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Softrock Lite 6.2
Adventures in Electronics and Radio
Elecraft K3 Transceiver Audio Output
Continuing in a series of measurements of my new K3
transceiver, this page examines the K3's receiver audio output.
Table of Contents
Originally written 30 August 2008
01 September 2008 - added single and dual tones within SSB passband
02 September 2008 - added LIN OUT = 2 and LIN OUT = 5 plots
02 September 2008 - added 60 Hz hum pickup versus K3 orientation
05 September 2008 - added section on TTC-108 transformer distortion and
06 September 2008 - added frequency response data for TTC-108
06 September 2008 - modified to suggest 47R series resistance
06 September 2008 - modified to include single tone at 500 Hz in 2.7 KHz
bandwidth SSB mode
20 September 2008 - Added cross reference to non linear transformer page
Cross-reference: A considerably
more detailed analysis of the Tamura TTC-108 transformer used in the K3's LINE
OUT port is now available at my web page
Non-Linear Transformer Behavior.
The figure below shows the test
configuration for the K3 audio output tests. The only piece of equipment
requiring additional description is the HP 3562A Dynamic Signal Analyzer. The
3562A is a dedicated Fast Fourier Transform instrument for audio spectrum and
swept frequency response analysis over the range 0 to 100 KHz. (Actually, the
lowest range is well under 1 Hz, close enough to 0 for our purposes.) I use it
in preference to a computer audio sound card because it has greater
frequency range and has calibrated audio levels.
The GR1840A power meter has switchable load resistances.
During headphone work, it is set to 50 ohms, the closest match to the 45 ohm
headphones I normally use. Speaker measurements are made at 4 ohms and line out
data is taken at 600 ohms.
For all tests, the K3 was set to CW mode, 600
Hz bandwidth, width centered at 600 Hz. The K3 is adjusted so that the
beat note is centered using the K3's "CWT" function. AGC is enabled and set to
Noise Characteristics and Artifacts
frequency hearing is not good enough to know whether the measured artifacts I
observed are audible to K3 owners. I invite comment on the subject.
In looking at other measurements described later on this
page, I noticed that the K3's audio output has noticeably more high frequency
noise and artifacts compared with other receivers, including Elecraft's K2
The 3562A spectrum analyzer plot below shows the K3's
headphone (rear panel) output with the audio level set for a comfortable to loud
audio level. The RF input is an unmodulated signal at -80 dBm and the K3 is in
CW mode, 600 Hz bandwidth, width centered at 600 Hz. The K3 is adjusted so
that the beat note is centered using the K3's "CWT" function.
Two points are of note. First, there are three discrete
tone artifacts around 12 KHz. The center tone is at 12 KHz and the two stronger
tones are approximately 600 Hz above and below 12 KHz. Their level is about 45
dB below the CW tone. With a separation of 600 Hz, this strongly
looks like signals related to the desired signal being aliased up and centered
at 12 KHz feeding through. This is puzzling since the K3's 2nd IF, where the DSP
work is done, is 15 KHz, not 12 KHz.
Second, note that the high frequency noise level is
essentially constant from 2 KHz to 20 KHz, the limit of the band I looked at in
this plot, as 20 KHz is normally the upper limit for human hearing.
Switching the signal generator's RF output off shows
the 12 KHz artifact, and also makes clear additional artifacts at just below 4
and 8 KHz. These are visible when the RF signal is applied as well, but are not
as noticeable. The paired signals centered around 12 KHz are not present,
leading further support to them being tied to the input signal.
The following plot is the same test setup with an Elecraft K2
transceiver, with the primary difference being the K2's CW bandwidth is
700 Hz, not 600 Hz.
I've carefully adjusted the K2's
audio output level to match the K3's, within 0.5 dB or so. Both the K2 and K3
show some 3rd harmonic distortion of the 600 Hz beat note, down about 60 dB in
both receivers, although the K3 is a few dB better than the K2 in this
More importantly, however, the 12 KHz artifacts are gone
and the high frequency noise, above say 6 KHz is lower.
To make the comparison easier, I've overlaid the two plots
below. Although the K3's DSP certainly provides better selectivity, and lower
noise up to 4 KHz, the K3 has greater high frequency noise. For those with good
high frequency hearing, these additional signals and high frequency noise may
prove annoying and fatiguing. One quick fix would be an LC filter with a 4 KHz
cutoff used between the K3 and headphones.
Line Output Level
Elecraft's K3 Owner's Manual recommends operating with line
output levels set below 10 as reflected in the excerpt to the right.
To assess the effect of various line out levels, I ran a
series of spectrum plots with the HP3562A for LIN OUT settings ranging from 2 to
100 (2 plus 5 to 100 in steps of 5.)
Rather than present nearly two dozen plots individually,
I've compiled them into an animated GIF image that steps through the LIN OUT
The spectrum analyzer images are with an RF input signal
of -80 dBm, corresponding to about S5. Stronger input signals will increase the
audio levels and likely will increase harmonic distortion. There's also an
interaction with the AGC slope and intercept as well, as those controls
determine the demodulated audio level for any particular RF signal level.
Note that most of the distortion products are odd order,
i.e., 3rd harmonic, 5th harmonic, etc. This is characteristic in several types
of device distortion. Transformers, for example, will exhibit odd order
distortion. Push pull audio amplifiers cancel even order distortion, so odd
order products are more pronounced. An amplifier stage driven into severe
clipping has an output resembling a square wave, which again is comprised of odd
order harmonics. Of course, none of the cancellation effects are perfect.
Note that the artifact we observed in the headphone output
around 4 KHz is quite clearly seen here as well. The frequency appears to be 3.9
KHz or so. It's about 60 db down from the desired signal, by the way.
The artifacts near the start of the spectrum analyzer plot
are 60 and 180 Hz from the power line. (The K3 is powered for these tests by an
HP E3610A DC power supply with very low hum and ripple. The power line signals
are likely induced from nearby equipment.)
The above animation shows that once LIN OUT is set to 10 or
greater (even up to 100), the odd order harmonics tend to remain at a constant
level with respect to the fundamental, at around -45 dB.
Since 10 is the recommended level, I'll provide a separate
image for it, as well as two lower settings, 2 and 5.
At LIN OUT = 2, the 3rd harmonic is down about 65 dB.
(Note 15 dB/vertical division).
At LIN OUT = 5, the 3rd harmonic is down about 55 dB.
LIN OUT = 10, the third
harmonic is stronger, down about 45 dB from the desired signal.
Speaker Output and THD
The K3's speaker output is rated at 2.5 watts into
either 4 or 8 ohms with a typical distortion of 2.5%.
Audio amplifiers generally produce maximum distortion into
lower impedance loads, as the currents are higher for a given output power.
Accordingly, I set the GR 1840A audo power meter for 4 ohms and took spectrum
analyzer images for a selection of power levels. With -80 dBm RF level, the
maximum audio output power I achieved was 1.25 watts.
The animated image below shows the spectrum changing with
increased audio power. I had to change the spectrum analyzer axis during
this test, so you'll notice an axis change for the highest power runs. The
indicated power is in milliwatts.
To assess the rated power output and distortion, I
increased the RF signal level to -50 dBm. I was able to achieve 2.0 watts into a
4 ohm load. The HP333A audio distortion analyzer reported total harmonic
distortion (THD) as 2.7% during this condition.
The HP333A, like other analog distortion analyzers of its
vintage, uses a narrow notch to remove the desired signal, with all remaining
signal being considered to arise from harmonic distortion. At the 2.7% level,
that's a reasonable assumption with the K3, but the K3's high frequency noise
and non-harmonic artifacts will also be read as THD on the 333A's meter.
I also looked at the output distortion for varying headphone
levels. The Sony headphones I use require only about 5 microwatts to provide a
comfortable sound level. At 5 microwatts, the K3's distortion is quite low, with
the first significant harmonic being about 70 dB below the desired signal.
The image below is of the headphone audio output at 1 mW,
which is an earsplitting level with my Sony headphones. Less efficient
headphones, of course, may require more output power. At 50 ohms, the
maximum headphone output level I found with -80 dBm input was around 2 mW. Note
how much the 3rd harmonic increases compared with the 5 microwatt setting.
It's still 50 dB down, which is more than decent, but the change is remarkable.
with Single and Dual Tones
on the Elecraft reflector caused me to look at the K3 (and at the K2 as a point
of comparison) when operated with SSB filter bandwidth and with a single carrier
and two carriers within the SSB passband. The diagram below illustrates the test
Although my HP8657A signal generators are quite good
performing equipment, both exhibit a group of 60 Hz powerline related spurious
signals around their output frequency. I've discussed this at
and reviewing this page first may help you understand some of the artifacts seen
in this analysis. I've made some measurements in this section with an HP 8640B
signal generator, which also has 60 Hz powerline related signals around its
output frequency, albeit at a considerably lower level than either of the two
8657A generators I own. (The referenced web page shows some 8640B data as well.)
In addition, the 8657A generators have some close in phase noise. With careful
attention to the plots, however, none of these signal generator imperfections
prevent accurate measurement of the audio performance of the K3 under the test
The tests were made with the K3 (and K2 for some tests) set to USB mode, tuned
to approximately 10.1 MHz. The two signal generators were set to 10.100000 MHz
and 10.100370 MHz, i.e., 370 Hz spacing. (The 8657A has 10 Hz increments. I
wanted the spacing to be 375 Hz.) From previous work with similar setups,
I know the intermodulation products generated in this setup are significantly
below a level to be at issue during these tests. AGC is set to slow (except for
a couple of tests with AGC off) and the audio output examined is from the
LIN OUT port on the K3 and the front headphones jack on the K2.
The K3 is equipped with the stock 2.7 KHz bandpass filter and
the selectivity was set at 2.7 KHz. I set the HP3562A for the range 0 - 2.5 KHz,
except as otherwise noted. I also was careful to adjust the 3562A's input
gain to avoid overload that might contribute instrument artifacts.
The K3's LIN OUT gain is set at 10, the default setting,
for these tests. The HP3562A has a 600 ohm termination across its input.
I've identified the main spectral features of the test
plot below. The plot is of my K3 with the HP8640B signal generator as the sole
input signal source, at -25 dBm, a very strong signal, S9 plus 40 dB or
thereabouts, with the K3's preamplifier off. At this signal level, the K3's
hardware AGC is operating.
- A are 60 Hz
related hum signals apparently coupled into the test setup, although
shielded cables are used and the 3562A is used in floating input mode to
break ground loops. These signals should be ignored in this and later
- B are the
two spurious sidebands associated with my HP8640B signal generator. Note
that these are about 68 dB below the carrier, which is not at all bad
performance for a general purpose signal generator.
- C is the
HP8640B's signal, as converted by the K3 into an audio beat tone output just
over 500 Hz in frequency.
- D is the second
harmonic of the beat note, down more than 60 dB from the fundamental (C).
- E is the third
harmonic of the beat note, down 43 dB from the fundamental.
- F is the fourth
harmonic of the beat note, down about 75 dB from the fundamental
- 1 and
2 are weak discrete signals of unknown
source. They appear to be spaced equally from D, with approximately 60 Hz
- The third harmonic at 43 dB below the fundamental is
fully consistent with measurements I made earlier, reported on this page, on
the LIN OUT port in CW mode. The headphone port performs much better if the
level is kept low, demonstrating the third harmonic at -70 dB from the
As a point of comparison, I connected the same RF test setup
to my K2. The K2's audio level is a bit higher, but the main points to be
observed relate to the relative levels.
- The 60 Hz related hum products are considerably
reduced, although the identical test setup is in place. This suggests
there is some coupling related to the K3.
- The second harmonic is not observable, indicating
that it is at least 68 dB below the fundamental.
- The third harmonic can be seen at -67 dB from the
fundamental, about 25 dB better than I see with the K3.
- Measurements reported earlier on this page
demonstrate that the K3's LIN OUT output has higher harmonic production than
seen in the headphone audio output.
Returning to the K3, I made a series of tests with two
input signals, separated by 370 Hz. The spectrum analyzer image below was taken
with the K3's AGC OFF and an applied RF level of -105 dBm (each tone). The trace
shows no evidence of harmonics or intermodulation.
Most operators will use AGC with their K3, so I made a series
of tests at different input signal levels with the AGC set to slow. The
signal level input is -45 dBm per RF signal.
plot is unfortunately cluttered with spurious signals from the two HP8657A
signal generators. I've identified the real signals.
- T1 and
T2 are the two input signals. As the K3's
dial is set, one signal provides a 500 Hz beat note and the second signal a
beat note 370 Hz higher at 870 Hz.
- The third harmonic of T1's beat note (3x
T1) is 50 dB down from T1 fundamental.
- The signal at the exact center (1250 Hz) marked
IMD? could be a third order intermodulation
product between T1 and T2.
- Additional discrete signals are visible at
approximately 1875 Hz and 2250 Hz. These are not harmonically related to
either T1 or T2 and might be higher order intermodulation products. I've
identified them as IMD? but their origin
is unclear. I don't believe they are signal generator spurious
signals, as the 8657A spurious signals drop in level as they space out from
the center frequency. The signals shown with the IMD?
mark are relatively constant level.
The spectrum analyzer image below has the same frequency
setup, but the signal level is 20 dB greater at -25 dBm. The display is quite
similar, as the hardware AGC has made the internal signal levels more or less
equal to those in the plot immediately above.
As a comparison point, I looked at the K2's output with an
input level of -65 dBm. The same close in signal generator spurious signals are
present, but not the higher order signals, nor the tone harmonics. This leads
further credence to the three discrete signals as being generated within the K3.
SSB Mode with 500 Hz Tone - Harmonics
received a request to look at the K3's headphone port audio in SSB mode with 2.7
KHz bandwidth and a single tone at around 500 Hz.
The test conditions are: USB mode, BW 2.7 KHz FC 1.5 KHz,
AGC-S, signal level into headphones set to a comfortable listening level with
Heil Pro Set. RF level into K3 -40 dBm. The audio level is -29.4 dBVrms across a
200 ohm resistor used as a substitute for the Heil headphones, or about 34 mV.
The 3rd harmonic is down 76 dB, which is quite impressive. I'm not sure if the
little blip just below 1 KHz is the 2nd harmonic or just a noise fluctuation. If
it's the 2nd harmonic, it's down close to 80 dB from the fundamental.
I put the X marker (the round dot) on the 3.9 KHz artifact. It's about 78 dB
down from the tone.
The same conditions, but with the RF signal turned off shows
the K3's passband response. Note that the 3.9 KHz artifact is still present.
The final spectrum analyzer image shows the tone applied, but
at a level of -80 dBm, 40 dB down from the first image in this series. The
second and third harmonics are below the noise level in this image.
60 Hz Hum
Pickup versus K3 Orientation
suggested in a post on the Elecraft reflector, that the TTC-108 isolation
transformers used in the K3's LIN OUT port, were unshielded and thus subject to
hum induced via magnetic coupling. The transformers have a directional hum
pickup characteristic, by the way.
I found that this is indeed the case with my K3, and that
by carefully rotating it on my workbench the hum levels would change 15 dB
consistently and, with just the right orientation by almost 20 dB, although that
was not stable.
The image below shows my K3 in the normal position, front
panel parallel with the front of my workbench. (The only connections to the K3
are DC power and the HP3562A dynamic signal analyzer.) This turns out to be
almost the worst case for hum pickup in my shop.
Rotating my K3, I can knock the 60 Hz noise down 15 dB,
although the 180 Hz noise only drops about 6 dB. The only difference
between the plot above and the plot below is the K3's orientation.
Distortion and Intermodulation
Cross-reference: A considerably more detailed analysis of the Tamura TTC-108
transformer used in the K3's LINE OUT port is now available at my web page
Non-Linear Transformer Behavior
audio amplification section is capable, according to the active device
specification sheets, of excellent performance. My measurements indicate that
the K3's LIN OUT signal is not living up to the expected level of performance,
and not by a small margin.
The K3's LIN OUT port is driven from a separate DAC,
U29 in the K3's schematic, a Texas Instruments TLV320DAC23, with quite
good specifications. (Elecraft uses two independent DACs; one for LIN OUT and a
second for headphone and speaker output.) THD is -60 dB (0.1%) at levels of 10
This specification is for a 32 ohm load. In the K3's
current configuration, U29's headphone amplifier sees at least a 600 ohm load at
all times. Hence the actual output power is considerably less. With 3.3 volt
supply voltage, and a small allowance for saturation at both power and ground
rails, we might expect a 3.0 V PP output from U29's headphone amplifier. Into a
600 ohm load, 3.0 V PP corresponds to 1.8 mW. Of course, the limiting factor is
going to be clipping at the positive and negative excursions, not power
U29's integrated headphone amplifier output has separate
sections for left and right channels and appear at the K3's rear panel through
the following arrangement. (Right channel is shown; left channel is identical.)
C15 is a blocking capacitor as U29's operates with a single ended 3.3V power
supply and hence its output is biased at V/2 or 1.65 volts. R20 is a 604 ohm
resistor with a purpose that is unclear to me, but which turns out to be the
source of significant performance impairments. The common side of the left and
right transformers are tied together and connected, through RFI suppression
chokes and bypass capacitors L3 and CN1. The high side of each channel is routed
through a similar RFC / bypass arrangement.
T2, and its left channel counterpart, T3, are Tamura TTC-108
parts, with relevant specifications as extracted below.
Of these specifications, the most important is number 11,
the "total harmonic distortion," quoted at 0.5%. 0.5% THD corresponds to
harmonic suppression of 46 dB. Strictly speaking, of course, it's "total"
harmonic distortion, i.e., the sum of all harmonics. However, usually one
harmonic (the third) is much stronger than others, so that it dominates the 46
dB suppression specification.
To obtain a sense of how the K3's LIN OUT audio chain
performs, I purchased a couple of TTC-108 transformers and built a simple test
driver circuit. Duplicating the K3's DAC isn't necessary; U29's headphone output
port is, for our purposes, a low impedance output audio amplifier. We'll use a
Microcircuits MCP6021 op-amp as a substitute. The test circuit I built is
illustrated below. It's a standard unity gain buffer amplifier with two inputs.
Deserving additional explanation is the bias circuit. In order to run from
a single supply voltage, the non-inverting input must be biased at Vdd/2 and
also the inverting input requires Vdd/2 reference voltage as well.
Obtaining Vdd/2 can be done with a resistive voltage divider, but the MCP6021
(in the 8-pin DIP package, at least) includes a voltage divider with Vdd/2
available at pin 5. Hence, all that's necessary to obtain Vdd/2 reference
bias is to add C1, a bypass capacitor and connect Pins 3 and 5.
Additionally, since the inverting input also should be a
Vdd/2 in the event of no input signal, R4 provides the necessary reference. Pin
2 is, for AC purposes, a virtual ground, so inputs 1 and 2 are isolated from
each other, permitting us to connect two signal generators without worrying too
much about interaction between the two.
It's important to keep in mind that the output of an
op-amp with feedback such as this mixer circuit, is essentially zero ohms. The
op-amp acts as a perfect voltage source, as the feedback keeps the output
voltage constant. Of course, the op-amp can only provide so much voltage or
power, but within these limits, and at the frequency range we are using it at,
it has a zero output impedance. The headphone amplifier within the TLV320DAC23
has the same zero output impedance characteristics. Hence the simple MCP6021
mixer and buffer amplifier circuit below serves as a good analog of the
TLV320DAC23's headphone amplifier.
One final point before we look at measured results. Even a rather poor
transformer is capable of excellent performance when driven by a zero ohm source
(or, at least a source with low impedance compared with the transformer's
primary winding resistance). I won't go into the details of why this is the
case, but Jensen Transformer has a good discussion of the effect at
Read this for more details.
To demonstrate the
difference, and to show that the K3 is capable of with a simple component value
change in the LIN OUT circuit, some data is taken with R6 in the
test circuit in place (duplicating the K3 configuration) and other data is taken
with R6 bypassed, demonstrating what a revised K3 is capable of.
The data is taken using two audio signal generators, an HP
200CD and an HP3312 function generator. Both have relatively good harmonic
performance, with the 200CD's harmonics typically 60 to 65 dB below the
fundamental. The 3312 is not quite as good. Hence, when looking at the test
data, in many cases the limiting factor in assessing performance is the harmonic
content of the signal generators, not the MCP6021 circuit.
The data is analyzed with an HP3562A dynamic signal
analyzer in spectrum analyzer mode.
The first image is of a two-tone intermodulation distortion
(IMD) test, 1300 and 1500 Hz approximately equal level at 100 mV RMS each. The
upper (green) trace is the output of the TTC-108 terminated with 10K to mimic a
typical sound card. The lower blue trace is the output of the MCP-6021 op amp.
Both signal generators (HP 200CD and HP3312 function generator) have some 120 Hz
ripple but the bottom trace shows zero IMD seen above the noise level. The
upper trace shows IMD products up and down the spectrum range, with the 3rd
order IMD products down about 45 dB from a single tone.
The next image is from directly connecting the transformer to
the op-amp, without the 620 ohm resistor. This image is from an earlier run with
a 620 ohm short-circuit protective resistor on the transformer secondary, and a
second 620 ohm on the spectrum analyzer input. The plot colors, green =
transformer output, blue = op amp output, are the same as in the plot above with
the 620 ohm resistor between the op-amp output and TTC-108 primary.
I've used a wider sweep on this image and generator harmonics are seen in both
plots. However, there are some IMD distortion products seen in the transformer
output, most noticeably at frequencies below the two test tones. The worse case
IMD, however, is around -75 dB with respect to a single tone, representing about
30 dB improvement over the K3's design placing 604 ohms in series with the
Lower frequencies are more difficult for transformers, so as
an experiment I ran a two tone IMD test at 130 and 150 Hz with a 620 ohm
resistor between the op-amp output and the TTC-108 transformer primary.
(The TTC-108 spec has a lower 3 dB point of 300 Hz and the 0.5% distortion
specification is valid over the range 300 - 3500 Hz @ 0 dBm, so testing at these
frequencies is perhaps a bit unfair.
The result is a sea of intermodulation products out of
the transformer (green trace). The blue trace, directly out of the op amp shows
the signal generator harmonics, around -50 dBc as my signal generators take a
bit of a performance hit in this frequency range as well. Note that the output
level is relatively low here— -30 dBV, which is 30 mV or so per tone (RMS). No
intermodulation products are shown in the op-amp output; all those in the green
image are generated in the transformer.
The next image is a two-tone IMD test using a direct op-amp
to transformer connection. The IMD test tones are 70 and 90 Hz, way outside the
TTC-108's normal operating range. Also note the test tone level - its 15 dB
hotter than the image above and the frequency is considerably lower, both
factors that generate even more IMD.
While the result isn't great, it's head and shoulders above the connection with
620 ohms between the op-amp and transformer primary in the image above. IMD in
the direct connection case is around 50 dB below the single tone level,
and the highest order product visible is considerably lower order than in the
The image below shows a harmonic analysis with the 620 ohm
resistor between the op-amp output and the TTC-108 primary winding.
The output tone level is -22 dBVrms, or just under 100 mV
RMS into a 10K load. Note that the 3rd harmonic is -45.6 dB with respect to the
fundamental. That's almost identical with the 3rd harmonic suppression I found
in the K3 once the LIN OUT level gets up in this range. The level of harmonic
suppression depends on the fundamental signal level, of course, but the range I
observed is on the order of -50 to -45 dBc.
The image below shows the same frequency range and test
signal frequency, but with the TTC-108 connected directly to the op-amp output.
The test signal applied in the image below is significantly stronger than
in the image above, by nearly 20 dB. Yet, the direct transformer connection
demonstrates a minimum harmonic suppression of 61.6 dB, which, in fact,
represents the limit of the HP 200CD signal generator's harmonic suppression.
With respect to harmonic and intermodulation distortion in
the K3's LIN OUT port, my conclusions are:
- The source of the interference is the TTC-108
- Operating the TTC-108 with the 604 ohm series
resistor as in the K3's design is the reason the TTC-108 demonstrates the
level of harmonic and intermodulation products seen.
- Replacing the 604 ohm series resistor in the K3 with
a 47 ohm parts should significantly improve the LIN OUT audio performance.
[Note: I had thought a 0 ohm part would be suitable but I've received a
report that 47 ohms will provide better results.]
Note that I have not tried the modification directly on my
K3, but the op-amp results give me high confidence that an improvement will
result from this change. Whether the full degree of improvement seen in my tests
will be seen in the K3 is unknown.
I also note that the TTC-108 transformer has a total
winding resistance of 100 ohms (44 ohms in one winding and 56 ohms in the other
winding) so if the 604 ohm resistors are replaced by 47R parts, no additional safety
resistors should be required at the TTC-108 output.
I also measured the frequency
response of the TTC-108 transformer when driven in the K3 arrangement with 620
ohms in series with the primary and when driven directly by a zero ohm op-amp.
Before looking at the frequency response plots, let us first consider why a
transformer has both an upper and lower frequency limit.
I've also discussed transformer frequency response in
The schematic below is a transformer model showing the
components that cause transformers to be less than perfect devices. (This is a
simplified model but quite adequate for our purposes.)
It is possible to model a transformer and consider the
imperfections as separately acting in the primary and secondary. However, the
model may be greatly simplified if all of the imperfections are considered to be
in the primary, as in the model depicted above. For example, suppose the
secondary has 10 ohms winding resistance and the primary has 20 ohms winding
resistance, and that the transformer in this example has 50 primary turns
and 100 secondary turns. The secondary's 10 ohms winding resistance appears to
the primary as (100/50)^2 * 10 = 40 ohms. Rw, in this example, is 20 ohms direct
primary resistance plus 40 ohms secondary resistance reflected back to the
primary, for a total of 60 ohms. Likewise, the secondary's leakage inductance,
etc. can be reflected back to the primary and combined with the primary's
The elements of the model are:
- Zs - the impedance of the signal source
- Lleakage - leakage inductance, i.e., some of the
lines of flux generated by the transformer primary escape, or "leak," and do
not cut the secondary windings. This leakage flux can be converted to an
equivalent series inductance, Lleakage.
- Rw - the transformer's winding resistance. (AC
- Cd - distributed capacitance across the primary.
- Rp - shunt resistance across the primary, due to
dielectric and core loss.
- Lp - the magnetization inductance, i.e., the
inductance due to the flux that links the primary and secondary windings.
- Cs - capacitance between the primary and secondary
- Zl - load impedance.
- An ideal transformer with turns ratio N.
As said earlier, these parasitic components are shown on
the primary side only and represent the net contribution of both primary and
secondary parasitic elements.
Looking at the low frequency response of a well
designed transformer, the leakage inductance and distributed capacitance are
negligible and may be omitted, further simplifying our model.
Looking at the model should reveal why the frequency
response rolls off below some frequency limit. Zs forms a voltage divider with
Rw and Rp paralleled with Lp. As the frequency drops, the inductive reactance Xp
of Lp drops and hence the voltage available to the secondary drops.
Likewise, it should be obvious why a low Z source will
improve the low frequency response. If Zs is zero ohms, the voltage divider
effect has reduced, with only Rw and Rp || Lp having an effect.
Exactly as our model predicts, driving the TTC-108 with a zero impedance source
boosts the low frequency response considerably compared with the series
resistance configuration. There's still the winding resistance effect limiting
the low frequency response, as well as the fact that our MCP6021 op-amp can only
source ±30 mA into a short circuit. Given the fact that the TTC-108's primary
resistance is 44 ohms, the MCP-6021 will, at some frequency, be current limited
as Xp drops. Looking at the direct connection plot below, we see a distinct
change in slope at 30 Hz, very likely representing the point at which the
MCP-6021 goes into current limiting.
The data is
taken with 10K secondary load, so the secondary winding resistance does not
enter into the current calculation.
One final point. Elecraft shunts the TTC-108 primary with
1000 pF bypass capacitance. To see whether this changes the frequency response,
I ran a sweep with and without a 1000 pF shunt capacitance across the TTC-108's
primary. Both plots are with the transformer primary driven through a series 620
ohm resistor, to match Elecraft's design. As the sweep data shows, there's a
very small difference at frequencies above 50 KHz. (The blue sweep is without
the capacitor; magenta with the capacitor.)
You may also ask "why is the high frequency response of the
TTC-108 so good? This is, after all, a part only rated between 300 Hz and 3500
Good question. The frequency response data I've
taken is into a relatively high impedance load, 10K ohm, representing a
typical computer sound card. (The HP3562A Dynamic Signal Analyzer I used for
these tests has an input impedance of 1 Mohm, so I shunt it with a 10K ohm
resistor during these sweeps.) Operating into a relatively high impedance load
negates much of the effect of the leakage inductance and winding capacitance
effect upon high frequency response.
At the high frequencies, the Lp drops out of the picture
and the same voltage divider concept picks up new elements, the transformer's
leakage inductance and the distributed winding capacitance. These parasitic
elements are, in effect, in series with the load resistance and hence
effectively limit the high frequency response only when their reactance becomes
an appreciable fraction of the load resistance.-
Working into a 620 ohm termination instead of the 10K produces the expected
result; the high frequency response drops. Instead of being flat to slightly
rising above 50 KHz when working into the 10K ohm load, we now see the amplitude
decrease. (There's also 6 dB extra loss with 620 ohm resistors in both the
primary and secondary windings, of course.) Still, the high frequency response
of the TTC-108 isn't all that bad. That's because it's relatively easy for a
physically small transformer to have low leakage reactance. Where the challenge
comes in is for a small transformer to have good low frequency response, as that
requires very high core permeability material.