Impendance - Resistance & the story of "Z"

I started to type out a very long explanation of voltage, current, inductance, reactance, impedance, etc... It is hard to explain exactly what Impedance (Z) is without knowing what the various factors that go into making it up really consist of. Needless to say, after typing up what would have been the longest post in the history of Agon, i stopped.

Resistance is but one simple part of Impedance. Impedance is a complex combination of Resistance, Inductance and Capacitance summed into one simple to navigate figure. Even though resistance and impedance are used interchangeably in many situations, they really have different meanings.

Resistance is the opposition to signal flow. Think of it as kind of an "amperage restrictor". Depending on the level of resistance involved, the amount of current flow ( amperage ) will vary according. More resistance equals less amperage in the circuit and vice-versa.

On the other hand, Impedance may actually oppose current flow in a much more active manner. This is because Impedance factors in both capacitive and inductive reactance of the circuit along with the simple opposition to signal flow that resistance by itself generates.

Think of "reactance" as the equivalent of "resistance" going through an alley and running into combatative thugs. Not only is it a lot trickier for the signal to push its way through the circuit, those "shady characters" won't let the signal pass without a major fight.

This is not to say that all "complex" impedances are "tough" to deal with, but when a circuit has a high level of reactance, the subsitution of the words "resistance" for "impedance" becomes more and more meaningless and less accurate of a description. This is why we say that some speakers that are tough to drive are "reactive" ( lot of "fighting" with the amp to deliver the signal to the speakers ). Easy to drive speakers offer a "resistive load" i.e. "non-reactive" because they don't put up much of a fight.

Having said that, it is quite possible for a low impedance load to be easy to drive. That is, so long as the amp can pass enough current on a steady state basis to keep up with the amount of signal flow required. When a speaker has both high levels of reactance AND a low impedance, it can be VERY tough to deal with. This is because the amp has to be able to provide gobs of power AND "fight" the reactance as it does so.

As far as the "Z" of a cable goes, it depends on what spec "Z" is being quoted for. A low "nominal impedance" with a speaker cable is a great thing. That's because the output of an amplifier has a very low impedance and the input impedance of most speakers is also quite low. Sticking with a speaker cable that has a very low "nominal impedance" has great benefits as far as i'm concerned.

The same may not be true for an interconnect, depending on the components being connected. As previously discussed, due to various input and output impedances on gear, the "nominal impedance" of a cable can act as somewhat of a "buffer" or "impedance transformer" between the components. What "nominal impedance" works best will depend on how stable the output circuit of the source component is and how reactive the input of the load component is. If all of this gear was properly designed, we would want to have the output impedance of the souce matching the input impedance of the load component with a cable of the same "nominal impedance" connecting them. Since we don't have this type of situation taking place in audio today, we've ended up in the situation that we have where cables do affect the sonics of a system. Rather than just being a passive device to carry signal from one active device to another active device, they become an active part of the complex impedances that the signal sees as it travels through-out the entire system. By changing the complex impedances ( inductance, capacitance and resistance ) that the signal sees, we change voltage to current ratios, loading characteristics, etc... This effects the linearity of the system as a whole. Sean
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Joperfi,

Impedance is a complex number - that is "complex" in the
mathematical sense - it has two components. The "real"
component is the resistance. The imaginary component -
which is the coefficient of "i" where "i" is the square
root of -1 [ yes I know they tell you in school that you
can't take the square root of a negative number - but the
concept exists in higher mathematics] and will be the amount
of capacitance, inductance, or "reactance" as Sean explained.

Think of impedance like a sailor thinks of his position -
there's both longitude and lattitude. Now lattitude will
tell him some things - like whether he's in the tropics
or a temperate region - but longitude is important too.

Sean.... B+..... See me after class.

A very simplified definition, though not technically correct, would be:

Resistance: opposition to current that is constant no matter what the frequency (60 hz, 2kHz, 1MHz, etc.)

Impedance: opposition to current that varies as frequency varies.

A resistor gives a constant resistance at all frequencies.
A capacitor gives more "resistance" as freqency decreases.
An inductor gives more "resistance" as frequency increases.

The audio signal has a varying frequency, from around 10Hz to well over 20kHz. So it becomes an issue with cable designs to account for this in order to minimize the effect of cable resistance. For speaker cables, a lower overall impedance improves the amplifers' damping factor which minimizes the distortion by spurious signal oscillation from speaker-to-amp-to-speaker. As far as interconnects go, Sean covers it very well.

Gs: Your comments about resistance being frequency independent and impedance acting the opposite i.e. changing as frequency is altered was a very good point and easy to understand in the manner presented. I had worked that into my original post, but when trimming things down, it got lost in the shuffle. Kudo's to you for highlighting this basic but very important aspect of understanding electronics.

This is why testing amplifiers into dummy loads ( resistive loads that remain constant with frequency ) isn't a very accurate representation of how amplifiers actually "load up" into various speakers. That's because speakers are complex impedances where reactance varies with frequency. In some cases, reactance and therefore the impedance can even change as the drive levels are altered. At 1 watt at 100 Hz or 10 KHz, the amp might see what appears to be an 8 ohm load. Increase the drive level to 10 watts at that same frequency and the amp may see what appears to be a very different impedance.

Trying to achieve a smooth or "flat" impedance curve* is something that many manufacturers attempt to do by adding parts to the crossover network, but in the real world, those parts only add more clutter between the amp and speaker. In most of the speakers that i've heard where the designers placed great importance on this aspect of design and performance, the end result was that it tended to "suck the life" out of the music. There is something to be said for designs using minimal or no crossover at all. Sean
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* a "flat" curve sounds kind of contradictory, doesn't it??? : )

the story of Z sound great and is very interesting and if this is true that the smaller the Z number the better then i hope that Jopherfi or someone can tell what co. this is so i can look into getting some of these cables to listen to. thank you .

I want to thank all who took the time to respond and educate the non-EE’s (me) on this complex topic. I now have a better understanding of things. The reason I asked in the first place was because the manufacturer of the pre-amp I just purchased suggested that a long interconnect to the amp would be OK if I used and IC that kept the resistance low. I will now go back and ask if he meant resistance or impedance. (Does anyone know what he may have meant? He does not publish an output impedance spec for the pre-amp).

Sean, in particular, thanks for explaining the concept of an impedance transformer as related to interconnects. I see now how the electrical parameters of the components connected along with IC’s have a big impact on the “complex impedances” of the system. Understanding that the impact of a cables “Z” (nominal impedance) depends on its application (amp-speaker or source-pre-amp) wouldn’t one now question the cable manufacture that say’s that a lower “Z” for both IC's and SC's is always better? Perhaps I missed something.

Regards,

Joperfi: As i mentioned, most amplifiers have a very low output impedance and most speakers have a relatively low ( several ohms ) input impedance. Using a cable that is somewhere between these two figures will typically provide the best results. If one is trying to alter the sonics of a poorly matched system, introducing some type of colouration via series resistance ( makes the cable sound leaner due to less current flow / reduced bass output ) and / or high inductance ( makes the cable sound warmer and smoother due to high frequency roll-off ) can do that. Using a cable that offers both high series resistance and is inductive would act somewhat like a band-pass filter i.e. reduced bass and soft highs with "reasonable" mids. This might be okay for a system or speaker that was very boomy and bright. Having said that, it would be better t fix the system than to have to band-aid it though.

As far as interconnects go, the source output impedance may be anywhere from a very low impedance ( 20 - 50 ohms ) up to several hundred ohms. The input impedance of most preamps or amps is quite high i.e. several thousand ohms up to 100 - 200 thousand ohms. You have to remember though that we are talking about complex impedances here, not just straight resistance. This complex impedance can consist of XXX ohms of resistane combined with XXX values of capacitance and / or inductance. As such, it is possible to find a cable that "cancels" or minimizes the reactive part of the complex impedance found on the input of the device, allowing the source component to see what effectively looks like "pure" resistance. Since reactance is equivalent to "active resistance" or the load "fighting back" against the source, minimizing this encourages power transfer and can improve linearity via reduced ringing / improved phase & transient response. Obviously, this can get phenomenally tricky and for most folks, becomes a matter of trial and error. As such, due to the differences in voltage to current ratios and the impedances that we are dealing with, the electrical characteristics for a speaker cable and an interconnect are different. As a side note, something that works well as a low impedance speaker cable will typically work pretty well as a power cord too. That is, so long as it can pass enough voltage / current without potential safety hazards coming into play. Sean
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I am intrigued by Sean's observation that complex crossovers, designed to flatten impedance curves, tend to suck the life out of the music. The man is always loathe to name names, but would anyone care to identify some speakers with very simple crossovers or no crossovers at all? In addition to single-driver designs, of course.

I know that some of Israel Bloom's past efforts used very simple "crossovers" ( if you want to call them that ). They are the first that came to mind. This is not to say that i agree with all of the design strategies used in those products, because i surely don't. I'm sure that others can fill in some of the blanks here. Sean
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Sen - good job, however mentioning characteristic impedance is also useful. For low-frequency analog signals, impedance is important, because is represents AC resistance. For high-frequency signals, a phenomenon know as characteristic impedance comes into play. It is defined as SQRT(L/C). Characterisitic impedance is a single number that represents the resistance and matching property of a transmission-line to a system, including a terminator, connectors, line drivers and cables. If such a system is matched impedance, no high-frequency reflections will occur anywhere in the system.

Audioengr: You've hit the nail on the head. When all your impedances match, you don't have reflections. You also get rid of ringing due to the lack of stored / decaying energy in those reflections. The differences in transparency and liquidity can be staggering. That is why i've stated many times before that people that think that transmission line theory in RF applications don't apply to audio circuits / installations have never taken any measurements or even listened to an impedance matched system. With such useful tools as a high resolution scope, spectrum analyzer and a TDR ( Time Domain Reflectometer ), one can basically see EVERYTHING that is going on in the circuit. Sean
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