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G8MNY > TECH 14.06.07 07:40l 150 Lines 7144 Bytes #999 (0) @ WW
BID : 18905_GB7CIP
Read: GUEST OE7FMI
Subj: Modem Bauds & Bits
Path: DB0FHN<DB0MRW<OK0PKL<DB0GRL<SR6BBA<SR7DWI<SR1BSZ<IW2OAZ<IK2XDE<DB0RES<
ON0AR<GB7CIP
Sent: 070613/2305Z @:GB7CIP.#32.GBR.EU #:18905 [Caterham] $:18905_GB7CIP
From: G8MNY@GB7CIP.#32.GBR.EU
To : TECH@WW
By G8MNY (New June 2007)
(8 Bit Graphics use Code page 437 or 850)
Do you know the difference between baud & data rate. BAUD is the changes per
second, & DATA RATE is the number of bits per second, say leaving the computer.
In simple AFSK or FSK there is a 1:1 relationship. eg. 1 bit = 1 baud.
FSK 1200B/S
This is fairly typical of what happens as
0 1 the FM idle carrier at 1800Hz causes 2 AM CW
³ 600Hz /³\ /³\ 600Hz signals to appear at the deviation set points
³ of / ³ \ / ³ \ of representing the data 0 & 1.
³ LSB / ³ \ / ³ \ USB Each of these carries full double AM side-
³ / ³ \ / ³ \ bands up to the baud rate/2 in Hz, as it
ÅÄÄÄÄÄÄÁÄÄÄÄÁÄÄÄÄÄÄÄÄÄÁÄÄÄÄÁÄ needs 2 bits to form a cycle.
0 300 600 1k2 1k8 2k4 3K (1800Hz carrier is used as it is the fastest)
(frequency on most telephone lines.)
For this FSK to work, a bandwidth of 600Hz - 3kHz is needed, it does not have
to be too level flat, as FM can be hard limited & remove most noise etc.
So a bad line/comms link with more than 15dB frequency spread & worse than 15dB
S/N is still error free despite being very poor for phone use.
However differing delay times in the 2 tones is critical, & a Group Delay
difference of less that 1mS between 1200Hz & 2400Hz will garble the data, as
the modem will Rx no tone, then 2 tones etc. This has no affect on comms audio!
Typical long loaded line, or via a comms Rx IF filter!
Delay
1200uS´ \ Transformers / Channel
900uS´ \ & caps / Low pass
600uS´ \ / Filtering
300uS´ ~~ÄÄ..__ _.Ä~
0uS´ ~~ÄÄ---Ä~
ÅÄÂÄÄÂÄÄÄÂÄÄÄÄÂÄÄÄÄÂÄÄÄÄÂÄÄÄÄÂÄÄÄÂÄÄÄÂÄÄÂÄÄÂÄÄ>Frequency
300 500 800 1k2 1k6 2k 2k4 2k7 3k 3k2 3k4 Hz
Sent data Rx Data with 833uS of group delay!
______~~~~~~____________~~~~~~~~~~~~ ______????????????______??????~~~~~~
0 1 0 0 1 1 0 no 0+1 1 no 1
1200 2400 1200 1200 2400 2400 1200 Sig 1k2+2k4 Sig 2400
This still is one of the simplest & robust standards around (this why it is
still used), but even so it is important to have all the sidebands that make up
the signal turning up all at the same time & at the same relative level & also
not drowned out with noise or distortions.
GOING FASTER
If we look at what a telecomms line can pass eg. 300Hz - 3.3KHz with some
frequency attenuation & group delay. Then that would support a max baud rate
of 3000 baud, eg. an 1800Hz carrier with double sidebands up to ñ1500Hz.
Alternating baud signals of 010101 @ 3000 baud form the highest side bands of
ñ1500Hz.
³ 1500Hz /³\
³ of / ³ \ 1500Hz
³ LSB / ³ \ of
³ / ³ \ USB
ÅÄÄÄÁÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÁÄÄÄ> Frequency
0 300 1k8 3k3 Hz
However this is not the data rate, but the max baud rate. So by using AM with
multiple levels & phase modulation with multiple angles of carrier together, it
is possible to make a single baud of carrier represent 1 of many states, eg. 16
AM levels & 16 phase angles, gives 256 states or symbols, which is equal to 8
bits of data per baud! That would make a data rate of 8x 3k = 24kB/S.
Phase & level diagram (dartboard vector) for just 4x 4 (16 symbols)
+4´ [0] [1]
+3´ [4] [5] This give 16 pigeon holes (0-F) for each
+2´ [8] [9] burst of carrier signal (baud) to drop into.
+1´ [C] [D]
0´ 0 In practice the 4 phase are rotated per
-1´ [F] [E] level shell to give the biggest pigeon
-2´ [B] [A] holes.
-3´ [7] [6]
-4´ [3] [2] Note that the carrier level of 0 can't be
ÀÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄ uses as it would not give any phase info.
LEVELS-4 -3 -2 -1 0 +1 +2 +3 +4
+4´ [ ][ ][ ][ ] [ ][ ][ ][ ]
+3´ [ ][ ][ ][ ] [ ][ ][ ][ ] By using variable number of phases per
+2´ [ ][ ][ ][ ] [ ][ ][ ][ ] carrier level, you can fill all the
+1´ [ ][ ][ ][ ] [ ][ ][ ][ ] pigeon holes as close as possible, giving
0´ 0 the biggest number of symbols, here 64,
-1´ [ ][ ][ ][ ] [ ][ ][ ][ ] or 6 bits per Baud.
-2´ [ ][ ][ ][ ] [ ][ ][ ][ ]
-3´ [ ][ ][ ][ ] [ ][ ][ ][ ] Noise, distortion, poor frequency/phase
-4´ [ ][ ][ ][ ] [ ][ ][ ][ ] response will move the carrier into the
ÀÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄÄÂÄ wrong pigeon hole, & produce 6 errors
LEVELS-4 -3 -2 -1 0 +1 +2 +3 +4 at once!
However you don't get something for nothing, using 16 levels means the
distortion & all noise must put the level into the next 6.25% level window, or
3.1% (-31dB peak). And the same goes for multiple phase mod, due to jitter &
multipath etc. that must not to exceed 1/32 of a cycle peak @ 1800Hz! A very
tight specification for radio path!
EQUALISING (training)
As the line will not be flat or have no group delay it is important that the
modem has an equaliser that has the opposite characteristics to the line. This
used to be an analogue nightmare, but with digital A-D convention of the line
audio it is relatively simple to flatten in software!
eg.. a Line with bump at 1K
Level Add in % of signal data from 500mS ago & the
³ /~\ bump will go. But then you get a bump @ 2kHz,
³ .-----~ ~----. so add in some signal data from 250mS ago, keep
³ / \ doing this until all bumps are above 3.4kHz.
ÅÄÄÄÂÄÄÄÄÂÄÄÄÄÂÄÄÄÄÂÄÄÄÄÂÄÄ
0 250 500 1k 2k 4k
Training can also be done on live data, by making small adjustments & seeing if
the data quality (how near Rx symbols are to their pigeon hole ideal centres)
Ideal Amplitude Phase Noise &
Pigeon hole Trouble Trouble Distortion
ÚÄÄÄÄÄÄÄ¿
³ ³ ± ±±±±
³ o ³ ± ±±±±± ±±±±±±
³ ³ ± ±±±±
ÀÄÄÄÄÄÄÄÙ zero zero
So you see that although modern modems are super at equalising & giving 56kB/S
max on a good line short, they can only do that over clean copper circuits, &
high quality PCM systems that give <1% THD >50dB S\N & no phase jitter.
In practice most lines can't do this the modem is designed to drop back the
baud, & or levels/phase angles (called symbols rate). Also the modem has error
detection/correction so missed errors passed through are low. The use of an
encryption algorithm in some modems also minimises continuous retries of data
patterns that have high error rates.
BROADBAND
These systems are different & use much wider frequency range & multiple
carriers. But there are similarities & nasty line problems will greatly reduce
the usable data rate.
Why Don't U send an interesting bul?
73 de John G8MNY @ GB7CIP
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