New HOWTO: Modem-HOWTO - page 20
Table of Contents
19. Appendix A: How Analog Modems Work (technical) (unfinished)
19.1. Modulation Details
19.1.1. Intro to Modulation
This part describes the modulation methods used for conventional
modems. It doesn't cover the high speed methods (modulus conversion)
sometimes used by ``56k Modems (v.90)''. But 56k modems also use the
modulation methods described here.
Modulation is the conversion of a digital signal represented by binary
binary (0 or 1) into an analog signal something like a sine wave. The
modulated signal consists pure sine wave "carrier" signal which is
modified to convey information. A pure carrier sine wave, unchanging
in frequency and voltage, provides no flow of information at all
(except that a carrier is present). To make it convey information we
modify (or modulate) this carrier. There are 3 basic types of
modulation: frequency, amplitude, and phase. They will be explained
19.1.2. Frequency Modulation
The simplest modulation method is frequency modulation. Frequency is
measured in cycles per second (of a sine wave). It's the count of the
number of times the sine wave shape repeats itself in a second. This
is the same as the number of times it reaches it peak value during a
second. The word "Hertz" (abbreviated Hz) is used to mean "cycles per
A simple example of frequency modulation is where one frequency means
a binary 0 and another means a 1. For example, for some obsolete 300
baud modems 1070 Hz meant a binary 0 while 1270 Hz meant a binary 1.
This was called "frequency shift keying". Instead of just two
possible frequencies, more could be used to allow more information to
be transmitted. If we had 4 different frequencies (call them A, B, C,
and D) then each frequency could stand for a pair of bits. For
example, to send 00 one would use frequency A. To send 01, use
frequency B; for 10 use C; for 11 use D. In like manner, by using 8
different frequencies we could send 3 bits with each shift in
frequency. Each time we double the number of possible frequencies we
increase the number of bits it can represent by 1.
19.1.3. Amplitude Modulation
Once one understands frequency modulation example above including the
possibilities of representing a few bits by a single shift in
frequency, it's easier to understand both amplitude modulation and
phase modulation. For amplitude modulation, one just changes the
height (voltage) of the sine wave analogous to changing the frequency
of the sine wave. For a simple case there could only be 2 allowed
amplitude levels, one representing a 0-bit and another representing a
1-bit. As explained for the case of frequency modulation, having more
possible amplitudes will result in more information being transmitted
per change in amplitude.
19.1.4. Phase Modulation
To change the phase of a sine wave at a certain instant of time, we
stop sending this old sine wave and immediately begin sending a new
sine wave of the same frequency and amplitude. If we started sending
the new sine wave at the same voltage level (and slope) as existed
when we stopped sending the old sine wave, there would be no change in
phase (and no detectable change at all). But suppose that we started
up the new sine wave at a different point on the sine wave curve.
Then there would likely be a sudden voltage jump at the point in time
where the old sine wave stopped and the new sine wave began. This is
a phase shift and it's measured in degrees (deg.) A 0 deg. (or a 360
deg.) phase shift means no change at all while a 180 deg. phase shift
just reverses the voltage (and slope) of the sine wave. Put another
way, a 180 deg. phase shift just skips over a half-period (180 deg.)
at the point of transition. Of course we could just skip over say 90
deg. or 135 deg. etc. As in the example for frequency modulation, the
more possible phase shifts, the more bits a single shift in phase can
19.1.5. Combination Modulation
Instead of just selecting either frequency, amplitude, or phase
modulation, we may chose to combine modulation methods. Suppose that
we have 256 possible frequencies and thus can send a byte (8 bits) for
each shift in frequency (since 2 to the 8 power is 256). Suppose also
that we have another 256 different amplitudes so that each shift in
amplitude represents a byte. Also suppose there are 256 possible
phase shifts. Then a certain points in time we may make a shift in
all 3 things: frequency, amplitude and phase. This would send out 3
bytes for each such transition.
No modulation method in use today actually does this. It's not
practical due to the relatively long time it would take to detect all
3 types of changes. The main problem is that frequent shifts in phase
can make it appear that a shift in frequency has happened when it
To avoid this difficulty one may simultaneous change only the phase
and amplitude (with no change in frequency). This is called phase-
amplitude modulation. It is also called quadrature amplitude
modulation (= QAM) since there were only 4 possible phases
(quadrature) in early versions of it. This method is used today for
the common modem speeds of 14.4k, 28.8k, and 33.6k. The only
significant case where this modulation method is not used today is for
56k modems. But even 56k modems exclusively use QAM (phase-amplitude
modulation) in the direction from your PC out the telephone line.
Sometimes even the other direction will also fall back to QAM when
line conditions are not good enough. Thus QAM (phase-amplitude
modulation) still remains the most widely used method on ordinary
19.2. 56k Modems (v.90)
The "modulation" method used above 33.6k is entirely different than
the common phase-amplitude modulation. Since ordinary telephone calls
are converted to digital signals at the local offices of the telephone
company, the fastest speed that you can send digital data by an
ordinary telephone call is the same speed that the telephone company
uses over its digital portion of the phone call transmission. What is
this speed? Well, it's close to 64kbps. It would be 64k but
sometimes bits are "stolen" for signalling purposes. But if the phone
Co. knows that the link is not for voice, bits may not get stolen.
The case of 64k will be presented and then it will be explained why
the actual speed is lower (56k or less --usually significantly less).
Thus 64k is the absolute top speed possible for an ordinary telephone
call using the digital portion of the circuit that was designed to
send digital encodings of the human voice. In order to use 64k, the
modem must know exactly how the telephone company is doing its digital
encoding of the analog signals. This task is far too complicated if
both sides of a telephone call have only an analog interface to the
telephone company. But if one side has a digital interface, then it's
possible (at least in one direction). Thus if your ISP has a digital
interface to the phone company, the ISP may send out a certain digital
signal over the phone lines toward your PC. The digital signal from
the ISP gets converted to analog at the local telephone office near
your PC's location (perhaps near your home). Then it's your modem's
task to try to figure out exactly what that digital signal was. If it
could do this then transmission at 64k (the speed of the telephone
company's digital signal) is possible in this direction.
What method does the telephone company use to digitally encode analog
signals? It uses a method of sampling the amplitude of the analog
signal at a rate of 8000 samples per second. Each sample amplitude is
encoded as a 8-bit (ASCII-like) byte. (Note: 8 x 8000 = 64k) This is
called "Pulse Code Modulation" = PCM. These bytes are then sent
digitally on the telephone company's digital circuits where many calls
share a single circuit using a time-sharing scheme known as "time
division multiplexing". Then finally at a local telephone office near
your home, the digital signal is de-multiplexed resulting in the same
digital signal as was originally created by PCM. Then this signal is
converted back to analog and sent to your home. Each 8-bit byte
creates a certain amplitude of the analog signal. Your modem's task
is to determine just what that PCM 8-bit byte was based on the analog
amplitude it detects.
This is (sort of) "amplitude demodulation" but not really. It's not
amplitude demodulation because there is no carrier. Actually, it's
called "modulus conversion" which is the inverse of PCM. In order to
determine the digital codes the telephone Co. used to create the
analog signal, the modem must sample this analog signal amplitude at
exactly the same points in time the phone Co. used when it created the
analog signal. To do this a timing signal is generated from a
residual 4kHz signal on the analog phone line. The creation of
amplitudes to go out to your home/office at 8k amplitudes/sec sort of
creates a 4kHz signal. Suppose every other amplitude was of opposite
polarity. Then there would be a 4kHz sine-like wave created. Each
amplitude is in a sense a 8-bit symbol and when to sample amplitudes
is known as "symbol timing".
Now the encoding of amplitudes in PCM is not linear. At low
amplitudes an increment of 1 in the PCM byte represents a much smaller
increment (delta) in analog signal amplitude than would be the case if
the amplitude being sampled were much higher. Thus for low amplitudes
it's difficult to distinguish between adjacent byte values. To make
it easier to do this (for 56k modems) certain PCM codes representing
very low amplitudes are not used. This gives a larger delta between
possible amplitudes and makes correct detection of them by your modem
easier. Thus half the amplitude levels are not used by v.90. This is
tantamount to each symbol (allowed amplitude level) representing 7
bits instead of 8. This is where 56k comes from: 7 bits/symbol x 8k
symbols/sec = 56k bps. Of course each symbol is actually generated by
8-bits but only 128 bytes of the possible 256 bytes are actually used.
There is a code table mapping these 128 8-bit bytes to 128 7-bit
But it's a little more complicated that this. If the line conditions
are not nearly perfect, then even fewer possible levels (symbols) are
used resulting in speeds under 56k. Also due to US government rules
prohibiting high power levels on phone lines, certain high amplitudes
levels can't be used resulting in only about 53.3k at best for "56k"
Note that the digital part of the telephone network is bi-directional.
Two such circuits are used for a phone call, one in each direction.
The 56k signal is only used in one of these directions: from your ISP
to your PC. The other direction, from your home/office to the ISP,
uses the conventional phase-amplitude modulation scheme with a maximum
of 36.6kbps (and not 53.3kbps). The analog portion of the circuit
from your home/office to the nearest telephone Co. office was never
intended to be bi-directional since it's only a single twisted pair.
But due to sophisticated cancellation methods it's able to convey data
simultaneously in both directions as explained in the next subsection.
19.3. Full Duplex on One Circuit
Modern modems are able to both send and receive signals
simultaneously. One could call this "bidirectional" or "full duplex".
This was once done by using one frequency for sending and another for
receiving. Today, the same frequency is used for both sending and
receiving. How this works is not easy to comprehend.
Most of the telephone system "main lines" are digital with two
channels in use when you make a telephone call. What you say goes
over one digital channel and what the other person says goes over the
other (reverse) digital channel. Unfortunately, the part of the
telephone system which goes to homes (and many offices) is not digital
but only a single analog channel. If both modems were directly
connected to the digital part of the phone system then bidirectional
communication (sending and receiving at the same time) would be no
problem because two channels would be available.
But the end portion of the signal path goes over just one circuit.
How can there be two-way communication on it simultaneously? It works
something like this. Suppose your modem is receiving a signal from
the other modem and is not transmitting. Then there's no problem.
But if your modem were to start transmitting (with the other received
signal still flowing into your modem) it would drown out the received
signal. If the transmitted signal was a "solid" voltage wave applied
to the end of the line then there is no way any received signal could
be present at that point.
But the transmitter has "internal impedance" and the transmitted
signal applied to the end of the line is not solid (or strong enough)
to completely eliminate the received signal coming from the other end.
Thus while the voltage at the end of the line is mostly the stronger
transmitted signal a small part of it is the desired received signal.
All that is needed is to filter out this stronger transmitted signal
and then what remains will be the signal from the other end which we
want. To do this, one only needs to get the pure transmitted signal
directly from the transmitter (before it's applied to the line)
amplify it a determined amount, and then subtract it from the total
signal present at the end of the line. Doing this in the receiver
circuits leaves a signal which mostly came from the other end of the
19.4. Echo Cancellation
A signal traveling down a line in one direction may encounter changes
in the line that will cause part of the signal to echo back in the
opposite direction. Since the same circuit is used for bi-directional
flow of data such echos will result in garbled reception. One way to
ameliorate this problem is to send training signals once in a while to
determine the echo characteristic of the line. This will enable one
to predict the echos that will be generated by any given signal. Then
this prediction method is used to predict what echos the transmitted
signal will cause. Then this predicted echo signal is subtracted
from the received signal. This cancels out the echoes.