Analytical table and recommendation for using headphones with different types of amplifiers based on the measured characteristics
About
For whom RAA made this: for those who is hard to understand graphs or/and for who want to see brief graph analysis in common words. RAA developed an algorithm to calculate the compatibility of sources and headphones. This table is the first step to create a simplified general report. We want to make two reports: first short simplified report for simple user and second report for a pro.
Such the algorithm became possible due to:
 Measuring the sensitivity of headphones and power characteristics of sources.
 Determination of the average statistical data for different headphones and sources (amplifiers).
 Direct comparison of headphones live and comparison of the received data after measurements.
From the idea of the table to the final implementation took about three years. And gradually the algorithm is being improved for modern products.
In this general table, we show the most common variations of sound sources and the field of headphones application. The compatibility rating is similar to car analysis based on its ground clearance  on which road the car will move optimal without evaluating the class of the car. On a race car of Formula 1 is difficult to drive on a ground road. The same foolish idea to use caterpillar allterrain vehicle on a highway.
The table allows to estimate the most complete opening of the potential of headphones while use with amplifiers of a similar class, but with different power parameters.
Analysis and recommendations for ASTRO Gaming A40 based on the measured characteristics 
Sources (what the headphones to be connected) 
Areas of using headphones 
Sensitivity 
Impedance 
The type of acoustic design 
Total 
113.30 dB/V SPL 
62.22 ohm 
Semiopen 

Lowpower sources
6dBV/15dB(mA):
a smartphone a player a tablet Examples 
Home or studio, where sound from the headphones does not bother anyone 
5 ★★★★★ 
5 ★★★★★ 
3 ★★★☆☆ 
4.3 ★★★★☆ 
Office and home, where people should not hear the sound from the headphones 
5 ★★★★★ 
5 ★★★★★ 
3 ★★★☆☆ 
4.3 ★★★★☆ 
Street with active traffic 
5 ★★★★★ 
4 ★★★★☆ 
3 ★★★☆☆ 
4.0 ★★★★☆ 
Metro (subway), public transport 
4 ★★★★☆ 
3 ★★★☆☆ 
3 ★★★☆☆ 
3.3 ★★★☆☆ 
Midpower sources
6dBV/27dB(mA):
a computer with sound card a HiFi player a portable amplifier a mixing console Examples 
Home or studio, where sound from the headphones does not bother anyone 
5 ★★★★★ 
5 ★★★★★ 
3 ★★★☆☆ 
4.3 ★★★★☆ 
Metro (subway), public transport 
5 ★★★★★ 
5 ★★★★★ 
3 ★★★☆☆ 
4.3 ★★★★☆ 
Recording a voice or instrument in the studio 
5 ★★★★★ 
5 ★★★★★ 
3 ★★★☆☆ 
4.3 ★★★★☆ 
Hipower sources 18dBV:
a home system with a headphone amplifier Examples 
Home or studio, where sound from the headphones does not bother anyone  5 ★★★★★ 
5 ★★★★★ 
3 ★★★☆☆ 
4.3 ★★★★☆ 
Office and home, where people should not hear the sound from the headphones 
5 ★★★★★ 
5 ★★★★★ 
3 ★★★☆☆ 
4.3 ★★★★☆ 
In the example below, the conditions for a low power source with an output level of 6 dBV, 5 mA under conditions of high ambient noise and the necessary noise insulation will be considered.
Optimum volume level
The combination of headphones and a source is ideal if it is possible to get the optimum volume level for listening to music.
The sensitivity parameters of the headphones and the power of the amplifier are not indicated to the musical signal. It is common that parameters are indicated to the sine. This gives distorted data while we calculate the sound pressure for music by the power of the amplifier and the sensitivity of the headphones.
In RAA we set a comfortable volume level and after determined, with which level it corresponds to the characteristics of headphones and amplifiers. At fixed values of the sound level meter, an average of 8590 dB SPL resulted in the equivalent of 110 dB SPL, if we summarize the output voltage at the amplifier output with the sensitivity of the headphones.
Analysis of the sensitivity of headphones
The optimal volume level we determined for ideal conditions, when there is no outside noise. In reality, the situation is different and an amendment is made for each specific situation.
If the headphones is with noise cancellation, the level is reduced by 6 dB, and with a partial noise cancellation by 3 dB.
The surrounding situation is estimated by a factor from 0 to 2. Then it is added to the optimal level by multiplying the coefficient by 6 dB.
Optimal = SPL
_{Optimal} + Environment•6  Noise cancellation
where
 SPL_{Optimal} = Optimal baseline 110 dB SPL
 Environment – noise environment factor
 Noise cancellation – amendment noise isolation headphones
Having received the value of the optimal level, we make an estimate of the capabilities of the source, based on its power parameters.
We can have two variants of poor compatibility: the source is too quiet or too loud.
For example, for headphones with partial noise insulation (semiopen type) in a noisy subway train environment, the optimal volume level will be:
Optimal = 110 dB SPL + 2•6 дБ – dB = 122 dB SPL
A source is too quiet
A source is too quiet and can not provide the required volume with specific headphones.
Calculate the difference between the source and the optimal level.
Delta = Sensitivity + Amp Voltage  Optimal
where
 Sensitivity  Headphone sensitivity of voltage
 Amp Voltage – Maximum voltage level in dBV
 Optimal – Previously calculated optimum required level
Mark = 5 +[Delta/6]
For example, for headphones with a sensitivity of 113.3 dB/V SPL and a player with a level of 6 dBV will be:
Delta = 113.3 dB/V SPL + 6 dBV  122 dB SPL = 14.7 dB
Thus, the maximum volume level differs from the desirable by 14.7 дБ.
Mark = 5[ 14.702875873197/6] = 5[2.4504793121995] =5 2 = 3
On a fivepoint scale, the difference by 6 dB decreases by one.
The source is too loud
A lot of modern devices use digital volume control, thus when you set a small volume level, the background noise at the output does not decrease and becomes more noticeable against the background of the music being played on a small volume level. Another case is devices with an analogue volume control; there is often an imbalance in volume level between the right and left channels due to imperfections of typical variable resistors that control the volume level.
If the previously calculated Delta is positive and no more than 20 dB, then the mark is 5 on a fivepoint scale. If Delta is over 20 dB, the mark is reduced by one for every 6 dB.
Mark = 5[(Delta – 20)/6]
For example, if the Delta was 30 dB, the mark would be 4.
Mark = 5 [(3020)/6] = 5 [10/6] = 5[1.6666666666667] = 51 = 4
Analysis of the headphones impedance
When analyzing the headphones impedance, we take optimum volume level (Optimal, see above) and estimate the source according to the maximum current, without considering the voltage. If source give enough current or have reserve by current, the mark is 5 on a fivepoint scale. If the current is not sufficient, the estimate is reduced. In those cases where the current level is insufficient, the sound of the source becomes less quality.
First consider the required voltage level at the source.
dBV = Optimal  Sensitivity
where
 Sensitivity  Headphone sensitivity of voltage
 Optimal – Previously calculated optimum required level
In our example, this will be: 113.3 dB/V SPL  122 dB SPL = 8.7 dBV
Convert voltage from dBV to V.
V = 10
^{8.7dBV/20} = 2.7 V rms (You can use
online calculator)
Now consider the current
I
_{Optimal} = 1000•V/R
where
 R – Resistance of headphones, in our example the resistance is 62.2 Ohm
 V  Voltage in volts
I
_{Optimal} =1000* 2.7 В/ 62.2 Ом = 43.8 мА
We compare the current with the maximum for the source in dB. Suppose that we have a lowpower smartphone with an output current of not more than 5 mA (when working is equivalent to class A)
The ratio of the currents will be:
Delta_I = 20•Log
_{10}(I
_{Sours}/I
_{Optimal}) = 20•Log
_{10}(5 мА/43.8 мА) = 18.8 дБ
By analogy with voltage, we calculate the mark, where a decrease by 6 dB decreases mark by 1 star.
Mark = 5 [Delta/6] = 5+[18.8/6] = 5[3.1407839807446] = 5  3 = 2
Mark of noise isolation headphones
The mark of headphones noise isolation depends from external conditions and requirements to noise isolation. For example, for a cyclist on the street among machines, noise insulation is contraindicated. In the subway in a noisy environment, noise insulation is a must.
 If the headphones have noise isolation and it is needed, then the mark is 5.
 If there is noise isolation and it is not needed or vice versa, there is no noise isolation and it is needed, then a mark is 1.
 For headphones with a partial noise isolation mark is 3.
In our example, headphones is semiopen and noise isolation is needed, thus the mark is 3
The final mark is the arithmetic mean of the three marks:
The final mark = (3 + 2 +3)/3 = 2.7