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Audient Headphone Amplifiers & Safe SPL Levels

The impedance of headphones can be a tricky concept to get your head around and many people are left wondering how much power is really needed to drive their favourite headphones.

The impedance of headphones can vary from 16Ω up to 600Ω, although most commonly you will find 32Ω and 600Ω types. this comes down mostly to the application in which the headphones are designed to be used. Lower impedance headphones typically require more current drive instead of voltage output, and are often supplied with portable battery powered devices such as phones and MP3 players, where voltage swing is limited, but some current delivery is available with modern driver IC chips. These are often your everyday headphones that you might use on the bus or while kicking back on the sofa, but some excellent studio headphones are also available in 32Ω - Grado for example.

Higher impedance headphones generally need greater voltage from the source to drive them  - which can be found in beefy headphone amps and audio interfaces with higher power rails, such as our very own iD14 & iD22. Higher impedances in headphones can often be caused by using thinner wire and more turns of wire in the voice coil. This translates to a stronger magnetic force required to drive the speaker diaphragm. In well designed headphones, this means a more accurate reproduction of audio as the stronger magnetic force gives more control over the moving diaphragm.

There are a few formulas that will come in useful when talking about powering headphones;  

  • R = V/I  (Resistance = Voltage / Current) or V = IR (Voltage = Current x Resistance)
  • P = IV  (Power = Current x Voltage) 

From these formulas, we can see that resistance (impedance) and power are related and as power is a product of voltage * current and resistance or impedance directly influences voltage or current transfer - we should treat a headphone amplifier as a Power Amplifier with a rating in Watts for a given load resistance. As impedance is a complex combination of resistance, capacitance and inductance (the coil in the headphone driver) - the nominal rating (such as 32Ω) will only be given for one frequency point.

The output of a headphone amplifier in its most simple form - a potential divider. A potential divider, if you are not familiar with this term, is one of the main building blocks of electronics and allows us to split voltages using resistors. Using two or more resistors, the voltage is split as a ratio of the values of the resistors.

 

For example, imagine a potential divider with a 1Ω resistor in series and and a 2Ω resistor to ground, with an output taken across the 2Ω resistor. This circuit is supplied with 1 Volt.

The output voltage is calculated by 1V * (R2/(R1+R2)) = 1V * (⅔) = 0.67V, or effectively it is split into ⅓ drop across R1 and ⅔ delivered to the load of R2 and thus available at the output.

If you then replace the second resistor with the impedance of a set of headphones it can be seen how the impedance of the headphones affects the voltage transfer, which in turn affects the power delivered to the load, which in the case of headphones will dramatically affect the dBSPL volume that is produced.

Using 32Ω and 600Ω headphones as examples with a 22Ω headphone amplifier output (iD14) and a maximum drive voltage of +12dBu = approx. 4V peak:

Impedance of Headphones

R1 = 22Ω (iD14 headphone output)

Voltage across R1

Voltage delivered to R2 (headphones)

Power delivered to R2 (headphones)

32Ω

1:16

1.63

2.37

176mW

600Ω

1:600

0.14

3.86

25mW

This shows that as the impedance of a set of headphones increases, the amount of voltage delivered to them via the potential divider is increased, and thus the power applied is reduced. Real world applications are never this tidy however and are dependent upon impedance and frequency variations - so the voltage differences may be even more profound.

Furthermore, since the voltage is changing relative to the impedance, the current must also change in order to keep power constant as according to the formula;

Power = Voltage x Current

This is why lower impedance headphones will draw a higher current than high impedance headphones and how thinner wires in a high impedance voice coil can be used without burning the wire out. We need to ensure that a good headphone amplifier design does not offer lots of voltage gain, but instead combines moderate voltage gain with increased output current drive capability to ensure power can be transferred to the low impedance headphones (Watts = energy).

(More information about impedance and how it affects your audio can be found here.)

To test this, we set up an iD14 with an iMac running Logic Pro 9. We then used a signal generator to produce a pink noise signal as loud as we possibly could without clipping using the iD14’s headphone amplifier. We used pink noise as it gives the best example of how the human ear perceives loudness. We then plugged in a series of headphones that we had lying around the office. Next, we placed a C-weighted SPL meter against the ear cup of the headphones and took a reading of the maximum SPL.

The results can be seen below;

Phones

Impedance

Sensitivity

SPL (dB c-weighted)

AKG K141

55 Ohms

101dB @ 1mW

100dB

ATH - M50

38 Ohms

99dB @ 1000mW

102dB

AKG K240 DF

600 Ohms

88dB @ 1mW

85dB

Grado SR325

32 Ohms

99.8dB @ 1mW

98dB

(Note: Although we did manage to get the AKG K240 DF up to 92dB before it clipped, we decided to use the lower value to keep the test fair) 

It can be seen that headphones with lower impedances can be driven somewhat louder by the amplifier with the 600 Ohm headphones being a little quieter than the others. 

The iD14 can quite easily push headphones to quite high volumes, more than enough to cause discomfort if listened to for long periods of time. For people working in audio or music, good hearing is one of the most valuable assets you can have. However, many people tend to listen to audio loud enough to cause hearing damage which could possibly become permanent.

The National Institute for Occupational Safety and Health has series of recommendation on how long an individual can be safely exposed to sustained SPLs before hearing damage could occur.

Sound Pressure Level (dB)

Safe Exposure Time

82

16 Hours

85

8 Hours

88

4 Hours

91

2 Hours

94

1 Hour

97

30 Minutes

100

15 Minutes

103

7.5 Minutes

106

3.75 Minutes

109

1.8 Minutes

112

0.9 Minutes

115

0.4 Minutes

At the highest levels, the iD14 could produce levels that could cause hearing damage after just only a few hours or less is listening to audio with a small dynamic range. Even more dynamic audio can cause issues if listened to over a long period of time.

It is therefore important during long sessions, that lower levels are used for monitoring and listening to ensure that hearing damage doesn't occur. If exposure to high SPL’s cannot be avoided, then its important to take frequent breaks or find other measures to protect your hearing because a set of good ears is most important part of any set-up. 

Conclusion 

The bottom line is, that iD14 (and also iD22) is more than capable of driving any professional headphone on the market loud enough for all comfortable and safe listening.


Be safe, preserve your ears! Enjoy life.

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