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Headphone sensitivity and cross-talk.


Headphone sensitivity.

Headphone sensitivity is specified as dBSPL @ 1 mW or as dBSPL @ 1 V.
Translating between the two:
dBSPL(V) = 10 * LOG * ( 1000 / R ) + dBSPL(mW) or
dBSPL(mW) = dBSPL(V) - 10 * LOG * ( 1000 / R ), where:
dBSPL(V) is the sensitivity in dBSPL @ 1 V
dBSPL(mW) is the sensitivity in dBSPL @ 1 mW
R is the nominal headphone impedance.

A 32 Ω headphone with a sensitivity of 100 dBSPL @ 1 mW has a sensitivity of:
10 * LOG ( 1000 / 32 ) + 100 = 115 dBSPL @ 1 V

Headphone cross-talk.

This is a very simplified calculation for the cross-talk in 3-wire headphone connections.

Headphone equivalent circuit.
Fig.1: Equivalent circuit for 3-wire headphone connection.

Ro: Amplifier output impedance. See amplifier data sheet.
Rg: Amplifier ground output impedance. This should be a very low value.
Rc: Connector resistance. This is normally only specified as a maximum value ( typically 50 mΩ ).
Rw1: Common cable resistance for the 2 channels.
Rw2: Cable resistance from output to each channel.
Rw3: Cable resistance from each transducer to common ground point A.
Rh: Nominal transducer impedance.

Assume one channel has signal and the other is muted and find the voltage in point A:
Rchannel = Ro + Rc + Rw2 + Rh + Rw3
Rground = 1 / ( 1 / ( Rg + Rc + Rw1 ) + 1 / Rchannel )
VA = Rground / ( Rground + Rchannel )
Find the voltage in the muted transducer:
V = VA * Rh / Rchannel

You can download a spread-sheet with the calculations here.

Table 1: Some calculated values.
1 Ω10 mΩ50 mΩ32 Ω0.33 Ω (1)0.33 Ω (1)17 mΩ (2)40 dB
1 Ω10 mΩ50 mΩ32 Ω00.33 Ω (1)0.33 Ω (1)65 dBA 4-wire connection with the 2 GND
wires connected in the 3-way connector.
1 Ω1 Ω50 mΩ32 Ω0.33 Ω (1)0.33 Ω (1)17 mΩ (2)25 dBA "3-channel" amplifier.

Note 1: 2 m 0.1 mm² wire.
Note 2: 10 cm 0.1 mm² wire.

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