About the Ohms law.
It still applies of course.
One would expect double the power when the impedance halves though.
But that would only be so if the power supply wouldn't sag in output voltage (or have a higher internal voltage drop) under higher current loads.
Ohms law tells me that into 8 Ohm it can deliver 70W (both channels driven most likely).
This means the output voltage under continous load is approx 23.5V.
into 4 Ohm it can deliver 100W into 8 Ohm (both channels driven most likely).
This means the output voltage under continous load is approx 20V.
The output voltage thus drops to 20V when double the current is drawn.
The HD650 and LCD2 sound about equally loud when driven from a voltage amplifier (both around 103dB at 1V).
That is using an amplifier with a low output R.
A power amp + low Ohmic resistors = low output R as well.
So the HD650 and LCD2 require equal voltages BUT because the impedances differ the efficiency differs.
But ONLY the efficiency in Watts, not so much the efficiency in voltage.
The DT1770 has a higher efficiency so will play slightly louder.
The question now is how LOUD do you want to go and what voltage would be allowed.
Power ratings dictate this.
The DT1770 is rated at 200mW, the HD650 at 500mW the LCD2 at 15W
So the DT1770 would have to be leading as that one needs to be limited in power.
BUT a headphone can easily handle double the music power because music is not continuous.
So 500mW is no problem.
Max 11V peaks is what it works out to.
The HD650 can handle 17V peaks.
LCD 2 can handle 27V so can be connected directly.
Now the calculations above are all about peak voltages.
The amplifier can probably reach 30V peak levels
To protect the DT1770 so it limits at 11V means a factor 3 in output voltage reduction is needed.
The other headphones thus will also be limited to 11V peak = 7.5V RMS.
The DT1770 will thus be safe as will the other headphones as it will be limited at 225mW continuous.
The HD650 will be limited to 175mW (Ember will be louder)
The LCD2 will be limited to 1.3W (About the same as Ember)
That means that peak SPL's will be reached at:
The DT1770 peak = 125dB SPL (pain limit)
The HD650 will be limited to 175mW = 120dB
The LCD2 will be limited to 122dB
Given that high quality recording has a Dynamic Range of 15dB that means that average levels of 105dB can be reached.
This is extremely loud (90dB average is already pretty loud !)
a factor 3 in voltage reduction = -10dB.
Then there is the question of noise.
Most power amplifiers are designed to drive rather insensitive speakers and noise is not an issue on speakers unless you have your ear against the tweeters.
BUT headphones are way more sensitive than speakers so the noise levels of a quiet speaker amp may be quite audible when not attenuated.
-10dB noise level lowering may not be enough.
The there is the question do we really need deafening levels when the volpot is at maximum setting ?
Do we rather not need a usable volpot range ?
To get a better volpot range a reduction of 20dB (10x attenuation) may possibly be better though.
In that case 110 dB peak levels will be reached.
This attenuation level may be needed to get better volume pot adjustment range and to ensure there will be no audible noise.
So I will make recommendations for a 10dB attenuator and a 20dB attenuator working from a 70W/8 Ohm power amp:
Where U1 is the amplifier output voltage (red to the top, black to the bottom) and U2 is the headphone plug (top is ring for right channel, or tip for left channel) and the bottom is the return (sleeve)
The load on the amplifier will be light so the amp doesn't need to work hard.
5W resistors will be used where R1 will dissipate the most.
with about 20V on it R1 needs to be 68 Ohm when the power is continuous.
BUT music is not continuous so the resistance value can be lower.
This means
R1 can be
33 OhmFor both the 10dB and the 20dB version R1 will be the same.
To have a factor 3 reduction (-10dB)
R2 needs to be
10 Ohm.
The output R will be 7 Ohm which is low enough (but not nearly as low as Ember) and the amp will have slightly less power than Ember.
To have a factor 10 reduction (-20dB)
R2 needs to be
3.9 OhmThe output R will be 3.5 Ohm.
So there you have it.
R1 = 33 Ohm (5W) and R2 could have values between 10 Ohm and 3.9 Ohm depending on how much attenuation you want/need.
Thus buy 2x 33, 2x 10 and 2x 3.9
resistors don't cost that much.
The box and connectors will define the build costs.
For the HD700 (and comparable power amp give or take 30W) R2 should probably be between 8.2 and 3.3 Ohm depending on potmeter usage/noise reduction.