# Do DSL / ADSL modems have an ADC with ~ 2 MHz sampling rate?

For fun and no real practical use, I'm trying to design a DIY modem that can transmit data over an audio line, like old 56k modems did. I'm studying how to pack bits of data efficiently in a 1k-15k audio spectrum, such that I'll be able to de-modulate it later.

During my readings, I saw that DSL modem use the 25 kHz - 1 MHz spectrum, in order to avoid interference with voice on the telephone line.

Question: on the demodulation side, in order to be able to do digital signal processing (FFT, etc.) to identify peaks of spectrum at, say 400 kHz or 800 kHz or 1 MHz, one needs a 2 MHz sampling rate (Nyquist).

Do (A)DSL modems have ADC (analog to digital converters) with 2 MHz sampling rate?

Same question for dial-up 56k modems: what kind of sampling frequency did they use at the ADC/DAC stage?

• The H in Hz is supposed to be capitalized, by the way. Because it is someone's name. – DKNguyen Sep 27 '20 at 19:23
• @BrianDrummond Do you mean, as high? Typical ADC/DAC I've seen for DSP have between 8 kHz and 100 kHz sampling-rate. Are there 2 mHz DAC/ADC easily available? – Basj Sep 27 '20 at 19:40
• @Basj lol, are you a time traveller from the 1970s? You can buy Gigasample/s ADCs on the free market... Every mid-range MCU has a > 1MS/s ADC, these days. – Marcus Müller Sep 27 '20 at 19:42
• @MarcusMüller Oops this might be because I've always worked with audio signals, so typical DACs I used were 8 / 16 / 48 / 96 / 192 kHz, with 24 bit resolution :) Outside of the audio world, what are typical DACs since, say 2000? Is a 1 Mhz DAC with 16 bit resolution something common? – Basj Sep 27 '20 at 19:45
• It's "MHz" and "GHz, not "mHz", "Mhz" or "Ghz". Capitals matter! Tip: SI units named after a person have their symbols capitalised but are lowercase when spelt out. – Transistor Sep 27 '20 at 19:56

They have a much faster ADCs. Also, ADSL2+ has its downlink up to maybe 2.2 MHz, so you'd need at least 4.4 MS/s to do that.

In reality, single-digit MHz ADCs are "old tech" and relatively cheap. Together with it being desirable to oversample the signal to apply digital filtering to increase your SNR, I'd presume that modern (as in: of the last 20 years!) ADSL modems have > 5 MS/s ADCs.

You'll probably not find a separate ADC on the board – typically, these things are integrated into AFE (analog front-end) ICs, integrating both ADC as well as DAC and a fair bit of analog and digital signal conditioning, and usually things like digital downconversion, sometimes clock recovery.

Such chips make highly-integrated and cheap DSL modems possible, but also make these devices less useful as general-purpose ADCs.

Also, because you ask like that, and because people will wonder anyway: No. This is not a clever way to circumvent export restrictions / technology embargoes. Officials in charge of export control aren't stupid, and companies want to sell millions of chips for DSL modems everywhere, so I'd assume it'll be practically impossible for the average engineer to convert these to general purpose ADCs/DACs.

• Not to mention that DSLs like ADSL, HDSL, etc., do something else -- they separately monitor on the order of 1000 (256 in ADSL, memory serving) individual frequency bands for their $Z_\text{LOAD}$ and actively optimize their $Z_\text{DRIVE}$ to maximize transmission performance, band by band, in real-time. Copper telephone lines are notoriously bad environments for data transfer (though they are well-equipped to handle lightening events at both ends.) – jonk Sep 27 '20 at 21:22
• I have never heard before of export restrictions on ADCs. Are you referring to something specific, or just speaking generally? – Nonny Moose Sep 28 '20 at 22:47

ADSL modems were usually >2Msps, often a multiple of 1.1Msps to simplify the signal processing later. E.g. the MTC20174 ADSL analog frontend had a 8.8Msps ADC/DAC. The reason for the higher than necessary sampling rate was the use the higher sampling rate to get more effective bits at signal frequency. This is a quite common trick as increasing sampling rate is often easier than reducing sampling noise in ADCs.

56k modems are ... special. They operated in an asynchronous fashion, something which ADSL later copied. They offered 56kbit/s down, but only 33.6kbit/s up. The reason of this lies in how they cheated. Back in the days of old, ISDN was considered the future and people who wanted to stay with current technology, upgraded to ISDN. ISDN could deliver two times 64kbit/s (plus a 16kbit/s signaling channel). Now to have ISDN available for customers, the whole telephone network has to support ISDN, or in other words has to be digital. V90 made use of that in that it knew the analog path in the connection was only that between the central and the last mile to the customer. The rest was digital. So, if your ISP had the equipment to interface digitally, they could inject digital samples into the phone network, which would be transmitted digitally until it reached the last central. This way it was possible to make use of the 64kbit/s that ISDN networks boasted, as you could, sample by sample transmit the analog signal and almost 100% recover it at the receiver end, as the analog wire was really short. The "encoding" used was simple PAM at the 8ksps / 8bits/sample that ISDN featured. But as signal noise and ADC/DAC linearity was far from offering perfect conditions, only 7bit of the 8bit samples were used. ADC/DACs used in these modems were usually 64ksps and 128ksps with 8bit (we are talking about the second half of the 90s, so these were state of the art chips that didn't cost an arm and a leg and could be used in a modem that should cost less than \$200).

So, why was this only used down stream? Because the receiver had to be synchronized to the sender. While it was possible to add a synchronizer (aka clock recovery and PLL) to the modem, nobody would have paid for the changes in telephone infrastructure to synchronize them. So upstream was still V34bis with its QAM.

And to answer the question you haven't asked:

If you really want to build a modem for digital data transfer I recommend you start small. Build an PAM system, that can do something like 2-100kbit/s over a few 100m. Then go to FSK and see how that increases wire length that you can use. Then upgrade to PSK and finally to QAM. And in the end, if you feel like it, you can go for OFDM like *DSL does. If you don't follow this path from simple encodings to more complex encodings, but try to build a complex encoding from the beginning, I can guarantee you that you will run into so many issues that you will have no idea how to fix any of them. You will need the experience from the simple systems.

And a word of caution: You are building a system which puts RF signals onto an ideal antenna. Any telephone wire, no matter whether you terminate it correctly or not, will act as an antenna with high emission rate. If you do not control the signal power and frequencies correctly, you will violate the emission limits and create interference that will annoy the heck out of other people and get you a nice fine.

• From an operational perspective, historically as the internet access technologies were developing, at a certain stage ISDN PRI was the natural next step to go in terms of integration / concentration at the interface between telephone technologies and the TCP/IP world. The PRI was digital, needed just a single signal pair instead of 30 individual analog phone lines, and the access router gear got equally integrated - the B-channels just got routed to an array of DSP's. No need for individual ADC/DAC per port. The ADC/DAC got offloaded to the phone network, the last mile copper interface... – frr Sep 28 '20 at 8:31
• BTW the 56k modems were asymmetrical. The downlink was faster than the uplink. But, unlike ADSL, where this is deliberate and probably based on frequency division multiplexing, in the 56k this was allowed/given by the principle that: 1) in the upstream direction, there was an actual ADC (where the analog copper was entering the CO = at the CO port) so the Nyquist limit applied, whereas 2) in the downstream direction, the DAC could play back whatever the digital channel brought from the ISP, and the CPE modem could ideally sync to individual samples and recover all the bits. – frr Sep 28 '20 at 9:38
• Woohoo, Attila! Nice, almost as nice as chocolate, seeing you – Marcus Müller Sep 28 '20 at 16:39

I recall taking a look at the spectrum of SHDSL modems once, those were capable of 15 Mbps over a single twisted pair. The spectrum had a steep roll-off above say 1.5 MHz if memory serves. So that's roughly 3 MBaud... times 5 bits per symbol? The modulation was called TC-PAM I guess... note that modern VDSL systems use very different modulation schemes, possibly OFDM-based.

Async modems operationg over telephone lines (V.90) were limited by the fixed sampling rate of the PDH and ISDN systems B-channels, which is 8 kSps (8 kHz) with 8bit depth and some coding on top (A-law/u-Law).