PHASE RESPONSE
We use the trade mark Coherent Source to describe the unusual technical performance of our products. This phrase is descriptive of the
time and phase coherence which gives THIEL products the unusual ability to accurately reproduce musical waveforms.
Usually, phase shifts are introduced by the crossover slopes, which change the musical waveform and result in the loss of spatial and
transient information. The fourth order Linkwitz-Riley crossover is sometimes promoted as being phase coherent. What is actually meant is
that the two drivers are in phase with each other through the crossover region. However, neither driver is in phase with the input signal nor
with the drivers’ output at other frequencies; there is a complete 360
°
phase rotation at each crossover point.
There is a type of crossover system that does not introduce any phase shift or time smear, although it is difficult and expensive to
execute. This crossover is the first order (6dB/octave) system that THIEL has employed since 1978 in all Coherent Source systems. A first
order system is the only type that can achieve perfect phase coherence, no time smear, uniform frequency response, and uniform power
response.
A first order system achieves its perfect results by keeping the phase shift of each roll-off to less than 90
°
so that it can be canceled by
the roll-off of the other driver that has an identical phase shift in the opposite direction. (Phase shifts greater than 90
°
cannot be canceled.)
The phase shift is kept low by using very gradual (6dB/octave) roll-off slopes which produce a phase lag of 45
°
for the low frequency
driver and a phase lead of 45
°
for the high frequency driver at the crossover point. Because the phase shift of each driver is much less than
90
°
and is equal and opposite, their outputs combine to produce a system output with no phase shift and perfect transient response.
Figure 7 graphically demonstrates how the outputs of each driver in a two-way speaker
system combine to produce the system’s output to a step input. The first graph shows the ideal
output. The second shows the operation of a time-corrected, fourth order crossover system.
The two drivers produce their output in the same polarity and both drivers start responding at
the same time. However, since the high-slope network produces a large amount of phase shift,
the tweeter’s output falls quickly and the woofer’s output increases only gradually. Therefore,
the two outputs do not combine to produce the input step signal well but instead greatly alter
the waveform. The third graph shows how, in a first order crossover system, the outputs of the
two drivers combine to reproduce the input waveform without alteration.
In practice the proper execution of a first order system requires very high quality, wide
bandwidth drivers and that the impedance and response variations of the drivers and the
cabinet be compensated across a wide range of frequencies. This task is complex since what is
necessary is that the acoustic outputs of the drivers roll off at 6 dB/octave and not simply for
the networks themselves to roll off at 6 dB/octave. For example, if a typical tweeter with a low
frequency roll-off of 12 dB/octave is combined
with a 6 dB/octave network, the resulting
acoustical output will roll off at 18 dB/octave.
Therefore in practice the required network
circuits are much more complex than might be
thought.
Figure 8 is a plot of the absolute phase
response of the CS1.5. It shows that the phase
response is within a very accurate
±
20
°
from 400
Hz to 17 KHz. Even more important is the
speakers’s phase deviation from the mathematical
“minimum” phase response of an ideal transducer
with the same frequency response. This deviation
is called the excess phase and is plotted for the CS1.5 in Figure 9. This graph shows the
excess phase to be less than
±
5
°
to beyond 10 KHz.
The result of phase coherence (in conjunction with time coherence) is that all waveforms
will be reproduced without major alterations. The speaker’s reproduction of a step waveform
best demonstrates this fact. Like musical waveforms, a step is made up of many frequencies
which have precise amplitude and phase relationships. For a step signal to be accurately
reproduced, phase, time and amplitude response must all be accurate. Because this waveform
is so valuable, it is commonly used to evaluate the performance of electronic components. It is
not typically used for speaker evaluation because most speakers are not able to reproduce it
recognizably. Figure 10 shows the CS1.5’s response to a step. That the step is reproduced so
recognizably is the result of accurate phase, time and amplitude response.
4
Time
Output
-
+
Ideal step response
Time corrected fourth order crossover system
First order crossover system
tweeter output
woofer output
combined output
Figure 7
Figure 9 CS1.5 excess phase
Figure 10 CS1.5 step response
Time – msec
0.5
1.0
Output
1.5
2.0
2.5
10
Frequency - KHz
1
100
80
60
40
20
0
-20
-40
-60
-80
-100
Transfer Function Phase - deg
Figure 8 CS1.5 phase response
Frequency - KHz
100
80
60
40
20
0
-20
-40
-60
-80
-100
Transfer Function Excess Phase - deg
10
1
0.1
