7 STEPs Find Out How Much Amplifier Power is Enough


Basically, it mainly depends on headphones' sensitivity and impedance.

For the sensitivity, dB/mW@1kHz and dB/V@1kHz are commonly found on the spec sheet. It represent the acoustical level that the headphone transducer can produces under 1 mini-watt or 1 volt.

For the impedance, the AC resistance of the coil of headphones in ohms. Since impedance depends on the frequency, it is usually specified at 1kHz.

These steps could be applied to both headphone and speaker.


Step 1: Find the Sensitive and Impedance on the specification sheet

Audio-Technica ATH-W1000X


Example: Audio-Technica ATH-W1000X
  1. Sensitive is 100dB/mW
  2. Impedance is 42Ohms


Step 2: Calculate the Loss on the output impedance

Assumption: Output Impedance of the headphone amplifier = 10Ohms


Where
  • Zhp is the impedance of the headphone 
  • Zout is the output impedance of a headphone amplifier


Step 3: Calculate the Voltage corresponding to the stated SPL

Where
  • PSPL is the power corresponding to the stated SPL of the headphone
  • VSPL is the voltage corresponding to the stated SPL of the headphone

Step 4: Calculate the Gain is required to achieve target dynamic range

Assumption: Target dynamic range = 110dB
(Warning: 1 min exposure to 110dB loud music can cause permanent damage to your ear!)



More about frequency and intensity of familiar sound...

Frequency and Intensity of Familiar Sound - The National Acoustic Laboratories


Step 5: Calculate the Output Voltage is required to achieve the target dynamic range


Where
  • Vout is the min output voltage is required to achieve the target dynamic range


Step 6: Calculate the Output Power is required to achieve the target dynamic range


Where
  • Pout is the min output power is required to achieve the target dynamic range


Step 7: Calculate the Operating Voltage (V) is required
Where
  • Vop is the min operating voltage is required to achieve a target dynamic range


Result 

For Audio-Technica ATH-W1000X, amplifier with below spec is good enough:
  • Power output = 12.38mW
  • Operating voltage = 2.27V

(Please refer to Headphone Amp Power Calculator to find out how much amplifier power is enough)

1 comment:

  1. Hi!

    Thanks for you work. There's only one thing I'm not sure about - most amps seems to indicate mW @ amperage, let's say an amp that outputs 130 mW at 300 ohms and 500 mW @ 32 ohm. How am I supposed to find out the operating voltage? It rarely seems to be shown. Why is that?

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