Clarity7 Electrical Performance
Technical
analysis and measurements:
In order to establish a baseline for comparison, we simulated
and measured a 4.86
meter (16 feet) section of 11 AWG (American Wire Gauge)
ZIP cord and the same length
Clarity7 speaker cable. The simulation models were
generated using a finite-element
field solver and the simulations were done using both
SPICE3 and HSPICE. These tools
take into account all of the relevant effects described
in Maxwell's electromagnetic wave
equations, rather than the innaccurate approximations of
simple circuit-solvers. The
models are distributed lumped lossy models with coupling
between all conductors. The
physical cross- sections of the 11 AWG ZIP and the
Clarity7 that were used to generate
the models are shown below:
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11 AWG ZIP-cord
(PVC insulation) |
Clarity7 11 AWG
equivalent
(Teflon insulation) |
To compare the
performance of Clarity7 to 11 AWG ZIP-cord, we need to
examine
frequency response, phase response, transient response
and understand the resonant
characteristics of both. All of these are important
characteristics for audio.
Frequency
Response Simulations
Frequency response plots were generated from simulations
for the ZIP and Clarity7
when driven from an ideal solid-state amp with .2 ohm
output impedance and an infinite
bandwidth. The plot of Figure 1 shows the response of
both cables:
 Figure
1
Figure 1 shows that the
frequency response of the Clarity7 is more than 4X that
of the 11 AWG ZIP-cord. The -1db point of the ZIP is
about 70KHz, whereas the
Clarity7 -1dB point is at 300KHz. From this result you
can see that the 11 AWG
barely stays linear through the audio range, falling off
dramatically after 20KHz.
Remember, this is the attenuation of the cable alone,
with no other contributors.
Most amplifiers do not have inifinite bandwidth and
speakers have their own
high-frequency response roll-off, so these will only add
to the attenuation that is
caused by the cable. Therefore, to minimize overall
high-frequency attenuation,
the cable should be as flat as possible through the audio
range.
Time-Domain
Measurements
So what kind of effect will this have on music waveforms?
To illustrate this, we
made actual measurements of a system consisting of a CODA
10.5 amplifier driving
each of the 16 foot cables to a KEF 104/2 loudspeaker
load. The waveform is a 9 KHz
square-wave at relatively low-level (to avoid tweeter
damage through resonance).
The waveform measurements of Figure 2 were taken at the
KEF loudspeaker binding
posts:
Figure
2
The superimposed
waveforms of Figure 2 show clearly that the leading edges
of
the squarewave are being rounded with the 11 AWG
ZIP-cord, but the fast
leading-edge is preserved in the Clarity7 waveform. There
is also high-frequency
noise riding on the waveforms because these signals were
at relatively low-level
(.8V peak-to-peak). Notice that the high-frequency noise
is attenuated by the
11 AWG ZIP as compared to the Clarity7. These effects are
all evidence of high-
frequency roll-off in the 11 AWG ZIP-cord. To more
clearly see the difference,
the waveforms above were mathematically filtered to
remove the high-frequency
"fuzz" to create the plot of Figure 3:
Figure
3
The rounding of the
leading edges in the 11 AWG ZIP-cord waveform is clearly
visible in Figure 3. The Clarity7 waveshape is virtually
identical to the pulse
generator output.
Phase Response
Simulations
Next, we compare the phase response of the Clarity7 to
the 11 AWG ZIP-cord.
The graph of Figure 4 performs a simulation of the
difference in phase from the
input to the output of each of the two cables. This is
the phase error:
Figure
4
The plot shows that the
phase error introduced by the 11 AWG ZIP-cord is more
than 5 degrees at 20 KHz. The Clarity7 introduces only
1.3 degrees of phase error
at 20 KHz in this case. This really should be the
worst-case in any system unless
the speaker impedance is lower than 3 ohms. The KEF 104/2
impedance is relatively
flat at 3 ohms.
Time-Domain
Measurements
To illustrate the effect of phase shift, we made some
actual measurements on a
system comprised of a CODA 10.5 amplifier driving both
cables to a KEF 104/2
loudspeaker load. This time, we use a real music waveform
burst: the first few
milliseconds of track 6 on the Spiro Gyra "Got the
Magic" album. This music burst
contains musical transients containing 8 KHz and 16 KHz
components. We measured
the music burst at the amplifier input (unbalanced) and
at the speaker with each
cable (Clarity7 and 11 AWG ZIP) connecting them. The
following plot shows the
waveform of the burst. The AMPIN signal was scaled-up to
be the same voltage
as the speaker voltage. 15K data points were captured for
each waveform of Figure 5
using a Digital Sampling Oscilloscope (DSO) with 500MHz
bandwidth (instrument and
probes):
Figure
5
The waveform overlay of
Figure 5 shows that the Clarity7 output tracks the
amplifier
input closely. To easily illustrate differences between
the signal at the amp input
and the signal at the speaker terminals, we subtract the
two signals mathematically
in the following plots creating an "error
voltage". First the 11 AWG ZIP plot in Figure 6:
Figure
6
The plot shows that the
11 AWG ZIP is not tracking the input waveform very well,
particularly at the high-amplitude transitions in Figure
5. Ideally, the yellow line
should be flat. Figure 7 is the same error voltage plot
for the Clarity7:
Figure
7
The plot of Figure 7
shows a much flatter difference voltage, indicating that
the
Clarity7 is not introducting as much phase error as the
11 AWG ZIP-cord. There is
likely some quantization error in the calculations, so
some of the small peaks are
likely a result of that. This means that the samples that
were taken for each cable
did not occur at exactly the same points in time, so some
errors will be present,
particularly where the waveform is changing at a high
rate.
Transient
Response Simulation
Good transient response is critical for accurate music
reproduction. Transient
response is very difficult to measure with anything other
than a square wave,
which is shown above. However, using simulation models,
it is possible to build
systems that would be difficult to implement in real
life. These simulations can
apply virtually any waveform and frequency to the cable
to better understand it's
characteristics. In the following simulations, we apply a
very fast (1 µsec risetime)
step to both the 11 AWG ZIP-cord and the Clarity7 cable.
Figure 8 shows the time-
domain response of both cables:
Figure
8
It is obvious from
Figure 8 that the 11AWG ZIP-cord cannot pass a step
voltage
this fast. The Clarity7, however reproduces the edge-rate
well, with only a small
delay. Now, lets look at the spectrum of these waveforms
to see how the cables
behave in the frequency domain. This is done
mathematically by performing a
discrete Fast-Fourier Transform (FFT) on the waveform
data above. This creates
a frequency plot of the spectral energy contained in the
voltage step. Figure 9 is
the spectral plot of the above voltage step waveforms:
Figure
9
In Figure 9 the
higher-order harmonics of the step are visible as humps.
The
spectrum of the Clarity7 tracks well under 1 MHz and has
the same general
shape as the amplifier output spectrum above 1 MHz. The
11AWG ZIP, however,
diverges from the amp-in spectrum well under 1 MHz and
has a "saddle" pattern
at higher frequencies that deviates from the shape of the
amp-in spectrum
significantly. This indicates some type of resonance is
occurring. Now, lets zoom-
in and take a closer look at what happens below 1 MHz in
Figure 10:
Figure
10
Figure 10 shows that the
Clarity7 accurately reproduces the waveform components
to at least 1 MHz, whereas the 11 AWG ZIP is having
trouble at less than 100KHz.
Note that the voltage scale is a log-scale in this case.
Resonance
Simulations
Resonance is a phenomena that is typically overlooked in
audio cable design. It
is always a serious consideration in digital link design,
however. All physical systems
that are not too lossy exhibit resonance, including
cables. See the Audio FAQ for more
general information on this. Resonance in audio cables is
a function of their length
and distributed impedance. We have determined empirically
that resonance is audible,
not as a primary effect, but that it becomes audible
through other secondary effects.
Because resonance can cause relatively high-amplitude
very high-frequency signals
that sustain themselves on the cable, this can apply
unexpected voltages and currents
to the amplifier output drivers. These voltages can cause
the apparent impedance of
the cable and speaker to vary beyond what the drivers can
handle and still remain
linear. Long before non-linearity occurs, the driver
circuit's crossover distortion may
also increase enough to be audible as well (not an
problem in single-ended designs).
To explore resonance effects in the 11 AWG ZIP-cord and
the Clarity7 speaker cable,
simulations were performed to generate frequency response
graphs, sweeping the
frequency high enough to observe the resonances. Figure
11 is a frequency response
plot of the 11 AWG ZIP-cord being driven by an ideal .2
ohm driver into a purely
resistive 3 ohm load:
Figure
11
In Figure 11 the
fundamental resonance of the 4.86 meter ZIP-cord is at 18
MHz
and its harmonics are all visible as well. The
fundamental peak is quite high,
therefore a resonance might be sustained. Figure 12 shows
the same plot for the
Clarity7 speaker cable with Anti-Resonance termination:
Figure
12
In Figure 12 the
fundamental resonant peak is reduced by at least 8 dB and
the
harmonics are 17-32 dB down. This is how the Clarity7
achieves its "jet-black"
background and crisply focused three-dimensional image.
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