How do I calculate sound pressure level (dB SPL) from headphones at a specific setting on my sound card?

Question

I am using headphones with sensitivity 102 dB SPL / 1 Vrms with impedance of 300 ohms. For a particular volume knob setting on my sound card embedded with a headphone pre-amplifier, I would like to determine the output in dB SPL from the headphones.

I played out a calibration tone of 1 kHz of peak amplitude 1 V (RMS 0.707 V). Using a multimeter, I measured the Open Voltage (Vo) from my sound card for different values on the volume knob. I then measured Voltage with the load (VL) connecting headphones to the soundcard for the same values on the volume knob.

I would like to determine the output impedance of the sound card (pre-amplifier) along with the Voltage input in order to get the power of the amplifier in driving the headphones. I am stuck here, can anyone help? (I can use the power to determine the value in db SPL for a particular volume knob value.)

Open Voltage (Vopen)	Voltage across load (VL)	Source Resistance (Rs)
0.0795	0.068	50.73
0.1	0.085	52.94

Answer 1

Since you already measured how much Vrms is sent to phones when they are connected, you can just convert that Vrms to decibels by using the 1Vrms as reference, and since you know the reference level of 102 dB SPL at 1 Vrms, just add the reference decibel level to your calculated decibels.

E.g if you measure 1 Vrms going to phones, you know that equals 102 dB SPL. 2 Vrms is double so +6 dB to reference. 0.5 Vrms is -6 dB to reference.

You don't need the phone impedace, output impedance or open voltage levels for this.

Answer 2

The output impedance of your sound card headphone should be close to zero but you can check.

• You have the open circuit voltage, \$ V_O \$.
• You have the voltage into 300 Ω, \$ V_{300} \$.
• The output impedance and the speakers form a potential divider.

$$ V_{300} = \frac {300}{R_S + 300} V_O $$

Therefore the source resistance will be given by

$$ R_S = \frac {300}{V_{300}} V_O - 300 $$

I'm not sure how much value this will be as the impedance will be frequency dependent. You could try different values such as 100 Hz, 1 kHz and 10 kHz to see. Remember that most multimeters are designed for power frequencies and won't be much use above 100 Hz.