Toroidal Step Up Transformers for Electrostatic Loudspeakers
By Menno van der Veen
Introduction
This article gives information about the
new range of toroidal step-up transformers,
to be used with electrostatic loudspeakers.
It explains the concept of a so called “step-up”
transformer; it explains how the transformer
behaves at low- and high frequencies and how
the transformer plus loudspeaker can be tuned
in such a way that any “ringing” of the speaker
system will be suppressed. Typical applications
are discussed.
Step Up transformers in general
Electrostatic loudspeakers need high voltages
(magnitudes of several kV) on their
perforated plates to move a thin charged
membrane in the rhythm of the music. Audio
amplifiers do not deliver such high voltages.
For instance a 100 Watt 4 ohm amp delivers
20 Vrms maximum at its speaker terminals.
Therefore a special “step-up” transformer is
used to convert the small amplifier output
voltages into the large voltages needed for
electrostatic loudspeakers.
Such a step-up transformer is not an easy
device. The electrostatic loudspeaker delivers
a complex load to the secondary side of the
step-up transformer. Take as example a
standard ESL with an effective plate
capacitance of 1 nF. Now consider a step-up
transformer with a step-up ratio of 50,
meaning that the number of secondary turns
(Ns) is fifty times larger than the number of
primary turns (Np). The capacitance of the
ESL will be converted to the primary side of
the step-up transformer (multiply by the
turns ratio squared), delivering an effective
load of 502 . 1 nF = 2,5 µF to the driving
amplifier. Not all amplifiers easily can handle
such heavy loads.
Especially tube amplifiers with small damping
factors are not able to send enough high
frequency energy into such difficult loads.
Take as an example a tube amplifier with a
damping factor of 2, meaning that its output
impedance equals almost 4 Ω. This output
impedance, combined with the 2,5 µF load,
creates a low pass filter with its -3dB corner
frequency at 16 kHz. This clearly shows that
such an amp experiences difficulties to deliver
high frequencies above 16 kHz into the
electrostatic loudspeaker.
Consequently, for the transfer of the complete
audio frequency range, amplifiers with larger
damping factors should be used. This can be
realised by the application of overall negative
feedback inside the tube or semiconductor
amplifier. No feedback amplifier designs are,
in general, not suited for driving electrostatic
loudspeakers.
The step-up transformer has an internal
capacitance as well, called Cis, which adds up
to the external ESL-capacitance Ces of the
loudspeaker and its membrane. In total the
load to the amplifier is the sum of Cis and Ces
times the turns ratio squared.
A step-up transformer has an internal
inductance, called Ls (measured on the
secondary side). This Ls should be as large
as possible for good low frequency response
and for an easy low frequency loading of the
amplifier. In this aspect toroidals are superior
due to their nice construction and high
permeability core materials selected, resulting
in large Ls values.
Some of the magnetic field lines leave the
transformer, resulting in the so called Leakage
Inductance Lss. Again, in this toroidals are
superior to EI- or C-type cores because they
capture almost all the field lines inside the
round core, resulting in small leakage.
The leakage inductance, combined with the
ESL-capacitance and the internal capacitance
of the transformer, creates a second order low
pass filter structure. This 2-nd order filter
should be tuned to optimal behaviour.
Not every ESL-loudspeaker has the same
capacitance, and therefore this tuning should
Plitron Manufacturing Inc. 8 – 601 Magnetic Dr. Toronto, Ontario, Canada M3J 3J3
take place outside the step-up transformer to
adapt the transformer to any type and
capacitance of an electrostatic loudspeaker.
In our designs this tuning can be optimised by
means of ONE external resistor Rep, placed at
the primary side of the step-up transformer,
in series with the primary. The power rating
of this resistor will be in the environment of
10 Watt, while the resistance can be selected
between 0.22 to 2.2 Ohms, depending on the
tuning selected. Anyway, this simple resistor
can prevent the ESL-loudspeaker from ringing.
Ringing means excess high frequency energy in
the environment of 20 kHz, which can make
the tonal character of the electrostatic
loudspeaker very irritating and sharp sounding.
By giving Rep the correct resistance (see later),
this ringing can be suppressed, resulting in a
correct and mild sounding tonal balance.
The step-up transformer must be able to
handle high voltages, into the kV range.
Careful isolation, combined with careful
construction make that our new step-up
transformer range can fulfil this task without
internal sparks.
Proprietary new computer programs have
been developed to combine the finest core
materials, winding techniques and audio
knowledge, leading to advanced and modern
up to date step-up transformer products.
About the specifications (numbers)
a) Step-up ratio: this numbers shows the
ratio of the secondary to primary turns,
and tells how much the secondary voltage
is enlarged with respect to the primary
input voltage. It is important to realise
that a step-up transformer is a voltage
step-up device, meaning that the voltage
transformation is the important item and
not the power transformation.
b) Nominal Power in 4 Ohm: Combining
the power of an amplifier and its optimal
loudspeaker impedance gives the maximal
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1
effective output voltage of the amplifier.
See for calculation remark (1) at the bottom
of the specs. This voltage combined with the
start frequency of the -3dB Power Bandwidth
shows exactly how much low frequency
voltage the core can handle without going
into severe distortion.
c) Ls and Lss: these numbers show the
inductance and leakage inductance of the
step-up transformer (seen from the
secondary side).
d) Rip and Ris are the DC-resistances of the
primary and secondary windings. In case of
a normal transformer these quantities would
represent losses. In the case of a step-up
transformer these quantities are part of the
tuning section for optimal high frequency
2-nd order roll-off behaviour.
e) Cis is the effective internal capacitance of the
transformer. In the design and manufacturing
stage Cis is optimised for a proper balance
between losses in the transformer and tuning
of the high frequency behaviour of the
electrostatic loudspeaker.
f) -3dB Power B andwidth starting at: In
remark (3) is explained how this frequency
combined with power should be interpreted.
In general, the higher the lowest frequency of
application, the more voltage (power) the
step-up transformer can handle without any
distortion. The general rule behind the
calculation sounds: raise the lowest frequency
of application by a factor of square root 2
(= 1.414), then the transformer can handle
the double amount of power.
g) Rep is the tuning resistor, placed in series
with the primary winding. In the
specifications an acceptable value is
proposed, however tuning can easily be
performed by the customer, see later. The
power capability of this external resistor
should be around 10 Watt.
h) At small input voltages the start of the
–3dB bandwidth is largely determined by Ls.
In the specifications f3L is calculated using
the maximum value of Ls. However, Ls is
2
dependant of the magnitude of the input
voltage and can vary with a factor of 6
maximal. This means that the lowest -3dB
frequency is signal level dependant and
can be up to 6 times larger (higher) at
small input voltage levels. Therefore we
have designed f3L to be far below 20 Hz
and consequently any dynamic changes in
this frequency will not be detected by our
human hearing.
i) Primary impedance at 10 Hz: the
impedance of the step-up transformer
combined with the electrostatic
loudspeaker is calculated at 10 Hz
(see note 6). In an average step-up
transformer design with a small
secondary inductance, this low frequency
impedance at 10 Hz mostly will be very
small, resulting in a very difficult load to
the amplifier. In our toroidal design the
large value of Ls prevents such a situation
from happening, even in the case of
small-signal conditions.
j) Ces indicates the capacitance of an
ESL-loudspeaker connected to the
step-up transformer. In practise values
between 500 pF and 2000 pF are met.
k) The second order resonance
frequency (note7) and the second
order Q-factor (note 8) are the
parameters for the high frequency
behaviour of the loudspeaker.
l) f3H gives the -3dB bandwidth at
the high frequency side. Its value is
independent of the input voltage. In our
toroidal transformers the –3dB bandwidth
is designed on purpose in the environment
of 20 to 30 kHz, because f3H values in
the 100 kHz range would disable the
possibility to suppress ringing with the
help of Rep.
m) The primary impedance of the
electrostatic loudspeaker plus step-up
transformer combined with Rep is calculated
at 20 kHz. This impedance can become
very small, however I designed for an
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PAT – 4 1 3 4 - E S
Ratings
Type & Applications
:
Step-Up Ratio (=Ns / Np)
:
PAT-VDV-75FB-ESL ; step-up
Ratio = 75
Nominal Power -
:
Pnom = 80
[Watt]
(1)
Nominal Power to be delivered in
:
Zout = 4
[Ω]
(1)
Secondary Inductance (maximum value)
:
Ls = 1.6•103
[H]
(2)
Effective Secondary Leakage Inductance
:
Lsse = 22
[mH]
Primary DC Resistance
:
Rip = 0.1
[Ω]
Secondary DC Resistance
:
Ris = 273
[Ω]
Effective Secondary Internal Capacitance
:
Cis = 8•10 -10
[F]
[]
Low Frequency Information:
-3 dB Power Bandwidth starting at
:
fu = 35.355
[Hz]
(3)
Tuning Resistor in series with Primary
:
Rep = 0.82
[Ω]
(4)
-3dB Bandwith (with Rep) starting at
:
f3L = 0.515
[Hz]
(5)
Primary Impedance at 10 Hz (with Rep)
:
z10 = 18.101
[Ω]
(6)
[F]
High Frequency Information (with Ces & Rep)
Capacitance of Electrostatic Loudspeaker
:
Ces = 1•10 -9
2-nd order Resonance Frequency
:
Fo = 25.291
[kHz]
(7)
Q-factor 2-nd order HF filter section
:
Q = 0.642
[]
(8)
(8)
-3dB High Frequency Bandwith
:
F3H = 22.741
[kHz ]
Effective Primary Impedance at 20 kHz
:
Z20k = 1.013
[Ω]
(1):
(2):
(3):
(4):
A step-up transformer transforms Voltages;V-primary = (Pnom.Zout)ˆ0.5
Ls is not constant; see M. van der Veen, Glass Audio 5/97 starting pp.20
-3dB means 1/2*Pnom at fu: Pnom at 1.4*fu: 2*Pnom at 2*fu: etc.
Rep (= series resistor with primary) stops High Frequency ringing.
This resistor is an important exernal High Frequency tuning device.
(5): With Ls,max (see (2) ) and Rep; values upto 6*f3L can be met in practice.
(6): This impedance is based on Ls,max (see (2) ) and Rep.
At small primary Voltages values of 1/6*z10 can be measured.
(7): This fundamental frequency is determined by Lss and Cis + Ces.
(8): Rep influences Q, f3H, Zp; Select Rep for 0.50 < Q < 0.74
Copyright: 1998 Menno van der Veen, Ir. buro Vanderveen; Design date: 25-3-98
electrical impedance phase angle of almost
zero degrees around this frequency, thus
preventing the driving amplifier from
becoming extremely hot.
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About the Characteristics
The next pages show several graphs of the
step-up transformers combined with a good
electrostatic loudspeaker. These graphs are
made with an optimal Rep resistor. A little
explanation might support the proper
understanding of this abundant amount of
information.
The first graph (H(x)) shows the on axis
acoustic response of the electrostatic
loudspeaker plus step-up transformer in dB.
A mild high frequency roll-of without ringing
is clearly visible in the environment of 20
kHz. The effective –3dB frequency is just one
division below the middle and is in the
environment of 30 kHz. This is more than
wide enough for any electrostatic loudspeaker.
The second graph shows the acoustic phase
response of the electrostatic loudspeaker plus
transformer. Phase unequal to zero means
delay, and it is clearly visible that above 3 kHz
the delay in transformer and loudspeaker can
be noticed. A lot can be said about this topic,
but phase deviations from zero don't have to
be harmful. In fact, this phase graph, when
taken alone, says very little about the time
behaviour of the loudspeaker plus transformer.
To learn and understand more, the third graph
is needed.
The third graph shows the Differential
Phase Distortion (in degrees). This is
essential time delay information! When reading
this graph correctly (vertical range from –90 to
plus 180 degrees, so “zero” is at the second
division from the bottom line), it is clearly
visible that from 10 Hz to almost 30 kHz, the
differential phase distortion equals “zero”.
What does this mean? It says that the delays
encountered by different frequencies (ranging
from 10 Hz to 30 kHz) in the transformer and
loudspeaker, are all equal. When a “burst” of
sound is going through this sound system, all
frequencies of the burst will be delayed by an
equal amount of time, and the relative time
positions of the different frequencies will not be
changed or distorted. The time behaviour of
this transformer and loudspeaker is
perfect in the acoustic domain and
the dynamic behaviour will not get
distorted (time wise). In practice
this means that transient sound
signals will maintain their
purity of the tonal balance.
The transient will sound as it was
and will not show any dynamic
coloration. In my opinion, this is
a very important quality of a
“good” loudspeaker system.
To summarise: the phase graph
shows that there is delay in the
speaker. However, the third graph
clearly proves that this time delay
is frequency independent and
constant in the audio range from
10 Hz to 30 kHz, and therefore
absolutely not harmful. The time
distortion is zero in the audio
range. This is one of the many
goals we set when designing our
high quality step-up transformers.
The fourth graph (impedance)
and the fifth (electrical phase)
tell the electrical story of the
transformer plus electrostatic
loudspeaker. They are important
for questions like: “can my amp
drive this speaker system?”. In the
fourth graph it is clearly visible
that the impedance at the
primary side of the transformer
(the amplifier side) is not constant
at all. For those who wish to
design a cross-over filter for their
ESL, this might cause severe
problems. Well, a smart solution
then is to apply an extra external
resistor PARALLEL to the primary, say with a
value of 10 Ohms. Then the total impedance
of transformer, speaker and extra parallel
resistor, will be close to 10 Ohms at
frequencies below 1 or 2 kHz, and smaller at
higher frequencies. Very often the cross-over is
designed to filter in the environment of
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300 Hz (supposing an electrostatic mid-highunit) and through this extra resistor “trick” the
cross-over can be designed with great accuracy.
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3
How to tune Rep correctly?
method is not expensive. After finding the
optimal Rep value, return to method 1 and
fine tune by ears.
There are three easy methods available
to find the optimal value of Rep for a
specific electrostatic loudspeaker panel.
Summary: always method 1 is the final
decision maker. In reality, measurements
are fine and can help you. But we have the
finest measurement devices already available
on the two sides of our head: our EARS, and
are not they fantastic? Well, use them and
rely on them!
METHOD 1: Use your ears, enlarge Rep
step by step (between 0.2 and 2.2 Ohm)
and listen to the high frequency balance
and sharpness of the high frequency
sound. Use CD's of which the musical
content is known and change Rep until
you like the high frequency character of
the sound. The costs of this method are
small: only a view resistors for testing
which can be replaced for high quality
resistors when the optimal value is found.
METHOD 2: use a frequency range
analyser with a high quality measuring
microphone in a dead room. A very good
system to do this measurement is
MELISSA, but that's rather expensive.
Well, give Rep several values, as indicated
by Method 1. Measure the acoustic
transfer function on axis, rejecting
reflections by selection of the proper part
of the impulse response (this creates a
dead room measurement in a normal
Figure: Three acoustic transfer function situations with Rep too small; with Rep correct and
living chamber). In the figure below
with Rep too large. Notice the clear influence of Rep on the high frequency behaviour.
three situations are shown with Rep too
small, Rep with the correct value and
thirdly Rep too large. The influence of
with little acoustic volume!! Now turn up the
Rep is clearly visible. After having found the
frequency of the oscillator and look at the
correct value of Rep by measurements, fine
current sine wave and the voltage sine wave at
tune Rep by listening as indicated in Method 1.
the screen of the oscilloscope. Change Rep to
(After all, method 1 is always the final decision
larger values, step by step, while raising the
maker; your ears tell you the truth).
frequency around the 20 kHz region, say by
METHOD 3: Measure (with a current clamp
around one of the wires from the amplifier to
the primary of the step-up transformer) the
primary current. Connect the output of this
current clamp to channel 1 of the oscilloscope.
Measure with channel 2 of the oscilloscope the
voltage over the loudspeaker terminals of the
driving amplifier. Connect a sine wave
oscillator to the amplifier input. Don't set the
amplifier too loud: perform this measurement
4
changing the frequency per measurement from
15 kHz to 40 kHz. When ringing occurs you
will see around the ringing frequency that the
current and voltage sine wave will change
quickly in magnitude and relative phase.
Without ringing, the changes in the two sine
waves will be mild and gradually when raising
the frequency. This adaptive, intuitive method
needs some experimentation to learn how to
interpret the measurement results, but the
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1-800-PLITRON (1-800-754-8766) Tel. 416-667-9914 FAX 416-667-8928