Is it better to have short interconnects and long speaker cables or visa-versa?
To answer this question, one must understand the difference in environments. The electrical environment of interconnects differs significantly from that of speaker cables. Let's examine interconnects first:
Components that drive interconnects are typically high-impedance, ranging from 7 ohms in high-end solid-state gear to around 300 ohms in tube gear. The impedance of the inputs are much higher, typically 10K-100K ohms. In this high-impedance environment even small cable capacitance will create a low-pass filter. This means that the highest audio frequencies can be attenuated or reduced in amplitude. Interconnects all have capacitance and this capacitance increases as they get longer. Another effect of added capacitance is phase shift. Phase-shift occurs when the position of the high-frequency part of musical waveforms is shifted in time relative to the other frequencies. This phase distortion will start to occur at much lower frequency than the frequency response roll off.
Another consideration is that the signals involved are less than one volt RMS. Signals in a high-impedance environment are more susceptible to noise pick-up from sources including ground-loops, strong RF fields and strong magnetic fields than those in a low-impedance environment. This is aggravated by the fact that the signals are small, which reduces the signal-to-noise ratio. Therefore, shielding can be important if these noise sources are present. Obviously, longer unshielded interconnects are more susceptible to these noise sources. Other characteristics such as resistance and inductance are less important in interconnects because the signal currents involved are so small and the capacitance swamps the other effects. In fact, adding inductance can actually be beneficial, extending the frequency response. Higher input impedance is generally better, but this only affects overall voltage drop, not really frequency or phase response. The driver impedance and cable capacitance are the primary contributors to frequency and phase response issues. So what's a good rule of thumb for maximum length given your cables capacitance?
To generate some guidelines, simulations were performed based upon a solid-state driver (TL072 op-amp) driving 100K input impedance at the receiving component, 20 pF output capacitance, 30 pF input capacitance and cable capacitances of:
1) 200pF/m (inexpensive cable - &lgt; $50/meter pair)
2) 40 pF/m (Empirical Microdynamic) and
3) 28pF/m (expensive cable - > $1000/meter pair)
Typical inductance is assumed to be .2µH/meter (Microdynamic is 1.0µH/meter) with typical resistance of 50 mW/meter for all cables. The data was derived from SPICE3 simulations of the following circuit:
The criteria for acceptability was established as: less than 1 dB attenuation at 20 KHz, since our skilled listeners can hear 1 dB amplitude changes. The following graph plots the frequencies at which a 1VRMS signal is attenuated -1dB as a function of cable length:
The Interconnect Length Guidelines above show that inexpensive interconnects have a useful limit of about 22 feet based upon the frequency response criteria alone. The graph also shows that optimized interconnects such as the Empirical Audio Microdynamic do not experience high-frequency audio response degradation until the length is greater than 100 feet.
Frequency response, however, is not the only effect that should be considered. Phase response can also become a problem, particularly when two channels are involved in developing the image of a single musical event. The following graph shows the phase response of the same three interconnects at varying lengths. The criteria for acceptability is 10 degrees of phase shift so all curves show the frequency at which 10 degrees of phase shift occurs as a function of length:
The phase graph above shows that unacceptable phase shift occurs in inexpensive interconnects longer than 7 feet. The optimized interconnects, on the other hand, do not exhibit the same phase shift until they are 30-40 feet long.
One conclusion from these graphs is that when inexpensive interconnects are used, they should be seven feet or shorter. It also shows that optimized interconnects, such as the Microdynamic can be up to 30 feet long before significant phase degradation occurs and more than 100 feet before significant frequency response degradation occurs. The other considerations mentioned previously, including ground-loop noise and poor signal-to-noise environment dictate that it might be prudent to limit these lengths even further. A fudge factor to compensate for these other effects can be applied to get a more realistic prediction of performance. Empirical Audio suggests cutting the guideline in half, which results in inexpensive interconnects having a useful maximum length of about one meter. Optimized high-end interconnects will have a useful maximum length of about 5 meters. Listening tests are highly recommended.
Speaker Cable Length
Cables that connect power amplifiers to loudspeakers are in a low-impedance environment. Amplifier output impedances are on the order of .2 ohms for solid-state and 3 ohms for some tube amplifiers. Most speaker impedances vary significantly, deviating from their published impedance by as much as 30 ohms. Typical numbers are 3-4 ohms at low-frequencies and 30-50 ohms at midrange and tweeter frequencies. Speaker cables transfer power to the speakers and the currents can be high at times, approaching 20 or 30 amperes in some systems. The requirement for power transfer means that the resistance and inductance must be low, similar to AC power transmission systems. Capacitance is of less concern since the drivers are very low impedance.
Monster-type ZIP cord is commonly used to connect loudspeakers to amplifiers. Many academics feel that you can't really improve upon ZIP of sufficient gauge, usually 11-12 AWG, and that more expensive cables are a waste of money. The following analysis shows that even 11 AWG ZIP has serious limitations because it has relatively high inductance compared to more optimized cable designs, such as Empirical Audio Clarity7. Cross-sections of 11 gauge ZIP and Clarity7 are shown below (drawings are not in relative scale):
11 AWG ZIP cord (PVC insulated)
Clarity7 11 AWG equivalent (Teflon insulated)
These cross-sections were used to develop analytical models for each cable using an electromagnetic field solver. To determine the behavior of these cables at different lengths, they were both simulated using both SPICE3 and HSPICE under the following conditions: the amplifier output impedance was .2 ohms and the speaker load was purely resistive at 3 ohms. The models for the cables are lossy distributed, lumped models with coupling between conductors as opposed to transmission-line models (which are interesting only at >30MHz). The following schematic was used for the simulations:
The acceptance criteria was identical to that used for the interconnect study above, -1dB attenuation at 20 KHz. First, the frequency response graph:
The graph above shows that 11 AWG ZIP cord is attenuated -1dB at 20 KHz at a length of less than 16 meters or about 50 feet. The Clarity7, an optimized cable, on the other hand has a -1dB 20KHz limit of more than 80 meters or 270 feet (off the graph and not shown for readability).
The phase response was simulated and is graphed below for the same two cables. Like the interconnect study done above, the criteria for acceptance is maximum of 10 degrees phase shift at 20 KHz.
The graph above shows that 11 AWG ZIP has a useful limit of about 8 meters or 25 feet based upon the phase acceptance criteria. The Clarity7 useful limit exceeds 80 meters or 270 feet. (10 degrees shift frequency is at >80 meters)
Speaker Cable Conclusions
For systems that are resolving, the previous analysis has shown that 11 gauge ZIP cord will likely cause audible degradation, both frequency and phase, unless the lengths are less than 25 feet. Like the interconnect study, it would be prudent to further limit this length by a factor of 1/2 to account for non-ideal amplifiers and speakers that are complex loads. Recall that the analysis assumed a perfect voltage and current source for the amplifier except for .2 ohms output impedance. The loudspeaker load was also purely resistive, which is never the case in the real world. In the case that tubed-amplifiers are used, these lengths should be reduced even more. This makes 11AWG ZIP impractical for high-end tube systems and some longer length solid-state systems. The performance advantages of optimized speaker cables become obvious from this study. We have proven that these effects are electrically measurable, can be analyzed using extremely accurate simulation tools and we believe that they are audible to most audiophiles.
Overall Length Guidelines
Since we now understand the limitations of both interconnects and speaker cables, both inexpensive and optimized, it is possible to create a guideline that allows optimization at the system-level of both interconnect and speaker cable lengths. This will answer the question once and for all "is it better to have shorter interconnects and longer speaker cables or visa-versa?" Since the same acceptance criteria established in the study was used for both interconnects and speaker cables, these can be both be plotted on a single graph. The following graphs plot interconnect length against speaker cable length with each point on the graph corresponding to identical -1dB frequency for the interconnect and speaker cable. Each point on the graphs also represents a combined length of interconnect and speaker cable used together. The first graph plots Empirical Audio Clarity7 speaker cable and Empirical Audio Microdynamic interconnect:
The graph shows that for medium cable lengths, the relationship of optimum speaker cable to interconnect length is (spkr) = 26+2.2(inter). This means that in order for both interconnects and speaker cables to be the optimum length, the speaker cable should be 2.2 times as long as the interconnect plus 26 feet. The obvious conclusion from this is that lengths shorter than 26 feet overall should be primarily speaker cable, with very short interconnects. If an overall length was 50 feet, then the optimum interconnect would be 7.5 feet and speaker cable would be 42.5 feet. The graph allows for more than 270 feet of speaker cable, but an abbreviated version of 150 feet is shown here for readability. Another conclusion that can be drawn from this is that it is more difficult and costly to manufacture a high-performance long interconnect than a high-performance long speaker cable.
Next we graph the same relationship, between interconnect length and speaker cable length, this time using frequency response data from the inexpensive interconnect and 11 AWG ZIP cord as speaker cable. Again, each point on the graph represents a length for each cable that corresponds to the same -1dB frequency for both cables:
The graph above shows that the relationship between the interconnect length and the speaker cable length is: (inter) = 4+0.343(spkr). The typical length ratio of speaker cable to interconnect ranges from 1.5:1 to 2.4:1. Like the previous high-end cable analysis, this shows that it is beneficial to make the speaker cable length at least 1.5-2.5 times the length of the interconnects. For very short overall lengths, such as 8 feet, the cables can be made equal length. The red overlay on the graph above represents the violation region of the -1dB at 20KHz acceptability criteria. The longest cable system recommended using these cables would be: 75 feet, where the interconnect would be 22.5 feet and the speaker cable would be 52.5 feet. Given that most systems are either mostly interconnect or mostly speaker, this further limits the overall length. If the system were mostly speaker cable, the limit would be ~55 feet with ~ 1 meter of interconnect. If the system were primarily interconnect, the limit would be ~30 feet overall, with ~2 meters of speaker cable. The conclusion to be drawn from this is that systems that are primarily interconnect should utilize more optimized interconnects. As before, Empirical Audio recommends cutting the maximum length guidelines in half, especially for the interconnects. These lengths are based upon the frequency response criteria alone, ignoring phase.
Summary of length guidelines
The following guidelines recap the results from the cable length study. Using the maximum length guidelines and the optimum relationship equations, one can fully optimize their system:
- Regardless of the cost of interconnect and speaker cables, it is always better to make the interconnects shorter and the speaker cable longer.
- Inexpensive interconnects should be limited to 1 meter or shorter overall based upon 1/2 the maximum length guidelines.
- 11 AWG ZIP used as speaker cable should be limited to 12 feet or shorter based upon 1/2 the maximum length guidelines.
- The optimum length relationship of inexpensive interconnect and speaker cable is approximately (inter) = 4+0.343(spkr) (in feet). Therefore, in general, inexpensive interconnects should be 1/3 the length of 11AWG ZIP speaker cables or shorter (1/3 rule).
- More optimized interconnects, such as the Empirical Audio Microdynamic can be as long as 15 meters or 50 feet without significant frequency or phase degradation based upon 1/2 the maximum length guidelines.
- More optimized speaker cables, such as the Empirical Audio Clarity7 can be as long as 40 meters or 130 feet without significant frequency or phase degradation based upon 1/2 the maximum length guidelines.
- The optimum length relationship of Microdynamic and Clarity7 cables is given by: (spkr) = 26+2.2(inter) (in feet, for systems with >26 feet overall).