WHEN IS A BAUD NOT A BIT
A DATA COMMUNICATIONS TUTORIAL
by
JAMES A. WALKER
AUGUST 27, 1987
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Much has been written over the years about the intricacies of data
communications. Most of them written by very knowledgeable authors.
Still, I question an author's credibility when he makes reference to
9600 baud modems. It has become more and more apparent that people are
using the terms bit and baud interchangeably. This usage, more times
than not, is incorrect. Additionally, I view BBS messages referencing
modem speeds at baud rates, not bits per second (bps). Perhaps it is
a pet peeve of mine but I wanted to do something for my new endeavor
(hobby wise) and make a contribution which could be considered
worthy. So, I decided to draft this tutorial. I hope it is of
benefit to those who read it and aides them in understanding the
difference between a "bit" and a "baud".
A FOUNDATION OF UNDERSTANDING
In order to proceed, a common ground of understanding must be
established. The purpose and function of a modem is to convert binary
information into a signal compatible with today's analog telephone
lines; and vise versa.
The term "modem" is derived from the major functions performed by a
modem. These are, MOdulation and DEModulation. Although this is not a
tutorial or text on analog transmission techniques, you must know that
modems can modulate a signal in a variety of ways. Common techniques
used are: Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK)
and Phase Shift Keying (PSK).
The easiest way to understand modulation, is to picture in your mind,
a Sine Wave. Through electronic technology, we are able to change or
alter the characteristics of a Sine Wave's shape, frequency, phase and
amplitude. Modulation, as it is implemented within a modem, is the
creation of a Sine Wave at a certain frequency (called a carrier
frequency), then alters or changes it's frequency, phase or
amplitude. A modem, when connected to a telephone line, transmits the
sine wave which is received at the distant end by another modem.
Now to complete the picture. Your PC or terminal sends binary "1's
and 0", or "bits" of data to the modem where it is received and then
converted to a modulated sine wave, transmitted to the distant modem
where the sine wave is demodulated and binary "1's and 0's" are sent
to the receiving PC or terminal. Job complete.
We all know that a "bit" is a binary 1 or 0 and when 7 or 8 of them
are grouped together, we have a byte or character of information.
Webster defines a baud as "a variable unit of data transmission speed
usu. equal to one bit per second." The two key words are "variable"
and "usu." meaning "usually", when Webster uses it. It is, indeed
variable but in today's technology and higher transmission speeds, it
is not usually equal to one bit per second.
A more correct definition for "baud" would be: a variable unit of data
transmission speed determined by the rate of change of a modulated
signal.
WHAT THEN IS A BAUD?
As we discussed, data, in it's analog form, is represented by a Sine
Wave. If we were to change or alter this Sine Wave in a predetermined
and meaningful manner, we can allow the Sine Wave to carry
information. A baud is very simply a change in amplitude, frequency
or phase of a sine wave. Baud rate is the speed at which we perform
this change.
Let's look at an example. Today's standard for transmitting at 300
bps was established many years ago by AT&T. We utilize the frequency
shift keying schemes developed for the Western Electric manufactured
103J modem. In order to simplify this discussion, I will deal only
with half of the full duplex link. When you originate a call to
another modem at 300 bps, you transmit to the other modem by shifting
the frequency of your sine wave between 1270 Hz and 1070 Hz. A binary
"1" is represented by the 1270 Hz signal and a "0" is represented by
the 1070 Hz signal. If you were to connect an oscilloscope to the
analog line, you would be able to see the sine wave change it's
frequency back and forth as data is transmitted. In this example, we
are transmitting at 300 bits per second and at 300 baud because each
change of the sine wave represented one bit of data.
This relationship between a bit and a baud being equal stops very
quickly. Why? You may ask. Well it was determined many years ago by
two acclaimed scientists and researchers, by the names of Shannon and
Nyquist, that the maximum allowable "changes of state" of a sine wave
was in direct relationship with the bandwidth of an analog line. They
developed, you guessed it, the Shannon/Nyquist theory; which is a
mathematical formula proving that the maximum baud rate for a
typical unconditioned line having a bandwidth of 2700 Hz is
approximately 3000 baud per second. So, only 3000 changes to a sine
wave per second can take place before you surpass the capabilities of
a typical analog line. How then, do we transmit at speeds in excess
of 2400 bits per second (bps)?
THE EVOLUTION OF SPEED AND TECHNOLOGY
The need to be able to communicate remotely with and between computers
dictated advancements in analog data communications. To do so
economically, meant that we would have to utilize the existing analog
network built by AT&T and it's Operating Companies. To do so
efficiently, required that we communicate at high speeds. To do so
accurately, meant that we could not exceed the limitations of the
analog network.
Modem manufacturers rose to the challenge by developing multi-level
modems. And here is where we truly delineate between a bit and baud.
Multi-level modem means that a single change to the sine wave can
represent more than one bit of data. Therefore, one baud can
represent two, three or perhaps four bits. Let's take a moment to see
how this takes place.
At a speed of 1200 bits per second, our modems utilize Phase Shift
Keying (PSK) as the method of modulation. The transmit carrier
frequency (after handshake) is 1200 Hz for the originator of the call
and 2400 Hz for the answerer of the call (for full duplex operation).
Our modems are also 4-level. That is, our modems use 4 different
shifts in the phase of the sine wave in order to transmit bits of
data. The question now is, in the binary world of 1's and 0's and
with a 4 level modem, how many bits can each of the 4 different phase
shifts carry? The answer of course, is 2. Let's look at all of the
possible combinations, 00, 01, 10 and 11.
Now to build the correlation between bits and bauds. In one change of
the phase of the sine wave, let's say 45 degrees, I am really
transmitting 2 bits of data (00). A change of 90 degrees conveys the
bits (01). A change of 135 degrees means (10). And last, a change of
180 degrees means (11). So, in this example, we are transmitting 1200
bits per second while actually transmitting at a baud rate of 600.
Half the bit rate. By the way, a 4-level modem transmitting two bits
of data for each baud is referred to as Di-bit modem.
Let's take this another step. Let's look at a tri-bit modem. That
is, a modem which transmits 3 data bits for each baud. Most modem
manufacturers utilize tri-bit technology for speeds of 4800 bits per
second. The modulation technique is usually Phase Shift Keying.
Eight different combinations of three bits can be transmitted.
Therefore, we have an 8-level modem. The three bit combinations of
course are: 000, 001, 010, 011, 100, 101, 110 and 111. The data rate
is 4800 bits per second, the baud rate is 1600.
One last modulation technique which must be discussed because it is
widely utilized in our modems at 2400 bits per second is Quadrature
Amplitude Modulation (QAM). This technique combines two modulation
techniques together. Phase Shift Keying and Amplitude Shift Keying.
In addition, it utilizes both the Sine and Cosine Wave forms. Each of
the Waves carries 2 bits of data and when received, are then combined
into 4 bit groups. So, at 2400 bits per second, we are actually
transmitting at a baud rate of 600.
SUMMARY
So is a bit and a baud the same? The correct answer is, sometimes.
But not really because they each should be used in referring to
different aspects of the speed at which data is transmitted. Can they
be used interchangeably? Absolutely not! Is there such a thing as a
9600 baud modem? There may be, but it won't work on Ma Bell's lines.
Shannon and Nyquist proved their theory in mathematical terms and the
industry has proven them to be correct. Last but not least, you might
be asking yourself, What is the baud rate of a 9600 bit per second
modem? Most 9600 modems are 16-level or 16-point, in which case they
are transferring data at a baud rate of 2400.
Questions or comments can be left on Compuserve #76266,3455, Wildcat
File Cabinet, (214) 351-9859 or Wildcat PC Help, (214) 680-2693.
4) 351-9859 or Wildcat PC Help, (214) 680-2693.