Tearing Into Delta Sigma ADCs Part 2

In part one, I compared the different Analog to Digital Converters (ADC) and the roles and properties of Delta Sigma ADC’s. I covered a lot of the theory behind these devices, so in this installment, I set out to find a design or two that would help me demonstrate the important points like oversampling, noise shaping and the relationship between the signal-to-noise ratio and resolution.

Modulator Implementation

modulatorCheck out part one to see the block diagrams of what what got us to here. The schematics shown below are of a couple of implementations that I played with depicting a single-order and a dual-order Delta Sigma modulators.

schematicBasically I used a clock enabled, high speed comparator, with two polarities in case I got it the logic backwards in my current state of burn out to grey matter ratio. The video includes the actual schematic used.

Since I wasn’t designing for production I accepted the need for three voltages since my bench supply was capable of providing them and this widget is destined for the drawer with the other widgets made for just a few minutes of video time anyway. Continue reading “Tearing Into Delta Sigma ADCs Part 2”

Tearing Into Delta Sigma ADC’s

It’s not surprising that Analog to Digital Converters (ADC’s) now employ several techniques to accomplish higher speeds and resolutions than their simpler counterparts. Enter the Delta-Sigma (Δ∑) ADC which combines a couple of techniques including oversampling, noise shaping and digital filtering. That’s not to say that you need several chips to accomplish this, these days single chip Delta-Sigma ADCs and very small and available for a few dollars. Sometimes they are called Sigma-Delta (∑Δ) just to confuse things, a measure I applaud as there aren’t enough sources of confusion in the engineering world already.

I’m making this a two-parter. I will be talking about some theory and show the builds that demonstrate Delta-Sigma properties and when you might want to use them.

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Grandma’s Phone, DSL, And The Copper They Share

My DSL line downloads at 6 megabits per second. I just ran the test. This is over a pair of copper twisted wires, the same Plain Old Telephone Service (POTS) twisted pair that connected your Grandmother’s phone to the rest of the world. In fact, if you had that phone you could connect and use it today.

18zbmki8n3xgkjpgI can remember the old 110 bps acoustic coupler modems. Maybe some of you can also. Do you remember upgrading to 300 bps? Wow! Triple the speed. Gradually the speed increased through 1200 to 2400, and then finally, 56.6k. All over the same  of wires. Now we feel short changed if were not getting multiple megabits from DSL over that same POTS line. How can we get such speeds over a system that still allows your grandmother’s phone to be connected and dialed? How did the engineers know these increased speeds were possible?

shannon_maze_hr
Claude Shannon with his maze running mechanical mouse

The answer lies back in 1948 with Dr. Claude Shannon who wrote a seminal paper, “A Mathematical Theory of Communication”. In that paper he laid the groundwork for Information Theory. Shannon also is recognized for applying Boolean algebra, developed by George Boole, to electrical circuits. Shannon recognized that switches, at that time, and today’s logic circuits followed the rules of Boolean Algebra. This was his Master’s Thesis written in 1937.

Shannon’s Theory of Communications explains how much information you can send through a communications channel at a specified error rate. In summary, the theory says:

  • There is a maximum channel capacity, C,
  • If the rate of transmission, R, is less than C, information can be transferred at a selected small error probability using smart coding techniques,
  • The coding techniques require intelligent encoding techniques with longer blocks of signal data.

What the theory doesn’t provide is information on the smart coding techniques. The theory says you can do it, but not how.

In this article I’m going to describe this work without getting into the mathematics of the derivations. In another article I’ll discuss some of the smart coding techniques used to approach channel capacity. If you can understand the mathematics, here is the first part of the paper as published in the Bell System Technical Journal in July 1948 and the remainder published later that year. To walk though the system used to fit so much information on a twisted copper pair, keep reading.

Continue reading “Grandma’s Phone, DSL, And The Copper They Share”