DAC direct to Monoblock Power Amplifier Gain Calculations (Number crunching needed)

mononoaware

Hi everyone, (Sorry mistakes edited)

After reading many forum threads online and with the help of calculators etc, calculations made but think I have some errors.
I apologise for the long post, I will do my best to keep it concise.

Objective:
With the limited specifications available, I would like to know how much each 'click' of the DAC volume (level 1-37) will come out of the 1x Monoblock Power Amplifier into the 1x speaker as "watts RMS into 8ohms".
Here is the setup I would like to try:
DAC (SMSL SU-8) RCA Output > RCA cable > Monoblock Power Amplifier RCA Input > Speaker wire > Low Power-handling Speaker (Fostex FE103NV driver in enclosure)

I am aware of the risks involved connecting DAC direct to Power Amp (unintended DAC volume level risk), and the risk of connecting High-Power Amplifier to Low Power-handling speaker (unintended gain level cooking speaker voice coils).

I would like to confirm calculations before I connect everything together.

Specifications (incomplete):
(1x Digital-to-Analog Converter)
- RCA Output at Max volume: (Unbalanced) 2.1Vrms
- Volume Control Steps: 37

(1x Monoblock Power Amplifier)
- Rated output power: 20Hz-20kHz, THD+N<0.1%, 4Ω 300W
- Voltage gain: 1 kHz 31 dB
- Input Impedance: 10 kΩ
I think this low-impedance input (for an Amplifier) will help in getting controllable gain from DAC for Low Power-handling Speakers.

(1x Speaker in enclosure)
- Impedance: 8Ω
- Rated Input: 5W
- Max Input: 15W
According to Fostex the "5W" Power rating was achieved using a square wave signal, so apparently actual Rated Power is slightly higher (8-10W?).
(Sorry currently misplaced the source of information)

1. Amateur Calculations:
Converting 1x Monoblock rated power into 8Ω should be around 150watts RMS (half).
= Converted Rated output power: 20Hz-20kHz, THD+N<0.1%, 8Ω @~150W

After reading online that Voltage is more important factor of power.

Using this calculator (Convert Decibels to Voltage Gain / Loss): http://www.sengpielaudio.com/calculator-gainloss.htm
31dB gain = 35.48 volts.

Then using calculator: https://www.rapidtables.com/calc/electric/watt-volt-amp-calculator.html
I entered 2 values: "8" ohms and "35.48" volts, clicked calculate which gives "4.435" amps and "157.35" watts.
Confirmed this by 35.48^2 / 8 = 157.35.

This makes sense so far right? since the watts RMS output result is accurate.

2. Next, my aim was to find out 1x Monoblock's input sensitivity in volts.
Vin (v) = Vmax/linear gain

To find "Maximum output voltage (Vmax)" of 157.35W @ 8Ω.
Vmax = sqrt (157.35x8) = 35.479v

Then this equation to find "Linear Gain (Y)":
"XdB: 10^(X/20) = Y" so "31dB: 10^(31/20) = 35.48x".)
So Linear Gain is 35.5x.
https://www.audiosciencereview.com/...rstanding-gain-on-power-amp.11309/post-322681
Then using the reverse to confirm 20 * log(35.5) = 31.004dB (31dB Specification).

Vin (v) = 35.479 / 35.5 = 0.999v
Input Sensitivity = 0.999v

Is there something wrong here at this point? it seems like I am just finding the 1v reference voltage.

So 1x Monoblock Vmax (157.35W / 8Ω / 35.48v) is achieved at just 0.999v RCA input.
0.999 / 2.11 x 100 = 47% volume level = 100% output from 1x Monoblock.
Which means only (slightly less than) half of the DAC's 2.1Vrms Max output can be used (37 x 0.47 = 17.52), which means only 17.52 steps of volume from volume level 1.
0.999 / 17.52 = 0.057v per step of DAC volume.

Then going back to the linked Calculator (Voltage and Gain): http://www.sengpielaudio.com/calculator-gainloss.htm
And entering 2 values: "31" dB, "0.057" volts. Gives 2.022 volts increase from Monoblock per step of DAC volume.

Then going back to this Calculator: https://www.rapidtables.com/calc/electric/watt-volt-amp-calculator.html
And entering 2 values: "8" ohms, "2.022" volts. Gives 0.511 watts RMS @ 8 ohms per step of DAC volume.

Conclusion:
So each volume "click" from "level 1" of the SMSL SU-8 DAC should theoretically increase the RMS output from the 1x Monoblock amplifier to 1x speaker by: 0.51 watts RMS.
Which means using the DAC volume, 10 clicks DAC volume = 5.1watts RMS, 18 clicks DAC volume = 9.2 watts RMS.

Does this all seem sound?
Are there are any errors, or do you notice I am doing something wrong?

Thanks again if you made it this far.

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1. Amateur Calculations:
...
Using this calculator (Convert Decibels to Voltage Gain / Loss): http://www.sengpielaudio.com/calculator-gainloss.htm
31dB gain = 35.48 volts.
...
31 dB gain = output voltage equals input voltage amplified by 35.48 times. Only when the input is 1 V you will get an output of 35.48 V. That's why you got back 0.999 V later in your calculations.

Using the 300 W 4 Ω output rating, the max output voltage is √(300 * 4) = 34.64 V. Therefore, the input sensitivity of the power amp is 34.64/35.48 = 0.976 V. (i.e. An input level of 0.976 V will drive the amp to full output power — which is close enough to 1 V.)

With the limited specifications available, I would like to know how much each 'click' of the DAC volume (level 1-37) will come out ...
...
So 1x Monoblock Vmax (157.35W / 8Ω / 35.48v) is achieved at just 0.999v RCA input.
0.999 / 2.11 x 100 = 47% volume level = 100% output from 1x Monoblock.
Which means only (slightly less than) half of the DAC's 2.1Vrms Max output can be used (37 x 0.47 = 17.52), which means only 17.52 steps of volume from volume level 1.
0.999 / 17.52 = 0.057v per step of DAC volume.
...
Volume control usually follows a logarithmic type scale, not linear scale. It means the voltage increase will not be 2.1/37 = 0.057 V per step. The step spacings are much finer at the low end than at the high end. The SMSL manual doesn't say how the volume control steps are related to the actual gain (or attenuation), so it is difficult to know without measurements where is the "safe level" for the Fostex.

Hi NTK, (Sorry edited this post many times keep finding mistakes)

NTK said:
31 dB gain = output voltage equals input voltage amplified by 35.48 times. Only when the input is 1 V you will get an output of 35.48 V.

Thanks for confirming.

NTK said:
Using the 300 W 4 Ω output rating, the max output voltage is √(300 * 4) = 34.64 V. Therefore, the input sensitivity of the power amp is 34.64/35.48 = 0.976 V. (i.e. An input level of 0.976 V will drive the amp to full output power — which is close enough to 1 V.)

This makes sense. Seems like I was doing a lot of extra calculations (trying to justify the numbers I was getting).

So 34.64v @ 8ohms = 149.99watts RMS.

NTK said:
Volume control usually follows a logarithmic type scale, not linear scale. It means the voltage increase will not be 2.1/37 = 0.057 V per step. The step spacings are much finer at the low end than at the high end. The SMSL manual doesn't say how the volume control steps are related to the actual gain (or attenuation), so it is difficult to know without measurements where is the "safe level" for the Fostex.

I understand the "exact" value is difficult to calculate.

Linear volume control Calculations:
0.976/2.11 x 100 = 46% volume
38 steps x 0.46 = 17.48 steps
(Just correcting myself here that SMSL volume levels are "mute", 1-37, "max". So 37 volume level steps + "max" = total 38 steps of volume)
0.976v / 17.48 = 0.0558v DAC RCA Output per volume level step.

Then with: http://www.sengpielaudio.com/calculator-gainloss.htm
Reference voltage 0.056v (DAC output) = Measured Voltage 1.98v (Monoblock output)

Then using: https://www.rapidtables.com/calc/electric/watt-volt-amp-calculator.html
Gives...
Monoblock Power Output:
1.98v @ 8ohms = 0.49watts at DAC volume level 1, rising linear with level 2, 3, 4 etc.
DAC volume level 2 = 1.97watts RMS @ 8ohms
DAC volume level 3 = 4.44watts RMS @ 8ohms
DAC volume level 4 = 7.89watts RMS @ 8ohms

So this being the worst case scenario.
I could conclude it would be best to keep the volume under level 3 on the DAC.

-

Regarding Logarithmic Volume control: I found these graphs from Texas Instruments website.
1. - Shows Linear vs Perfect Logarithmic Volume Pot

2. - Shows Linear pot with a fixed resistor (Blue /Red)

So SMSL likely would have implemented the digital volume attenuation as a "virtual" Log Pot.

Is there are way to estimate the Monoblock output levels (watts RMS @ 8ohms) of the Blue and Red scale by calculating?
Sorry I spent a lot of time here trying to get results but I struggled.
I can try again when I come back. Any help would be appreciated.

Update: So the variance between the Blue and Red line in volts is a large swing, and the graph is not from SMSL, so it is pointless to calculate "estimates" from using the graph I linked.

Quickly calculated the first step of Logarithmic volume level (level 1 on SMSL), which should be -40dB gain loss of the DAC max output, which is 0.01x.
So DAC output @ lowest volume (level 1): 2.11v x 0.01 = 0.0211v
0.0211v DAC output = 0.7486v Monoblock output
Monoblock output: 0.7486v @ 8ohms = 0.07watts RMS

Note: I always take the careful step of turning DAC on first, so I can double confirm the Volume level.
Then I will proceed to turn on the Monoblocks once Volume level has been confirmed.
Also I am aware that my SU-8 (version 2) has some quiet audible noises (like a muffled pop) in the signal when changing "sound color" settings (I noticed the sound when first using the DAC with Active Studio monitors and trying the "sound color" settings).
I always use the same input source with fixed sample rate, and only use the remote to control the volume level so I do not cause any "unusual noises" in the audio signal.
Also the DAC remembers volume level even after power loss, so that's a good safety feature.

I just thought anyone else thinking of connecting the SU-8 direct to Power Amp should be aware of this unusual behaviour of the DAC.
- There was a short YouTube video by a Russian guy, who had the SU-8 (version 1) and he showed the voltage spikes when changing inputs & other settings. He basically said he will not be using the DAC with his Monoblocks.

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The following is just an (inaccurate) estimate calculation for myself, please avoid using it as a reference.

Reference from Texas Instruments Logarithmic volume scale:

30% Perfect Logarithmic volume = ~3% DAC output voltage.

Max DAC output x 0.03 = 3% DAC output voltage
2.11v x 0.03 = 0.0844v

http://www.sengpielaudio.com/calculator-gainloss.htm
0.0844v @ 31dB gain (35.5x) = Monoblock output voltage
0.0844v @ 31dB gain = 2.994v

https://www.rapidtables.com/calc/electric/watt-volt-amp-calculator.html
Monoblock output in watts RMS:
2.994v @ 8ohms = 1.12watts RMS

30% volume in steps (volume level):
38 volume steps x 0.3 = level 11.4

Volume position @ 11.4 steps = 1.1watts RMS

So Volume position @ 11 steps = <1.1watts RMS

The SMSL manual doesn't say how the volume control steps are related to the actual gain (or attenuation), so it is difficult to know without measurements where is the "safe level" for the Fostex.

Hi NTK,

I just stumbled upon some new information that the SU-8 attenuates by approx -38dB @ minimum volume level, which is awfully close to the -40dB attenuation achieved by a Logarithmic Pot (?).

Could you gloss over the calculations and confirm it if makes sense. Thanks.

Update: New calculations based on Multimeter information (approx -1dB loss with each volume step).

SMSL SU-8:
- Volume control information is missing about whether it is Linear or Logarithmic
- A user in this forum stated they used a multi-meter to measure a SMSL (V1.0), and each "step" down from Max (38/38) corresponds to approximately -1dB loss in gain.
(down to level 32 which was -6dB) (an indication that the volume control is Linear?)

If there are 38 steps, and each step corresponds to -1dB in gain.
Then at lowest DAC volume (1) = Max output 2.11v signal @ -38dB gain.

Using: http://www.sengpielaudio.com/calculator-gainloss.htm
-38dB gain = 0.012589x

So 2.11v (Max DAC output) x 0.012 = 0.02532v (volume level 1 DAC output)

Then going back to calculator: http://www.sengpielaudio.com/calculator-gainloss.htm
Amplifier gain = 31dB
0.025v Reference voltage (DAC output) = 0.887v Amplifier voltage (Amp output)

So each DAC volume step = 0.025v Linear increase in DAC output voltage.

Multimeter Gain Reference Results (assuming linear):
DAC volume level 1 output = 0.025v = Monoblock output = 0.887v.

0.887v @ 8ohms = 0.098watts RMS

-

DAC volume level 2 output = 0.05v = Monoblock output = 1.77v.

1.77v @ 8ohms = 0.39watts RMS

-

DAC volume level 4 output = 0.1v = Monoblock output = 3.548v.

3.548v @ 8ohms = 1.57watts RMS

-

DAC volume level 7 output = 0.175v = Monoblock output = 6.209v.

6.209v @ 8ohms = 4.8watts RMS

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It makes sense that the volume display of SU-8 correspond to attenuation in dB. If the attenuation scale is linear in dB, it is automatically logarithmic in absolute levels.

Below is a plot I made with this assumption. The plot is calculated based on a digital signal at digital full-scale (0 dBFS), and the power amplifier gain of 31 dB = 35.48 X.

The method of calculation is:
With zero attenuation at the SU-8 and a signal at digital full scale, the output voltage is 2.1 Vrms. If the amplifier doesn't clip, the output voltage would be 74.5 Vrms, and power into an 8 Ω load will be 74.5^2/8 = 694 W. Since the max rated output is 150 W @ 8 Ω, the smaller of the two values is taken.

With every 1 dB attenuation, power is reduced by 10^(-0.1) = 0.794 X. Therefore, at 1 dB attenuation, the output power should be 551 W (which is still well above the amp's rated power). It is not until 7 dB attenuation that the amp output goes below clipping level.

With full 38 dB attenuation, the amp output power is 0.11 W. Remember that the 0.11 W is with a digital full scale signal. Average power at 38 dB attenuation should be significantly below 0.11 W.

The other noteworthy points (FWIW) are:
17 dB attenuation -- max power = 13.8 W (will not exceed speaker max input power)
22 dB attenuation -- max power = 4.4 W (will not exceed speaker rated input power)

 The above graph gives the maximum power your amp will output given the SU-8 attenuator settings (provided that my assumptions are valid).
...
So each DAC volume step = 0.025v Linear increase in DAC output voltage.
...
If the attenuation goes down in steps of 1 dB, it will not be a linear decrease in the voltage. Each step will decrease the voltage by a ratio, which is 10^(-1/20) = 0.89 X. So if 0 dB (no attenuation) is 2.1 Vrms, then -1 dB is 2.1 * 0.89 = 1.87 Vrms, -2 dB is 2.1 * 0.89^2 = 1.67 Vrms, -3 dB is 2.1 * 0.89^3 = 1.49 Vrms, etc.

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There's almost no way to predict output power when you are playing actual music because it depends on the recording/ mastering level and it's not steady state. This calculation will only help repeatable measurements with a test tone that has a given amplitude.

In reality if the amp is not clipping you're probably fine so long as you can't hear distortion or signs of distress.

Just my 2c.

So I understand the top right of the scale where the graph is flat is the attenuation levels at which the Power Amplifier is clipping.
And the entire scale (graph) up to that point shows as Linear (a straight line), because the evenly spaced Y-axis markers are Logarithmic values.

With zero attenuation at the SU-8 and a signal at digital full scale, the output voltage is 2.1 Vrms. If the amplifier doesn't clip, the output voltage would be 74.5 Vrms, and power into an 8 Ω load will be 74.5^2/8 = 694 W.

Ok so theoretical Max output Power is 694w, I understand you used this in the Power calculation below.

Since the max rated output is 150 W @ 8 Ω, the smaller of the two values is taken.

"the smaller of the two values is taken." What do you mean by this? Taken as in "accepted"?

-

With every 1 dB attenuation, power is reduced by 10^(-0.1) = 0.794 X.

Ok so from the information "Power ratio (gain in decibel)" from this previous link.

"Every 10:1 in power is 10 dB." -- so every 10/0.1 in power is 1dB.

-1dB: 10^(-1/10) = Y

Volume level 1 Power Amplifier output = -38dB: 10^(-38/10)
10^(-3.8) = 0.000158x.
8 ohms @ 694w RMS x 0.000158 = 0.11w RMS

Volume level 16 (-22dB) = -22dB: 10^(-22/10)
10^(-2.2) = 0.0063x
8 ohms @ 694w RMS x 0.0063 = 4.4w RMS

Remember that the 0.11 W is with a digital full scale signal. Average power at 38 dB attenuation should be significantly below 0.11 W.

I assume you mean the difference between pink noise with all frequencies 20hz-20khz played at high levels and actual music file content. So I will consider these calculations as "worst case" and so a good maximum limit to have as a reference.
Edit: or maybe this gain specification is telling "1 kHz 31 dB", so 1khz signal at max.

-

If the attenuation goes down in steps of 1 dB, it will not be a linear decrease in the voltage. Each step will decrease the voltage by a ratio, which is 10^(-1/20) = 0.89 X. So if 0 dB (no attenuation) is 2.1 Vrms, then -1 dB is 2.1 * 0.89 = 1.87 Vrms, -2 dB is 2.1 * 0.89^2 = 1.67 Vrms, -3 dB is 2.1 * 0.89^3 = 1.49 Vrms, etc.

Thanks for including this.
So yes Voltage Ratio (gain in voltage) is going back to "XdB: 10^(X/20) = Y".
2.1v x 0.89 = 1.869v
Power Amp output = 1.869v x 35.5 (voltage gain) = 66.3495v

P = V^2/R
P = 66.3495^2/8 = 4402.25/8 = 550w RMS.

1 dB attenuation, the output power should be 551 W

Thank you for all your help. I think this is as far as I need to go.

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There's almost no way to predict output power when you are playing actual music because it depends on the recording/ mastering level and it's not steady state. This calculation will only help repeatable measurements with a test tone that has a given amplitude.

In reality if the amp is not clipping you're probably fine so long as you can't hear distortion or signs of distress.

Hi raindance,

Yes I am aware of different tracks of music needing different volume levels to match, and some music having more dynamic range etc.
I thought it was worthwhile / good idea to calculate an estimate with the available information, since a Power Amplifier would be used with speakers that are such low power-handling (5w-15w max) and the DAC specifications surrounding its volume control were missing.
One thing is for certain I will not be playing the beginning of "Concerto For Clarinet And Orchestra No. 1 In F Minor, Op. 73- 1. Allegro" (Von Weber) until I have well learned the appropriate volume position.
I will watch out for signs of duress thank you !

Not knowing the sensitivity of your speakers, but having some familiarity with the drivers, I'd hazard a guess that they're going to be running at around a watt or three most of the time.

a watt or three most of the time.

Yes that is also my estimate.
Have been powering them with an integrated amplifier. If I was to guess how much power was being used, I would say slightly under 1 watt.
(they are brand new drivers so I am still being cautious)

This discussion is all rather academic. What about: just don't play too loud

Also, a few assumptions are just not correct:
- For one, the power rating is just the thermal limit of the driver. There are other things to consider. Depending on the usage of the driver, it could already bottom out with less than 5 Watt's with lower bass signals. And if not, it would at least distort heavily. I would highpass the thing at 70hz or higher to protect it. How are you using the driver?
- Another thing is the fact that music has a crest factor of 10 to 20 dB, so you can actually play 10 to 20 dB louder (so factor 10 to 100 in power) than that 5W. Even a 50W amp at full power would probably not be too much of an issue of the little Fostex with most music.

You can also just measure the in-room SPL. On the safe side would be about 97 dB at 1m. That should already be plenty loud.

This discussion is all rather academic. What about: just don't play too loud

Hi voodooless,

Yes you probably need to always use common sense, but in this case I thought some calculations were worthwhile to get an idea of how sensitive the DAC's volume control would turn out to be.
But I guess you are right in a way, since they are just calculated "estimates" common sense must be used anyway.

Depending on the usage of the driver, it could already bottom out with less than 5 Watt's with lower bass signals. And if not, it would at least distort heavily. I would highpass the thing at 70hz or higher to protect it.

Based on my gentle use so far of the brand-new FE103NV with an integrated amplifier, the driver simply makes zero attempt to play anything under 70hz anyway.
I fed some content which I knew to have sub-50hz bass, and turned the volume up a bit. It simply just puts out what it can (mostly 90-100hz and up), "this is what you get" it says.
Zero cone excursion as far as I could see, so it is not even trying to play those low frequencies.

I actually considered getting an amplifier with a output frequency response of 50hz-20khz (Yamaha PA2030a) but they are sold out everywhere.

How are you using the driver?
Just as a single full-range driver.

Even a 50W amp at full power would probably not be too much of an issue of the little Fostex with most music.
Yes I have read online they are tough little drivers (although this may be based on previous generations of FE103).

You can also just measure the in-room SPL. On the safe side would be about 97 dB at 1m. That should already be plenty loud.
The only measurement device I currently have access to is a dB level meter App on the iPhone. If it is worth anything I recall it was made by some university people and calibrated for the iPhone model you are using.

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Just as a single full-range driver.

Sure, but how is it implemented? Naked, closed box, horn…?

The only measurement device I currently have access to is a dB level meter App on the iPhone. If it is worth anything I recall it was made by some university people and calibrated for the iPhone model you are using.

That’s an okay start I guess.

Sure, but how is it implemented? Naked, closed box, horn…?

That should reduce excursion at the low end a bit. Should be fine. I’d say measure with your iPhone, let’s say 1 kHz tone. Put yourself at 1m from one speaker and dial up the volume until you measure about 97 dB. That is your very safe lower bound. With real music you can probably go much louder though.

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