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Calculation of Output Transformers
The output transformer
is probably the most expensive part in the amplifier and something
you have to live with if you like classic tube amplification.
To separate the high voltage and match the speaker impendance
with the tube impendance we need audio grade /output/ transformer.
Single Ended /SE/ Amplifiers also run unbalanced DC through load
and even if we somehow manage to connect a special very high impedance
custom made speaker - that will introduce at least significant
losses /speaker most probably will overheat and burn in smoke/.
Output transformers are transferring certain power to the speaker
so they are closer to their cousins - the power /mains/ transformers
and in many cases good outputs are way larger than mains for the
same rated power. There are circuits of Output Transformerless
amplifiers /OTL/ which properly made nave really great sound but
are harder to maintain and less reliable /some designs use up
to 16 paralleled low impedance power tubes per channel to do the
job/. Most tubes have high output impedance and unfortunately
all of contemporary dynamic loudspeakers have low impedance. So
we have to match them with tube impedance and if we need good
performance - wide bandpass, low distortions and low losses we
have to take special care of preliminary calculations and design.
It is not easy task and takes a lot of experience but if you have
a calculator on hand you could DIY and even wind it yourself.
All Equations here are for Hi-FI Class A amplifiers - that is
even better if you design AB or B amps. Here is how is made the
simplest practical way:
First you have to choose output
tube/s/ and desired power to achieve. Determine tube/s/ Load Resistance
or Plate Resistance - RP from the tube data sheet. The tube RL optimum
is usually listed there. If you don't know it look here choosing optimum load...
We are going to perform SE transformer
calculations without negative feedback and my goal is to simplify the equations. We
need to determine minimal size of the necessary core E - I type
lamination is most economical "no waste" iron and is
also classic for outputs.
Two coils C-core transformer
is probably better for reduced leakage inductance but the iron
is expensive and harder to obtain. There are also ironless "AIR-CORE"
transformers shown on some sites - they need many pounds of copper,
have an increased losses up to 60 % and not very good bass response,
but are very linear /no distortions is introduced/ that's deriving
from the linear magnetic properties of the air itself.
Now - we have Pout chosen and we
have to calculate and choose core size - Q in square centimeters
- Pout is the output power in VA /Watt/
- Q - core size in sq. cm. /For square inches divide the result
- Now increase Q with 10 % and choose a standard E-I
size lamination. /For cheeper Hi-FI /with feedback/ or guitar
amps you may reduce the size twice/. For
longer equation - look here.
- Now lets calculate number of primary Turns/Volt -
- /for feedback guitar amps you may reduce n1 twice/ Basic longer equation for
Turns/Volt - look here.
- The AC voltage on RL in the primary is
- N1 - number of primary
turns we need to wound is
- Next we have to to match the loudspeaker impedance
to tube impedance look
again here /or to determine reflected impedance ratio/
and the basic formulae for transformer without losses is:
- n1; n2 - number of Turns/Volt for primary and secondary
N2 - total
number of turns for primary and secondary
- U1 -
AC voltage on primary
- Z is loudspeaker impedance
- d - wire diameter in millimeters
- I - current in Amperes
- Now calculate N2 and to reflect the losses in copper and iron
we need to increase number of secondary turns - N2 with 5% to 15 % (the lower the power - the
higher the percentage). Now the transformer is almost ready to
- Wire diameters depends mainly on Is
A/sq.mm. you choose. To calculate the diameter in mm we use the
- I is higher tube current in Amperes
- t = 0.7 when Is = 2.5 A/sq.mm;
- t = 0.8 when Is
= 2 A/sq. mm;
- t = 0.9 when Is
= 1.5 A/sq.mm
- The thicker the wire the less power is lost and less
heat is produced in both windings /primary and secondary/. So
if possible choose wire thicker than calculated above, but keep
in mind that physically you may not be able to fit all the numbers
of turns when you start winding the coil.
- Now we have to calculate how our transformer can
be made in the real world with the calculated parameters or we
have to go back and choose different core or wire size. We choose
square stack with following sizes:
- h - that the longest side of
the coil former in millimeters.
- H = / h - 2mm /
we have to to fit and secure the leads with strong tape - that
is why we cannot use total h size
and have to reduce it with 2-5 mm. /In Millimeters/
- b - shortest side /usually
1/4 of the flange size/ in mm. /Only one flange shown here/.
- B =0.5 - 0.9 . (b
- 1 mm) that comes from
the inter turn/inter winding insulations and interleaving we
need to include in the coil /mixed primary and secondary - that
reduces leakage inductance and is important for band pass of
the transformer/. That again reduced size - but that real life.
All windings have to be well electrically insulated with paper,
cloth or insulation tape which adds up significant thickness
and reduces inter winding capacity. That important for the higher
frequency of interest and the electrical stability. /If you are
making very "high voltage" transformers B could go
- D - wire diameter with lacquer
insulation in millimeters/a bit thicker 5% - 10% aprox. more
- N11; N22 - number of
turns per layer
- number of layers
- Now we have to calculate if the number of turns we
have calculated will fit our design:
- for number of turns per layer we take closest smaller
number /example if calculated 29.47 = 29/
- for number of layers we take closest bigger number
/example if calculated 9.47 = 10/. That the calculation for primary.
- The same way you calculate secondary N22= H/D ; M22= B/D
- if it calculation does not
fit the coil former - select thinner wire and insulation or bigger
core size and start over.
- We may well split primary in series /high voltage
side/ and split secondary in parallels /high current side/ in
at least three or four equal parts each and interleave them for
best frequency response - result from lower leakage induction.
- Start winding - secure leads tightly with glue or
insulation tape and remember turns nave to be very tight
and as close as possible to each other. You may start
with the secondary and finish again with it - that interleaving
is good for reducing overall leakage induction; parasitic capacity
to ground and also increases safety - low voltage side is on
top. That's four secondaries and three primary windings. This
design method is proven over times and gives extremely good results
for Ultra - Fi SE amps. Finally you have to complete you transformer
stacking the iron on the coil /for SE amps adding "air gap"
between E and I sections of the iron is a must/. Air - gap is
introducing an increased resistance in the magnetic path which
shows increase in iron losses. There's complicated formulas for
calculating "air-gaps" but in practice it boils down
to the following:
- The "air gap" is not usually "air"
but precut piece of non magnetic material such as thick paper
or "shoe box cardboard" /0.2 - 0.5 mm/ for reducing
DC magnetic saturation of the iron and linearizing the magnetic
hysteresys curve. Insert 0.3 mm thick material between E part
and I part of the iron for best results /up to 15W SE output/.
- That is practical way to do a output transformer
for SE amplifier. After completing the transformer test it the
simplest way - connect the primary to the mains - if does not
go out in smoke or burn in flames it is ready to be connected
to the tubes in your schematics. If buzzing occurs tight the
screws and look at the coil former - the transformer may need
few more laminations.
- For Push-pull stages you may use same methods and
equations and use the reduced core size since there is no standing
current in the primary. Plate resistance here is:
- Rpp = 2Rp.
- Reflected impedance per tube is 1/4 of total impedance
plate to plate. No unbalanced DC flowing so no "air gap"
is used here E-I laminations piece by piece is inserted from
both sides of the coil former/some folks may like to use air-gap
for more linear response - that may create other problems with
the low level induction and somewhat increased losses/. For Class
AB or B you may need to split the coil former in two "disks"
and wind first one of the "disks" interleaving primary
and secondary and later take the coil out, turn it over and put
it back for winding the second "disk". Here is how
coil former looks in that case:
- There are equations to check induction
of primary; frequency response and other parameters - that's
no object of our practical transformer calculations. and it also
difficult to do without exact iron parameters /such as magnetic
permeability, flux density, exact B-H curve, iron per kilo/pound/
losses which varies from steel to steel/ specified by the silicon
grade steel manufacturers.
- Regards P.G.
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