Speaker Matching Transformers. 2013

This page is about speaker matching transformers.
Fig 1 to 13 show details of transformers and all is explained.  

There is sometimes a good reason
to use a transformer between an amplifier and speaker
to improve the sound quality and improve all measured parameters in terms of power ceiling range,
distortion, bandwidth, and damping factor..
The transformer is called a Speaker Matching Transformer, or SMT, and is usually a black box
connected by short cables from amplifier and to which existing speaker cables may be plugged in.

In most cases, the transformer effectively converts a low impedance speaker to a higher impedance.

Definitions of terms used here :-

R is resistance in ohms, and R = V / I where V is voltage in volts applied across R, and I is amps
of current flowing through R as a result of applied V.
RL is Resistance Load, which is the resistance of a wire or manufactured resistor used in a circuit
where active devices such as vacuum tubes or solid state cause a change of current to to liberate
RLdc = load between a DC supply rail and a device to change current,
RLa = load for ac power at an anode,
RLa-a = load for two push-pull anodes of two tubes supplying opposite phased voltages to RLa-a.
P is the symbol of power is in the form of heat measured in Watts and may be calculated P = V x I,
or V squared / R or I squared / R.
Po = power output, Pin = power input.
L = inductance in Henrys, millihenrys, mH, or millionths of a Henry, uH.
Lp = primary inductance of a primary winding, Lsec = secondary winding inductance.
LL = leakage inductance between two windings.
C = capacitance in Farads, F, millionths of Farads, uF, or billionths of Farads, nF,
or 1,000 billionths of a Farad, a pico Farad, pF.
X is Reactance in ohms for either L or C. The ohm value is only valid for only one particular
sine wave frequency.
Reactance value of C = XC, and of L = XL.
XC = 1,000,000 / ( 2 x pye x Frequency in Hertz x C in uF ) = 159,000 / ( F x CuF ) ohms.
Hertz = frequency measured in cycles per second, Hz, or kilocycles per second, kHz, or millions
of cycles per second, MHz..
XL = 2 x pye x F in Hertz x L in Henrys = 6.28 x F x L ohms.
Ra = dynamic anode resistance on ohms.
µ = amplification factor of a vacuum tube.
µ = also means iron core permeability, a number that varies with F and applied Vac so context of µ
must be remembered.
gm = device transconductance in A/V or mA/V.
Z = impedance, nominated in ohms, and for any combination of R, L or C connected together,
and such parts of circuits with R plus L and/or C are called networks. The impedance of any
network measured between any two points is dependent on frequency of the sine wave voltage
applied from one point to another. The calculation of impedance between two points connected to
more than one R and L and C can be almost impossible to work out, and is best worked by
use of applied software and PC, although simple R+C and L+R networks can be easily calculated.
But without computing, an approximate estimation of Z may be made and values trimmed by measurement
until wanted F response and Z is obtained.

The following formulas don't include frequency F. But ohm values of XC or XL do include frequency.
I make no apologies for saying you have to consider many things if you
are to make accurate calculations
about L&C&R networks, and you must be careful when measuring them. Its no use chucking a tantrum
when I expect
you to understand details and to calculate and consider things that are not simple!!!!!.
For example, For R + C in parallel, Z (R//C) of network = 1 / square root of ( 1/R squared + 1/XC squared ),
Z in ohms, R in ohms, C in Farads.
For R+C in series, Z ( R+C) = square root of ( XC squared + R squared ) in ohms where R is ohms,
C in Farads and XC in ohms.
Similarly, for R + L in parallel, Z (R//L) = 1 / square root of ( 1 / R squared + 1 / XL squared ) ohms.
For R+L in series, Z(R+L) =  square root of ( R squared + XL squared ).

Eg, XC for 2uF is 79.5 ohms at 1kHz. Impedance of say R = 79.5 ohms plus 2uF in parallel

is 56.2 ohms. Where XC = R then XR//C = 0.707 x R.
In series, 79.5 ohms plus 2uF has Z = 112.4 ohms. Notice the XC+R = R x 1.414.
You will have to study many more examples plus a mountain of theory and equations for which
I don't have time or space to include here. Many keen audiophiles are utterly dumb and unable to
consider the world in terms of applied mathematics, and its why their own attempts and designing
gear are so ineptly incompetent and bad sounding, and likely to generate smoke.

A typical speaker may have an impedance of  4 ohms printed impedance on the label.

But the construction of the speakers include drivers which have complex R+L components and some
C  if the box effect is added. A simple 2 way crossover network board may have 15 L, C and R parts
included, and the final actual Z cannot be easily calculated by anyone on the Planet. But the Z will
be a finite value at each frequency considered and the"average" Z between input terminals is the
"nominal impedance". But Z may in fact vary between 2 ohms and 30 ohms depending on any single
frequency applied. There may be a region of say between 100Hz and 500Hz where Z = 4 ohms,
+/- 1 ohms, so the speaker is called a "4 ohm speaker" There are speakers which have Z which may be
"difficult to drive" and these may have their lowest Z in the band of frequencies where most audio music
energy occurs between 100Hz and 1kHz. Old AR9 had two awful quality 3.6 ohm x 11" bass drivers
in parallel and with the crossover the Z input was just above 1 ohm at 120Hz. This caused many
amplifiers to fail from overheating. But AR9 sold for $4,500 in 1975 and ppl bought them because
manufacturers know how to market garbage product, and buyers are so damn gullible.

There are reasons why it is not wise to connect a speaker with any low Z down to say 2 ohms

to any amp that has been designed to work with 8 ohms. If you wish to damage your amplifier,
this is what you do, and it defies common sense. Common sense says less ohms are easier to drive.
Like less bricks on the truck mean the truck can drive up the hill easier. No matter what I say,
ppl don't remember MORE Ohms = easier for amp, LESS ohms = harder for amp.

The lower the speaker ohms, the higher the current needed to produce the same power output and

sound level. If a speaker sensitivity is rated for SPL = 88dB/W at 1M, then for a "4 ohm" speaker
the amp voltage is 2Vrms and amp current is 0.5Arms. ( This assumes the Z is constant for all F and that
the sensitivity is constant, but both vary considerably, so manufacturers just give the nominal or average value.)
For 10 Watts into 4 ohms you need 6.3Vrms and 1.58Arms. There may be a dip in Z to 2 ohms
at say 200Hz and where sensitivity is much less. The same amp voltage of 6.3Vrms generates 3.15Arms.
The speaker may have a high reactive L or C component in its "load nature" which is the sum
of  L, C and R elements in drivers and crossover filters all acting together. Some amps would not
perform well with 2 ohms and high currents even though they have a high maximum power output

This previous paragraph has bamboozled everyone reading it, so its time to look at diagrams

which may break through the "clouds of dumbness" which affect your brain every time someone
rattles off a pile of figures in text.

Fig 1.


The above shows a typical set up where someone may wish to ensure that a speaker with a nominal
Z that is either above or below the ideal load value for the amp can be converted into an impedance
that is ideal for the amplifier, and hopefully the resulting music replay will include less amplifier distortion,
will not cause tubes to overheat, and will give better damping factor, and all of this without winding losses
exceeding 5%, and without reducing the bandwidth of signal applied to the speaker.

Let us suppose we have a fairly well made tube amp such as one channel of my 5050 at


For this amp, 8 ohms is a very nice load for each channel. In fact, all speaker loads between 4 and 16

ohms are very well tolerated, and one would not really need a SMT at all.
Suppose the 5050 had only one one pair of output terminals labelled "8 ohms".
Suppose I wanted to power a two ohm speaker, or 2 x 4 ohm speakers in parallel.
Then the SMT would be a good idea, because 2 ohms is a dangerous and bad sounding load to connect,
especially if it has low sensitivity needing high power to generate a wanted sound level.

Many people will purchase the most powerful amplifier they can afford, and then buy the most expensive

speakers without worrying about sensitivity, impedance, load matching, or power, or anything else at all,
except how to get it home and hook it all up. What a dumb and uneducated approach!

Well, 95% of the world's people cannot be expected to be fully educated on how things work.

So they have to use guesswork or salesman's advice and/or user manuals and perhaps online information
to set up their system. Advice is all minimized if they buy a complete 3 in 1 box of electronics and speakers
as a matching package. 5% of music listeners expect more hi-fi than is available from bargain basement mass
produced "packages" costing under $500. Some are extremely fussy about sensitivity,  impedance,
load matching, and power because they know that if they understand these issues and apply the knowledge
they don't have to spend so much as those who buy far more expensive amps and speakers.

Fig 2.


Here is a nice tricky little picky if ever there was one!!

Before 1955, it was established by authors of the 1955 Radiotron Designer's Handbook, 4th Ed,

on page 623, that maximum sound levels for men and women was 78dB for symphonic music.
Maximum levels for musicians was 88dB, and highest levels for male "programme engineers"
was 90dB. Today, any tests may show men and women may prefer slightly higher levels especially
since higher levels of bass exist in much pop music and film sound tracks et all. Older people
like lower SPL than younger people, unless they have gone deaf.
My tests using simple SPL meters in lounge-rooms reveals that 85dB is a maximum average for
most people, for most music. Classical orchestral music may linger at average levels much lower
than 85dB, but also soar briefly to 100dB. Much pop music will sit between 85dB and 91dB, with
very little change to level because of compression and repetitive drum and bass levels and because
of young people's preferences for continual Boom-Chikka-Boom & rap garbage.

For most serious hi-fi listeners, their speakers and amp must be able to make SPL = 100dB at least.

Their average level may be say 85dB.

So let us suppose you buy a pair of speakers, say X-Brand, rated for 88dB/W/M, ie, the speakers

produce SPL = 88dB with say 1kHz sine wave at distance of 1 metre with 1.0 watts applied,
and all done in an anechoic chamber. Inside a nicely carpeted room with lounge chairs and some absorbent
furnishings to reduce unpleasant reverberations, the 1.0 Watts applied may produce 88dB SPL at 3 metres,
allowing for reflected sound. Music energy is a mix of very many frequencies in dynamically varying levels
and one should find the quantities mentioned so far will be about correct. Hi-fi systems will have two
speakers for stereo so that to make an SPL of 88 dB, only 0.5 Watts need be applied to each of two
speakers to make an SPL of 85dB in each. Each change of +/-3dB of SPL measured requires a power
change of +/- 6dB of power, in other words, to increase SPL +3dB, twice the power is applied,
and to reduce the SPL -3dB means 1/2 the power is needed.

Now because average room SPL may not be more than 85dB, we need only have each speaker

produce 82dB, and if we look at the table 1 in Fig 2 we see only 0.25 Watts is needed for each speaker
and together, 2 speakers produce 85d.

Table 2 in Fig confirms the power needed for average 85dB and only 8 Watts per channel is needed for

total room SPL of 100dB. If each amp can make 24 Watts, then max SPL will reach 106dB which usually
is plenty for most ppl. Most recorded music has had its dynamic range limited or compressed and the
85dB to 106dB is enough, although in the real world without electronics some acoustic instruments may
produce SPLs much higher where microphones are placed near instruments, and sitting in among the brass
section of a large orchestra requires ear protection.

Therefore, the use of 2 x 6550/KT88/KT90/KT120 in each amp channel usually gives "enough" power.

But whether it really is enough can depend on impedances, not just sensitivity. The more sensitive the speakers,

the less power you need. Most are now made at about 88dB/W/M and many are 4 ohms, with dips to 2.5 ohms.
Fig 3.

The two graphs show what power may be expected from 2 x 6550 ( or KT88 etc ).
The graphs are prepared from tests carried out on an amp with given operating
conditions and with OPT matching giving 8k0 : 8r load matching setting.

The PP amp
can give up to 55 Watts with a 3 ohm load, but that doesn't mean you must use
a 3 ohm load. With loads less than 4 ohms, THD becomes high because class A working portion
is a low % of total possible class AB power. And the amount of effectively applied NFB is low.
Damping factor is worse.
With 8 ohms, you get 35 Watts, and perceived SPL maximum at clipping is only -2dB and almost
a negligible amount compared to having 55 Watts. 35W of class A power, low THD, and good DF
will sound better.
The variations with THD when using different loads can be seen in THD graph in Fig 2.
The THD levels have been drawn on a logarithmic scale, so you need to read the variations carefully.
Basically, the higher the speaker ohms, the lower the THD and lower all other distortions as well.
But if load is say 16 ohms, then available max PO is only 18 Watts. But it is all pure class A PO and
with low THD, so if clipping does not occur, music may sound best with the 16 ohm speakers
- if the speakers don't create distortions.
My PP amps have maximum PO possible with a load of less than 1/2 the nominal speaker Z, ie,
max PO occurs with 3 ohms, although terminals are labelled "8 ohms". Many amps make the maximum
PO of say 55 Watts occur with the labelled 8 ohm load, ie, their OPT would have a Z ratio of 3k0 : 8 ohms,
not 8k0 : 8.
This means that the amp with 3k0 : 8r OPT surely would not work well if a 4 ohm speaker with dip to
2 ohms was connected. The tube load then drops to1k5, with dip to 1k0. The THD/IMD with a "4 ohm load"
would be many times greater than with 8 ohms or to anything I would make.

Many mass made amps may have output terminals labelled 4 ohms and 8 ohms, but what works best is

8 ohms and 16 ohms respectively. To overcome such a problem, the SMT with 2:1 turn ratio can make a
4 ohm speaker look like 16 ohms. Then the tubes work with a higher RLa-a ohm load value which
gives lower THD/IMD and better DF and bandwidth etc.

The SE amp
with 2 parallel 6550 has a very different OPT, and the tubes always work in class A.
Load matching is more critical than for any PP amp of the same Po, because SE amps cannot generate
class AB Po that can be up to 3 times the maximum pure class A Po maximum
In the SE amp case, maximum class A power = 22 Watts is made when load is 8 ohms, and loads of
more or less ohms will always give less power. If a speaker was 4 ohms with a dip to 2.0r then you may
expect a poor sound at high levels because only 12 Watts is available, and any signal F where Z = 2.0r
gives only 8 Watts. The impedance dip in speaker Z character will cause terrible IMD and THD at all
but very low levels.The max power with 16r will also be less at 13Watts but at least this power will have
low distortion and DF will be high.

Consider old Quad-II amps.
These have a pair of KT66 with OPT arranged to give a Z ratio
of 4k0 : 9 ohms or 16 ohms. But many ppl try to use 4 ohm speakers connected to the OPT when
terminals under the chassis have been strapped to suit 8 ohms. The RLa-a on tubes becomes only 2k0,
and this is far too low for fidelity. But best lowest winding loss connection is the "16 ohm" setting of the
OPT strappings. The best load is 32 ohms that gives 18Watts, all class A with RLa-a tube load of
8k0. Using a 4 ohm speaker with SMT which has a ratio of 32r : 4r, ie, ZR 8 : 1, TR = 2.83 : 1
means the 4r speaker looks like 32r at the amp and sound will be excellent, ( providing all other
old things in the old Quad amps have been serviced or replaced.

OTL amps.

An OTL amp is said to be usable with a "4 ohm" speaker. 
My experience tells me just about all OTL amps work better with a much higher load value, maybe 16 or 32 ohms.
There are OTL amps where the use of a 16 ohm speaker will increase available maximum output power,
increase damping factor by 4, and reduce THD/IMD by 1/4. Let us examine why raising the RL ohms improves
the sound, and all measured functions.
Fig 4.

The Fig 4 shows the Ra curves and class A and B load lines for one 6AS7 with both its triodes
paralleled. As you can see, loadline A-Q1-B shows near linear intersection of Ra curves gives 
7 Watts of pure class A1 with RL = 630 ohms and with total Pda at idle = 18 Watts.
Using two tubes in PP and class A1 would give 14Watts and 2H is cancelled leaving a probable
1% 3H with RLa-a = 1,260 ohms.

Using 4 tubes with OTL seriesed PP tubes or Circlotron use in class A1 will give 28 Watts

with THD < 2% 3H and load of 630r / 4 = 157r.

With 4 tubes in series/parallel with Technics Futterman circuit or Circlotron, Ra effectively

is about 20r so damping factor = 157 / 20 = 7.8 approximately.

The class B1 operation shows RLa = 32r with peak Ia = 740mA, and Ea swing = 22Vpk.

I would never risk class using class B2 by forcing grids positive. In the example, pure class B with zero
Iadc at idle is not used; there is some low idle Iadc at idle, but Pda calculations then become the same
as for pure class B.  
2 x 6AS7 could manage 7Watts in class B1 with RLa-a = 128 ohms using a normal PP OPT.
With a Circlotron, primary OPT load becomes 32 ohms, and with 8 tubes primary load = 8 ohms
and there seems to be no need of an OPT, ( but of course there is, afaiac ).
Pda a rises to 24W max for each tube in such an amp. It could be higher depending on the idle Iadc.
Tube current production is not very linear, and the low power region of a few Watts has high THD%.
Tubes work in a region of borderline safe working. The use of a 4 ohm load could push peak Ia max
in class B1 to about 0.9Amps with each tube having a load of 16 ohms. Pda could be at least 28W
in each tube. PO for 8 tubes loaded with 4 ohms is 24Watts max and less than PO for 8 ohms.
Distortion damping factor is very poor for all loads without any OPT.

Most OTL need to have 40dB of GNFB applied to force the circuit to measure acceptably.

This is possible because there is no OPT with its inherent phase shift at LF and HF which is included in
the FB loop. An SMT does not need to be included in any NFB loop. The SMT can reduce the
amount of GNFB needed to 12dB, and at least one gain stage may be omitted. Output power maximum
can be doubled, with mach more class A1 Po. 

I can conclude that class B1 with 6AS7 is the worst way to use tubes, especially with a very low value

of RL. an SMT will allow better operation for an amp set up for B1 and can have increased idle tube
current for class AB1 and a much higher % of class A power.

High power tube amps or SS amps may be more load tolerant because people use the same power

for the same sound level regardless of the power amp capability.

Nearly all high power tube amps capable of  say 70 Watts+ will be found to produce say 0.4 % THD

at the 70Watt level or just before the wave form begins to develop visible flats on the crests of sine waves
which is usually about 2% THD. So if speaker is 8 ohms, then amp Vo = 23.6Vrms. But average
listening levels may be at 0.5Watt which is 2.0Vrms, and THD is approximately proportional to
Vo, so THD at 0.5W = 0.4% x ( 2 / 23.6 ) = 0.034%, and by calculation THD is quite negligible.
If a 2 ohm speaker is used, and volume is adjusted to make the same power of 0.5W, then Vo = 1.0Vrms.
What would THD be then? One may find max 2 ohm power = 35Watts, at say 1.0% at Vo = 8.3Vrms,
so at 1.0Vrms, expect THD = 1% x ( 1 / 8.3 ) = 0.12%.

THD has quadrupled because load value has been quartered - for the same sound level.

If the amp has maximum 22Watt capability for 8 ohms with 2 x 6550 in PSE, expect Vo = 13.2Vrms,

with THD = 1%, a higher amount than for a PP amp because all SE amps tend to make much more
THD because there is no cancellation on even H from push-pull operation.
Expect the 0.5Watt THD level to be 0.15%, more than 4 times the 70Watt capable PP amp.
If speaker is 2 ohms, max PO = 6Watts at 3.5Vrms and 1.5% THD.
At 0.5Watts with 2 ohms, THD = 0.43%.

Again we see a huge THD increase just because 2 ohms is used instead of the correct design load

of 8 ohms.

And we also need to say the lower the maximum power is for the amp, the higher the distortion

becomes for the same listening levels.

To avoid the THD and resulting IMD increase, the use of SMT is well justified!

When the amplifier power is close to the minimum we think we ever would need, we might

then remember these considerations :-

1. We should always try to provide the amp with a speaker load ohm value it prefers.

2. The speaker ohms between 50Hz and 1kHz should always be higher than what is labelled on the

amp terminals.

3. Use of SMT to reduce amp Vo but increase Io between amp and speaker will give the amp the

higher load ohms it prefers.

4. Impedance matches available with SMT should be approximately as in the table :-


Primary Input load ohms
Sec = 0.5 x Pri load 
Sec = 0.25 x Pri
Sec = 0.125 x Pri
Sec = 0.0625 x Pri
64 Ohms 32 Ohms 16 Ohms 8 Ohms
4 Ohms
32.0    16.0    8.0   4.0 2.0
16.0 8.0 4.0 2.0 1.0
8.0 4.0 2.0 1.0 0.5

The power handling ability of the SMT must allow at least 50 Watts with any load value and winding
resistance losses to not be less than 5%. The cost of manufacturing SMT with a 50Watt rating will be
little different to a 25Watt rating.

For 50 Watts of input power for 64 ohms, primary input voltage will be higher than for any other load value

and be 56.6 Vrms. The core saturation at 56.6Vrms should not occur above 14Hz. This requirement
for voltage capability is independent of current ability. This means the maximum permitted Bac < 1.6Tesla
at 14Hz.

The number of turns in the auto transformer winding is determined by the formulas elsewhere at this website

for PP OPT design.
But the following formula from the OPT design pages applies :-

Fsat  = 22.6 x V x 10,000 / ( S x T x Np x B )

where Bac is in Tesla, with 1 Tesla = 10,000 gauss,
22.6 and 10,000 are constants for all transformer equations,
V = Vrms signal voltage across the primary, or sq.rt ( PO x PRL )
S = core stack height,
T = core tongue width,
Np = primary turns,
F = frequency at which B is to be measured.
All dimensions in mm!!

Many DIYers may find they have a pile of old transformers from which they think they might make
something useful, such as a SMT.
Usually, the most common old E&I lamination size useful for this application will be "wasteless pattern"
with tongue = 38mm and window size of 19mm x 57mm. The iron quality of most old transformers is
mostly quite poor. This is because the core has low maximum permeability, µ, often below 2,000,
and has high hysteresis losses and generates high THD at F below 100Hz.
And this is because the iron may have a low silicon % content and it has not been cold rolled and
annealed to align metal crystals, ie, worked and heat treated. So I can't really recommend that
you try to use the iron from old mains transformers with poor quality iron.

For the best SMT or for any OPT handling audio F signals, you need GOSS laminations, and GOSS

means "grain oriented silicon steel" and this is much harder to ever find among old piles of fused
transformers which nobody wants.

So, for SMT, you need to BUY core material, and that upsets hobbyists who hate paying for anything.

You need to know what weight you need, perhaps 10Kg, and if price is $25 per Kg, there's $250,
and does not include freight. Finding a supplier willing to supply less than 50Kg of core material is difficult,
and you must expect to pay far more per Kg than if you were to buy 1,000Kg, an amount that may be
a minimum quantity from large makers of laminations.

The issue of transformer generated distortion cannot be treated lightly. Iron in all audio transformer cores

can generate distortion harmonics greater than the vacuum tubes where the amplifier output resistance
is high. In the 100Watt SMT described in detail below, the iron distortion even with GOSS may over 10%
at typical levels of listening where the signal source resistance is over 100 ohms. The distortion is
a mainly odd H harmonics, 3H, 5H etc. The 100W SMT below has primary Lp = 4H at 50Hz so the
XL = 1,256 ohms. Let us say the signal source R = 600r. One may find THD = 12%.
The current flow in the winding without any load with 5Vrms applied and 50Hz is only 4mArms, and
distortion current at 12% is 0.048mA, a very small current. One can say that the the primary winding
has the properties of a linear perfect primary inductance where 4mArms flows, and also has a  network
of equivalent non linear circuit elements which produce 0.048mA of distortion currents.One may say
the non linear network causing distortion has a high impedance averaging V / I = 5V / 0.048mA =
104kohms, a quite high impedance. The SMT is designed to be used with an existing amplifier with Rout
of less than 1 ohm, and when this is done the distortion current and its impedance still exists, but the
distortion voltage is shunted by 1 ohm, and its hard to measure the iron caused distortion as a result.
With low grade iron with lower Si content and less cold rolling to align crystals, iron caused THD
may be 50 times worse than figures I have mentioned for GOSS here. So hence low grade iron
will show some distortion with the low signal source resistance.
One will find that where iron cored items are used with vacuum tubes, OPTs, and choke loadings,
pentodes are not used without NFB because because their Ra is a high Z current source and THD
will be atrocious. It is also bad practice to use the drain circuit of a mosfet to drive a transformer unless
there is a good amount of loop NFB.

The inductive reactance of a winding with turns around an iron core show that the primary inductance

Lp is low at low levels of amp Vo, and then Lp becomes higher as the sine wave amplitude increases,
and then Lp becomes lower when the core material reaches onset of saturation. This is the nature
of non linear iron behaviour. High enough Vac across the winding results in a cessation of change
in magnetic field beyond say 1.6Tesla. When this occurs, magnetic field is static, and cannot
cause the opposition of current flow and reactance reduces to zero, and core has become
"magnetically saturated". This can occur for part of a sine wave for where Bac is forced above
1.6Tesla, but magnetic field cannot increase. Thus for the section of sine wave where applied voltage
would cause Bac to exceed 1.6T, the actual impedance becomes no more than the wire resistance.
Saturation is proportional to frequency, so the lower the F, the higher the Bac and the easier it is to
have saturation. LF caused saturation can cause a sudden enormous rise in THD and IMD and
complete lack of fidelity with music. SMTs should allow full 100 Watts into the primary load of say
8ohms and at just above the Fsat which should be close to 10Hz. It is saturation behaviour that determines
the turns and Afe needed for a primary winding's "turns per volt", and not the calculated primary inductance.

To minimize the distortion caused by iron which is always worst at F below 100Hz, GOSS should be

used, and to reduce sudden onset of core saturation the core µ should be reduced from the high values
found with GOSS, perhaps 15,000 with some E&I samples, to no less than 3,000. This makes the iron
behave as an inductance with less sudden saturation at LF, and is better than having a high inductance
that becomes a short circuit if the core is saturated if stray LF below 20Hz are applied at high voltage
The amplifier driving a SMT must have low output resistance, preferably less than 1/10 of the load value
to be driven, easy to obtain from most amps where NFB is applied within the amp.
But some OTL amps have quite high Rout and quite a poor damping factor. However, if you connected
a SMT with 64 ohms input load to drive a 4 ohm speaker, then Rout of the amp need only be as low
as 6.4 ohms to get a DF = 10. Iron caused harmonics will be suppressed by whatever FB is operative,
including that which exists in the triodes without the NFB loop added. Using solid state devices such as
mosfets in source follower mode and with global NFB can mean Rout < 0.1 ohm, and iron caused
distortion is easily reduced to utterly negligible levels, and the iron ceases to "get in the way of the music".

THERE ARE EXAMPLES of other speaker matching trannies which use an auto transformer with ONE

winding to give input as 8 ohms and with with taps offering use of speakers with Z = 4, 2, 1, 0.5 ohms.
A classic modern example is made by Paul Speltz at http://www.zeroimpedance.com
I have tested one of Paul's toroidal transformers. I found it had excellent bandwidth. Two audiophiles here in
Canberra bought them and were well pleased. One bought the simple un-boxed version which I was
asked to enclose in a box. I made a wooden box and mounted the tranny inside and surrounded with
compacted dry sand. The lid had foam between lid underside and sand surface to keep some active pressure on the
contents. Transformer was siliconed to bottom of box so movement creep is not possible.

I found toroidal windings were very messily wound but the measurements were very good. It may be difficult

for any DIYer to duplicate this performance of wide bandwidth unless he knew the secrets of the sequence
of layers of windings and their relative position around the toroid circle. Inherently, toroidal transformers
offer broad bandwidth because a primary and secondary windings are well interleaved if each are wound
around the toroid in several layers which overlap all the way around.

THE DIY SMT BUILDER will probably find it easier to use E&I laminations or C-cores and use a

preformed plastic winding bobbin.   

Any single winding transformer with taps, ie, auto-transformer that you may be tempted to wind at home may

suffer much reduced HF response at secondary taps especially if secondary load is lower than 1/2 the input load.
Despite auto transformers having only one winding, as the the portion of shared winding used for a secondary
winding becomes smaller, the transformer behaves like an isolation transformer which has a low number of primary
and secondary interleaved sections. Consider you have 8 layers of wire on a given bobbin for one winding, occupying
a window size of 19mm x 57mm. Say you devote the bottom two layers for a secondary for 2 ohms. The TR
will be 8L to 2L, or 4:1, so primary load input = 8 ohms. You may find than HF bandwidth does not reach 8kHz.
To increase the bandwidth, the 2 layers used for 2 ohms should be from 3rd up and 6th up from bottom. the series
connection is the same, with 6 layers from top to 2 ohm tap, and then two layers to 0V. But then you will find
winding losses will be high and BW still rather low, so then you need to increase total layers and have maybe 2
extra layers in parallel with the 2 layers for 2 ohms. Then the core window needs to be increased, or stack height
increased to reduce Np, and then the design exercize will take a week, not just one evening with pocket calculator
using print-outs of my design pages on your kitchen table.

There are some toroidal mains transformers which have 2 x 115Vac primary windings with say 2 x 50Vac secondary

windings and rated for 300VA. These are used for PT in solid state amps where +/- 70Vdc is wanted. There are those
who may be tempted to use these as SMT. But the range of available load matches is very low, and many problems
will remain and I cannot recommend the use of any mains transformers for audio hi-fi applications.

To test a SMT, I found it necessary to use an amp with Rout less than 2 ohms and bandwidth of 2Hz to 3MHz.

Most amplifiers cannot produce the necessary bandwidth, 10Hz to 65kHz is common. But for TESTING
audio transformers one always should explore behaviour beyond ordinary bandwidth.

Test signal levels do not have to exceed 3Vrms for SMT. This means that an elaborate multi stage amplifier need

not be used for a test signal. All that is needed is a mosfet based buffer amp with no voltage gain and which merely
lowers the source resistance of the test signal voltage from a standard 600 ohms to less than 2 ohms.
Here is what I have used :-

Fig 5.


The buffer stage allows adequate testing of any audio transformer at F above core saturation, say 10Hz to
over 4MHz when secondary is loaded with specified RL, or not loaded at all with R, or loaded by any
R+C network or with a pure C load. Test loading with L may also be done with caution at low F.

However, when using such a buffer, LF core saturation performance may be difficult to test with signals taken to

the primary input where signals across windings is the highest . The 100W SMT below is rated for 100Watts into
8 ohms which means 28Vrms may be applied across the primary and at 10Hz when calculated Bac = 1.5Tesla.
At this condition the core should produce distortion exceeding 3% and easily seen on the oscilloscope.
Therefore one would need an un-distorted input signal to the buffer stage of about 30Vrms and going down
to 2Hz. The buffer shown here cannot produce more than 10Vrms, so core saturation may not be able to
be tested using the primary winding. However, it is possible to use a secondary winding which has far fewer
turns than primary. For testing to confirm Fsat, the transformer may be tested without any R loading at all
across any winding. But the there should be a small 1r0 current sensing resistance connected between
earthy end of a secondary or a portion of primary and 0V. The voltage across the 1r0 is then fed to
an oscilloscope, and when saturation begins to occur, there will be a very rapid rise in THD as F is

Suppose you have calculated that Fsat = 10Hz at 28Vrms across the primary winding.

Suppose you have a secondary winding has 1/4 of the turns of the primary. You should find that Fsat
= 10Hz when 7Vrms is applied across the secondary winding. The only worry is about the secondary
winding inductance, and that its reactance not be too low at such low F.
In the case of the 100W SMT, primary Lp = 4H, and with a sec = 1/4 of the turns the sec L
will be 4H x 1 / (4 x 4) = 0.25H. The reactance of 0.25H at 10Hz = 15.7 ohms and this will not
cause excessive amplifier currents and overheating. But when saturation does begin to occur
for parts of the sine wave applied, there will be very high current produced which may well
cause mosfet overheating if sustained for longer than a few seconds. So the measurement
of Fsat must be done very carefully.

There are TWO basic options for SMT, either Isolation transformer OR Auto-transformer.

My experience tells me its easier to design the isolation type for best predictable fair HF response than design the

auto-transformer, but both will be discussed here.

Let me deal with basic issues with an auto-transformer.......

Fig 6.

This shows a very basic set of amplifier powering a speaker with an SMT connected.
The advantages of auto-transformer are that winding resistance losses are lower than isolation transformers for
where the secondary load is not less than 1/2 the primary load. Consider the winding currents in the above
auto transformer. In the non-shared portion of A to E and F to B the primary input current = 1.75A for the
120 turns, and if the Rw = 0.5 ohms, the power lost = 1.53Watts.
But the current in the remaining E to F secondary winding which powers the speaker will be found to be
the difference between speaker current and primary current = 5.25 - 1.75 = 3.5A.
The turns for E-F = 60t, and if the same dia wire exists for all windings, Rw = 0.25 ohms and losses = 3.06 Watts.
Therefore total P&S losses would be 4.6 Watts, ie 9.2% of 50Watts applied to input. The above diagram shows
Po at sec = 49 Watts, which is extremely optimistic and in fact one would get about Po = 45.4Watts.

If an isolation transformer were to have a primary winding of 180t using the same wire wire size then more bobbin

window area must be found for the 60t for isolated secondary, so the window size must be larger. This involves
a larger core size, but with lower stack height to keep Afe the same. But weight has increased. And turn length
may increase. The 180t for primary carries 1.75A and Rw may become 0.9r so losses = 2.75Watts.
With 60t for secondary using same wire size, Rw = 0.3r and current is the same as for speaker at 5.25A
so sec winding losses = 8.27Watts, so total P+S losses = 11.0 Watts. Total losses are 22%.
Po at sec = 39 Watts. 

To reduce losses for BOTH types of transformers requires slightly different methods.

For the auto transformer, the winding E to F would in fact comprise two paralleled windings each 60t.
This would halve sec losses to 1.53 Watts, and total P+S loss = 3.06 Watts, or 5.7% of 50Watts of input power.
This means that there would be 8 layers of wire with two of them paralleled with another two for between E and F
and these 4 windings would then be spread out among the remaining 4 to minimize leakage inductance to get
best bandwidth.

The isolation transformer would need to have a much bigger window, AND to get lower resistance losses the

wire size must also be increased AND to reduce the number of turns for same Fsat the stack height must increase.
The secondary would need to have paralleled windings and/orlarger wire size than the primary.
I cannot give all details but you will find the conventional isolation transformer will need to be twice the weight
of the auto transformer to achieve the same power handling, Fsat, and winding losses, and an example of isolation
transformer is below......

Fig 7.

In order to get reasonably low winding losses with the isolation SMT, the core size must have a larger

window size to accommodate larger winding wire.
Should anyone wish to have the primary used with a Vdc potential of say up to 100Vdc, they can do
so safely without worrying about the secondary and speaker also being at a Vdc potential.
But I draw the above with both P and S windings taken to 0V at one end.
The method of changing the load matching is done by changing secondary connections with soldered
wire links or bolted metal strappings. I suggest this is rather inconvenient for 99% of audiophiles.

There are 12 primary connections numbered 1 to 12 in winding order and all connected in series.

There are 12 secondary connections, A to L. I have not included details of how you would arrange a
circuit board allow an easy change of P to S turn ratios, but one way is to have an octal tube socket
on the SMT board for banana sockets for amp and speaker cables.
The strapping pattern may be varied using octal plugs with prepared linking patterns within the
8 pins. Suppose you wanted to make most available speakers between 3 and 9 ohms appear
as about 16 ohms to an amp.
One octal plug would be strapped for 72 turns to give 16r0 : 2r6, ok for all low Z speakers
between 2r0 and 5r0.
One octal plug would be strapped for 108 turns to give 16r0 : 5r8, ok for all speaker Z between
5r0 and 10r0.
Higher speaker Z can be connected directly to the amp without SMT.

So probably, only two octal strapping sockets need to be used, and to avoid losing the unused plug
it should be plugged into a second octal socket labelled "Spare".

One might be tempted to make the SMT secondary in the form of say
4 parallel windings each with taps and just like a tapped secondary on a tube amp OPT.
But this means the core window must be even bigger to accommodate more turns, and by then the use
of a plain old auto SMT with no isolation between P and S begins to make a whole lot more sense.
So I have not given any more details, and I leave that to others.

Fig 8. A fairly simple auto-transformer for 50 Watts :-
This is a brief diagram-schematic of a speaker matching transformer used with an amplifier to make a range of speaker
ohms "look just like" a higher Z speaker from the amplifier's view point.

There are 5 sets of load matches shown for 3 nominal values of SMT input load.

Suppose you wish the amplifier load to be 32 ohms. Plug cables from amp to A & B on SMT input.
Plug cables from speaker to the terminals shown :-
14.2 ohm speaker to C & H, 8 ohm speaker to C & G, 3.55 ohm speaker to D & G, 2.0 ohm speaker to E & G,
0.89 ohm speaker to F & G.

Because there are so many possible load ratios are so numerous, it would be very easy for someone to use the wrong

terminals, or have different terminals used for each channel. So unless you are able to confirm what you are doing
with well labelled terminals and / or by means of measuring a test signal of 1 kHz, then just remember I have mentioned
that the marriage of knowledge and a fool can lead to smoke.
However, as long as amp cables go to A & B, then connection of any speaker to between any of the terminals C to H
will always give a higher ohm load value between A & B. Many might guess what they are doing and find they cannot
hear what sounds best. And they just can't understand ohms, voltage, current or impedance, or why smoke and blow fuses
happen so often. I suggest they confer with a more logical friend.

The input voltage is limited to 40Vrms by core saturation at 12Hz when Bmax = 1.5Tesla. It means that the SMT

could cope with 200Watts of input to 8 ohms looking into the SMT A & B input. 
Winding losses are 5.2% when the input Z is 8 ohms, and speaker load is 2 ohms. 

Fig 9. For those confused by so many connections, here is a board layout and label :-


Table 2. Range of primary : secondary loads available from "Simple" SMT above.
Terminals A - B
Primary input load SMT,
Primary turns = 180t,
C to H
Sec load ohms,
C to G
D to G
 E to G
F to G
32 ohms 200W 14.2
3.55 2.0
16 ohms 100W
8 ohms 50W
Load Factor A to B = x 1.0. x 2.25 
x 4.0
 x 9.0
x 16.0
x 36.0

The highest winding losses are just over 10% when primary input load is 8 ohms due to whatever speaker
is connected, say 3.55 ohms connected to the C-H terminals. The input load = 3.55 x 2.25 = 8.0 ohms at A-B.

If the same 3.55 ohms was moved to the C - G terminals, the load which appears at AB becomes

4 x 3.55 = 14.2 ohms. If the 3.55 ohms is moved to D - G terminals, load at A - B becomes 9 x 3.55 = 32 ohms. 

Some people get very nervous about connection of a speaker load with very low DC resistance  across the output

terminals of any amp. Most audiophiles would be entirely unaware of any danger to the amp especially if it is a solid
state amp. The low winding resistance of the primary of the SMT is much lower than the winding resistance of a
speaker coil. This is no problem for a tube amp, but could be for an SS amp which becomes faulty with a DC offset
at its output directly from SS devices. If DC offset was say 0.5Vdc, and primary resistance of SMT shown above
is 0.5 ohms, then the NFB circuit of the amp may try to keep the 0.5Vdc constant, so 1Adc will flow in output devices
in addition to whatever other idle current may be so that maybe only 1/2 the output devices are biased with too much
current and may overheat while the other 1/2 have far too little bias current. This causes the amp to perform as
a badly designed single ended amp for the first watt or two and THD&IMD will be much too high.

To avoid such problems with SS amps, a DC blocking cap can be soldered inside the amp between amp output
terminals and output from devices. A usual value to suit low loads down to 4 ohms without affecting bass response
is 10,000uF, rated for ripple current of 7 amps. The simplest way to do this is use multiple parallel non polarized
electrolytic caps - if you can find them. The other way is to use 2 x normal 63V rated 22,000uF electrolytic
caps in series, with +end of one to amp, and +end of other to speaker terminal. The -ends are commoned and
biased with -50Vdc from an amp PSU rail. Thus you get C = 11,000uF, and caps are properly biased with Vdc.
LF pole with 8r0 input to SMT = 1.8Hz.
The 2 electro caps should each be bypassed with 2uF and 0.1uF polypropylene or polyester caps rated for
250V min.
Many early solid state amps used a single PSU rail of say +50Vdc and had seriesed power transistors where
the collector/emitter output was at +25Vdc. There needed to be a large capacitor between SS devices and
speaker connected to 0V.
Sugden amps still being made using the same basic topology of 1969 and use 10,000 uF electro-caps to couple
speakers to the collector/emitter join which has a bias voltage of  23Vdc which is 1/2 the single rail of +47Vdc
used for these class AB solid state amps.

Fig 10. Now here is a more sophisticated SMT for 100 Watts. I have wound this design.


Excuse the somewhat messy appearance. This is a prototype under test.

Fig 11. Transformer core and Bobbin windings for pictured auto-transformer.


The above shows my pictured 100W prototype speaker matching auto-transformer. All details are shown as clearly as I can
arrange for you all and I hope that nobody becomes completely confused with what is being attempted here.

The bifilar winding of each layer is not hard to achieve. One then avoids having wires leading in across a previous layer

of turns to half way across the bobbin for the ends of the two windings per layer. For bifilar windings with thick wire,
I found it easy to wind on 17 turns across the bobbin with a a gap between all turns. Then a second winding of 17
turns was wound on slowly between the gaps between turns of the previous 17 turns. Turns of both windings were
pushed tight together using a plastic paddle to remove all gaps.
That's how 34 turns can be wound on in two windings, each having the full traverse width of  bobbin.  

Fig 12. More details of 100 auto-transformer..


Although it is not obvious in the above schematic of the transformer, there are in fact two of the eight layers
connected in parallel with two central layers among the other six layers.
This means that low Z speaker loads are connected to paralleled windings which are symmetrically distributed in the height
of the bobbin windings to give low leakage inductance and low winding losses.
For example, winding 1,2,3,4 is in parallel with 9,10,11,12, and 29,30,31,32 is similarly in parallel with 21,22,23,24.

The single winding transformer has more copper section in its central area to suit low loads, and to gain symmetrical
winding layout either side of the centre tap. The CT could be taken to 0V and the two input points driven by a pair of
balanced voltage sources, as indicated here as +/- 14.1Vrms. Such use will very well suit suit Circlotron topology
or simple balanced source follower with N channel mosfets.
Many tube amps have 3 speaker terminals labelled Com, 4 and 8, and the Com terminal is usually connected to the
0V rail of the amplifier. The Com to 8 ohm terminal gives the maximum number of turns of the amp's OPT secondary
winding, and gives the highest Vout.
The Com to 4 ohm terminal from a tap on the winding gives approx 0.7 x total turns for 8 ohms, and  0.7 x max Vout.
The best use of above SMT is where the SMT primary from A&B are connected to Com and 8.
If a 4 ohm speaker is connected to G&H, then input load to SMT becomes 16 ohms, which may be a load for the
amp that gives better performance than if the 4 ohm speaker was connected to Com & 4 amp terminals.
Notice that where A&B are used between Com & 8, and Com is at 0V inside the amp, then the CT connection
on SMT winding MUST be ignored, and left unconnected to anything.

Fig 13.

The above shows the wire link connections made on the 32 terminals mounted on the transformer with

16 on each side. Also shown are the additional wire links to the underside of 4mm banana sockets
for amp and speaker cable banana plugs. The banana sockets are mounted on a board fixed above the
winding with rows of winding terminations each side. The board overall L x W is made to suit the box
enclosing the SMT. A suitable box made to enclose the E&I laminated transformer can be made using
1.2mm steel sheet, but with minimum distance from to any winding or core = 12mm, thus avoiding any
magnetic interaction, while also providing enough room for dry sand filling, and while giving magnetic
shielding against stray magnetic field coupling with other transformers etc nearby. Ideally, SMT should be
placed 400mm away from any other audio components.

Test Results.
I tested the above transformer using the mosfet buffer and 3Vrms sine wave signal source generators giving
2Hz to 4MHz bandwidth, with Rout of buffer = 1.3ohms.
With no load of any kind connected, bandwidth for between G&H was dead flat from well below 10Hz to
1MHz, with a =1dB peak at 900kHz. There was a peak of +3dB at 2MHz and then output declined at
more than 12dB/octave with other peaks and nulls of lessening levels.
Use of a 465kHz square wave showed some slight ringing frequencies between 4MHz and 10MHz.
There were no problem resonances below 1MHz.
Pure C load of 2uF produced no large amount of ringing, and was better than many other audio transformers.

F2 -3dB points at HF with pure R loads at G-H were 4r0 = 240kHz, 2r0 = 140kHz, 1r0 = 70kHz.
 4ro8r016r0, 220kHz,  gave F2 = 220kHz, 8r0 gave F2  

Leakage L at primary < 10uH. Shunt Capacitance = negligible. 

With Np = 204 turns for the SMT, Afe = 44x 50, µ max = 8,000, and ML = 245mm, and at high signal

levels below 50Hz, max Lp = 4Henry at 50Hz. Lp is far larger than we need it to be, and one may think
Np could be far lower than 204 turns, or the µ could be a lot lower. Indeed µ would need to be
MUCH lower if the core were used for an SE design with say 3 amps Idc present.
But this SMT is to be capable of far more power than possible with SE and having Idc present.
Without Idc, the Vac levels are high enough to need to have high Np to avoid core Bac exceeding
1.5 Tesla above 14Hz at voltage for rated power power. It is core saturation behaviour which
determines quantities of iron and turns, not Lp.

The core with maximum interleaving has µ = 17,000. The core E&I lams are each 0.35mm thick and
were bundled in stacks of 7E and 7I and each bundle assembled in opposite directions into bobbin
window. This gave the µ = 9,000, and if the core had bundles of say 15e&15I then perhaps µ would
be between 3,000 and 5,000, thus further reducing risk of saturation with stray LF signals below
10Hz with high amplitude. Most audio recordings do not contain such stray LF waves.

The SMT is configured as shown with a CT winding which suggests the input should be supplied
by a balanced pair of oppositely phased signals from an amp output stage or from balanced
PP tubes or SS devices.
But there is no need for the SMT to have its CT taken to ground where there is just two amp
output terminals with one at 0V and the other being singularly active. The input signal can be applied
with each Input connected to 2 output terminals and speaker signal voltage will be the same as for
a balanced pair of signals with CT at 0V.

The transformer has numerous other uses and possible configurations, and may be used for

OTL with many 6AS7 or 6C33c triodes.

Have I covered this subject well enough? Any questions?

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