Listening setup optimisation

[chrissugar]

I read for a long time many posts about the following situation and because I never heard a complete and correct analysis from a technical point of view I think it is the best place to ask the math and electronics gurus.

Let's say we have a mastering setup where the active loudspeakers are 5meter (15 feet) away from the mastering console. I mean we have five meter cables from the stepped attenuators to the amplifier input.
I'm interested what is in your opinion the best compromise for this situation, because if the stepped attenuator has large value the cable will act as a low pass filter, if the value is too low there is the risk that the stage before it will be loaded too much, if we use a unity gain buffer we loose some transparency of the signal.
Keep in mind that in any situation there should be no significant attenuation at 20K (lower then 0.5dB)
Let's say the input Z of the active speaker is 10K.

What is in your opinion (based on calculus and personal experience) the best value for the attenuator, the maximum acceptable capacitance of the cable, the length of the cable and if you feel the need for the buffer.
I know Bob Katz use a buffer made by Fred Forssell and others opt for similar solutions but also I know that others avoid the buffer.
What do you think.

chrissugar

 

[bcarso]

What's the impedance and drive current capability of the thing driving the attenuator, that is, what does the console output look like?

And what is you cable capacitance?

 

[Samuel Groner]

Assuming 1 nF for 5 m, we get a worst-case BW of 30 kHz for a 10k attenuator. That's a bit too low.

If we use low-cap. cable and a 5k pot, things look better. Still no DC-to-daylight, though. And lower than 5k seems dangerous without knowing your gear.

An ideal solution would be remote controlled attenuation in your active speaker. They have some attenuation anyway, so why not make it variable?

Samuel

 

[chrissugar]

Brad, the cable I use has 70p/meter , it is a quality cable but I would like to avoid to drift the discussion in the direction of optimising for a specific situation, I'm more interested in an analysis for a general situation. Let's say one extreme would be for a setup that can drive without problem very low impedances and the other only high impedances. It is clear that the first situation is much easyer and there is no need for a buffer. I'm more curious where is the point where the value of the attenuator, cable capacitance, cable length is significant and when a buffer is the only optimal solution (compromise between loss of transparency and loss of high freq and maybe other problems).


Samuel, the speakers have no attenuation, the remote attenuator is a a good solution but that needs some relay based system like the one designed by Mikkel. Let's stay with the mechanical stepped attenuators at the console for now.


chrissugar

 

[bcarso]

OK. Then we want a general expression, which should be straightforward enough. At least we can presume that the console Z is lower than the powered speaker Z. But there are a lot of parameters.

There is also another option, which is an intentional shelving R-C when the capacitance of the cable is known, to pull up that last dB or so at 20kHz.

I have to run now.

 

[chrissugar]

No Brad, no shelving, I want the least possible modification of the original signal in the audio range, so no compensation devices. It should be less then 0.5dB attenuation at 20k.

Lets say that the cable capacitance is 100p/m because most of the quality cables have less. Although It would be interesting an analysis depending on the cable capacitance/meter.

chrissugar

 

[Samuel Groner]

Without starting the simlulator or getting a filter design book I don't remember which -3 dB point gives -0.5 dB @ 20 kHz, but a first assumption is 50 kHz.

A simple stepped attenuator with impedance Z has a max. output impedance of Z/2. The -3 dB point of a RC filter is given by 1/(2*pi*R*C), so it's simple to put values in and see whether we are above or below 50 kHz.

Somehow I got the feeling that this is not what you want, as this is rather basic and I'm sure you could have done that yourself; so maybe you could be a bit more specific?

Samuel

 

[Samuel Groner]

Too late for good posting: max. output imp. of an attenuator is of course Z/4, not Z/2. The BW in my first post makes it to 60 kHz instead of 30.

Samuel

 

[bcarso]

A closed-form expression may get hairy and lead to negative values for R's if my intuition is trustworthy*, so it might be better to do this exercise as a flow chart.

Another approach is start with cable C, input Z, and the bandwidth constraint, figure out the maximum output Z of the attenuator. Then put in the attenuation and see what the input Z of the attentuator becomes, and determine if that can be driven. If not you are SOL.



(*reminds me of Spys Like Us, where the Chevy Chase character is trying to convince the Dan Ackroyd character to follow the woman they have just parted from. Chevy gives his rationale, and Ackroyd says "You're thinkin' with your d*ck", to which Chevy rejoins "Got me through high school.")

 

[bcarso]

Here is the solution for a single-ended situation and associated pad, which can be readily extended to the balanced case.

Find the sum of the cable C and input C.

Call this Ctot.

Take your bandwidth criterion as 0.5dB down at 20 kHz, which, for a single-pole rolloff, is-3dB at 57.3 kHz, or a τ of 2.78us. Find R sub τ = τ/Ctot. If you don't like to lose 0.5dB then find a loss you like and a corresponding τ.

Let your desired attenuation be expressed as a numerical fractional gain, and call this A. So for example -20dB means A = 0.100.

Form the quantity Q = (1-A)/A.

Let the input Z of the powered speaker etc. be Rin.

Let the resistance of the input resistor of the pad, plus the source impedance, be R1. Let the shunt R to common be R2. The junction of the physical resistor, whose value is (R1 ? Rsource), and R2, is the output of the attenuator, i.e., the node that drives the cable.

Then R2 is given by the expression

[(Rin)(R sub τ)(Q+1)]/[(Rin)Q ? (R sub τ)(Q+1)]

And having gotten R2, R1 is

(R2)(Rin)Q/(R2+Rin), that is, Q times R2||Rin.

(this could be worked out as just involving Q and Rin and R sub τ )

For the actual input resistor value, subtract the output Z of the source from the value of R1. If the answer is negative then you definitely need a buffer. If the value of the source Z is anywhere close to the value for R1, then maybe you should consider a buffer. Most of the time you won't have to.

 

[chrissugar]

Thank you Brad. Of course the math part is very good. That made me think about a little software that can calculate every parameter depending on the other known factors. Maybe some excel or something like those javascript calculators.
Another factor that made me think about this problem is where is the active zone of the stepped attenuator, in the first half (-infinity to -20dB) or the second half (-20 to 0dB) because depending on it the high freq response will be affected. I should calculate what is the worst case situation and optimise everything taking that in acount. What do you think?

chrissugar

 

[TomWaterman]

[quote author="chrissugar"]That made me think about a little software that can calculate every parameter depending on the other known factors. Maybe some excel or something like those javascript calculators.[/quote]

Hmmm good idea Chris I may have to have a go in Excel sometime, could try and add that to attenuator calcs too.

[quote author="chrissugar"]Another factor that made me think about this problem is where is the active zone of the stepped attenuator, in the first half (-infinity to -20dB) or the second half (-20 to 0dB) because depending on it the high freq response will be affected.[/quote]

Won't that only matter if you're using cumlative attenuators such as the series shunt, ladder etc? Where the output Z-changes....

If you use a bridged-T then the in/out Z remains constant no matter what the attenuation and the signal path is only limited to one resistor stage, as opposed to cumlatively going through 23.

Surely that will assure a stable HF response no matter where the active zone is?

-Tom

 

[chrissugar]

Tom, bridged-T attenuator is too simple.
The situation I'm considering is the one when you use a series stepped attenuator as a replacement for a pot.
By the way I built tons of series attenuators and they are much, much more precise and better sounding then a pot even with 23 resistors in series, so I don't want to overcomplicate the problem.
So let's continue the discussion with series stepped attenuators.
http://207.228.241.188/schm_ser.html

chrissugar

 

[chrissugar]

I almost forgot to say, that I visited a site where I was last time long ago, and they have an attenuator calculator. You can enter cable capacitance values and load resistance:
http://www.dact.com/html/ac_calculator.html

http://www.dact.com/DACT_Attenuation_Curve_Calculator.xls

chrissugar

 

[TomWaterman]

Fair enough.

Most monitor amps seem to have input Z in the range of 10-20k...so I guess you're going to need a lowZ attenuator if you want to have decent HF repsonse over 50k into 5m cable @ approx.500pF.

Hard to tell from the graph what the response is at 20k in the DAC-T file (can't find a way to hack into the values in excel either??) but as an example a 10k atty into 5m cable (approx 500pF) feeding the input to a Pass-X at 11k unbalanced Z it looks like its down at 20k until we reach -21dB on the attenuator.

So I guess the place of operation needs to be in the last half of the attenuator or a 5k attenuator used.

Out of interest if it was a 10k bridged-t would it be reasonable to assume that the freq performance would be in the magnitude of the -60 line (orange) in the DACT calc. i.e greater than 100k at all settings?

-Tom

 

[bcarso]

"I almost forgot to say, that I visited a site where I was last time long ago, and they have an attenuator calculator. You can enter cable capacitance values and load resistance: "

Note that Dact assumes a zero source Z, with unlimited current drive available. If one can make the attenuator Z arbitrarily low then there's no issue.

As Samuel pointed out the maximum output Z of a simple attenuator like the Dact, or for that matter a plain old potentiometer, occurs at A = 0.500 or about -6dB, and is 1/4 of the end-to-end resistance. Anywhere else Z out is lower, again assuming a zero source Z.

It would seem that what one really wants is a constant output Z so the cable rolloff is constant.

 

[bcarso]

Just to put this in persepective a bit: here's an example using the formulae:

Rin = 20kohm; C cable and input, "Ctot" = 500pF; Attenuation 20dB, A = 0.100; The R2 = 8.939kohm and R1 = 55.6kohm. If the source Z is 100 ohms the actual series R is 55.5kohm.

This is based on the 0.5dB down at 20kHz criterion.

Clearly at this attentuation we would probably use a lower Z overall and take less of a h.f. cut, since this is an easy load for anything to drive.