Hi
SNR Margin
See 2 attached Graphs plotted on natural log 3 cycle Graph.
x represents SNR =Psignal/Pnoise that is the straight signal to noise ratio. I will refer to this as the
actual SNR SNRdb= 10log(Psignal/Pnoise) Commonly shortened to SNR OR SNR margin
Graph 1
The graph plots the
actual SNR against the SNR(db) plots . It shows that each 3db increase there is a doubling of the
actual SNR . for example 3db = 2x(x is any start value ) and 6db = 4x . So it can be seen that between 3db and say 12 db
actual SNR margin has increase by a factor of 8
I have also shown the relationship between SNR margin and synch speed ,for a line where the attenuation is such that full 8 max connection can be made . Lines with lower potential connection speed will show smaller average bit loading .
The right hand line indicates a line with an average SNR of 33db.
edit :(after allowing for overheads )The horizontal lines show the
average number of
Data bits carrier bins per tone that can be loaded .
For any given SNR margin the available room for data = total SNR-SNR margin
Take the 6db SNR margin as an example then 33db(total SNR) - 6db(SNR margin) = 9
data bits carrier bins can be loaded across the 223 tones .
The QAM rate is said to be 4000Kbps per
data bit carrier bin
(quote :
http://www.kitz.co.uk/adsl/adsl_technology.htm)
What this means is that this line will be able to synch at 8028Kbps
that is 223 tones * 4Kbits * 9 . A similar calculation for any SNR Margin can be calculated in this way
so
with this line with a 33db
average SNR , the following are the maximum calculated synch speeds .
SNR Margin(db) carrier bins synch speed
3 10 8920Kbps
6 9 8029 Kbps
9 8 7136 Kbps
12 7 6244 Kbps
15 6 5352 Kbps
Quite often ,it is said that the reduction in synch speed makes the line more stable . The reduction in synch speed is an unavoidable by product of increasing the Target SNR margin . What is stabilising the connection is the increased SNR margin.
references Graph 2 is an attempt to illustrate the effect of increased SNR margin has on line noise
Graph 2
The SNR margin is again showing the same relationship between SNRdb scale and the
actual SNR values .For every 3db of SNR there is a doubling of the
actual SNR .
The second plot identified as +3db noise is a curve that shows the effects of an increase of 3db of noise will have on the SNR margin . This plot is a curve not a straight line ,as plotting a constant value on log axis will produce a curve .
Results taken from the plot showing the effect of a 3db increase in noise
Original SNR margin Approx new SNR margin with
3db 0db
6db 4.8db
9db 8.56db
12db 11.62db
As the SNR margin increases ,the effect of the noise is minimised .The opposite will also be true.
This helps to explain why a very stable line at say Target SNR margin of 12 db showing spikes /drops of 1 db whilst having little or no effect ,can be so unstable when the Target SNR margin is reset to 6db.Reading from the graph the 1db drop from 12 db to 11db translate into a 4x decrease in
actual SNR and this is equivalent to a 6db drop against a Target SNR of 6db .result 0db margin .
Reading from the graph is NOT exact but it does show the general relationship.
EDIT in the graphs please read
data bits as
carrier bins Regards Jeff
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