Bandwidth is one of those technical terms that has been overloaded in popular speech: as an example, an editor might ask if you have the bandwidth to write a Hackaday piece about bandwidth. Besides this colloquial usage, there are several very specific meanings in an engineering context. We might speak about the bandwidth of a signal like the human voice, or of a system like a filter or an oscilloscope — or, we might consider the bandwidth of our internet connection. But, while the latter example might seem fundamentally different from the others, there’s actually a very deep and interesting connection that we’ll uncover before we’re done.
Let’s have a look at what we mean by the term bandwidth in various contexts.
Turn the clock back six decades or so and imagine you’re in the nascent computer business. You know your product has immense value, but only to a limited customer base with the means to afford such devices and the ability to understand them and put them to use. You know that the market will eventually saturate unless you can create a self-sustaining computer culture. But how does one accomplish such a thing in 1961?
Enter the Minivac 601. The brainchild of no less a computer luminary than Claude Shannon, the father of information theory, the Minivac 601 was ostensibly a toy in the vein of the “100-in-1” electronics kits that would appear later. It used electromechanical circuits to teach basic logic, and now [Mike Gardi] has created a replica of the original Minivac 601.
Both the original and the replica use relays as logic switches, which can be wired in various configurations through jumpers. [Mike]’s version is as faithful to the original as possible with modern parts, and gets an extra authenticity boost through the use of 3D-printed panels and a laser-cut wood frame to recreate the look of the original. Sadly, the unique motorized rotary switch, used for both input and output on the original, has yet to be fully implemented on the replica. But everything else is spot on, and the vintage look is great. Extra points to [Mike] for laboriously recreating the original programming terminals with solder lugs and brass eyelets.
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.
I 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?
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.