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Nonlinear transformer behavior
Table of
Contents
Introduction_
Transformer_Fundamentals
Magnetic_Flux_Inside_the_Transformer_
BH_Curve_
Why_Does_OddOrder_Distortion_Predominate_in_a_Transformer
NonLinear_Transformer_Modeling_in_SPICE
Zero_Impedance_Driver_Circuit
Measurement_Setup�BH_Curves_
Measurement_Setup__Pulse_Ringing
Transformers_Studied
Tamura_TTC108_Transformer
TTC108_Distortion_versus_Driving_Resistance
TTC108_Frequency_Response
TTC108_Square_Wave_Response
Western_Electric_�Repeating_Coils�_THD_
Western_Electric_119C_Repeating_Coil_Frequency_Response
Western_Electric_119C_Coil_Square_Wave_Response
Triad_SP70_THD
SP70_Frequency_Response
SP70_Square_Wave_Response
Bourns_LMNP1001B1_THD_
Bourns_LMNP1001B1_Frequency Response
Bourns_LMNP1001B1_Square_Wave_Response
Walters_OEP8000_Frequency_Response
OEP8000_Harmonic_Distortion
Comparisons_and_Conclusions
Primary_Inductance_Variation_with_Level
Frequency_Response_Compared
Stancor_TTCP2._TTCP6_and_TTCP8
Effect_of_DC_Bias_on_TTPC6_and_8_Transformers
Jensen_DIN2LI
BH_Curve_Analysis_of_Stancor_and_Jensen_Transformers
TTC108_BH
TTPC2_BH
Western_Electric_119C_Repeat_Coil
Jensen_DIN2LI_BH
BG_Incorporated_KS_Transformer
BG_Inc._KS_Frequency_Response
BG_Inc._KS_THD
KS_Transformer_Driven_by_OpAmp_Zero_ohms_Source
KS_THD_Comparison_to_Other_Transformers
How_Does_All_This_Relate_to_the_K3_LINE_OUT_Audo_Distortion
Revision
History
Created 19 September 2008
Revised 20 September 2008  added K3 LINE OUT section at end of document
Revised 20 September 2008  added 1 KHz square wave ringing tests & 50 ohm
source data for three transformers
Revised 21 September 2008  had wrong plot for Bourns LMNP1001 THD; now
corrected
Revised 02 November 2008  added data for Walters OEP8000 transformer
Revised 23 April 2009  added data for three Stancor transformers and Jensen
DIN2LI transformer module
Revised 25/26 July 2009  added data for BG Incorporated KS transformer

Introduction
I've written about linear
transformer models at Audio
Transformer Data and Modeling,
and at Softrock Lite 6.2
and about ferrite core based RF transformers at
Ferrite Transformers.
And, I've explored in some detail the problems stemming from Elecraft's choice
of a Tamura TTC108 audio transformer to provide LINE OUT isolation in its K3
transceiver at Elecraft K3 Receive Audio.
My Elecraft K3 Receive Audio page
has a great deal of additional nonlinear performance measurements for the
Tamura TTC108 transformer and should be read as a supplement to this page
for a full understanding of nonlinear transformer behavior.
My Elecraft K3 studies,
unlike the other pages, looked at both linear and nonlinear problems with the
TTC108. Linear transformer concerns are most commonly related to frequency
response and, less commonly, phase shift. Nonlinear behavior results in
waveform distortion, evidenced by harmonic generation and intermodulation
distortion.
This page focuses on
nonlinear transformer behavior. Although started as an extension to my Elecraft
K3 audio explorations, I've expanded the scope of these studies to other
transformers and hence decided the topic justifies its own web page.
Albert Einstein one
saidalthough in more formal language�everything should be made as simple as
possible, but no simpler.� To understand why transformers produce nonlinear
distortion requires a detailed look at magnetic material behavior. I'll make the
explanations and mathematics as simple as possible, erring on the side of
oversimplification.
I'll also add that I've
written many magazine articles, an 800 page book on computer programming as well
as this web page, not to mention thousands of documents I've worked on
professionally whilst practicing law for 30 years. This web page turns out to be
among the most difficult I've written, and fails to meet my standards of
clarity. Generally this means I don't understand the subject as well as I
should, and I apologize in advance. When growing up, I recall an expression
used in my family, �he doesn't understand all he knows about it.� This
expression applies here�I have learned quite a bit about transformers in my
measurements and research, but I fear that I don't quite understand all that
I've learned.
If you are interested in
only the measured results, skip the next sections and jump right to the measured
data.

Transformer Fundamentals
Before considering
nonlinear effects, we'll quickly review how a transformer works. Consider the
case of a transformer with a primary, or exciting, winding with N_{1}
turns and a secondary, or second, winding
of
N_{2} turns as illustrated to the right.
Assume, for the moment,
that the secondary winding has no connection to the load and hence no current
flows through it. If an AC voltage source is applied across the exciting
winding, an AC current, i_{1}, flows through the winding,
producing an alternating magnetic flux φ in the core, as provided in Ampere's
law. The flux φ is proportional to i_{1} and the number of turns
on the exciting winding.
Faraday's law says that a
time changing magnetic flux induces an alternating voltage in the turns of any
coil threaded by the flux, in this case both the exciting winding and the second
winding. Mathematically, each turn of the coil has a voltage e induced
across it of e = dφ /dt, where dφ /dt is the derivative of the
flux, i.e., the instantaneous rate of change of the flux with time.
(Faraday's law has a minus sign indicating the polarity with respect to the flux
change. Our discussion will ignore the sign.)
Assuming an ideal
transformer, the same flux threads both the exciting and second windings.
The exciting winding's
(winding 1) induced voltage is thus e_{1} = N_{1}dφ /dt
The second winding
(winding 2) has a similar voltage induced across its turns e_{2} = N_{2}dφ
/dt
N_{1} and N_{2}
are the number of turns on the exciting and second windings, respectively.
Since we've assumed an
ideal transformer with the same flux linking both windings, dφ /dt is the
same for both windings and the standard transformer relationship of turns and
voltages can be found:
e_{1}/e_{2}
= N_{1}/N_{2}
For many applications,
this simple relationship is all we need to know�the voltage ratio is
proportional to the turns ratio.
We can, however, obtain a
better understanding of real world transformers by adding the more important
parasitic elements to this theoretically perfect transformer. The schematic
below identifies the principle parasitic elements of a real transformer.
Remember, this is still a linear model�these parasitic elements only alter the
frequency and phase response and do not model nonlinear responses.
l
Lleakage is the leakage
inductance
l
Rs is the series resistance of
the winding
l
Cd is the distributed capacitance
l
Rc is the core loss
l
Lp is the magnetizing inductance
These parameters are
usually "reflected back" to the primary, e.g.., we assume the series
resistance is all in the primary, by treating it as the sum of the true primary
resistance plus the secondary resistance scale by the square of transformer's
turns ratio (N_{1}/N_{2})^{2}. Likewise for the
secondary leakage inductance.
In the same fashion,
Zload is transformed back by multiplying by (N_{1}/N_{2})^{2}.
For example, if the load is a 1000 ohm resistor, and if the secondary winding N_{2}
has four times as many turns as the primary, N_{1}, then the primary
side �sees� a resistance of 1000 x (1/4)^{2}, or 62.5 ohms. Although
our example uses a pure resistance, the N^{2} transformation ratio
applies to the general Z = R+jX case as well.
My
Audio Transformer Data and
Modeling
page compares the predicted response against measured response of an audio
transformer using this model. In general, if the parameters are accurately
determined (and if they don't change too much over the frequency and amplitude
range measured) very good agreement between model and measured data is possible.

Magnetic Flux Inside the
Transformer
In order to understand why
transformers cause nonlinear distortion, we'll look in more detail at the
relationship between applied exciting current and magnetic flux. The following
discussion is from Snelling, �Soft Ferrites Properties and Applications.�
The magnetic field strength, H, inside a very
long uniform solenoid having N_{1} turns per axial length
l and
carrying I amperes is given by:
H=N_{1}I/l
A m^{1}
Its direction is parallel to the axis of the
solenoid and is uniform across the cross section.
The associated flux density, B, is given by
B = μ_{0}H tesla (T)
where μ_{0} is the magnetic constant or
the permeability of free space. It has the numerical value 4π x 10^{7}
and has the dimensions henries/meter or [LMT^{2}I^{2}]. Thus
in the SI units, flux density is dimensionally different from field strength.
If the solenoid is now filled with a magnetic
material, the applied magnetic field will act upon the magnetic moments of the
ions composing the material ... the ions, by virtue of the spinning electrons,
behave as microscopic current loops each having a magnetic moment. ... Under the
influence of an applied field, the ion moments are reorientated ... so that the
ionic moments augment the applied field. This increase in magnetic field is
called the magnetization, M, and it is expressed in A m1 ... The internal
magnetic field becomes
Hi = N1I/l + M A m1
and the flux density becomes
B = μ_{0}H_{i} = μ_{0}(H+M)
T
or
B = μ_{0}H + J T
where J is the magnetic polarization in teslas;
it is sometimes referred to as intrinsic flux density
J = μ_{0}M T
...
B/H = μ_{0}μ_{ }
where μ is relative
permeability.
As more usually stated, B
= μ_{0}μH
If the B is uniform across
the cross section of the core, the magnetic flux, φ, is:
φ = BA webers (Wb)
A is the cross sectional
area of the core in square meters.
From Faraday's law, the
induced voltage, e_{2}, into a coil of N_{2} turns from a
varying flux is
e_{2 }= N_{2}A
dB/dt volts (V)
The negative sign is
because the induced voltage is such that it (assuming a closed circuit) creates
a current opposing the changed flux.
Stated in terms of the
driving magnetic field strength, H, the induced voltage (and dropping the
negative sign for convenience) is
e_{2} = N_{2}Aμ_{0}μ
dH/dt
Inductance, L, is related
to flux linkage per unit current
L = NΦ/I henries
(H)
where I is the peak AC
current in amperes.

BH Curve
From these relationships,
therefore, the transformer's output voltage is a function of the rate of change
of the input current multiplied by the permeability.
From our discussion, it
might seem that μ is a constant
and thus the relationship between B and H is linear. This is far from the case
with practical magnetic core materials. The relationship between B and H is
commonly shown through a �BH� plot, such as the one illustrated at the right.
(This BH curve is data I've measured of a Bourns LMNP1001B1 audio
transformer further analyzed below.)
The horizontal axis is
proportional to the winding current and, for our purposes can be considered to
be H, the magnetic field strength. the current I. The vertical axis is the
integral of the applied voltage, and is thus proportional to the magnetic flux,
B.
Looking at the BH
relationship shows that for any H (or for any current i), there are two possible
B values, depending upon H's historywas H increasing or decreasing from its
peak? It also reveals that significant parts of the BH curve are nonlinear.
The area within the BH
curve represents hysteresis energy loss, which is a component of the total "core
loss" along with eddy currents and other losses. Hysteresis can be defined as
�The phenomenon by which an effect in a component depends not only on the
present stimulus, but also on the previous state of the component.� In other
words, which B state corresponds to a particular H depends on how the H value is
arrived at ,i.e., its history.
If BH is so nonlinear,
how can a transformer deliver even relatively low distortion output? The answer
is that a feedback mechanism helps make the output waveform match the input
waveform.
The transformer's input
voltage causes a current to flow through the primary windings and as discussed
earlier generates a magnetic flux B flowing through the core. B threads both the
primary and secondary windings more or less equally, and hence dB/dt induces an
opposing voltage in the primary winding, even where there is no current flowing
in the secondary because it's open circuited. This opposing primary voltage, in
a well designed transformer, almost equals the applied voltage when the
secondary is open circuited, with the difference causing the �magnetization
current� to flow.
When a load is placed on
the secondary, current flows through it and a magnetic flux is generated
opposing the flux generated by the primary current. The secondary's opposing
flux causes a reduction in dB/dt at the primary and the corresponding induced
opposing voltage, thus causing increased primary current flow, so that the net
flux through the core is unchanged from the noload condition. (This should be
understood to be working instantaneously.) If the primary's source can
supply the necessary current, the output waveform reflects the input waveform,
since the same dB/dt is seen by both the primary and secondary windings,
regardless of how linearly or nonlinearly B and H are related.
Let's return for a moment
to our linear transformer model. This demonstrates several reasons why the
primary winding cannot supply exactly the correct current to cause the
transformer's inherent feedback mechanism to work perfectly.
One major problem is the
series impedance, comprising the winding resistance Rw, the leakage
inductance Lleakage and the source driving impedance Zs. As the load on the
secondary requires greater or lesser current in the primary at any given
instant, the ability of the driving voltage source Es to deliver the correct
current current to the primary winding is constrained by this series impedance.
Even if we make Es a very
low impedance source, such as a feedback amplifier, the transformer's internal
impedance limits the ability of the primary winding to provide the required
current and corresponding magnetic flux to exactly match the value required for
distortionless operation. Since Faraday's law applies, the secondary waveform
distorts to match the available dB/dt.
If the driving impedance
Zs is large compared with the transformer's internal impedance, distortion
increases for this reason; if Zs is small compared with the transformer's
impedance, distortion can be reduced. Of course, the transformer's internal
impedance places a lower bound on the distortion improvement resulting from a
zero ohm driving source. (A feedback amplifier, such as an opamp buffer can
have an output impedance of a fraction of an ohm and approaches a perfect
voltage source within its current limits.)
One additional point
before proceeding to the measured data. For a given sinusoidal voltage applied
across the transformer primary, the current�and H, of course�is inversely
proportional to the frequency. This is because dB/dt increases directly with
frequency. For a sinusoidal of the form B sin(ωt), dB/dt is B ω cos(ωt). Hence
for a given induced voltage, i.e., constant dB/dt, B (and, of course H)
must decrease as ω increases. (The symbol ω is the frequency in
radians/second, or ω = 2πf where f is the frequency in Hz.) Therefore, as the
applied frequency increases, H and B decrease. This means that a transformer's
core material related nonlinearities are most pronounced at low frequencies as
increased H drives B into nonlinear portions of the BH curve.

Why Does
OddOrder Distortion Predominate in a Transformer?
Data at my page
http://www.cliftonlaboratories.com/elecraft_k3_receive_audio.htm
presents spectrum analyzer plots of the K3's LINE OUT audio (which uses a
TTC108 transformer), a typical example of which appears below.
The second harmonic in
this example is down approximately 70 dB from the 600 Hz fundamental, whilst the
third harmonic is down less than 40 dB. A similar effect is visible with the
fourth harmonic�not visible above the noise�and fifth harmonic, as well as the
sixth and seventh harmonics. Odd order harmonics are 30 dB or so stronger than
even order harmonics.
The reason for this
behavior may be summarized in one word�symmetry. Mathematically speaking, the
BH curve can be regarded as a transfer function. We may consider the
transformer's input waveform as consisting of a series of discrete voltage
points x. (x is a function of time, of course). The output voltage x' is a
function of the BH curve, so that x' = f(x), where the function f describes how
a signal point on the transformer primary is modified into a signal point on the
secondary. In engineering, f(x) is called the �transfer function,� as describes
how an input signal is transferred to the output.
Transfer functions have
three possible symmetries:
Symmetry Type 
Sample Plot 
Distortion Type

Even symmetry�where f(x) = f(x) 

Only even order distortion is created 
Odd symmetry�where f(x)
= f(x) 

Only odd order distortion is created. 
No symmetry�where the function has
neither even nor odd symmetry 

Both even and odd order distortion is
created. 
These plots are from
http://www.rsmet.com/documents/tutorials/Waveshaping.pdf
which contains a more mathematically detailed analysis of symmetry and
distortion.
Comparing the odd symmetry
example with one of my measured BH curves should convince you that the BH
curve possesses odd symmetry and thus transformers will demonstrate odd order
harmonic generation. Of course, the BH curve is not perfectly odd symmetrical,
but it's close enough that the even order harmonics are down 30 to 40 db from
the odd order harmonics.
Odd
Symmetry Example 
BH Curve for Bourns
Transformer 



NonLinear Transformer
Modeling in SPICE
This is as good a place
as any to mention that SPICE circuit modeling tools include nonlinear
transformer modeling as well as linear transformer models. LTspice, the program
I use, has two nonlinear inductor (and transformer) models:
There are two forms of nonlinear inductors
available in LTspice. One is a behavioral inductance specified with an
expression for the flux. The inductor's current is referred to by the keyword
"x" in the expression. Below is an example in a netlist:
*
L1 N001 0 Flux=1m*tanh(5*x)
I1 0 N001 PWL(0 0 1 1)
.tran 1
.end
There other nonlinear inductor available in
LTspice is a hysteretic core model based on a model first proposed in by John
Chan et la. in IEEE Transactions On ComputerAided Design, Vol. 10. No. 4, April
1991. This model defines the hysteresis loop with only three parameters:
Hc Coercive force
Ampturns/meter
Br Remnant flux density Tesla
Bs Saturation flux density Tesla
In addition to these magnetic properties, the
mechanical dimensions of the core are required:
Lm Magnetic Length(excl.
Gap) meter
Lg Length of
gap meter
A Cross sectional
area meter**2
N Number of
turns 
This information is not
simply obtained when reverse engineering a transformer, at least not without
disassembling a couple of samples, so the practicality of nonlinear modeling of
an existing offtheshelf transformer remains problematic for the casual
experimenter.

Measurement Setup�Distortion Data
The distortion data (and
frequency response data) is taken with an HP 8903B audio analyzer,
controlled with software I've written.
The 8903B has a
lowdistortion signal generator with a range of 20 Hz � 100 KHz, with output
impedance of 50 or 600 ohms selectable by GPIB command. Maximum open circuit
voltage is 6V RMS. The 8903B's generator is specified as having harmonics and
noise < 80 dB below the carrier over the frequency range 20 Hz � 20 KHz.
The 8903B's analyzer
section works in the same fashion as a classic analog distortion meter. The
applied test signal frequency is notched out and the residue, consisting
of test signal harmonics, hum and noise is measured. The ratio between the test
signal and the residue is the �total harmonic distortion� or THD ratio. The
analyzer section has switchable low pass filters of 30 KHz and 80 KHz, along
with a �full bandwidth� mode of 750 KHz. Reducing the analyzer bandwidth is
appropriate for the tests I've run as noise and harmonics above 30 KHz are not
meaningful. (Distortion data over the range 20 Hz  20 KHz uses the 80 KHz
low pass filter.)
In interpreting the test
data, it's necessary to understand how the test signal level influences the
minimum measurable THD. The analyzer cannot distinguish broadband noise from
harmonics. Likewise, if the applied test signal is not notched down below the
instrument's noise floor, its contribution will also appear as part of the
reported THD. Accordingly, the dynamic range available is a function of the
signal level at the 8903B's analyzer section input.
The plot below shows a
loopback test of the 8903B, where the instrument's audio generator output is
connected directly to its analyzer input.
At 100 mV, the instrument
is limited by the 8903B's analyzer section noise floor. (All data taken with 30
KHz low pass filter enabled.) The noise floor is about 86 dB below 100 mV, or
5.01 μV summed over a 30 KHz bandwidth. The 8903B's noise floor specification is
less than 15 μV with 80 KHz bandwidth, so after adjusting for the narrower
bandwidth, the measured noise floor is well below the maximum specification.
The instrument's noise
floor does not change with input signal level, but as the test signal level
increases, the reported ratio between the test signal and residue (the THD
ratio) naturally increases. With 1000 mV test signal, the reported THD is about
95 dB at 1 KHz, corresponding to 17.8 μV. We thus see about 13 μV contribution
of source harmonics and possibly fundamental leakage through the notch
filter, plus 5.1 µV noise. At 5000 mV, the reported THD is 97 dB, or 70.6 μV,
comprising a mix of source harmonics and fundamental leakage due to finite notch
depth.
All these figures are well
below the 8903B's maximum specifications.
The point to remember is
that some data will be limited by the 8903B's noise floor, particularly where
the input signal is relatively low.

"Zero Impedance" Driver Circuit
In addition to connecting
the transformer directly to the 8903B's signal source, I've taken some data with
a zero ohm driving source, as discussed at
Elecraft K3 Receive Audio
The schematic below shows the zero ohm driving source.
Of course, the MCP6021's
output impedance is not truly zero ohms, but its sufficiently low that we can
consider it to be zero ohms without introducing significant error.
To verify that the opamp
was not adding distortion or noise, I ran a series of tests with the MCP 6021's
output directly connected to the 8903B audio analyzer. The opamp driver is
normally powered from an HP E3610A variable voltage power supply, so to see if
that introduced additional hum and noise, I also ran tests with the opamp
circuit powered by a 9 volt battery. (The circuit has an onboard voltage
regulator not shown in the schematic.)
The data shows that
there's very little hum and noise added by AC power, perhaps 1 to 1.5 dB, so for
convenience the transformer tests were run with the E3610A power supply.
The plot also shows the
8903B's loopthrough THD. We see that the opamp circuit adds about 4 to 4.5 dB
THD to the test circuit at the 100 mV level. At 1000 mV, however, there's about
1 dB difference between the opamp and the instrument loopthrough data. This
suggests that the opamp circuit adds about 4 to 5 dB broadband noise, but very
little harmonic distortion. (An alternative explanation is that at low signal
levels, the MC) 6021 exhibits crossover distortion.)

Measurement Setup�BH Curves
The BH curves presented
were taken with the simple circuit shown below, originally published in
Electronic Design.
http://electronicdesign.com/Articles/Index.cfm?AD=1&ArticleID=6155
R2 provides a sample of
the drive current, and thus the voltage at �To Scope X� is proportional to H.
Obtaining a B sample is slightly more difficult. The voltage across the
transformer primary is proportional to dB/dt, so by integration, we obtain a
voltage proportional to B. R1 and C1 are a simple RC integrator.
The B and H values are not
calibrated, but rather provide data proportional to the real B and H. For
our purposes, that's adequate.

Measurement
Setup  Pulse Ringing
I've also looked at the response of the these transformers
to a 1 KHz bipolar square wave. This may be argued as an unrealistic test,
since audio does not consist of square waves. Moreover, a bandwidth limited
communications receiver is incapable of generating fast rise/fall waveforms.
I've included the data because (a) I collected it and (b) there seems to be a
belief in certain audio circles that ringing generated by a square wave is an
important evaluation criterion.
The oscilloscope image below shows the test signal (trace
1). Trace 2 is a synchronization pulse from the Telulex SG100 function
generator used in this test.
Four configurations were studied for each transformer
tested with square waves:
 50 Ohm drive resistance; high Z (oscilloscope input)
termination
 50 Ohm drive resistance; 620R termination
 610 Ohm drive resistance; high Z (oscilloscope input)
termination
 610 Ohm drive resistance; 620R termination.
The 610 drive resistance was obtained by a series 560 ohm
resistor in the SG100's output. The 620 ohm termination is a 5% carbon film
resistor of that value installed in the body of a male BNC connector, mounted at
the oscilloscope input with a BNC "T" connector. The oscilloscope used is a
Tektronix TDS430.
I also looked a the transformers with what I regard as a
more realistic case, a burst of 10 cycles of 1000 Hz sine wave, as illustrated
in the oscilloscope image below. Because the sine burst ends at a zero crossing,
there is no ringing observed in any of the transformers tested.
Transformers Studied
I looked at ten transformers, four of which are shown in the photograph at the
right.
 Tamura TTC108
 Triad SP70
 Bourns LMNP1001B1
 Western Electric 111C
 Western Electric 119C
 Walters OEP8000
 Stancor TTPC2
 Stancor TTPC6
 Stancor TTPC8
 Jensen DIN2LI
The first three transformers are physically small (the red and yellow parts
shown in the photograph) lowcost parts intended for telephone line isolation in
telephone answering machines, fax machines and modems. The Tamura and Bourns
parts are under US$ 5.00 each and the SP70 is around $15 in single lot
prices. These parts are available from the usual suppliers such as DigiKey
and Mouser.
I studied the two Western Electric parts because I had them in my junkbox.
They weigh several pounds each and have a reputation of being superb
transformers. In the telephone network, these are used to isolate subscriber
line drops from transmission circuits in a few special instances. (They are not
and have not been used routinely in residential or business telephone service.)
For example, many broadcast leased line program circuits historically used 111C
and 119C coils. I use the term "coil" because both these parts bear the
nomenclature "repeating coils," not transformers. I have no idea what these
repeating coils cost. The 111C coil (in the oval case) was manufactured in
1956, whilst the 119C coil carries a 1972 production date. When these parts are
available on Ebay, for example, the going price for a 111C coil is around $75
plus shipping.
Except for the 119C coil, are the tested parts are 600 ohm : 600 ohm
transformers. (The 119C coil is 600 ohm : 520 ohm.)

Tamura TTC108 Transformer
The TTC108 is a small
transformer for telephone interfaces aimed at the modem and fax market. The
relevant specifications are reproduced below.
The term �dry coupling�
means that the TTC108 specifications are based
on zero DC current through the
transformer.
As discussed at
Elecraft K3 Receive Audio,
Elecraft's K3 uses a TTC108 in both the left and right LINE OUT channels for
ground loop isolation. As currently manufactured (mid September 2008) the K3
drives the TTC108 primaries with 604 ohm series resistance.
For audio levels exceeding
about 10 mV RMS, I've measured third harmonic distortion consistently around 45
dB from the carrier from the K3's LINE OUT port.
Elecraft K3 Receive Audio
has details.
An alternative assessment
of nonlinear transformer response is intermodulation distortion. My
Elecraft K3 Receive Audio page has
extensive intermodulation measurements of the TTC108 transformer.
The HP8903B has a minimum
input signal level of 50 mV RMS, so all the tests I've made start with 100 mV.
The plot below shows how
THD varies as a function of frequency and output levels over the range 100 Hz 
6 KHz. This data is taken with the MCP6021 opamp driving source and 620 ohms
series resistance between the opamp output and the TTC108 primary.
Tamura's data sheet quotes
the TTC108's THD as �less than 0.5%, 300 Hz � 3.5 KHz at 0 dBm.� 0 dBm at 600
ohms is 0.775 volts, and 0.5% THD corresponds to 46 dB. [THD quoted as a
percentage is on a voltage basis and may be converted to dB with the formula THD_{dB}
= 20*Log(THD%).] For 800 mV, the THD at 300 Hz is almost exactly 46 dB, meeting
Tamura's specification on the money. At 3.5 KHz, the THD is about 62 dB down
from the reference signal.
For frequencies commonly
used with CW and data communications, say 500 Hz to 2500 Hz, the data is broadly
consistent with the 45 dB figure I measured in the K3's output. However, note
that there's a clear trend to lower distortion with higher output levels. Also,
there's a marked turnover at lower amplitudes with frequency. Compare, for
example, distortion at 50 mV and 200 mV. Below 1000 Hz, the distortion at 50 mV
is greater than that at 200 mV, but above 1000 Hz, the distortion at 50 mV is
less than at 200 mV.
If we look at a typical
BH curve, the reason for this effect can be ascertained. The sketch at the
right shows a single valued BH curve for simplicity. It is divided into three
regions, origin to A, A to B and above B. These correspond to:
l
OrigintoA�reversible growth in
domains. The relationship between B and H follows a cubic law relationship.
l
AtoB�irreversible growth in
domains. This region is approximately linear.
l
Bandabove�rotation of the
domains, gentler slope and not linear. At some point, B saturation occurs and
the only increase in B is due to μ_{0}, i.e., the incremental
permeability is reduced to that of vacuum.
How does this relate to
the distortion data?
As the signal amplitude
increases, operation picks up more and more of the linear BH curve. At any
particular frequency, as the amplitude increases, more operation is in the
linear portion, until the onset of saturation at point B on the BH curve. Hence
we see a decrease in THD as amplitude increases. This is true for all
frequencies, once the �worst case� THD frequency is passed.
On the reduced amplitude
of the worst case frequency, a different mechanism is at work, where THD
decreases with decreasing amplitude. This is related to the reversible growth
region where the BH curve is roughly cubic, i.e., B is proportional to H^{3}.
If H is small, then B is closer to linear than when H is greater. Accordingly,
the smaller the applied voltage the smaller is the corresponding magnetic field
H and the closer to linear is the relationship of B to H. Accordingly, we expect
the THD to start at a lower level and increase as the applied voltage increases.
This behavior is seen in the plot for 1500 Hz and higher frequencies. The reason
it is not seen at lower frequencies is that the applied test voltage of 50 mV is
not sufficiently low, at frequencies below 1500 Hz, to keep the H field �small�
enough to make its relationship with B even approximately linear.
The crossover point, or
point of maximum THD, occurs where the magnetic flux B is so large as to place
major parts of B near the cubic/linear transition point but no so large as to
make major parts of B in the linear region.
The BH plots below are
all taken with a TTC108 transformer at 150 Hz, with the test voltage as
indicated above the image.
100 mV RMS 
2.2 V RMS 
13.8 V RMS 



With 100 mV RMS applied at
150 Hz, the plot is at the limits of my oscilloscope's vertical gain to decently
display the B field. Within the limits of the display, the BH relationship
looks quite linear.
Increasing the applied
voltage to 2.2V RMS (center image) shows a more interesting plot. There's no
sign yet of saturation, but we see a clear nonlinear relationship between B and
H.
The right image applies
13.8 V RMS at 150 Hz to the TTC108 transformer. It shows a clear knee but even
at this level of magnetic field, total saturation has not quite been achieved.
Looking at the right hand
figure, the knee point (point B in the sketch) is approximately 4 V RMS, well
above the maximum test voltage applied in the center plot.
To see what happens when
driven as hard as is possible with the 8903B analyzer, I ran a series of plots
with just the transformer connected to the 8903B's audio generator section; the
MCP6021 opamp circuit is not used in this plot.
The highest test voltage I
used is 5.477 volts, corresponding to 50 milliwatts power into 600 ohms. At the
lowest test frequency, 100 Hz, we see the distortion is clearly climbing,
although not quite to the level seen at 100 mV, where the BH curve is operating
in the cubic law region. At 100 Hz and 5.477 volts, the BH curve was being
cycled past the knee region, but not too much into the nonlinear area.
As the test frequency increases, the BH curve
is not pushed to the knee region, even at the maximum test voltage.

TTC108 Distortion versus
Driving Resistance
In the theoretical
discussion section, I suggested that a zero ohm driving source would
significantly reduce transformer distortion. Of course, it's not possible to
have a true zero ohm driving source for two reasons. One is that all amplifiers
have some output impedance, and, more importantly here, the transformer's
winding resistance and leakage inductance form a minimum driving impedance. The
output impedance of the MCP6021 opamp at audio frequencies for small signals
is a fraction of an ohm, but the TTC108's winding resistance (pins 13) is 44
ohms (56 ohms for the winding between pins 46).
The plot below shows
measured THD when the TTC108 is driven by the MCP6021 opamp buffer with one
of four resistances between the MCP6021 and the TTC108:
The measured data confirms
our theoretical analysis�the lower the driving series resistance, the lower the
measured THD. This is true for both high and low voltage levels. Removing the
620 ohm resistor and substituting a direct connection, for example, lowers
distortion at 100 Hz by 20 dB.

TTC108 Frequency Response
The plot below shows the TTC108's frequency response over
the range 20 Hz  20 KHz, into a 620 ohm termination and into the 100 Kohm
termination of the HP 9803B's analyzer section. In both cases, the 8903B's
source is set to 600 ohms.
The test condition applies 0 dBm (775 mV) as measured into
an open circuit. With a 620 ohm termination, therefore, zero insertion loss
corresponds to 5.88 dB loss, so a perfect transformer will show 5.88 dBm
output. Into a high impedance load, the theoretical insertion loss is
effectively zero, so a perfect transformer will show 0 dBm output.
It's common to see a rising response when a transformer is
terminated into a high impedance, due to winding capacitance resonance.
Tamura quotes the TTC108 as being ±0.5 dB measured at 0
dBm from 300 Hz to 3.5 KHz, with an insertion loss of 1.4 dB (maximum) at 1 KHz,
also measured at 0 dBm. This data is for the 600 ohm terminated
case, of course.
The measured data shows an insertion loss of 1.0 dB at 1
KHz, and just under 0.5 dB at 300 Hz, so the TTC108 meets its frequency
response and insertion specifications.
TTC108 Square Wave Response
The data shows moderate ringing only for the case of 50 ohm
drive and high impedance termination. The ringing results from a dampened
oscillation at the resonant frequency of the transformer secondary inductance
and stray capacitance, including the test lead from the transformer to the
oscilloscope. (The test does not use 10x probes, but rather a 6 ft length of
RG174 coaxial cable in an attempt to mimic how the transformer might be used in
practice.) The ringing frequency is around 120 KHz.
50 Ohm drive, high impedance termination 

50 Ohm drive, 620 ohm termination 

610 Ohm drive, high impedance termination 

610 Ohm drive, 620 ohm termination 


Western Electric �Repeating Coils�
THD
Western Electric
�repeating coils� have long had a reputation of low distortion. A �repeating
coil� is a transformer in Bell System terminology. I have two WeCo repeating
coils in my junk box:
Both the 111C and 119C
repeating coils have split coil windings. The test configuration I used is
600:600 for the 111C coil and 600:520 for the 119C coil.
Specifications on these
coils are hard to find, with frequency response
and power levels about all that's available.
Since
the Western Electric coils have a much
wider frequency
response than the other transformers
examined on this page, I ran a distortion plot over the
range 20 Hz � 20 KHz, representing the traditional �high fidelity� frequency
range. (These sweeps are with the 8903B's 80 KHz low pass filter engaged.)
As the plot below
demonstrates, neither of the Western Electric coils disappoint, with THD at or
below my ability to measure for frequencies over 200 Hz.
The newer 119C coil shows
considerable improvement over the 111C coil at lower frequencies, being at my
measurement floor until nearly 100 Hz and providing 65 dB THD at 20 Hz.
The test voltage applied,
775 mV, corresponds to 0 dBm at 600 ohms.
The plot below shows the
111C repeat coil with varying test voltages from 100 mV (17.8 dBm) to 5477 mV
(+17 dBm). At the two lowest voltage levels, 100 and 250 mV, the 111C�s THD is
below the ability of my HP8903B�s ability to resolve. Likewise, at the higher
test voltages, the THD is below the HP 8903B's resolution above 500 Hz or so.
I did not run a similar
plot for the 119C coil, but, based upon the 0 dBm test, there's little reason to
expect it to be anything but better than the 111C coil.
With higher voltage
levels, THD can be seen, but even at +17 dBm, it disappears below the 8903B�s
resolution at 98 dB. Above 600 Hz or so, the THD is at or below the distortion
analyzer�s floor.
To see whether the
excellent distortion performance results from a linear BH curve, I ran two BH
curves on the 119C coil, one at 0 dBm (775 mV) and the second at the maximum
output my HP 200CD oscillator could supply, 20.4 volts (+28.4 dBm) with the
results displayed below.
0 dBm (775
mV) 
+28.4 dBm (20.4V) 


These BH curves are
remarkable. The shape of the curves are essentially identical. (Of course, the
sizes are different; I've adjusted the oscilloscope's X and Y axis gain settings
to keep the images on the screen.) In neither case is there even a hint of
saturation. The 0 dBm curve has a fair bit of noise as the the signal is only a
few millivolts. The right hand curve can be seen to just start to tilt to the
right, but otherwise has a shape almost indistinguishable from the 0 dBm case.
These BH curves are not linear but they are highly symmetric and without
discontinuities, which contribute to excellent THD performance.
Western
Electric 119C Repeating Coil Frequency Response
I ran a 20 Hz  20 KHz frequency response sweep on
the 119C coil, with the results shown below. With a 620 ohm termination, the
response varied less than ±0.1 dB over the full 20 Hz  20 KHz range, with an
insertion loss around 0.5 dB. All in all, an excellent transformer, particularly
considering the technology is 40 years or more old.
Western Electric 119C
Coil Square Wave Response The data shows moderate
ringing for the case of 50 ohm drive and high impedance termination, and limited
ringing for 620 ohm drive and high impedance termination. The ringing results
from a dampened oscillation at the resonant frequency of the transformer
secondary inductance and stray capacitance, including the test lead from the
transformer to the oscilloscope. (The test does not use 10x probes, but rather a
6 ft length of RG174 coaxial cable in an attempt to mimic how the transformer
might be used in practice.) The ringing frequency is around 120 KHz.
50 Ohm drive, high impedance termination 

50 Ohm drive, 620 ohm termination 

610 Ohm drive, high impedance termination 

610 Ohm drive, 620 ohm termination 


Triad SP70 THD
I've used Triad SP70 audio transformers
with my Softrock Lite receivers after measuring several prospective candidates.
It's a 600:600 ohm transformer, of roughly similar size to the TTC108. My web
page
http://www.cliftonlaboratories.com/audio_transformer_data_and_modeling.htm
provides considerable measuredversuspredicted data for the SP70. 
Triad provides a limited
set of performance specifications for the SP70:
Notably, Triad provides no
distortion specification. I collected distortion data for the SP70 by directly
connecting the transformer to the HP 8903B distortion analyzer, without using
the MCP6021 opamp driver.
Looking at the lower
signal level performance, at 100 mV and 250 mV RMS, the SP70 provides lower THD
than the TTC108. At 500 Hz, for example, the SP70 has 10 dB lower THD at 100
mV and likewise at 250 mV.
At higher signal levels,
1000 mV and 5477 mV, particularly at lower frequencies, however, something goes
rather badly in the SP70. At 100 Hz, for example, at 1000 mV, the SP70 shows
25 dB THD, compared with 38 dB for the TTC108.
One possible explanation
for this behavior immediately springs to mind�the SP70 core is entering
saturation at a much lower voltage than does the TTC108, even though the SP70
is rated at 50 mW (5477 mV at 600 ohms).
To verify this assumption,
I ran three BH curve on the SP70 with the results shown below.
With 2.2 V RMS applied
across the primary at 150 Hz, the core is well into nonlinear operation and
indeed not far from saturation at the tips of the BH curve. Judging from the
center portion of the 2.2 V BH curve, with 1000 mV applied at 150 Hz the
BH curve is well into the nonlinear region.
With 5.5 V RMS applied,
the situation is even worse, as reflected in the right image. The core is deep
into saturation. Note that B remains flat over large portions of H, i.e.,
the core's magnetic elements are fully aligned with the H field and hence cannot
amplify H. The consequence of a horizontal BH curve is that the output waveform
sags or flat tops or even decays. dB/dt is close to zero, so the induced
secondary voltage is likewise close to zero. It's not surprising, therefore,
that the THD is very high under these conditions.

SP70 Frequency Response
The
plot below shows the SP70's response under the same test conditions as used for
earlier frequency response sweeps.
Triad rates the SP70 as ±2 dB from 300 Hz to 100 KHz.
(I've provided plots out to 100 KHz on my
http://www.cliftonlaboratories.com/softrock_lite_6_2.htm page, should you be
interested in seeing the full range data.
At 300 Hz, the SP70 is down about 0.5 dB from the 1000 Hz
value, so it easily meets the published low frequency response specification.
Triad does not provide an insertion loss specification, but the measured
data shows about 1 dB, which is quite typical of this size transformer.
SP70 Square Wave Response
The data shows moderate ringing for the case of 50 ohm drive
and high impedance termination, and limited ringing for 620 ohm drive and
high impedance termination. The ringing results from a dampened oscillation at
the resonant frequency of the transformer secondary inductance and stray
capacitance, including the test lead from the transformer to the oscilloscope.
(The test does not use 10x probes, but rather a 6 ft length of RG174 coaxial
cable in an attempt to mimic how the transformer might be used in practice.) The
ringing frequency is around 330 KHz, a considerably higher frequency than seen
in the Bourns or Tamura transformers.
50 Ohm drive, high impedance termination 

50 Ohm drive, 620 ohm termination 

610 Ohm drive, high impedance termination 

610 Ohm drive, 620 ohm termination 


Bourns LMNP1001B1 THD
The Bourns LMNP1001B1 transformer is aimed
at the same market as the TTC108, modems, faxes and other devices that connect
to telephone lines. The transformer has a recommended operating impedance of
600 ohms, with the following other specifications of interest.
Compared with the
TTC108, the LMNP1001 has a wider frequency range and lower quoted distortion,
0.1% versus 0.5%. (0.1% distortion is 60 dB from the fundamental.) Note,
however, that Bourns is playing �specsmanship� as the quoted value is for 1 KHz,
where we expect the THD to be low, whilst Tamura's 0.5% THD rating applies over
the entire frequency range
300 Hz � 3.5 KHz, a more stringent specification.
Regardless of whether Bourns was engaging in
specsmanship with the 0.1% THD figure, as the plot below demonstrates, the
LMNP1001 provides better THD performance at 100 and 250 mV than either the
SP70 or the TTC108 parts. Indeed, at 100 Hz and 100 mV, the LMNP1001 has a
THD of 56 dB, compared with 40 for the SP70 and 31 for the TTC108. Quite a
remarkable improvement.
Bourn's data sheet quotes
0.1% (60 dB) THD at 1 KHz with a 0 dBm test signal. The data shows THD at 1000
mV (+2.2 dBm) running at 75 dBm, more than comfortably over the quoted
performance.
There's more of a problem,
however, at lower frequencies, with the THD being only 29 dBm at 100 Hz. And,
there�s a gross problem at 5477 mV, which at +17 dBm, is admittedly way over the
transformer�s +3 dBm maximum rating.
As usual, when we see high
distortion, the BH curve will help us understand what is going on.
775 mV (0
dBm) 
1.84 V 


The BH image at the left
is the LMNP1001 with 775 mV RMS( 0 dBM) test voltage at 150 Hz. It shows
reasonable linearity over perhaps half the horizontal (H field) range, some
distortion at the extremities. The THD under these conditions is around 40 dB.
The left image applies
1840 mV RMS to the LMNP1001 transformer. The tips of the BH curve show severe
saturation, and indeed saturation occurs over a major part of the H range. This
behavior certainly explains the gross distortion seen at 5477 mV in the earlier
plot.

Bourns LMNP1001B1
Frequency Response
The plot below shows the LMNP1001B1's response under the same test
conditions as used for earlier frequency response sweeps.
Bourns quotes the frequency response range as 0.2 dB from
300 Hz to 3500 Hz, which the test sample easily meets.
The insertion loss is quoted as "less than 1.5 db at 2
KHz" which again it easily meets, being about 1.0 db at this frequency.
Bourns
LMNP1001B1 Square Wave Response The data
shows severe ringing when driven either with 50 or 610 ohms and high impedance
termination. The ringing results from a dampened oscillation at the resonant
frequency of the transformer secondary inductance and stray capacitance,
including the test lead from the transformer to the oscilloscope. (The test does
not use 10x probes, but rather a 6 ft length of RG174 coaxial cable in an
attempt to mimic how the transformer might be used in practice.) The ringing
frequency is around 100 KHz. The ringing is
eliminated with 620 ohm termination regardless of the drive impedance.
50 Ohm drive, high impedance termination 

50 Ohm drive, 620 ohm termination 

610 Ohm drive, high impedance termination 

610 Ohm drive, 620 ohm termination 



Walters
OEP8000 Frequency Response The OEP8000 is a
physically small, surface mount 600 ohm : 600 ohm transformer designed for
telephone coupling and similar applications, manufactured by Walters OEP Ltd.,
in Oxfordshire, UK. It may be purchased in the United States from Newark
Electronics for $5.81 in singlelot quantities, or through Farnell in the UK.
When purchased from Newark, the OEP8000 is shipped from Farnell (Newark acquired
Farnell several years ago) and a $20 service charge instead of
international freight shipping is applied.
The OEP8000's electrical specifications are reproduced
below. I've highlighted the most intriguing spec�THD of 89 dBm when 0 dBm is
applied. In the distortion section of this analysis, we'll see that this
specification must be read quite carefully however.
Electrical specification:
Ratio: 1 to 1
Primary DC
resistance: 111 ohms +/ 15%
Secondary DC
resistance: 111 ohms +/ 15%
Impedance
matching: 600 ohms to 600 ohms
Inductance
(270mVrms, 100Hz parallel) Pins 1  3: 3.6H min.
Leakage
inductance: (10mVrms, 200Hz series) pins 1  3: 4.1mH nom.
Return loss:
(ref. 600 ohms) 200 to 4kHz: 18dB min.
Insertion
loss: (ref. 600 ohms, 2kHz): 4dB max.
(ref. 430
ohms, 2kHz): 2dB max.
Frequency
response: 200  4kHz: +/ 0.2dB
Longitudinal
balance: 200Hz  4kHz: 80dB min.
Turns ratio
(@ 6kHz, 0.1Vrms), pins 1  3 & 6  4:1.00+/ 1%
Distortion: 600Hz, 0dBm: 89dBm nom.
Saturation:
<10Vrms, 65V peak, 50Hz
Hipot,
primary to secondary: 3.3kV min., 1mA for 1 minute
Operating
temperature range: 10 to +85 C
Storage
temperature range: 40 to + +125 C
Certified to
EN609501: 2001
RoHS
compliant.
Note: Do not pass DC current through windings.

The plot below shows the OEP8000's frequency response when
tested in the factory recommended test fixture. The factoryrecommended test
fixture introduces about 7.58 dB excess loss into the data, so I've subtracted
that from my measured value to derive the transformer's net insertion
loss. The specification is 4 dB maximum at 2 KHz, and my data shows this to be
comfortably met. The overall frequency response from 100 Hz to 10 KHz is
relatively flat, with less than 0.5 dB variance over this range.

OEP8000 Harmonic
Distortion The schematic below is the
recommended test fixture for the OEP8000 and I used it for the frequency
response data above and the THD data presented below. I believe the secondary
loading of 430R paralleled with 6.8 nF represents a typical British Telecom
analog subscriber telephone loop impedance. The 6.8 uF capacitor on the primary
side must be to block DC from the windings.
If the OEP8000 is replaced by a perfect 1:1 transformer,
over most of the normal audio frequency band, the result of the test fixture is
a resistive voltage divider, a perfect audio signal source and a 430 / (430 +
600) resistive voltage divider, resulting in 7.6 dB loss. At 1 KHz, the 6.8 nF
capacitors have a reactance of 23 Kohm, and may be disregarded in this analysis.
Likewise, the 6.8 uF series capacitor has a very low reactance at 1 KHz and may
also be disregarded. These approximations become less accurate as the frequency
increases, but are good enough through 3 or 4 KHz.
One point of concern is that the shunting capacitors will
roll off high frequency signals, thus reducing the measured harmonic distortion
where the test frequency is above a few KHz. As seen below, however, the
measured data shows no sign of that effect. 
The THD plot above show four measurements. The blue curve
is the noise floor of the HP8903B analyzer with a coaxial cable between the
generator output section and the analyzer input section, shunted with 430 ohms
resistance and 6.8nF capacitance, so as to duplicate the factory test fixture
loading. The applied signal generator voltage in this test was adjusted to
deliver 261 mV to the analyzer's input, which is the voltage seen on the output
side of the The instrument is capable of 90 dB THD at this voltage level.
The green and red traces are run using the same protocol
as the other THD measurements on this page. The transformer's secondary is
terminated with the HP8903B's analyzer input stage, which is 100 Kohm. The cyan
plot is the THD measured with the OEP8000 mounted in the test fixture. The
HP8903B's signal generator section is set to deliver 0 dBm (775 mV) open
circuit, with 600 ohm output impedance. When connected to the transformer and
fixture, the actual voltage delivered to the 8903B's analyzer section is around
261 mV.
At the specified 600 Hz test frequency, in the test
fixture, the measured THD is 75.4 dB with respect to the 600 Hz signal level
at the 8903B analyzer input section. The measured 600 Hz signal level was
260 mV. We may therefore compute the total THD voltage as 260 mV * 10^{75.4/20
} or 44.1 microvolts. In an instrument reading voltage, but calibrated
in terms of power delivered at 600 ohms, the resulting power is 3.25x10^{12}
watts or 84.9 dBm.
Measured this way, we might say that the THD is 85 dBm,
which compares reasonably well to the OEP8000's quoted specification of 89 dBm
nominal. The 4 dB discrepancy is likely subsumed within the "nominal"
terminology.
However, in my personal view, quoting THD as a dBm level
is more an attempt to make the product look better than to enlighten the
purchaser. It's far more common to quote TDH as a percentage of the output or X
dB down from the output. In fact, the OEP8000 is the only transformer of
the dozen or so I looked at that quotes an absolute value for THD. And,
there's no need to embellish the OEP8000's distortion figures by "specsmanship"
as it is quite a good performing transformer.
I should also add that dBm measurements presuppose a
specific impedance, usually 50 ohms for RF and 600 ohms for audio. Since the
voltage in the test circuit is being developed across 430 ohms (ignoring the
shunt capacitance) it is not correct to refer to any measured voltage level in
dBm where the reference level is (as is almost certainly the case) 600 ohms. I
realize common usage often ignores the impedance into which a dB referenced
value is measured, but ignoring the impedance does not make the usage correct. 
I also measured distortion in the OEP8000 with 600 and 50 ohm driving source
impedances into 100K termination. As with the other transformers examined,
lower driving impedance improves the distortion considerably.

Finally, I swept the voltage at an applied 600 Hz frequency
with both 50 and 600 ohm driving source impedance, with the results shown below.
These datasets are with 620 ohm termination on the transformer secondary.


Comparisons and Conclusions
As they say around the
race track, �there are horses for courses.� Leaving aside the Western Electric
repeat coils, and very expensive audio transformers such as those made by
Jensen,
http://www.jensentransformers.com/, what are we to make of the Tamura,
Triad, Walters and Bourns offerings tested?
Assuming THD is the
primary selection criterion, then we must know the expected signal level. All
three plots presented are taken with the distortion analyzer�s audio source
driving the transformer. As we�ve seen, major improvements in THD are possible
when a transformer is drive by a low impedance �zero ohm� source, so these
comparison plots are worst case in that regard.
If we can be assured that
the signal level will remain low, say 100 mV or less, Bourns� LMNP1001B1
provides exceptionally low THD, as does the OEP8000. In fact, over 2000 Hz, the THD measurement is
limited by the HP 8903B distortion analyzer�s performance.
At 250 mV, the relative
ranking of these four transformers remain unchanged, although we see the Bourns
LMNP1001B1 and Walters OEP8000 start to loose some of their comparative advantage over the other
two transformers. At 100 Hz, all four transformers are closer together in THD,
although the Bourns product is still 15 dB better than the TTC108.
The picture is more mixed
at 1000 mV RMS (+2.2 dBm), however. At lower frequencies, the OEP8000 is the
best performer. However, above 400 Hz, the relative performance seen at lower
voltage levels is restored, although the difference amongst the transformers is
less than at lower voltage levels.
It�s also informative to
look at the BH curves for three transformers under the same test conditions
and same oscilloscope gain settings. (I have not run BH data for the OEP8000,
as I acquired the sample parts after completing the BH analysis.) The data is for 0 dBm (775 mV) applied at
150 Hz.
Transformer 
BH Image 775 mV (0 dBm) 
Insertion Loss @ 150 Hz 
THD @ 150 Hz / 1000 mV 
Western Electric 119C 

0.49 dB 
90.14 dB 
Bourns LMNP1001B1 

1.12 dB 
39.9 dB 
Triad SP70 

1.71 dB 
33.13 
Tamura TTC108 

1.72 dB 
41.78 
The area within the ellipse is proportional to hysteresis
core loss and the larger the area, the greater the 150 Hz insertion loss.
However, the series resistance of the primary and secondary windings have a much
larger effect on insertion loss at this frequency and swamp the small
differences in hysteresis loss.
Distortion should be proportional to the symmetry and
linearity of the BH curve, and the curves back this up to a large degree.
Primary Inductance Variation with Level
It occurred to me that a surrogate for distortion might be
how the primary winding inductance varies with voltage. Accordingly, I measured
the primary winding inductance for the Bourns, Triad and Tamura transformers
over a range of test voltages. I used a General Radio GR1650B RLC bridge, which
has a variable oscillator drive that is convenient for this sort of test.
The frequency used is 1 KHz.
The plot below shows the measured inductance versus test
voltage for the three transformers. There's a clear difference between the
Bourns and the Triad and Tamura transformers, with the Bourns showing
essentially no change in inductance with applied voltage.
To make it easier to see the difference amongst the three
transformers, I've plotted the normalized inductance, i.e., with the
inductance at 700 mV = 1.00
Based on the change of inductance with test voltage data,
we would expect the Bourns transformer to have much lower THD at low voltage
levels, followed by the SP70, in turn followed by the TTC108. In fact, this is
exactly the order of THD performance for low voltage levels.

Frequency Response
Compared The plot below shows the frequency
response of four transformers, driven with 600 ohms and terminated with
620 ohms. Leaving aside the 119C coil's nearly ruler flat response, the TTC108
and SP70 have almost identical frequency response characteristics. The Bourns
LMNP1001B1 has better low frequency response, but at the price of less high
frequency response.
I've been asked to compare the frequency responses of
the three inexpensive 600:600 transformers when driven by 600 ohms and 50
ohms, terminated into a 100K load.
Since the interesting part of this data is the relative
performance of the transformers, I've normalized the data so that each
transformer has 0.0 dB loss at 1000 Hz. Although the normalization washes out
the insertion loss differences amongst the configurations, insertion loss is not
a major consideration in this application.
The data shows considerable low end extension when driven
with 50 ohms, save for the Bourns transformer, where the extension is more
modest.
There's an anomaly with the Tamura TTC108 data for 50 ohm
drive. It's considerably better at low frequencies than when I measured it with
different test equipment a couple weeks ago. I'll run it again and see why the
discrepancy exists.

Stancor
TTCP2. TTCP6 and TTCP8 Paul Christensen,
W9AC, sent me three Stancor telephone coupling transformers for analysis, models
TTPC2, 6 and 8. Because all three transformers are quite similar, I'll treat
them together. These parts are quite similar in size to the TTC108 I've covered
above and are in the same price category and serve the same market; telephone
coupling.
The differences amongst the three parts are related to
center tap windings and, interestingly, the TTPC6's ability to carry DC
current. DC current rating is intriguing because it suggest a "beefier" core
(also indicated by the TTPC6 weighing twice as much as the 2 and 8 parts)
and/or better core material with the prospect of improved low frequency response
and lower distortion. Alas, the TTPC6 isn't much different than the 2 and 8
parts and all three are close to the TTC108.
The full specifications are available from Stancor at
http://www.stancor.com/wrdstc/pdfs/Catalog_2006/Pg_019_20.pdf and I've
extracted the key elements below. 
The photo below shows the three
Stancor transformers along with the Tamura TTC108. At the rear is a DIN rail
standard package with two Jensen audio isolation transformers, loaned to
me for measurements by Ronald Wagner of Dynamic Research, Inc. Data for the
DIN2LI is presented later on this page. The DIN2LI's enclosure size does not
mean the transformers occupy the full space; the box is rather light. 

It may not be clear from the angle of the photo, but the TTPC2 is around half
the height of the other two Stancor products and the TTC108. The photograph
below provides a better view of the relative height of the transformers. The
TTPC2's core is more rectangular than the other three transformers which are
nearly square.


The figure below shows the frequency response of the three
transformers over the range 20 Hz  20 KHz. The data is taken with an HP8903B
audio analyzer, driving the transformers with the internal audio generator set
for 600 ohm impedance. The transformer is terminated into the 8903B's input
section, representing a 100K impedance.
Interestingly, the TTPC6 has the worst low frequency response, which can be
understood as a side effect of it's DC current rating.
First, telephone coupling transformers are designed
with a low frequency response target around 300 Hz, and at 300 Hz the TTPC6 is
down 3.8 dB, about 2 dB worse than the 2 and 8 devices. Still, the TTPC6's
low frequency response is more than acceptable for a telephone coupling
transformer.
In order to accommodate DC current, the transformer
designer must prevent the core from being driven into a nonlinear range by the
sum of the DC static magnetization field and the imposed AC signal.
(Looking at the BH curves, imagine the starting point being shifted. Clearly
one polarity of the incoming AC waveform will drive the core closer to
saturation whilst the opposite polarity will take the core away from saturation.
Hence the output will exhibit a different response for each waveform half.)
The
designer's bag of tricks include using a larger core, or different core
material, or introducing an air gap
in the core, or reducing the number of turns. Since the TTPC6 is similar sized
to the 2 and 8 parts, and since there seems to be no visible air gap, it is
most likely that the TTPC6's designer reduced the number of turns. This reduces
the magnetizing inductance and also means the low frequency response will
impaired. 

I measured the four transformers (three Stancor and the
TTC108) primary inductance at 100 Hz and 1 KHz with a General Radio 1658
Digibridge. As the data shows, the TTPC6 has considerably less inductance than
either the 2 or 8 parts or, for that matter, the TTC108. This suggests that
the designer has solved the DC current dilemma by opting for fewer turns or by a
core with lower permeability, or a combination of both. The DC resistance
specification shows the TTPC6 with nearly twice the DC resistance of the 2 and
8 transformers. If the 6 simply had fewer turns, then one would expect the DC
resistance to be less than seen in the 2 or 8 transformers. This not being the
case, the more logical answer is that the designer has opted for a different
core material with lower permeability and higher resistance to saturation (or
perhaps a gap core) and has added turns to bring the inductance back towards the
minimum acceptable value to maintain a 300 Hz lower frequency 3 dB point.
The difference in inductance between 100 Hz and 1000 Hz
represents at least two factors. One is that the 1658 Digibridge applies
different voltage levels at these two frequencies and incremental inductance
depends on the applied test signal level. See
Primary_Inductance_Variation_with_Level earlier on this page. Second, it's
possible that the core material's permeability has some frequency dependency,
although this is less likely to account for all the variation.
Transformer 
100 Hz Inductance (H) 
1 KHz Inductance (H) 
Predicted 100 Hz Loss (dB) 
Measured 100 Hz Loss (dB) 
TTPC2 
0.80 
0.38 
3.88 
4.7 
TTPC6 
0.34 
0.28 
9.50 
10.4 
TTPC8 
1.27 
0.44 
1.93 
2.6 
TTC108 
0.97 
0.46 
2.95 
3.08 
Incidentally, we can crosscheck the measured 100 Hz
inductance measurement against the observed 100 Hz insertion loss. With an open
circuited secondary, the voltage developed is given by analyzing the transformer
as a RL series network, with 600 ohms signal generator impedance and L being the
measured value. (This ignores the winding series resistance, but this won't
introduce too much error given the magnitude of the transformer resistance
compared with the 600 ohm generator resistance. It also assumes the transformer
turns ratio is 1.00:1.00.)
The simplistic prediction shows reasonably good agreement
with the measured data If we enhance the model, for example, adding the TTPC6's DC
resistance, the predicted loss becomes 9.92 dB, bringing it
considerably closer to the measured 10.4 db. When one considers the inductance
versus drive level factor, we can't expect perfect agreement.
The next plot sequence shows the THD for the three Stancor
transformers at the same drive levels in the earlier measurements. In all cases,
the drive is applied with the 8903B source impedance set to 600 ohms and the
transformer secondary unterminated, other than by the 100K input impedance
of the 8903B's analyzer section. 



Of perhaps more interest than the individual plots is how these three Stancor
products compare with the Tamura TTC108 at an applied signal level typical of
what one might find when used for a sound card input, as is the case in the K3's
line output stage.
The plot shows the TTPC6 is slightly�a matter of a dB or
two�better than the TTC108 up to 2 KHz. In fact, there's very
little to chose from amongst these transformers. Above 1 KHz, the TTPC2 is the
best performer, but it's the worse below 1 KHz. Performance above 4 KHz is not
material as the K3's bandwidth is limited to 4 KHz. 

I've also run a square wave ringing test on the three
Stancor transformers. Since the results are similar for all three, I'll just
provide the TTPC6 oscilloscope captures. As the image capture indicates, the
first capture is with the transformer secondary terminated only by the
oscilloscope 10X probe. The second terminates the secondary with 620 ohms. In
both cases, the transformer is driven with a bipolar square wave with a 50 ohm
source, an HP8904A multifunction synthesizer. The
data is generally similar to the other inexpensive transformers; unless
terminated all exhibit a great deal of ringing. Of course, a microsecond
rise/fall square wave is not a possible exciting signal when connected to a
radio receiver, so this test may be of more academic than practical interest.
If ringing is of concern, the simple answer is to
terminate the transformer with a suitable resistance, assuming other
considerations permit. 


Effect of DC Bias on TTPC6 and 8 Transformers
Is there a difference between the TTPC6 and 8 transformers
when DC current is applied to a winding, or does the 0 mA rating of the TTPC8
mean anything? These are otherwise physically and electrically similar devices. To answer this question, I applied a 100 Hz 1 volt peaktopeak
sine wave with variable DC offset from an HP 8904A synthesized multifunction
generator to one winding and looked at the resulting waveform on the
transformer's other winding for a range of DC offset voltages and resulting
current. I did not look at the effect of DC bias on THD.
The first image shows the effect of DC bias on a
transformer not designed to accommodate DC current. As the DC bias increases,
the output signal level drops some 10 dB between 0 mA DC current and 100 mA DC
current. Most of the drop occurs at low current levels, with little change
between 33 mA and 100 mA. There's also phase shift seen due to variation
in the transformer's magnetizing inductance with current. (The 0 mA blue trace
was not aligned with the center graticule line when I captured the data, so
you'll have to mentally correct for my error.) As a
historical footnote, the effect of DC current in changing an iron core device's
AC response is the principle behind magnetic amplifiers and saturable reactors.
The DC bias shifts the operating point along the BH curve and thus varies the
inductance and hence device impedance and gain.


In contrast, the TTPC6 shows nearly negligible change in
amplitude level as DC current is added to the winding. There's a very small but
real phase shift also visible, a consequence of a small change in the
transformer's magnetizing inductance with DC current. (The oscilloscope is
triggered on a synchronization pulse from the HP 8904A synthesized source.) 

So whatever the designer did to offset the harmful effects of
DC on transformer response was successful in the TTPC6. 

Jensen DIN2LI Thanks to
Ronald Wagner of Dynamic Research, Inc, I've been loaned a Jensen DIN2LI dual
isolation transformer to analyze. The 2LI's specifications are available at
http://www.jensentransformers.com/datashts/din2li.pdf and the performance
specifications are eye popping. Note, for example, the THD figure; less than
0.001% (100 dB) at 1 KHz and less than 0.04% (68 dB) at 20 Hz


The 2LI has two independent transformers within the plastic enclosure. I believe
these are JT11P1HPC transformers, with a different housing.
http://www.jensentransformers.com/datashts/11p1hpc.pdf
The 3 dB stated frequency response is from 0.25 Hz to 80
KHz, an incredibly impressive specification as well.
I should add that these performance levels are not without
cost. The 2LI is roughly $200 each, or $100 per transformer. If you wish
to purchase a single JT110KHPC without the fancy DIN enclosure, the price is
$78. For comparison, the Stancor and Tamura parts are in the $34 range.
One additional point is that Jensen's transformers have a
30 dB magnetic shield. This is a very useful addition as I've noticed induced
hum pickup in my K3's audio line transformers.
I also will add that these specifications are
difficult or impossible for me to accurately measure in all respects, as they
are better than the test equipment available to me. I'll identify where the
measurements are test equipment limited.
The plot below shows the 2LI's frequency response from 20
Hz to 100 KHz taken with the HP 8903B, with the transformer terminated by
the recommended 10K resistance. With other equipment, I could have looked at the
response below 20 Hz to verify the 0.25 Hz 3 dB point, but did not do so.
Quite an impressive response curve; ruler straight from 20
Hz to 10 KHz with a quarter dB or so rise up to 50 KHz and a measured 3 dB upper
point of 75 KHz. That's a hair below the specification, but my test setup does
not exactly duplicate the manufacturer's test protocol. 

The figure below shows my measured THD data for the 2LI. I've added horizontal
lines with the HP 8903B's noise floor for the particular drive level, taken by
connecting the 8903B's output directly to the input (loopback). The Jensen data shows
slightly less noise and distortion than the loopback test, which is due to the
level and terminating impedance differences between the transformer in
place and the loopback cables.
In essence, at 100 mV applied, all measured distortion is actually the noise
floor of my 8903B. At 250 mV applied signal and stronger, there are areas of
measured distortion above the noise floor for low frequencies.
With 5477 mV (RMS) applied, at 100 Hz I measured THD of 86 dB, or 0.005%.
5477 mV is +15 dBV, and at this combination of test frequency and signal level
Jensen's data sheet shows 0.006% THD, interpolating between Jensen's +10 and +19
dBV data curves. This provides confidence that my data is correct, at least
where the transformer's parameters are within the limits of my test gear. 


I also looked at the DIN2LI's response to a square wave,
with the results shown below. Even unterminated, the 2LI's response exhibits
much less ringing than the other transformers, a characteristic it shares
with the Western Electric 119C repeat coil. This square wave response is a
function of the transformer's inductance, stray capacitance and resistance. The
higher resistance seen in the 2LI means greater damping of the induced ringing. 


BH Curve
Analysis of Stancor, Jensen and Western Electric Transformers
I wondered how the Jensen transformer's performance would
show up in its BH curve, and how it compares with my previous best performing
transformer, the Western Electric 119C. I revised the BH circuit used earlier
to reflect direct current measurement via a Tektronix TCP202 current probe, but
the concept is unchanged. The horizontal axis is proportional to the
transformer's current and the vertical axis is proportional to the magnetic
flux, as sensed by integrating the voltage with a simple RC integrator. The
tests are done at 150 Hz and the data captured with a Tektronix TDS430 digital
oscilloscope. The exciting signal is obtained from an HP 8904A synthesized
multifunction generator driving a Kepco BOP 1001M bipolar power supply /
amplifier. This permits applying up to 200V PP across the transformer
winding, with a maximum current of 1A, although the actual current levels are
much lower than the maximum permitted by the power supply / amplifier limit.
The horizontal axis (Ch 1) is in millamperes x 5, so the
scale 50mVΩ corresponds to 10 mA per division. (The factor of 5 exists
because I wrapped five turns of wire around the TCP202's pickup jaw to increase
its sensitivity.) Channel 2 is the integrator output voltage.

TTC108 BH
As a point of comparison, I also ran the Tamura TTC108
transformer at 10 and 40 volts PP excitation, with the results illustrated
below.
At 10 volts, the BH curve is elliptical with no signs of
saturation; at 40 volts, the TTC108 exhibits major saturation, with the break
point occurring with less than 10 mA current.

10V PP Excitation

40V PP Excitation

TTPC2 BH
At 10V PP excitation, the TTC108 and TTPC2 BH ellipses are
quite similar, and the more traditional BH waveform appears in the 20V PP
capture. At 30V PP, the TTPC2 shows gross saturation, which becomes even worse
at 40V. (Note the change in scale in the last plot.)
Comparing the TTC108 and TTPC2 at 40V, it appears that
the the TTPC2 is driven further into saturation and that the linear region of
the BH curve is smaller. 
10V PP Excitation

20V PP Excitation

30V PP Excitation

40V PP Excitation

Western
Electric 119C Repeat Coil With 40V PP
excitation, the 119C repeat coil is a small ellipse. Note that I've increased
the horizontal axis gain to 2 mA/division in both 119C plots below. The area
within the BH curve represents hysteresis loss and it's gratifyingly small
compared with either the TTC108 or the TTPC2 parts. There's no hint of
saturation in the BH curve.
Even with 200V PP applied�the maximum output of the BOP
1001M amplifier�the 119C's BH curve shows no signs of saturation. The
ellipse is certainly not symmetrical, but it's not saturated. 
40V PP Excitation

200V PP Excitation

Jensen DIN2LI BH
As good as the 119C coil is�and it's good indeed�Jensen's 2LI
transformer is significantly better. Indeed, the BH curve is not
resolvable beyond what appears to be a single line with 40V PP excitation. Even
at 100V PP excitation, the BH curve is just starting to open.
At 150V, however, we see clear signs of saturation.
Indeed, the BH curve looks almost like of a square loop material, linear to the
break and then nearly horizontal. More of this behavior is visible at 175 and
200V PP excitation.

40V PP Excitation

100V PP Excitation

150V PP Excitation

175V PP Excitation

200V PP Excitation

BG Incorporated KS Transformer
Joop, PE1CQP, sent several BG Industries model "KS" transformers for evaluation.
These are data coupling transformers for telephone modems up to 56K BPS. The
particular transformer is available in several variants relating to pin
placement and height, but with identical electrical specifications.
The "KS" designation indicates, by the way, indicates the
part was designed for and supplied to Western Electric for Bell System
equipment. (These parts are identified with a multidigit KSxxxx sequence,
sometimes followed by a Lx suffix for variants.) This is a
small surface mount transformer, so thin, in fact, that the laminations are
easily counted. The ruler in the photograph is in inches and tenths. (The height
is less than 0.200 inches.) 

The relevant specifications are:
Impedance Source/Load 
600/280 Ohms 
DC
Resistance PRI/SEC 
160/190 Ohms 
Insertion Loss 
3.53.7 dB 
Frequency Response 
±0.2 dB 50Hz50KHz, 10 dBm OUTPUT 
Harmonic Distortion 
73 dB, 150 Hz, 280 Ohm Source, 3 dBm
across 600 ohm load 
Max
Output Power 
+9 dBm 
Turns Ratio 
1:1 ±2% 
I don't understand how a transformer with a 1:1 winding ratio matches
600 to 280 ohms, but perhaps it's related to an intentional mismatch for
a reason unknown to me. 


BG Inc. KS
Frequency Response The specifications sheet
rates the KS transformer's frequency response as ±0.2 dB, 50 Hz  50 KHz, and in fact it's remarkably flat over the
frequency range 20 Hz  100 KHz, as reflected below. Over this frequency range,
the level response varies from 1.5 dB to +0.8 dB, and over the more usable
range 50 Hz  50 KHz, the level varies less than 0.2 dB. While not in the same
league as Jensen's offering, it's much better than any of the inexpensive
transformers reviewed on this page, particularly considering the data reflects
600 ohm drive. 

BG Inc. KS THD
The KS transformer is not a bad performer in terms of THD, at
least so long as some attention is paid to signal levels. Note that the
data presented is for a wider frequency range (20 Hz  20 KHz) than in some
earlier plots.


KS Transformer Driven
by OpAmp "Zero ohms" Source I've been asked
to comment on the KS transformer performance when driven by a "zero ohms" source
such as an opamp with negative feedback. I used the MCP6021 voltage follower
circuit discussed earlier on this page, modified for better low frequency
performance by increased input blocking capacitor value. The MCP6021 follower
is powered by an analog bench power supply in the tests below. Direct opamp
drive models how the transformer will behave when used to isolate the audio
outputs of a Softrock receiver. (Harmonic distortion and frequency
response is not the end of the suitability requirement when used to isolate a
Softrock receiver, of course. Amplitude and phase balance between two
randomly selected KS transformers are also important but I have not yet looked
at this aspect of these transformers.)
The plot below shows the improvement in harmonic
distortion achieved when driven with a low impedance source (dotted line),
compared with the 600 ohm source (solid line).


In fact, the improvement in THD obtained from low impedance
drive is better than indicated in the plot above, as the low impedance results
are limited by the test equipment and broadband noise from the opamp and power
supply. The plot below shows the measured low impedance transformer THD and the
THD floor (dotted lines) when the transformer is removed and the opamp
output connected directly to the 8903B's input section.
Above a few hundred Hz, the test setup's noise and distortion
floor limits the measurement. 

I also looked at the harmonic distortion performance over a
wider frequency range, 20 Hz to 100 KHz, with the results shown below.
In order to make meaningful harmonic distortion measurements
over this wide frequency range, I had to operate the 8903B with the low pass
filters switched out. (Earlier measurements used the 80 KHz low pass filter
mode.) This increases the noise floor around 10 dB, as may be seen by comparing
the plot above (80 KHz filter engaged) and the plot below. The plot seems to
show the transformer improves the opamp performance by 1 dB or so, but this is
almost certainly a measurement artifact and should be disregarded. 

KS THD
Comparison to Other Transformers The two
figures below compare the THD of five physically small transformers measured at
signal levels of 250 and 1000 mV RMS.
At 1000 mV drive, the KS part is clearly superior to all
the similar size transformers plotted, in some cases by 25 dB, in other cases by
lesser amounts, but still superior.
At 250 mV drive, a different story emerges, with the KS
part being superior up to 1 KHz with the THD then becoming constant at 77 dB.
This is odd and is a performance not seen in other transformers studied. A
similar plateau is seen at 100 mV in the KS distortion plot above. 



How
Does All This Relate to the K3 LINE OUT Audio Distortion?
How does this
mass (or, some may think "mess") of data and analysis relate to Elecraft's use
of a TTC108 transformer in the K3's LINE OUT port?
I've demonstrated at
http://www.cliftonlaboratories.com/elecraft_k3_receive_audio.htm that the
K3's LINE OUT exhibits a oddorder harmonic problem, with the 3rd harmonic
typically down 45 dB or so over a reasonable range of audio output levels.
Further, similar levels of harmonic distortion are not present in the K3's
headphone and speaker outputs. Between the data at that page and the information
on this page, it's quite clear that the Tamura TTC108 transformer is the source
of the harmonic distortion, compounded by Elecraft's decision to drive the
TTC108 through a 604 ohm resistor.
There's no evidence that the TTC108 is being driven into "magnetic
saturation" at the audio levels available from the K3. Indeed, the BH curves
and THD data on this page show that the K3's maximum LINE OUT voltage level does
not come close to moving the BH curves into saturation or even into the
saturation knee, particularly at the frequencies involved. Remember, magnetic
saturation is a phenomenon of high signal levels and low frequencies�in
the case of the K3, magnetic saturation of the TTC108 is not possible, given
the normal lower limit of communications receivers frequency response and the
maximum output voltage.
Rather than from magnetic saturation, the TTC108's mediocre harmonic
distortion performance seems to be a product of its designers choice of magnetic
core material and core size. The data presented on this page shows that similar
size transformers, such as the Bourns LMNP1001, can provide 20 dB or so lower
harmonic distortion, at least so long as the levels are kept down. Unlike the
TTC108, however, it is possible to drive the LMNP1001 into magnetic
saturation, or at least the outskirts of saturation at levels not too far from
normal, although only at frequencies below the normal communications receiver
cutoff. The TTC108's mediocre harmonic distortion performance is, moreover,
compounded by the K3's use of 604 ohm series driver resistance.
With respect to the Stancor transformers studied, there is
little to recommend them as a replacement for Elecraft's TTC108.
The Jensen transformers embodied within the DIN2LI package
represent an extreme end of the price/performance curve with extraordinary
performance at a price roughly 20 times the low end transformers. This is
one example of "you get what you pay for" in the
transformer world.
BG Incorporated's KS transformer demonstrates some oddities.
At 1000 mV, for example, it shows excellent harmonic distortion from 100 Hz to
10 KHz, clearly superior to other low cost telephone transformers. Likewise, the
KS transformer has very good frequency response. At lower drive levels, however,
the KS part's THD plateaus for frequencies above 1 KHz and is not as good as
certain of the other similar parts studied. 

