Sound output of the Raspberry Pi

© 2014 Marcel Müller

Abstract:
There are many statements about the bad analog sound output of the Raspberry Pi around. Most of them are predication rather than knowledge. Let's come clean and add some facts!
Short answer: there are two things the Raspberry suffers from: enough bits and a reasonable reconstruction filter. Everything else is OK for audio playback.
There is a work around available for the reconstruction filter but not for the limited resolution.

Topics: frequency response, signal to noise, resampling, DC offset, reconstruction filter, measurement equipment, contact

Frequency response and aliasing

Fig. 1: frequency response of Raspberry Pi's analog sound output, measured at 48 kHz sampling rate and white noise at -3 dB FSR for the left channel and -23 dB FSR and inverted gain for the right one. The FFTs are smoothed by a Blackman-Harris window function.
left channel, right channel, FFT of left channel, FFT of right channel

From the result to the right it is obvious that there is no reconstruction filter behind the ADC except for a simple capacitator. The 48 kHz sampling rate of the DAC is clearly visible in the output. This results in significant high frequency noise up to ≈ 80 kHz and an amplitude drop of up to 5 dB at the Nyquist frequency (24 kHz). All frequency components above 24 kHz are mirrors of the audio signal (aliasing).

Hopefully your audio equipment is not capable of reproducing all this high frequency noise. It will drive your pets crazy and put unexpected power to your tweeters. Fortunately most electrodynamic tweeters will have higher impedance at these frequencies and so add some damping. But be careful if you feed the output to a Piezo tweeter. This one has very low impedance at high frequencies. Amplifiers usually dislike low impedance together with output power (at the relevant frequencies).

See reconstruction filter for a way to compensate for the high frequency noise and also the sinc degraded response.

Fig. 2: frequency response of Raspberry Pi's analog sound output, measured at 24 kHz sampling rate with 50 Hz bandwidth limited white noise at -3 dB FSR. The right channel gets the inverted signal. Additionally the right channel drives a load of 100 Ω while the left channel is left at high impedance. The FFTs have a linear Y axis and are smoothed by a Blackman-Harris window function. The M3 graph shows the relative amplitude of right and left channel.
left channel, right channel, FFT of left channel, FFT of right channel, FFT right / FFT left

Low frequency response and output impedance

There is no evidence of any significant high pass filtering done by the sound output. The response is perfectly flat. To show whether this also applies to lower impedance inputs I put a load resistor of 100 Ω to the right channel only. Fig. 2 shows the effect. The cut of frequency becomes ≈ 3 Hz which corresponds to a coupling capacitor of 470 µF (most PC sound card have less). The output is obviously intended to drive headphones directly.

Note: I had to reduce the sampling rate to 24 kHz (which does not impact this measurement) because the Raspberry's FFT library cannot deal with more than 131,072 points.

Signal to noise and distortion

Fig. 3: frequency response of Raspberry Pi's analog sound output, measured at 48 kHz sampling rate and 1 kHz sine wave signal at -3 dB FSR. The right channel gets the inverted signal. The FFTs are smoothed by a Blackman-Harris window function.
left channel, right channel, FFT of left channel, FFT of right channel
Note: the regular pattern at the floor of the left channel's FFT with 250 Hz repetition has no special meaning. The amplitude is in the order of 1 LSB in the internal representation. It is simply round off noise during the FFT calculation in the scope that happened to have some structure.

How linear is the output?

Fig. 3 pink graph shows the result when playing a 1 kHz sine wave. The only significant distortion is the 3^rd order harmonic (H3) at ≈ -53 dB.

Unlike other sound devices at low output levels the non linearity increases (see green graph). It is quantization noise. But is must be somehow asymmetric because of the even harmonics. Still the amplitude is below -53 dB (of the reference signal) but for the 7^th order harmonics that is not that pretty. Practically it will be less when using odd frequencies like 1.01 kHz which causes most of the harmonics except for H2 to vanish. From the level of the distortion I would guess that there are about 10 to 11 bits available for output. This is in the order of the first generation CD players.

There is an interesting side effect of the way the Raspi's DAC works. If you lower the sampling frequency of the 1 kHz test tone to 24 kHz the THD decreases by about 6 dB. This is because of the fixed PWM frequency (98 MHz) of the 1 bit DAC. Having a lower sampling rate the additional time can be used to add another bit of resolution which results in 6 dB less quantization noise.

Fig. 4: frequency response of Raspberry Pi's analog sound output, measured at 48 kHz sampling rate and 1 kHz sine wave signal at 0 dB FSR. The right channel gets the inverted signal. The FFTs are smoothed by a Blackman-Harris window function.
left channel, right channel, FFT of left channel, FFT of right channel

Overdriving

The situation changes dramatically if you raise the amplitude to 0 dB FSR. This causes the output to overdrive and odd harmonics with significant level appear. The analog output is not capable of driving the entire value domain of 16 bit samples. It saturates at ≈ 1,1 V_SS.

This is a bad news because many pop songs are normalized to 0 dB FSR you will like run into this pitfall. 0 dB FSR is a bad idea for other reasons (see loudness war) but it is reality. However, taking back the volume by only 1 dB solves the problem. There is no significant distortion at -1 dB FSR.

Resampling

Fig. 5: frequency response of Raspberry Pi's analog sound output, measured at 44.1 kHz sampling rate and white noise at -3 dB FSR for the left channel and -23 dB FSR inverted for the right one. The FFTs are smoothed by a Blackman-Harris window function.
left channel, right channel, FFT of left channel, FFT of right channel

Most audio material around is sampled at 44.1 kHz rather than 48 kHz. So what about 44.1 kHz playback?

Obviously the playback of the RPI is always at 48 kHz and the resampling is done in software. Probably the video core does the job because I can't see any significant CPU load (in contrast to software resampling by the PulseAudio daemon).

The good news is that the used resampling algorithm does it's job quite well - better than the following 48 kHz DAC by far. The low pass filter starts at 18 kHz and drops almost to zero at 22 kHz. The cut-off frequency is about 19 kHz. That's OK for audio playback.
Now the bad news: I don't know any reason why the Raspberry cannot play 44.1 kHz natively.

Fig. 6: frequency response of Raspberry Pi's analog sound output, measured at 44.1 kHz sampling rate and 15 kHz sine wave signal at -3 dB FSR for the left channel and -23 dB FSR inverted for the right one. The FFTs are smoothed by a Blackman-Harris window function.
left channel, right channel, FFT of left channel, FFT of right channel

And what about resampling artifacts?
Well, there are some. But don't worry, you will survive them. The 15 kHz test signal in Fig. 4 has an aliasing frequency at ≈ 3 kHz. At lower amplitude quantization noise comes into play as already mentioned above.

DC offset

Fig. 7: startup of playback of 50 Hz sine wave at Raspberry Pi's analog sound output, measured at 48 kHz sampling rate at -3 dB FSR: left channel, right channel

The Raspberry Pi has a DC offset at the output. Normally this is compensated by decoupling capacitors. However, the bias vanishes when playback has completely stopped. This caused popping sounds. Newer firmware compensate for that by slowly changing the bias to move the frequencies into the subsonic range of 5 Hz and less. Although this is a hack, it works as expected. You wont hear anything on start of playback. You simply shouldn't care about this topic.

Fig. 7 shows how the offset built up after start of playback. After about 1 second everything is done.

Cross talk and symmetry

I got no indication that either cross talk or differences between the left and the right channel are relevant in any way.

Build a reconstruction filter

Fig. 8: reconstruction filter for analog output of Raspberry Pi.

The missing reconstruction filter can be added externally with reasonable effort. The circuit in fig. 8 will provide the missing filter. It is a second order Sallen-Key filter with f₀ = 19.6 kHz and Q = 1.23. It has been optimized exactly for the Raspberry Pi not for any other device. Beside the compensation for the sinc function it also takes care of the built-in low-pass with 3 µs time constant.

• You need two instances of the circuit. One for the left channel and one for the right.
• One NJM4558 is sufficient as it contains two operational amplifiers. Other 4558 clones like RC4558 (RCA), LM4558 (National/TI) will do their job as well but the NJM4558 from New Japan Radio is one of the cheapest. But avoid very simple opamps like LM358. If you need to drive headphones directly replace the chip by the power opamp NJM4556, but I don't recommend that because the sound quality of the Raspberry is not sufficient for headphones.
• Be sure to use low tolerance capacitors for the filter, i.e. the 3,3 nF and the 20 nF. 5 % tolerance should be fine. If you can't get 20 nF use two with 10 nF in parallel.
• The circuit need a negative supply voltage. The Raspberry Pi only has positive supply. So you need either some power supply that provides negative voltages as well or use a voltage inverter that converts the +5 V from the Raspi to -5 V. Simple charge pump converters like LTC1046 or MAX829 are sufficient. Usually they have a bit less output. That don't care, -4 V is just as fine.

Fig. 9: frequency response of Raspberry Pi's analog sound output with (right channel) and without (left channel) external  reconstruction filter, measured at 48 kHz sampling rate with white noise at -3 dB FSR. The right channel is inverted. The FFTs are smoothed by a Blackman-Harris window function.
left channel, right channel, FFT of left channel, FFT of right channel

Result

The filter is by far not perfect but it significantly improves the frequency response. Up to 20 kHz the response is closer to linear and above 20 kHz high frequency noise is reduced. Even in the time domain any visible steps have vanished. There is a slight overshoot at the resonance around 13 kHz and also some group delay. But no problem, you won't hear either of them.

For sure an elliptical filter would perform better but they are difficult to build and hey, it's a Raspberry not Harman Kardon.

Measurement equipment

All measurements are done with a Tectronix TDS 754A digital oscilloscope. The test signal are generated by this software on the fly. Calculations are done with Mathematica.

Contact

If you have remarks or complaints (not too much, of course ;) feel free to contact me: