# Digital vs. Analog Volume Controls

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1 Digital vs. Analog Volume Controls October 2011 AMM ESS 10/11

2 Summary of this Presentation In a Digital Audio System what is the trade-off between using a digital or an analog volume control? To answer this question we need to know: How a digital volume control works and what are its limitations How an analog volume control works and what are its limitations D vs A Volume 2 of 39

3 Digital Volume Control -10dB Here is the number 30,003 shown as it appears to a 16 bit DAC: = 30,003 How do we turn its volume down - ie reduce its amplitude? We simply multiply it by say -10dB -10db is and here is the result: = 9,488 Any problem? Shouldn t the answer actually have been 30,003 * = ? Its close, it is only wrong by 23 parts per million, but it is not right D vs A Volume 3 of 39

4 Digital Volume Control -35dB Here is the number 30,003 shown as it appears to a 16 bit DAC: = 30,003 How do we turn its volume down even more, say by -35dB -35db is and here is the result: = 534 Any problem? Shouldn t the answer actually have been 30,003 * = ? Its close, but not so close, it is wrong by 866 parts per million D vs A Volume 4 of 39

5 866ppm surely no problem? Why worry about 23ppm at -10dB, and 866ppm at -35db? Surely these are small errors? No they are not small: 866ppm has degraded the performance of that 16 bit DAC by a factor of more than 50! As a digital volume control operates on a fixed-width field (ie on that 16 bit number that the DAC receives) it creates noise because the DAC cannot make the fractional part of the number. And this is a large noise! D vs A Volume 5 of 39

6 Digital (Frequency Domain) -1dB We will learn more if we are prepared to look at signals in the Frequency Domain. Here is a 16bit DAC in time and in frequency: ENOB SN The amplitude here is -1dB D vs A Volume 6 of 39

7 Digital (Frequency Domain) -10dB We will learn more if we are prepared to look at signals in the Frequency Domain. Here is a 16bit DAC in time and in frequency: ENOB SN The amplitude here is -10dB D vs A Volume 7 of 39

8 Digital (Frequency Domain) -35dB We will learn more if we are prepared to look at signals in the Frequency Domain. Here is a 16bit DAC in time and in frequency: ENOB SN The amplitude here is -35dB D vs A Volume 8 of 39

9 Digital Volume Control fixed noise Clearly, the noise is not moving! The signal is decreasing as we requested But the noise is not going down! Consequently, the signal-to-noise ratio is getting worse as digital volume control is reduced This is why audiophiles generally avoid digital volume control D vs A Volume 9 of 39

10 Analog (Frequency Domain) -1dB We will learn more if we are prepared to look at signals in the Frequency Domain. Here is a 16bit DAC in time and in frequency: ENOB SN The amplitude here is -1dB D vs A Volume 10 of 39

11 Analog (Frequency Domain) -10dB We will learn more if we are prepared to look at signals in the Frequency Domain. Here is a 16bit DAC in time and in frequency: ENOB SN The amplitude here is -10dB D vs A Volume 11 of 39

12 Analog (Frequency Domain) -35dB We will learn more if we are prepared to look at signals in the Frequency Domain. Here is a 16bit DAC in time and in frequency: ENOB SN 91.8 The amplitude here is -35dB D vs A Volume 12 of 39

13 Analog Volume - variable noise Now the noise moves down as well The signal is decreasing as we requested Now the noise is going down as well The signal to noise ratio is being maintained This is why audiophiles generally like analog volume control D vs A Volume 13 of 39

14 Can Digital be Improved? Analog appears to be a clear winner. But can we improve digital? The digital volume control is limited because the DAC (and the data source in the last example) were both 16bits. What happens when a 16 bit number is fed to a 32 bit DAC? Internally 32 bits, externally 16/24 D vs A Volume 14 of 39

15 Volume Control internal to DAC Here is the number 30,003 shown as it appears to a 32 bit DAC: = 30,003 How do we turn its volume down even more, say by -35dB -35db is and here is the result: = Any problem? Shouldn t the answer actually have been 30,003 * = ? As indeed it is... When the volume control has access to the additional bits in the DAC data path, there is no numerical loss of accuracy D vs A Volume 15 of 39

16 Optimum Digital Volume Control A Digital volume control with access to the DAC internal data path will behave just And the noise like the analog one until it will fall as well reaches the noise floor until the DAC noise floor is of the analog components reached of the DAC. -135dB in the ESS Sabre DAC The signal is decreasing as we requested D vs A Volume 16 of 39

17 Analog still better? In fact, yes it is. As long as the analog volume control has a noise floor better than the DAC noise floor, the analog one will win Conclusion: Analog volume controls easily outperform digital, unless the digital control has access to the data path of the DAC (ie is internal to the DAC) Exquisitely well designed analog volume controls can still beat even the very best internal digital volume controls if they have a lower noise floor than the DAC itself The -135dB of the ESS Sabre DAC would need an exceptionally low noise analog volume control to beat its internal digital one D vs A Volume 17 of 39

18 End of Volume Control Presentation Any questions? D vs A Volume 18 of 39

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