[faultfracture]

After reading Tyll's article on output impedance and how it "EQ's" the headphone to its impedance curve I wanted to figure out a way to mathmatically predict the results on different sets of headphones. I made this spreadsheet with the voltage divider networks discussed by Tyll and added some basic loudness calcs (with constant sensitivity) to try to predict this. These are based on the HD800 that Tyll measured...
 

HD800 (102 DB/V)
Freq	Vamp	Zamp	Zhp	Vhp	db (102db/v)	Diff
1000	1	1	361	0.997238	101.9664
100	1	1	635	0.998428	101.9809	0.014503
1000	1	100	361	0.78308	99.02658
100	1	100	635	0.863946	100.2216	1.195043
1000	1	200	361	0.643494	96.63924
100	1	200	635	0.760479	98.67044	2.031201
PX100-Iii (115 DB/V)
Freq	Vamp	Zamp	Zhp	Vhp	db
1000	0.25	1	37	0.243421	97.81803
100	0.25	1	82	0.246988	97.99492	0.176894
1000	0.25	10	37	0.196809	95.23323
100	0.25	10	82	0.222826	96.74305	1.50982
1000	0.25	20	37	0.162281	92.88747
100	0.25	20	82	0.20098	95.4883	2.600831

 
So the PX100 suffers more of a boost to the point of its impedance peak with only a 20 ohm output impedance than that of the HD800 with a 200 ohm output impedance. How should I correlate these values to figure the boost I could expect over a 1-ohm output impedance with any variable amp output impedance and a headphone's impedance characteristics?

 

[MindsMirror]

  How should I correlate these values to figure the boost I could expect over a 1-ohm output impedance with any variable amp output impedance and a headphone's impedance characteristics?

I don't understand what you're asking here.
 
 
You don't need to calculate the absolute voltage or level of the output, only the relative difference, so you can take out the intermediate calculations involving the absolute voltage level, sensitivity, and SPL.
 
For example, with the HD800 and a 100Ohm output impedance, you only need to calculate:

[ 361/(361+100) ] / [ 635/(635+100) ] = 0.90640 = -0.85360 dB

 
 
 
It appears you have made some mistake in the conversion to decibels. The formula for the conversion to dB is:

20*log₁₀(V₁/V₂)

 
Going through the numbers and intermediate steps that you did, you should have gotten this:

0.78308 V = -2.12388 dBV = 99.87612 dB SPL
 
0.863946 V = -1.27026 dBV = 100.72974 dB SPL
 
Diff = 0.85362 dB

 

[faultfracture]

Thank you so much for your help! I do see now that I fat fingered the constant to 28 instead of 20 in my loudness calcs. It is good to see that by changing that constant that my calculations were correct but in a roundabout way that could be eliminated with just the voltage ratio in a relative approach! I've simplified things some with this below, this is more of what I wanted to have for a spreadsheet! (my question that was a little vague before
 

Amplifier Output Impedance:	200	ohm
Headphone Impedance:	361	ohm	at	1000	Hz
Peak Imp. 1	635	ohm	at	110	Hz
Peak Imp. 2	440	ohm	at	20000	Hz
Peak Imp. 3		ohm	at		Hz
Nominal Loudness:	-3.81	db	at	1000	Hz
Gain at Peak 1:	1.45	db	at	110	Hz
Gain at Peak 2:	0.57	db	at	20000	Hz
Gain at Peak 3:	#DIV/0!	db	at	0	Hz

 

[faultfracture]

Then I wanted to be able to use a spreadsheet like this to compare other cans (especially armature driver iems) with higher output impedance... Like this example:
 

Headphone Name:	Marley Legend
Amplifier Output Impedance:	10	ohm
Headphone Impedance:	20	ohm	at	100	Hz
Peak Imp. 1	70	ohm	at	1900	Hz
Peak Imp. 2	100	ohm	at	6500	Hz
Peak Imp. 3	300	ohm	at	20000	Hz
Nominal Loudness (vs 1 ohm OI):	-3.10	db	at	100	Hz
Gain at Peak 1:	2.36	db	at	1900	Hz
Gain at Peak 2:	2.69	db	at	6500	Hz
Gain at Peak 3:	3.24	db	at	20000	Hz

 
I see that this single balanced armature might benefit from a little more than 1 ohm output imepdance as its measured response by Tyll normally is pretty dark! Thanks again!

 

[reginalb]

Not to be a pedant, or anything, but headphones have input impedance, as they don't output anything. So, are you just trying to get at the same thing that you could get by measuring a test tone, that is, the frequency response of the source with your headphones as a load?

 

[faultfracture]

If you could hook me up with a reasonably priced acoustic measuring setup id be all over it!

 

[reginalb]

If you could hook me up with a reasonably priced acoustic measuring setup id be all over it!

 
For frequency response I've been using RMAA, and a Behringer UCA222 (which was $30 off Amazon). Seems to work pretty well. But it's just going to be accurate for frequency response of the DAP/Amp/DAC, not terribly accurate for anything else. 

 

[castleofargh]

I second the idea to get a few resistors and try yourself if what you're looking for is the actual result. predicting the voltages works fin, after all electricity isn't such a mystery. but I found that my estimates almost never fit my measurements with IEMs, I imagine in part because not everything is fully resistive, but also because my pair or IEM didn't necessarily have the same impedance response as measured online on some other pair. sometime the difference is negligible, but sometimes not. when fooling around to tune a frequency response, being off by 1ohm on the IEM can be a lot.

now just to guess the overall signature, predictions based on impedance and voltage work perfectly fine and I still use that before buying something if I see a messed up impedance curve online.

and if you want more than only the electrical measurement, you can use even the crappiest microphone. if the purpose if only to measure variations from one impedance to another into the IEM, it should work fine(at least in the midrange).