Need help with Preamp to PowerAmp compatibility calculation

[supertech]

My understanding is that to drive an external PowerAmp to its maximum capacity, output voltage of PreAmp needs to be same or exceeds the input sensitivity of PowerAmplifier.

Let consider the following scenario in which I have a PreAmp with 1.0V (Yamaha AVR) output voltage and I have PowerAmp with 1.6V input sensitivity (Outlaw monoblock 2220, 200W at 8 ohm). If I use them together how much power my monoblock will be delivering before PreAmp runs out of juice and clips.

The following article was useful but it tells me if PreAmp or Amp are perfectly compatible or not.

Amplifier Voltage Gain Explained – Matching Amp to Preamp

Interested in a separate amplifier? Amplifier voltage gain and sensitivity are important specs to know about. This article explains the concept to help identify how to match your amp to a preamp.

www.audioholics.com

I am more interested in learning how to do these calculations so that I can calculate how much PowerAmp power I am wasting if I happen to match the equipment described above. Pointers will be much appriciated. I am math deficient person. Thank you very much.

 

[Chrispy]

I think you need to work with more than the Yamaha nominal pre-out voltage to make a good decision. Look to actual third party testing where for several brands the capabilities of the pre-out are beyond the nominal figure provided by the manufacturer (e.g. the RX-A6A tested to 4V without clipping at Audioholics).

 

[NTK]

Here is the long way (but straight from the basic electrical circuit laws):

Power = Output_voltage^2 / load_impedance​

Your Outlaw amp is rated at 200 W into 8 ohm load, therefore:

200 = Output_voltage^2 / 8​

or

Output_voltage = sqrt(8 * 200) = 40 volts​

Since the input voltage required to output 40 volts is 1.6 volts, the Outlaw gain is 40/1.6 = 25 times.

If your preamp can only provide 1.0 volt, then your Outlaw can only output 25 volts. Going back to the first formula, then the power output = 25^2 / 8 = 78.1 W.

Therefore, you'll get maximum 78.1 W from your preamp / power amp combo.


Here is the shorter way:

Since we know from the first formula that power is related (proportional) to the square of voltage, therefore, with your Yamaha preamp, the output power will be scaled down by the square of the ratio of the 2 voltages: Power = 200 * (1.0/1.6)^2 = 78.1 W.

 

[DVDdoug]

Yeah... It would be unusual for a preamp to clip at 1V. The maximum output voltage can probably go higher depending on the input voltage.

I am more interested in learning how to do these calculations

I'll give you some more formulas that you can save in a spreadsheet. (You'll have to reformat them from regular text.)

Since power (wattage) is proportional to the square of the voltage (when impedance remains constant) I started with the "basic" 1(squared)/1.6(squared) = 39%.

If you take an electronics class the 1st thing you learn is Ohm's law which describes the relationship between voltage, resistance (or impedance), and current:
Current = Voltage/ Resistance.

From algebra, there are 3 variations depending on what's known or unknown.

(Resistance and impedance are both measured in Ohms and our purposes are generally interchangeable.)

Power = Voltage X Current.
Since current is proportional to voltage, doubling the voltage also doubles the current for 4X the power (or the power is proportional to the square of the voltage).

Using simultaneous equations we can simplify the power calculation:
Power = Voltage(squared)/Resistance or Voltage(squared)/Impedance. (This one is often handy, and of course it be manipulated in case you know the power and impedance and you want to find the voltage.)

Then there's dB, and there are different calculations for voltage & power: The decibel result is the same and a 3dB difference in the electrical signal or the digital level results in a 3dB change in the SPL level (as long as everything stays linear). It's just a matter of how you calculate it, usually depending on if we happen to know the power or the voltage. We usually don't know the impedance load on a preamp so do we don't know the power, and power doesn't have any meaning with digital audio files.

dB = 20 X log (V/Vref)
If we take 1.6V as your reference we can calculate 20 X log (1/1.6) = -4dB. Or if we flip that around and choose 1V as the reference we would calculate +4dB.

dB = 10 X log (P/Pref)

Going the other way...
Voltage Ratio = 10 to the power of (dB/20)

Power Ratio = 10 to the power of (dB/10)

Some numbers that are handy to remember, and you can also use these to check your spread sheet formulas:
3dB is (approximately) a power factor of 2 (+3dB is twice the power and -3dB is half the power).
6dB is (approximately) a voltage factor of 2 and a power factor of 4.
10dB is a power factor of 10.
20dB is a voltage factor of 10.

And something that might be "educational"...
With Audacity you can open a file and reduce the gain by -3dB or -6dB, etc., to see what that much change sounds like. And with -6dB you'll see the wave height cut in half.

I recommend cutting instead of boosting because most files are 0dB normalized (or nearly 0dB normalized) and if you go over 0dB you'll clip your DAC. Audacity itself essentially has no internal limits, but the scale won't show you anything over 0dB. DACs and regular WAV files are also limited to 0dB and will clip (distort) if you "try" to go over. With regular (integer) WAV files, the reference of 0dBFS (0 decibels full-scale) is defined as the maximum you can "count to" with a given number of bits. 24-bit files have bigger numbers than 8-bit files but at playback time everything is scaled up or down to match the DAC.

 

[supertech]

Here is the long way (but straight from the basic electrical circuit laws):

Power = Output_voltage^2 / load_impedance​

Your Outlaw amp is rated at 200 W into 8 ohm load, therefore:

200 = Output_voltage^2 / 8​

or

Output_voltage = sqrt(8 * 200) = 40 volts​

Since the input voltage required to output 40 volts is 1.6 volts, the Outlaw gain is 40/1.6 = 25 times.

If your preamp can only provide 1.0 volt, then your Outlaw can only output 25 volts. Going back to the first formula, then the power output = 25^2 / 8 = 78.1 W.

Therefore, you'll get maximum 78.1 W from your preamp / power amp combo.


Here is the shorter way:

Since we know from the first formula that power is related (proportional) to the square of voltage, therefore, with your Yamaha preamp, the output power will be scaled down by the square of the ratio of the 2 voltages: Power = 200 * (1.0/1.6)^2 = 78.1 W.

You are my hero. I do not believe anyone else could explain in a simpler and more informative way. I do appriciate the longer way. Thank you so much.