Electronics > Beginners
Does cable impedance add to source or load impedance?
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David Hess:

--- Quote from: Richard Crowley on February 15, 2019, 04:08:03 pm ---OTOH, at the other end of the audio chain, for a connection between a power amplifier and a speaker, we are talking about very low source and load impedance (on the order of 10 ohms)  In that scenario, parallel capacitance is of no practical significance.
--- End quote ---

The cable capacitance has no significance to the low impedance driver at audio frequencies but it can cause the output stage to oscillate above the audio band if not properly handled.
Kleinstein:
The damping of the speaker depends on the speaker impedance at resonance, the speakers own ohmic resistance, that cable resistance and the amplifiers output resistance. If there is a passive cross over network this also can add quite a bit.

Here the resistance insider the speaker, wire and amplifier are added. Quite often of the resistance is due to the speaker itself so some 2 Ohms of wire resistance would not add that much and the actual damping factor would not change very much. The extra resistance still have a slight effect on the cross over network.

With modern speakers the ohmic resistance may be quite a bit lower than the speaker impedance, but it's usually still more than the wire or amplifier.
larry42:

--- Quote from: fonograph on February 14, 2019, 10:45:15 pm ---Lets imagine we have amplifier with 2 ohm output impedance connected to 8 ohm impedance load, headphone for example. Becose the amp impedance is 2 and headphone is 8, then the damping factor is 4.

How will the cable affect our system? If the cable has 2 ohm resistance, does it add up to the source impedance and decrease damping factor from 4 to 2 becose 2 ohm source + 2 ohm cable = 4 ohm output impedance divides 8 ohm load = 2x damping factor.

Or does it add to the load impedance and increase the damping factor becose 8 ohm headphone + 2 ohm cable = 10 ohm load divided 2 ohm amp output impedance = 5x damping factor?

--- End quote ---

My understanding (after 2 decades of RF design) is:
The characteristic impedance, Z0, of a transmission line, such as coaxial cable, is a notional concept that relates the current flowing through the line with the voltage across it. Heaviside and later Maxwell showed that a transmission line can be considered as a concatenation of short RLGC sections (series R and L, shunt G and C) and Z0 is given by
Z0 = sqrt((R+j*w*L)/(G+j*w*C))
where j = sqrt(-1)
w = 2*pi*frequency (omega)
and R,L,G,C are per unit length

For practical cables made from good conductors and good insulators the physical values of the R,L,G,C work out mean that for f>100kHz, say, Z0 ~= (sqrt(L/C))

Thus at HF the char. impedance is real and fairly constant.

At medium and audio freq. it is complex and varying.
with RG-58
R = 39mOhm/m
L = 250nH/m
C = 100pF/m
At f> 250kHz, j*w*L ~= 10*R and Z0 is quite constant 50Ohm.
At audio frequencies therefore the char. impedance is complex and a function of freq (i.e. Z0(f))

But what is the effect of this impedance? Modeled as a two port:
https://en.wikipedia.org/wiki/Transmission_line

Then using ABCD parameters, you will probably be able to see how the output inpedance of the amplifier (Port 1) is transformed via https://en.wikipedia.org/wiki/Two-port_network
to V1, I1 = ABCD V2, I2
and so see how much of an effect your tx line has. It's not a simple resitive addition, as the shunt capacitance is usually non negliable.
This will give you an effective Zsource that is connected to your load.
But Zsource is a function of freq. (due to the tx line) and because your amplifier will have a damping factor (output impedance) that rises with freq.
So... basically, IMO damping factor is just a fairly meaningless marketing term (which is is freq. dependent). Your speaker network as funkloads of resonances, and will be 8Ohm restive at 1 single point probably and unless you are using very long (say >5m) lines the tx line's characteristics are not interesting to consider, and cannot be regarded as  a simple resistance in any case.

larry42:
I just want to add - that this all assumes that you are at a freq. such that jwL is >> R and jwc >> G. below that you may need to think about transmission line effects, but the char. impedance is not constant.
Johnny B Good:

--- Quote from: fonograph on February 14, 2019, 10:45:15 pm ---Lets imagine we have amplifier with 2 ohm output impedance connected to 8 ohm impedance load, headphone for example. Becose the amp impedance is 2 and headphone is 8, then the damping factor is 4.

How will the cable affect our system? If the cable has 2 ohm resistance, does it add up to the source impedance and decrease damping factor from 4 to 2 becose 2 ohm source + 2 ohm cable = 4 ohm output impedance divides 8 ohm load = 2x damping factor.

Or does it add to the load impedance and increase the damping factor becose 8 ohm headphone + 2 ohm cable = 10 ohm load divided 2 ohm amp output impedance = 5x damping factor?

--- End quote ---

 The term "Damping Factor" must be the most abused "Figure of Merit" invented by the amplifier manufacturing industrys' marketing departments since the advent of transistorised power amplifiers with output impedances two to three orders of magnitude lower than the one to three ohms output impedance  typical of the valve (tube) amplifiers of the day.

 A myth was created that the 'Damping Factor" (DF) was the ratio of speaker load impedance to that of the amplifier's output impedance, neglecting the inconvenient truth that some 95% or more of the typical moving coil speaker's impedance was simply the ohmic resistance of its voice coil which is effectively in series with that of the amplifier's output Z and the connecting cable's loop resistance.

 All such signal carrying cables (two wire balanced circuits or unbalanced shielded co-axial circuits) have a "characteristic impedance" (not to be confused with "loop resistance") which, in the case of Hi-Fi wiring, is typically not a critical matter. That's not to say there isn't any need to consider its impact on audio frequency circuits such as the telephone trunk lines of old and local land line circuits which can be several miles in length. In this case, a more accurate phrasing of your question in the subject line would have been achieved by replacing the the first occurrence of the word "impedance" with the word "resistance" since in this case, the cable "impedance" is immaterial to this question.

 The myth that an amplifier with an output impedance of 0.02 ohms provides a damping factor of 400 on an 8 ohm speaker load is just that, a myth. At best you might see an effective DF of circa 4 on the typical 32 ohm resonant impedance (the characteristic behaviour that is being damped) of an eight ohm voice coil driven speaker cone (roughly the sum total of amplifier impedance plus maybe half an ohm loop resistance of cable plus 7.5 ohms or so of voice resistance versus the 32 or so ohms resonant impedance of the speaker).

 Such wonderful transistorised amplifiers do NOT improve the DF a hundredfold over that of a valved (tubed) amp with an output Z of 2 ohm with a half ohm loop resistance cable driving the same speaker voice coil load. In the transistorised amp case, the actual DF is only around 4 versus the valved (tubed) amp case of 3.2 which is a mere 25% improvement by the transistorised amp over that of its valved predecessors.

 In short, the DF figures published by the solid state amplifier manufacturers were (are still?) pure marketing bullshit designed to persuade their target demographic to give up their treasured valved amps for these nice shiny new wonders of solid state technological excellence in amplification. Unfortunately for those who fell for the false advertising claims back in the 1970s, those solid state technological wonders of amplification had far worse vices than the less than perfect valved amplifiers they were supposedly superior to.

 However, in the intervening four decades or so since those dark days, the industry has learnt a lot of valuable lessons and high power mosfet transistors became available many years since (two decades or so?) to address the limitations of the early bi-polar power transistors such as the classic 2N3055s so commonly employed in those early designs. Modern solid state amplifiers are a world away from those early amplifier designs and do now offer genuine improvements over the classic valved amplifiers from the late 20th century.

 The short answer to your question btw, is that unless you're planning on using several hundreds of yards of the thinnest of thin headphone cables, I wouldn't worry about it. it'll make bugger all difference. It's only the resonant impedance of the drive unit as explained above that's being damped everything else, the voice coil resistance (typically 95% or more of the drive unit's nominal impedance), the cable loop resistance and the amplifier's output impedance are all effectively in series across the resonant impedance which, for a speaker drive unit might be as high as 4 or 5 times its nominal impedance (headphone drive units may be even lower than this). It's not the nominal drive impedance you're trying to damp out but its much higher resonant impedance.

 Your main concern with the additional 2 ohms will be over the matter of the dB or so loss this will introduce, not the imperceptible reduction in damping effect on the resonance peak at the bottom end of the drive unit's frequency response plot.

 HTH & HAND  :)

JBG
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