You are using the same formula dude!
No I did not, I used the right formula.
You are calculating what the power should be given a gain number and input voltage reversing that formula to calculate Vout and then using the load to calculate power. This assumes a constant gain at any load.
Actually it looks to me you are the one doing the "reversing" sort of calculation by using the 4 ohm, or 8 ohm rated power output to "back" calculate the gain based on the 1.6 V that is given as "input sensitivity". The trouble is, how do you know their basis/definition of that 1.6 V input sensitivity, it could be for 28.18 V output, 30 V, 50 V, could be anything, or could be for the 8 ohm rated 200 W, or 4 ohm rated 300 W. So you tried it with the 4 ohm rated 300 W and thought the calculated gain was 33.4, close enough to the 34 dB specified for the AT2000, but then how about the 28 dB specified for the AT4000 that is also rated 300 W for 4 ohm and the same input sensitivity 1.6 V?
And besides, you have an error in your formula, if you had the formula right, your results would been 26.7 dB. More to follow...
I am using the simple formula, by definition Voltage gain = 20 Log (Output V/Input V) in dB, or just Output V/Input V in multiples. Okay, I also have to make an assumption, that is, assume the 1.6 V is defined as the input voltage for the amp output to reach 200 W into 8 ohm.
I calculated what the gain is at max power at a given load using that formula given the input voltage by calculating what the Vout would be into a specific load using Vout = P/R.
As mentioned earlier, you have an error in that formula and so I can see why your calculations (the 33.4 calculated gain) in your post#587 is incorrect because Vout = P/R is wrong, it should be Vout = square root of PXR, if you had used the right formula, your calculated gain in post#587 would have been 26.7 dB, not 33.4 dB. Nothing serious there, you just forgot the square relationship, P = V^2/R, that is V²/R in case you don't like the ^ symbol spreadsheet formula uses.
As far as I know, the latter is how amp manufactures report gain/sensitivity in their specs (typically from max power into 8ohms). That is when you would find your calculation consistent regardless of which way you went. Max power can be limited by current capability and so the gain at max output could be different from the gain at no load (as measured by Vout).
That's an interesting point, but I have to disagree, but that's only after I lose sleep thinking about it, thanks to you
..
Here's my counter point, a well designed power amp such as the AT2000, as long as it is operating within its designed limit, the voltage gain should in fact be constant, or very close to being constant, because hifi audio power amplifiers are linear amplifiers such that the output voltage will vary linearly with the input voltage, until it approaches it maximum/limit and starts to clip.
For example, the AT4000 is rated 200 W 8 ohm and 300 W 4 ohm, gain is 28 dB. That should be the same whether you load it with an 8 ohm or 4 ohm test resistor when operating within its linear range.
The input sensitivity is given as 1.6 V so using the formula Vout = Vin X (10^(28/20)) = 1.6 X 25.119 = 40.19 V, and P = (V^2)/R = 40.19X40.19/8 = 201.91 W, so the AT4000's specs of 28 dB gain and input sensitivity 1.6 V would work out, but the AT2000's 34 dB gain and input sensitivity 1.6 V clearly wouldn't. Will do the 4 ohm rated 300 W scenario later..
Otherwise, for every amp the power developed into 4ohms should be exactly twice that of power into 8ohms using your calculation. This isn't true for almost every amp (with a few exceptions). So, you could claim almost every amp spec is dubious with the same logic because the amp does not output as much power as your calculations would indicate for the lower load supported (unless they are lying about the power specs) using the reported gain number typically calculated for max power at 8ohms.
That is a different and separate issue. It has to do with the current and heat dissipation capability of the amp when driving low impedance loads. The gain of the AT4000 is still 28 dB, but using the same formula:
P = Vout^2/R, that is Vout = square root (P X R)
Vout = Vin X 10^(28/20), that is Vin = Vout/ (10^(28/20)
Substituting the power output, P = 300 W and load resistance, R = 4 ohms,
Vout = square root (300 X 4) =
34.64 V
Vin = 34.64/25.119 =
1.379 V
So you can see that the gain is still the same for both 8 ohm and 4 ohm resistor load, but if we assume ATI's specified input sensitivity voltage is 1.6 V to output the 8 ohm rated 200 W, then it will take only 1.379 V to output the 4 ohm rated 300 W.
Just to check: Gain = 20 X log(Vout/Vin) = 20 X log(34.64/1.379) = 20 X log(25.1189) = 28 dB, everything works out!!
Obviously voltage gain and input sensitivity are directly related, but there is a subtle difference. Gain is always defined as Output voltage/Input voltage, whereas input sensitivity is generally defined as the input voltage required to output 28.18 V (as we discussed before), or the input voltage required for the amp to output its rated power, and we both know the rated power outputs are different for different test load resistance .
So if we use the rated power for 4 ohm load, the input voltage will be lower than that required for an 8 ohm load. (the voltage gain remains the same as we are not considering output beyond "rated", that is, within the linear range only). Once the amp started to clip, then all bets are off and distortions will start to rise sharply.
What seems to have confused you is that ATI appears to have calculated the gain for the max power it can develop at 4ohms. That amp would have 24db unbalanced gain and 18db balanced gain at max power into 8 ohms. May be the marketing felt that magical 28.8-29 number would look better! Of course, this gain in the spec wouldn't be consistent with the stated power into 8ohms if you worked backwards to find power output. So, no perfect solution.
I don't really think so, and if I am confused, it is only because of the inconsistency and lack of clarity in the two specification sheets I attached earlier. The fact is, as you can see from the attached ATI spec sheets, the AT4000 and AT2000 amps are both rated 200 W 8 ohms and 300 W 4 ohms, yet one has 34 dB gain RCA input and the other 28 dB gain RCA input, the gain for XLR input for both are 28 dB, and input sensitivity are also the same 1.6 V for both.
So how can you reconcile the difference for the RCA input gain? 34 dB vs 28 dB is very different!
In practice, most people buying an amp don't look at the gain number. What they want to know is the max power output and for the few that venture into matching pre-amps and amps or doing gain staging with variable gain controls, what the input sensitivity is (along with noise and distortion numbers). As long as they are honest and correct, amp voltage gain is just a computed entity for all practical purposes that neither makes or breaks the amp.
Thank goodness, at least and at long last we finally have a lot to agree on.
Just realize I missed your post as we were cross posting, it would have saved me this super lengthy post. Sorry!