On the Effectiveness of a Simple Headphone Amplifier

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If the input-output relation is modeled as a cascaded transfer function H(s) = O(s)Hl (s)I(s) where O(s) is the soundcard line-out transfer function, Hl (s) is the voltage transfer function of the load and I(s) is the soundcard line-in transfer function, the line-in and line-out errors can be factored out, as long as the voltage to be measured is a linear function of the line-out voltage. It is found that under such setup, the input signal has a peak value of 0. The measurement amplifier circuit is shown in Figure 2 and it has a 15. 5 dB within audible range; Apple EarPods shows a 1 dB uniform voltage drop at all frequencies, for it having the smallest impedance among all products tested. As for the amplitude, Etymotic ER4SR, Sony EX, Superlux HD681 and Beats Studio perfectly meets the designed voltage gain of −9. 3 0 |Hsl | [dB] −5 −10 Etymotic ER4SR Sony EX Apple EarPods Superlux HD681 Beats Studio −15 −20 102 103 Frequency [Hz] 104 103 Frequency [Hz] 104 0 6 Hsl [rad] 2 −2 102 Figure 4: Soundcard loaded voltage transfer function for various headphones and earphones. Vl (s) = Vs (s) Zl (s) Rs + Zl (s) (1) Assuming the impedance of the load is constant across frequency, and in our case plugging in the values Rs = 40Ω, Zl = 45Ω, the loaded voltage is expected to be 53% of the input according to Eq. On the other hand, the phase distortion is generally below 1 rad in audible range, and almost flat under 10 kHz. In practice the result could be worse as the impedance of speakers, especially earphones often changes with respect to frequency; in such case the voltage gain of the voltage divider basically becomes a damped version of the load impedance, giving non-uniform amplification and phase shifts on the audio spectrum. For most of the headphones and earphones tested, the influence from the load is reduced to a negligible level. The test signal is a 10 Hz to 48 kHz chrip signal at 0. It comes clear that Hfb = O(s)I(s), in terms of the cascaded input-output model. 5 when the rms voltage at the measurement port is 0. Results are discussed in the end and serveral implications on practical aspects of high-fidelity audio playback are listed. Unless otherwise noted, in this report the data is obtained form the left channel as the two channels should be identical. Measurement Calibration The filtering and DAC/ADC components in the soundcard could introduce a slightly non-flat frequency response to the measured signal. 6 Although it is important to note that in the case of small impedance loads (≤ 10Ω), voltage drop is observed before reaching the maximum output current. However, the transfer function of ER4SR has a spectral slope that increases by 4 dB at high frequency and a 1 dB bump at 2. 2 Performance Evaluation The headphone amplifier circuit in Figure 6 has an input impedance of 6 kΩ. A refined test procedure should adjust the input level with respect to the sensitivity of the device being tested