
spectacular 464VA at 290V. Assuming the typical primary resistance
of 4.7 ohms for a 300VA transformer, the power loss in the primary
at each voltage (in turn) is250uW, 8.2mW, 0.9W and 12W at 290V.As
you can see from the graphs (B, C & D), the current is highly
non-linear, so cannot be corrected for power factor. While this is
a common error made all over the
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Internet, there is no way that a non-linear waveform can be
corrected for power factor by adding a capacitor. At best, you
might be able to add a capacitor that creates afilter which reduces
the peak current and improves the PF very marginally, but it will
only be effective at one location and/or voltage. Any such filter
will rely on the mainsimpedance, and is guaranteed overall to make
matters worse, never better.Adding a power factor correction
capacitor will only work if the cap is sized to draw a leading
current of around 14mA (for this transformer). This is the only
linear part ofthe magnetising current, being double the 'nice
sinewave' current drawn at 120V. True magnetising current is a
linear function of voltage, based on the reactance of thewinding.
This would imply a capacitor of around about 180nF - unlikely to be
useful (ok, it's completely pointless ).The actual magnetising
current drawn (including that caused by core saturation) is a
non-linear function, and is extremely difficult to simulate unless
one has access to asimulator that handles iron cores properly.
While such a thing may exist for transformer designers, I've not
seen any simulation that comes even close to reality as shownabove.
Note that these are actual captured waveforms from a real
transformer connected to a high power Variac. As you can see, the
saturation current waveformremains much the same once the core is
thoroughly saturated, but the magnitude increases exponentially
with voltage increase.With 290V applied, the peak current is about
5A (2A per division on the screen). You will see that the vertical
resolution has been changed for each capture, and thecurrent
monitor also has variable gain to maximise resolution. That is why
the measured current may seem to be different from the oscilloscope
display, but the reading involts has been converted into mA.When
the transformer is loaded with a resistance, the voltage and
current waveforms are in phase. Contrary to popular belief, a
linearly loaded transformer (i.e. resistiveload) does not produce a
lagging power factor, except for the small magnetising current's
contribution. As we can see from the above, this is negligible. I
tested the sametransformer with a 16 ohm load across one of the
nominal 20V secondaries, and the input voltage and current waveform
were perfectly in phase at any input - from lessthan 5V RMS up to
the full rated primary voltage.
12.2 Inrush CurrentWhen powered on, many transformers draw a
very high initial current. This phenomenon may not be noticeable
with smaller transformers, but as the component getslarger (above
~300VA) it tends to occur most of the time. You may see lights dim
momentarily when a large transformer is switched on, and now you
know why. The coresaturates when power is applied, so very high
current is drawn until normal operation is established (after
around 20 complete mains cycles). The magnitude of the
inrushcurrent is a combination of several factors ...
What was the polarity and magnitude of the mains at switch
offWhat is the polarity and magnitude of the mains at switch onTo
what extent has the core de-magnetised itself between
eventsTransformer type (toroidals have greater inrush than E-I
cores)The resistance of the transformer primary and the mains -
right back to the sub-station
The longer a transformer is left unpowered, the lower the
remanent flux, and the less likelihood there is of an excessively
high inrush current. This is a nice theory, but inreality it makes
no practical difference. Of far more importance is the point on the
mains waveform where the power is actually applied. If the mains is
applied when at itspeak value, inrush current is at its lowest.
Conversely, if the mains is applied at the zero crossing point,
inrush current will be maximum - this is exactly the reverse of
whatyou might expect, and is shown below. The inrush current lasts
for several cycles, and is made much worse with a rectifier and
filter capacitor on the output. The capacitoris a short circuit
when discharged, and large capacitors will take longer to charge.
The inrush current due to capacitors charging is not asymmetrical -
that privilege isreserved for core saturation at power-on.
Figure 12.2 - Transformer Inrush CurrentThe above is an
oscilloscope capture of the current in a 200 VA E-Core transformer,
when power is applied at the zero crossing of the mains waveform.
This is the worstcase, and can result in an initial current spike
that is limited only by the winding and mains wiring resistance.
For a large toroidal, peak currents can easily exceed 150A. Ifthe
mains is applied at the peak of the AC waveform (325V in 230V AC
countries, 170V in the US), the peak inrush current for the same
transformer is typically reducedto less than 1/4 of the worst case
value ... 4.4A (both can be measured with good repeatability for
the transformer tested).As you can see, the inrush current is one
polarity (it could be positive or negative), so superimposes a
transient 'DC' event onto the mains. Other transformers that
arealready powered may also saturate (and often growl) during the
inrush period. This is often known as 'sympathetic interaction'. To
minimise the effects of inrush currentand flow-on effects with
other equipment, any toroidal transformer over 300VA should use a
soft-start circuit such as that described in Project 39.
12.3 InductanceThe inductance of a transformer is not normally
part of its specifications, unless it's designed for a switchmode
power supply. For normal mains frequency applications,the figure we
are interested in is the magnetising current. As shown above in
Figure 12.1.1, the magnetising current is non-linear, so if you do
need to know theinductance you must take the measurement at a
voltage that's well below the nominal primary voltage. If you have
a way to monitor the current waveform, you can verifythat there is
no evidence of saturation at the test voltage (see Project 39 or
Project 39A for suitable current monitors).Once you know the
voltage and current you can calculate the impedance, and from that
you can work out the inductance ...
XL = V / I (where V is applied RMS voltage and I is RMS
current)L = XL / ( 2 * * f ) (where f is the applied frequency)
For example, the transformer I used to produce the oscilloscope
captures in Figure 12.1.1 draws 7.31mA with a mains voltage of 120V
at 50Hz.XL = 120 / 7.31 = 16.41 kL = 16.41 k / ( 6.283 * 50 ) =
52.25 Henrys
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This is an interesting 'figure of merit', but is not actually
useful for anything. Of course, if you have a need for a 52H
inductor you can use the primary winding to get it, butremember
that it will start to saturate at not much more than 10mA. If you
tried to use it for audio, the distortion will be quite high at
even lower currents, especially as thefrequency is reduced below
50Hz. In addition, the inductance will probably be non-linear,
because the core may not magnetise properly at very low current.
The testtransformer's inductance fell to 42H with a voltage of
35.2V and a current of 2.64mA.As noted above, inductance is part of
the specification for switchmode power supply transformers. That's
because they are operated in a somewhat different way fromlinear
transformers. One area of commonality is that saturation must be
avoided, and like linear transformers saturation is worse with no
load. For the same power output,a switchmode transformer will be a
great deal smaller than a conventional transformer operating at 50
or 60Hz. Typical operating frequencies range from a few kHz up
to100kHz or more. As a rough guide, the necessary size of a
transformer will halve for each doubling of frequency (and vice
versa of course), but there are many otherinfluences that must also
be considered. A complete discussion of this is way outside the
intent of this article.
13. Core StylesThere is a huge array of different core shapes,
and each has its own advantages and disadvantages. The two most
common for commercial and DIY audio equipment arethe standard E-I
core and the toroidal core, but there are many others. Occasionally
you will see C-cores, double-C-cores and R-cores, but these are not
as common asthe two most popular types.Ferrites in particular are
moulded, and therefore have many specialised shapes to suit various
applications, as well as the more traditional shapes shown
below.Toroidal cores are made from a continuous strip grain
oriented silicon steel, and are bonded to prevent vibration and
maximise the "packing density". It is important thatthere are no
gaps between the individual layers, which will lower the
performance of the core. The sharp corners are rounded off, and
they are usually coated with asuitable insulating material to
prevent the primary (which is always wound on first) from
contacting the core itself.I don't propose to even attempt them
all, but one iron core that warrants special mention is the 'C'
core. These were once very popular, but have lost favour since
suitablewinding machines became available for toroids. They are
still a very good core design, and are especially suited where an
intrinsically safe transformer is required (i.e.where the primary
and secondary windings are physically separated), and this
technique also ensures that the inter-winding capacitance is
minimal. C-cores are made byrolling a continuous strip into the
desired shape, and after bonding, it is cut in half. To ensure the
best possible magnetic coupling (i.e. no air gap), the cut ends
aremachined and polished as a pair - it is very important to ensure
that the two are properly mated or unacceptable losses will occur.
The core halves are commonly heldtogether with steel banding,
similar to that used for large transport boxes.
Figure 13.1 - C-Core TransformerThe main disadvantage of the
single c-core arrangement shown above is that its leakage
inductance is rather high. Although both windings could be placed
onto a singlebobbin with a pair of cores, it is more common to use
four 'C' sections as shown below. This provides more iron (twice as
much) and allows fewer turns for a givenvoltage. Naturally, the
double c-core as shown below is not intrinsically safe, because
both windings are wound together in the same way as for an
equivalent E-Itransformer. While not intrinsically safe, as with
any bobbin-wound windings it's still fairly easy to build one that
complies with all double insulation standards.C-cores are not quite
as efficient as toroidal cores, but are easier to wind with
conventional coil winding machines. The overall efficiency lies
between the E-I core and thetoroidal. Note that toroidal
transformers are very difficult to build so they comply with double
insulation standards. I've never seen a double insulated toroidal
transformer,except for those that are used in electronic
transformers intended for halogen downlights. These have a plastic
case that fully encloses the primary.
Figure 13.1A - Double C-Core TransformerA sample of ferrite
cores is shown in Figure 13.2 - this is but a small indication of
the selections available, and most styles are also available in
many different grades tosuit specific applications.
Figure 13.2 - Some Ferrite Core StylesThe diagram in Figure 13.3
shows the correct way to stack an E-I transformer. Sometimes
manufacturers will use 2 or 3 laminations in the same direction,
then the samein the other. This cuts costs, but the transformer
performance will never be as good. Alternate laminations minimise
the air gap created between the E and I sections dueto imperfect
mating of the two. It is essential that the laminations are packed
as tightly as possible so that the effects of the air gaps are
minimal.For maximum transformer efficiency, the stack should be
square if possible. A square stack is one where the height of the
lamination stack is the same as the width of thecentre leg (the
tongue), so the centre looks like a square from end-on. This gives
the best possible wire resistance for the core size. Thicker and
thinner stacks arecommonly used, but this is for expedience (or to
minimise inventory) rather than to improve performance.
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Figure 13.3 - E-I Lamination StackingWhen a transformer using
E-I laminations is bolted together, it is important that the bolts
are insulated from the core. If not, this would allow large eddy
currents tocirculate through the end laminations and the bolts,
reducing performance dramatically. For safety, the core should
always be bonded to mains earth unless thetransformer is rated as
"double insulated"."Yes, but what good is that? The laminations are
insulated from each other anyway." The inter-lamination insulation
is sufficient to prevent eddy currents, but cannotwithstand the
mains voltage, so in case of electrical breakdown, the core may
become 'live' if not earthed.In order to reduce the radiated flux
from an E-I transformer core, you will sometimes see a copper or
brass band* wrapped around the winding and the outside of thecore,
as shown in Figure 13.4. This acts as a shorted turn to the leakage
flux only, and greatly reduces magnetic interference to adjacent
equipment. The band must besoldered where it overlaps to ensure a
very low resistance. Such measures are usually not needed with
toroidal transformers, as leakage flux is very much lower, and
thecore is completely enclosed by the windings.However, in critical
applications a flux band can still be used. For a toroidal, the
band is simply wrapped around the outside of the winding and
soldered to give a lowresistance connection. The band must not be
allowed to touch other metal parts that are connected to the
mounting bolt in such a way as to form a shorted turn. This
willcause a huge circulating current - the fuse will blow if
properly sized, or the transformer will burn out if not. It is
alright to earth the flux band though, and this will
minimiseradiation of any HF noise (rectifier noise for
example).
(* While I am sure that many people would love to see their
local brass band wrapped around a transformer, this is not what I
had in mind. It does create aninteresting mental picture though
.)
Figure 13.4 - Flux Banded TransformerJust in case you were
wondering, the dimensions of E-I laminations are worked out so that
the laminations can be created with no material waste (other than
the holes).The relative dimensions are shown below, and are just a
ratio of the real dimensions, which will naturally be in
millimetres or inches. This arrangement is known as a'scrapless'
lamination because there is an absolute minimum of waste
material.
Figure 13.5 - Assembled Laminations and Punching DimensionsThe
magnetic path length is the average for the dual path shown in the
assembled lamination drawing, and is generally assumed to be 12
(units). This may be thought alittle pessimistic, but is the
commonly accepted figure. The winding window size is restricted by
the punching dimensions, and it is critical that the maximum usage
ismade of the limited area available. Should the winding wire be
too thin, there will be plenty of room, but copper losses will be
excessive. Make the winding wire too thick,and the completed
winding will not fit into the available space. Additional space
must be allowed for the winding bobbin, and for inter-winding
insulation and the finalinsulation layer.
13.1 Air GapsDC flows in the windings for any transformer that
is used for 'flyback' switching supplies or SET power amplifiers,
to name but two. The effect is that the DC creates amagnetomotive
force that is unidirectional, and this reduces the maximum AC
signal that can be carried before saturation in one direction.
Indeed, the DC componentmay cause saturation by itself, so the
transformer would be rendered useless as a means of passing the AC
signal without severe degradation. Even the use of a halfwave
rectifier will introduce an effective DC component into the
windings, and these should be avoided at any significant power
level (i.e. more than a few milliamps).To combat this, transformers
that are subject to DC in the windings use an air gap in the core,
so it is no longer a complete magnetic circuit, but is broken by
the gap. Thislowers the inductance, and means that a larger core
must be used because of the reduced permeability of the core
material due to the gap. An air gap also increasesleakage
inductance because of the flux 'fringing' around the gap, and
resistive (copper) losses are increased as well, because more turns
will be needed.It is beyond the scope of this article to cover this
in great detail, but it does impose some severe restrictions on the
design of transformers where DC is present. This is(IMO) one of the
biggest disadvantages of the SET amplifier so popular with
audiophiles, as it almost invariably leads to unacceptable
compromises and equallyunacceptable distortion (both harmonic and
frequency).In some designs, it is possible to eliminate the DC
component by using a tertiary winding that carries ... DC. If the
additional winding can be made to induce a flux that isequal and
opposite that of the bias current, then the quiescent flux in the
transformer can be reduced to zero (where it belongs). The
disadvantage with this is that itrequires an extra winding, and
that takes up valuable winding space on the core. It is also a
difficult technique to get right, and is not often seen these days.
It was apopular technique in telecommunications equipment at one
time, and meant that smaller transformers could be used for the
same performance.
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E-I transformers all have a minuscule 'air gap' because of the
way the laminations are assembled. With care, this can be almost be
considered negligible, but it cannot beeliminated. C-cores will
have their cut ends machined to minimise the effect, but again, it
cannot be eliminated entirely. The toroidal core has no air gap at
all, and istherefore more efficient (magnetically speaking) - they
are utterly intolerant of DC in the windings. With large toroidal
transformers the primary resistance is very low, andeven tiny DC
voltages on the mains will cause partial saturation.This is
commonly heard as a growling noise from the transformer, and if bad
enough you'll hear it just before the fuse or circuit breaker
opens. It's easy to get severaltimes the normal full load current
to flow in the primary with asymmetrical mains waveforms that have
an effective DC component. See Blocking Mains DC Offset for
moreinformation on the problem and how to fix it.
14. MaterialsThere is an enormous range of core materials, even
within the same basic class, so I will mention only a few of the
most common. All materials have some basicrequirements if they are
to be used with AC (for transformers, rather than solenoids or
relays, which can operate with DC). The core cannot be solid and
electricallyconductive, or excessive eddy current will flow,
heating the core and causing very high losses. Therefore, all cores
use either thin metal laminations, each electricallyinsulated from
the next, or powdered magnetic material in an insulating filler.
The list below is far from exhaustive - there are a great many
variations of alloys, and I havementioned only a few of those that
are in common use.GOSSCommonly thought to be an acronym for 'Grain
Oriented Silicon Steel', it's actually the name of the man who
invented it - Norman P. Goss (US Patent 1965559). SeeWikipedia for
a bit more.Silicon Steel (General Information)Typically, soft (i.e.
low remanence) magnetic steel will contain about 4% to 4.5%
silicon, which lowers the remanence of the steel and reduces
hysteresis losses. Normalmild steel, carbon steel or pure iron has
quite a high remanence, and this is easily demonstrated by stroking
a nail (or screwdriver) with a magnet. The nail will
becomemagnetised, and will retain enough magnetism to enable it to
pick up other nails. The addition of silicon reduces this effect,
and it is very difficult to magnetise atransformer lamination
strongly enough so it can pick things up.This is not to say that
the remanence is zero - far from it. When a transformer is turned
off, there will often be residual magnetism in the core, and when
next powered on,it is common for the transformer to make noise -
both toroids and E-I transformers can sometimes make a noise
(sometimes rather loud) when power is applied. This isdue to core
saturation and inrush current - see Section 12.1 above for a more
complete description.Silicon steel and other metal (as opposed to
ferrite) materials are normally annealed by heating and then
cooling slowly after stamping and forming. This removes most ofthe
internal mechanical stresses caused by the stamping or rolling
operation(s) - these stresses reduce the magnetic properties of the
material, sometimes verydramatically.CRGO - Cold Rolled Grain
Oriented Silicon SteelLike many steels, this version is cold-rolled
to obtain the required thickness and flatness needed for a
transformer core. The magnetic "grain" of the steel is aligned in
onedirection, allowing a higher permeability than would otherwise
be possible. This material is ideal for toroids and C-cores, since
the grain can be aligned in the direction ofmagnetic flux (i.e. in
a circular pattern around the core). It is less suited to E-I
laminations, because the flux must travel across the "grain" at the
ends of the lamination,reducing permeability.CRNGO - Cold Rolled
Non Grain Oriented Silicon SteelGenerally more suited to E-I
laminations, this is essentially the same process as the CRGO, but
the magnetic grain is left random, with no alignment of the
magneticdomains. Although this reduces overall permeability, the
effective permeability may be better with stamped laminations (as
opposed to rolled, as with toroids andC-cores).Powdered IronA soft
ferrite ceramic material, used where there is significant DC in the
winding. Powdered iron cores have relatively low permeability
(about 90, maximum), and aredesigned for high frequency operation.
These cores are most commonly used with no air-gap, and will not
saturate easily. Typically used as filter chokes in switchingpower
supplies, and as EMI (Electro-Magnetic Interference) filters - the
toroid is the most common shape.FerriteSoft ferrites are the
mainstay of switching power supplies, and low level high speed
transformers (such as might be used for network interface cards and
small switchingtransformers. Ferrites are available with
outstanding permeability, which allows small cores with very high
power capability. Flyback (a type of switchmode
operation)transformers in particular are usually gapped because of
the DC component in the primary current.High permeability ferrites
are also very common in telecommunications and for other small
audio frequency transformers where very high inductance and small
size isrequired.MuMetalNamed after the symbol for permeability, as
one might expect, this material has an extraordinarily high
permeability - typically in the order of 30,000. It is commonly
usedas magnetic shielding for cathode ray tubes in high quality
oscilloscopes, screening cans for microphone transformers, and as
laminations for low level transformers. Themaximum flux density is
quite low compared to other metallic materials. Apart from being
relatively soft, if dropped, the magnetic properties may be
adversely affected(MuMetal requires careful annealing to ensure
that its magnetic properties are optimised).
15. Transformer DistortionAn ideal transformer has zero
distortion, but there are zero ideal transformers. Therefore, it
can be deduced that transformers do have distortion, but how
much?The answer depends entirely on how the transformer is used.
When supplied from a voltage source of zero ohms impedance, the
real life transformer has very littledistortion. The winding
resistance of the transformer itself is effectively in series with
the 'ideal' winding, so to get a true 'zero resistance' source you
need a negativeimpedance driver. If the negative impedance is made
to be the same magnitude as the winding resistance (a positive
resistance/ impedance), the two cancel. This is nottrivial, but it
can be done, and there is some information about the technique in
the Audio Transformers article.Any transformer operating at low
flux density, and with a low impedance source, will contribute very
little distortion to the signal. As frequency decreases, and/
oroperating level increases, the limits of saturation will
eventually be reached in any transformer, and distortion will
become a problem. This is not really an issue with mainspower
transformers, but is very important for valve output and line level
coupling/ isolation transformers, particularly at low
frequencies.The distortion characteristics of transformers used as
valve output devices is a complex subject, and will not be covered
here. Suffice to say that the normal methods ofdetermining the
turns per volt, based on the bare minimum lowest frequency response
will give unacceptably high distortion levels at low
frequencies.There is a discussion of valve audio output
transformers in the valves section. See the Valves Index for a
listing of the articles available. The 'Design
Considerations'articles in particular look at transformer behaviour
and requirements.
16. Reusing TransformersTransformers can often be reused, with
the new usage completely different from what was intended. Great
care needs to be taken though, as there are a few traps withsome
transformers used in consumer equipment. In general, a transformer
taken from an old amplifier will be fine to use in a new amplifier,
but not all transformers foundin consumer goods are usable for
anything unless you know exactly what you are doing.A question that
was raised on the ESP forum some time ago related to the use of old
microwave oven transformers (MOT for brevity). While the secondary
voltage ismuch too high (typically around 1.1 to 1.5kV RMS), it was
suggested that the high tension winding could simply be removed and
a new secondary wound to give thevoltage needed. While this will
work, beware of current (cost cutting) manufacturing trends!It is
very common that an MOT taken from an oven that is less than 15
years old will be wound such that the transformer is well into
saturation at no load. In one unit I
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tested, the unloaded current was 1.2A (yes, 1.2A - not a
misprint). The core started to saturate at only 150V, and by 240V
was very heavily saturated. In its intended use,this will not cause
a problem - remember that core flux decreases when the transformer
is loaded, and a microwave oven also has a fan, and normally never
runs for verylong. The transformer is never operated unloaded
unless the magnetron supply circuit is faulty or the magnetron
itself is dead.An amplifier normally applies very light loading
most of the time. Operating a transformer such as the one I tested
in an amp would result in the transformer overheating(288VA of
no-load heat), as well as unacceptable overall efficiency for the
amp itself. In addition, a MOT is not designed for low leakage
flux, so will dramatically increasehum levels because of induced
currents in the wiring and chassis. To add insult to injury, the
transformer was also quite noisy (mechanical noise due to
magnetostriction),and that alone would make it unsuitable for use
in a hi-fi system (assuming that it was electrically suitable).As
you can see from the above, the transformer is completely
unsuitable for continuous duty at light loading - in fact, it is
not designed for continuous duty at all. While it ispossible to add
more turns to the primary, a great many additional turns would be
needed to reduce the flux to below saturation. In addition, adding
primary turns meansthat the insulation must be perfect to prevent
potentially fatal mishaps.All transformers that you intend for
reuse should be examined on their merits, and tested in a
controlled environment to ensure that they will survive in their
new role. Justbecause a transformer was used in one piece of
equipment does not mean that it can be used in any other equipment,
as the design criteria are often very differentindeed.If you are
satisfied that a transformer is suitable for the new task you are
about to set it towards, then turns can be removed from or added to
the secondary to get thevoltage you need. Do not tamper with the
primary unless you understand the insulation requirements, and can
ensure that the final transformer is at least as safe as itwas when
you found it. This article will not even try to cover the task of
rewiring the secondary - if you don't know how, and can't work it
out, then you shouldn't bemessing with transformers in the first
place.
VA Resistance ()