Johan Potgieter said:
Perhaps I can have a try here (getting jealous of Andrew)
It has to do with the way we hear different sound intensities, which is logarithmic. That is, equal steps of subjective loudness are not steps in output of say 2W, 4W, 6W, 8W, 10W and so on. These are equal steps in electrical output, thus linear.
If you advance a volume control in what will appear to you to be 'equal' steps of loudness, an output meter attached to the amplifer will register (say) 1/2W, 1W, 2W, 4W, 8W, 16W and so on.
That means that the 'law' that an 'even' (logarithmic) volume control will have to follow will be to first increase the signal in small steps, becoming larger all the time. You might have experienced the 'quickly loud' sensation in e.g. portable transistor radios, where a linear control increases loudness as per my first example. (Linear controls are cheaper to make.)
If you measure a center-tapped potentiometer, a linear pot will show 50% of the total resistance from each end of the pot, but a log pot will show only 10% of the total resistance from the 'cold' side. (As a true log scale does not have a zero or maximum, log pots are tapered off close to each end.)
Thanks Johan,
That explains it well. How would you use the "log law" this to calculate resistor values in the attenuator?
Turns out I don't know the source impedance ( Denon DVD player or Creative sound card), but I do know that the Zin of the amplifier is 100k ohms and the output to the speakers is at 4ohms. The pot that this will be replacing is 100k.
Thanks.
Here are the values from Glassware's catalog. What values must be changed to get the sought after ratio? Assume Zin of the amp as 100k.
An externally hosted image should be here but it was not working when we last tested it.
if the resistor numbers start the same as my old one then it's the top group that need to be lowered. The extra resistors shown from R17 to R21 must be for the extra steps in the new shunt attenuator.
I have R1 to R10 in pairs to set the series attenuator to 4k
I have the next group R11 to R16 to set the shunt attenuator to 20k.
This gives me a choice of using a buffer after the attenuator or not.
I tried the unbuffered, but it has exactly the same problems as any passive pot.
Go buffered or go very low in impedance. But, very low Zin will require a headphone buffer on all your sources to feed the attenuator.
A 1k0 followed by a 5k0 might be a nice combination that will work unbuffered. It might also be good buffered. But look at how low the load is that must be driven by the source.
I have R1 to R10 in pairs to set the series attenuator to 4k
I have the next group R11 to R16 to set the shunt attenuator to 20k.
This gives me a choice of using a buffer after the attenuator or not.
I tried the unbuffered, but it has exactly the same problems as any passive pot.
Go buffered or go very low in impedance. But, very low Zin will require a headphone buffer on all your sources to feed the attenuator.
A 1k0 followed by a 5k0 might be a nice combination that will work unbuffered. It might also be good buffered. But look at how low the load is that must be driven by the source.
I found a resistor value calculator for the stepped attenuator, below:
Series Attenuator
Shunt Attenuator
For the series part, what would the total value of attenuator (= Rx + Ry) be?
And will the number of steps be 6 each for Left and Right channel with identical resistor values?
For the shunt part, what would the series value of attenuator (Rx) be?
(six steps I assume)
Thanks.
Series Attenuator
Shunt Attenuator
For the series part, what would the total value of attenuator (= Rx + Ry) be?
And will the number of steps be 6 each for Left and Right channel with identical resistor values?
For the shunt part, what would the series value of attenuator (Rx) be?
(six steps I assume)
Thanks.
with a buffer on the output you can keep the standard 100k in the second stage.
The first stage should be reduced to somewhere between 5k and 20k.
If your source can drive 10k, then that's what you should choose.
I notice the web calculation sheet uses the opposite definitions for series and shunt. I'm not sure which is which.
Certainly the second stage is a string of resistors of decreasing value with the wiper tapping off the junctions between the resistors.
The first stage is just a pair of resistors with the wiper tapping off that junction. Different pairs are selected for the fine control.
The first stage should be reduced to somewhere between 5k and 20k.
If your source can drive 10k, then that's what you should choose.
I notice the web calculation sheet uses the opposite definitions for series and shunt. I'm not sure which is which.
Certainly the second stage is a string of resistors of decreasing value with the wiper tapping off the junctions between the resistors.
The first stage is just a pair of resistors with the wiper tapping off that junction. Different pairs are selected for the fine control.
I know this is an old thread, but I am curious about one aspect of the two stage stepped attenuator. Are the resistors to ground of the two stages in parallel with each other? Do you have to take that into account in calculating the ry/(rx + ry) values? From the chart, it is not clear how the resistor values are obtained for each db step.
Thanks
Thanks
Your answer is in the previous post.
The first stage is:
The second stage is:
Remember that EVERY Source connects to it's receiver via a TWO WIRE connection. There are no exceptions.
The Signal Hot and the Signal Return. There is no ground !!!!!
Actually, we have to love spreadsheets for solving these kind(s) of problems.
FIRST remember that [ dB = 20 × log₁₀( V₁ / V₂ ) ]. This is key … it means if you divide the input by 10, that 20 log₁₀( 0.1 ÷ 1.0 ) = –20 dB. So, cutting voltage by 10 drops output by 20 audible decibels.
SECOND, you have "practical switches". Much though you might want 0.1 dB steps, when you realize that over a range of say 50 or 60 dB, this would require 500 to 600 steps … obviously there's some compromises in order. The main one is, do you want to have the steps be the minimum that most people can perceive (about 1 dB), which requires a LOT of resistors and switch sections, or something more practical like "a nice small step that can be heard, but not 'hugely'"? (Somewhere between 1.5 dB and 3 dB)
I see merit in "2 dB per step", as being a good compromise.
Say you have a rotary with 27 section stops. Well, then at 2 dB, that becomes about 54 dB of total attenuation. Moreover, for reasons that are design choices only, you might want to have wider gaps at both the loud, and the very quiet end. Stretch out the range a bit.
What you need next to do is just to set up a column that contains "the stops", and what their negative dB rating will be. Negative, because you'll be cutting the signal by that amount. Use the EXCEL formula (in the next column to the dBs) of
=10 ^ ( dB ÷ 20 )
That (in visual terms) is the RATIO between all the resistors below the wiper, to the whole stack of resistors. A very cool number.
Taking the difference between this number, and the next one (next row) will give you the relative resistance value for the step position. The only time this breaks down is at the last position (quietest); actually it doesn't break down, it just points to the fact that the last resistor is apparently anomalously high compared to its neighbors. No worries.
Once these ratios and differences are computed, just multiply them by the "total value for the impedance of the stack" is going to be. Now you have your values. Couldn't be more straight forward.
The opportunity to make your volume control have a reproducible, customized log-volume curve is something I rarely read about. The "God of Linearity" being so powerful, it seems like everyone is just slavishly trying to make the most linear of stepped volume controls, forgetting that really, just really, "linear in apparent volume level" isn't what's exactly ideal, but what is is having both channels very, very closely achieving the same curve, whatever it is chosen to be.
As an example of an intentionally non-uniform stepping dB sequence, that broadens the range of 27 position stepper to 75 dB:
R1 29,200 0
R2 20,700 –3
R3 10,300 –6
R4 8,200 –8
R5 6,500 –10
R6 5,100 –12
R7 4,200 –14
R8 3,200 –16
R9 2,600 –18
R10 2,100 –20
R11 1,590 –22
R12 1,300 –24
R13 1,030 –26
R14 820 –28
R15 920 –30
R16 660 –33
R17 460 –36
R18 330 –39
R19 230 –42
R20 160 –45
R21 118 –48
R22 104 –51
R23 78 –55
R24 44 –60
R25 24 –65
R26 14 –70
R27 18 –75
(PS: the "sum of the resistors" is 100,000 ohms)
Let's see if this looks like shish-kebab or not.
GoatGuy
FIRST remember that [ dB = 20 × log₁₀( V₁ / V₂ ) ]. This is key … it means if you divide the input by 10, that 20 log₁₀( 0.1 ÷ 1.0 ) = –20 dB. So, cutting voltage by 10 drops output by 20 audible decibels.
SECOND, you have "practical switches". Much though you might want 0.1 dB steps, when you realize that over a range of say 50 or 60 dB, this would require 500 to 600 steps … obviously there's some compromises in order. The main one is, do you want to have the steps be the minimum that most people can perceive (about 1 dB), which requires a LOT of resistors and switch sections, or something more practical like "a nice small step that can be heard, but not 'hugely'"? (Somewhere between 1.5 dB and 3 dB)
I see merit in "2 dB per step", as being a good compromise.
Say you have a rotary with 27 section stops. Well, then at 2 dB, that becomes about 54 dB of total attenuation. Moreover, for reasons that are design choices only, you might want to have wider gaps at both the loud, and the very quiet end. Stretch out the range a bit.
What you need next to do is just to set up a column that contains "the stops", and what their negative dB rating will be. Negative, because you'll be cutting the signal by that amount. Use the EXCEL formula (in the next column to the dBs) of
=10 ^ ( dB ÷ 20 )
That (in visual terms) is the RATIO between all the resistors below the wiper, to the whole stack of resistors. A very cool number.
Taking the difference between this number, and the next one (next row) will give you the relative resistance value for the step position. The only time this breaks down is at the last position (quietest); actually it doesn't break down, it just points to the fact that the last resistor is apparently anomalously high compared to its neighbors. No worries.
Once these ratios and differences are computed, just multiply them by the "total value for the impedance of the stack" is going to be. Now you have your values. Couldn't be more straight forward.
The opportunity to make your volume control have a reproducible, customized log-volume curve is something I rarely read about. The "God of Linearity" being so powerful, it seems like everyone is just slavishly trying to make the most linear of stepped volume controls, forgetting that really, just really, "linear in apparent volume level" isn't what's exactly ideal, but what is is having both channels very, very closely achieving the same curve, whatever it is chosen to be.
As an example of an intentionally non-uniform stepping dB sequence, that broadens the range of 27 position stepper to 75 dB:
R1 29,200 0
R2 20,700 –3
R3 10,300 –6
R4 8,200 –8
R5 6,500 –10
R6 5,100 –12
R7 4,200 –14
R8 3,200 –16
R9 2,600 –18
R10 2,100 –20
R11 1,590 –22
R12 1,300 –24
R13 1,030 –26
R14 820 –28
R15 920 –30
R16 660 –33
R17 460 –36
R18 330 –39
R19 230 –42
R20 160 –45
R21 118 –48
R22 104 –51
R23 78 –55
R24 44 –60
R25 24 –65
R26 14 –70
R27 18 –75
(PS: the "sum of the resistors" is 100,000 ohms)
Let's see if this looks like shish-kebab or not.
GoatGuy
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Very nice numbers...largest absolute error 0.05dB, largest step error 0.07dB
I would not be able to tell...had to use a spreadsheet.
The second stage is the receiver, or load presented to the first stage. The amplifier Rin is the load presented to the second stage.
If you have a resistive divider say 5k + 5k from a 10k vol pot with the wiper at the geometric centre, then you will find that the load affects the attenuation.
When the load is infinite the output is exactly 50% of the input, i.e. ~-6.02dB
As the load is reduced the attenuation changes.
A 100k load on that same 5+5 divider gives -6.235dB
10k load gives -7.959dB
Note that with a 10k vol pot and a 100k load, the error is only 0.215dB for a -6dB setting. Whereas with a 10k load the error is 1.939dB (more than 9times bigger).
The formula for calculating the attenuation should take account of the load that is applied.
With this cascaded two stage attenuator, the Builder can choose the step sizes.
eg.
the fine steps could be 1dB. There are 11 of them, giving 0 to -10dB in steps of 1dB
The coarse steps could be 10dB. There are 6 of these, giving 0 to -50dB in steps of 10dB.
The combination gives 0 to -60dB in steps of 1dB.
These 1dB steps might be a bit too coarse for adjusting balance. ½dB steps might better suit fine balance adjustment.
The accuracy of the steps depends on how one loads each stage.
If the load is always the same, then the stage steps can be quite accurate, you can dial up -37dB and end up pretty close to that.
The attenuation is given by
20{log[(Rlower||Rload)/[Rupper+(Rlower||Rload)]]}, where Rlower||Rload = Rlower*Rupper/{Rlower+Rupper}
Most just ignore Rload when Rload >>5times [Rupper+Rlower]
Finally
for an amplifier Rin=100k the second stage could be made to have a maximum output impedance of 100/20, i.e. 5k. A 20k vol pot has a maximum output impedance of 5k.
The first stage seeing that 20k as a load could be made to have a maximum output impedance of 20/20 = 1k. A 4k vol pot has a maximum output impedance of 1k
The Source sees a first stage impedance of 4k
The first stage sees a second stage impedance of 20k
The second stage sees an amplifier input impedance of 100k.
Each of the sources sees a load that is more than 20times it's own output impedance.
If the Source can drive 4k, then all stages can achieve at least a 1:20 ratio of source to load impedance.
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Fabulous Goatguy and Andrew! Andrew, your explanation was exactly what I wanted to know. I will have to chew on it for a bit, but at first blush it appears the best way to go is to maintain the ratios you suggest.
Although he does not maintain the ratios, and I am not sure how he arrives at Rin of 11k and 22k, here is a variation of the 2 stage attenuator that looks interesting.
On Stepped Attenuators II
Thanks again for your help.
Although he does not maintain the ratios, and I am not sure how he arrives at Rin of 11k and 22k, here is a variation of the 2 stage attenuator that looks interesting.
On Stepped Attenuators II
Thanks again for your help.
related question re balance control
Would not the same considerations apply if I use a balance control with a stereo volume pot? I see that Rod Elliott states the balance control should have an impedance of 2 to 2.5 times the impedance of the volume control. ESP - A Better Volume Control (at end of page, fig. 7 looks like a typical configuration, but fig 8 looks like the two controls are in parallel rather than series). But it seems to me that using a balance control (in series) would essentially be the same implementation discussed in this thread. Therefore, the output impedance of the balance control should be one tenth to one twentieth the input impedance of the volume pot, not two to two and half times the impedance of the volume pot. Am I wrong on that?
I was thinking of making a stepped balance control so there would be no attenuation at the middle position, then increasing attenuation on one channel as the control is rotated CW and increasing attenuation in the other channel as the control is rotated CCW. Something similar to this: DACT audio balance controls
Andrew and Goatguy, do you have any thoughts on the correct relative impedances?
Thanks in advance.
Jazzzman
Would not the same considerations apply if I use a balance control with a stereo volume pot? I see that Rod Elliott states the balance control should have an impedance of 2 to 2.5 times the impedance of the volume control. ESP - A Better Volume Control (at end of page, fig. 7 looks like a typical configuration, but fig 8 looks like the two controls are in parallel rather than series). But it seems to me that using a balance control (in series) would essentially be the same implementation discussed in this thread. Therefore, the output impedance of the balance control should be one tenth to one twentieth the input impedance of the volume pot, not two to two and half times the impedance of the volume pot. Am I wrong on that?
I was thinking of making a stepped balance control so there would be no attenuation at the middle position, then increasing attenuation on one channel as the control is rotated CW and increasing attenuation in the other channel as the control is rotated CCW. Something similar to this: DACT audio balance controls
Andrew and Goatguy, do you have any thoughts on the correct relative impedances?
Thanks in advance.
Jazzzman
Some balance controls use a resistance track that has zero resistance along 50% of the track length.
They fit two of these into the control, so that (when turning in one direction) one wiper is attenuating that channel's output while the other wiper is on the zero resistance track, giving zero attneuation. When turned in the other direction the attenuation and zero attenuation swap over.
You could mimic this very easily with a switched atenauator.
They fit two of these into the control, so that (when turning in one direction) one wiper is attenuating that channel's output while the other wiper is on the zero resistance track, giving zero attneuation. When turned in the other direction the attenuation and zero attenuation swap over.
You could mimic this very easily with a switched atenauator.
It's not that important.
Does it matter that attenuation looks like it should be -10dB, but is actually -8.2dB? i.e. an error of 1.8dB
If you need realistic calibration markings on the attenuator, it makes a difference.
But for listening, we use our ears to tell us whether it's about right for that moment.
Does it matter that attenuation looks like it should be -10dB, but is actually -8.2dB? i.e. an error of 1.8dB
If you need realistic calibration markings on the attenuator, it makes a difference.
But for listening, we use our ears to tell us whether it's about right for that moment.
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