## some leftover maths

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##### some leftover maths

##### some leftover maths

28-11-2010 6:58 PM

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G.992.1 Full Rate ADSLor G.dmt = 4000 times 15 (60Kb/s for each tone.)times 256

If all 256 tones are used in parallel, the total theoretical data rate can be as fast as 15.36Mb/s

and G.992.2, a lower data rate approach often called G.Lite

For G.Lite, only 8 bits are used per symbol with only half of the carrier tones used for a theoretical maximum data rate

of 4.096Mb/s.

4000 times 8 (32Kb/s for each tone.)times 128

If all 128 tones are used in parallel, the total theoretical data rate can be as fast as 4.096Mb/s

==============================================================================================

=================================part two===========================================================

The SNR Margin is the difference between the actual SNR and the SNR required to run at a specific speed. For example, if your line needs 35dB of SNR to run at 8Mbps, and the actual line SNR is 41dB, then the SNR Margin would be 6dB.

=====================================================================================================

the above is correct

but

the help i need is in two other parts

(part 1)

as each data bit represents a 3dB SNR (see part one 992.1 formula)

and 15 bits :: a 45db sNR

then if my line SNR is 51 it can carry max number of bits, and has a safety SNR Margin of 6dB

one problem i see is that for every 3dB increase in the SNR Margin

it reduces the number of bits that all my dsl buckets(or bins or tones) will carry by 1 bit

each time

ie total bits per bin for G.dmt

15(bits) - (SNR)/3 dB

total bits per bin for G.lite(see part one G.992.2 formula)

8(bits) - (SNR) / 3

is (part 1) all correct

(part 2)

can i just add the line length dB (attenuation ) to the dB(SNR + SNR Margin) to calculate final bit allocation

to go on to formulate total dsl speeds for both types?

what i'm doing is creating a max speed formula

##
##### Re: some leftover maths

##### Re: some leftover maths

28-11-2010 7:02 PM

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------------------------------------part 3 ------------------------------------------

calculating power gains in dB

example A

10 log (P1/P2) where P1 = power 1 and P2 = power 2

if P1 is twice P2

then dB increase = 10 log (2/1)

dB = 10 times 0.3010299 = 3

so P1 times 2 = a 3dB increase

example B

now for the situation when P1 is four times P2

dB = 10 log(P1/P2)

dB = 10 log(4/1)

dB = 10 log 4

dB = 10 times 0.602059 = 6dB

example 3

now for the situation when P1 is 8 times P2

dB = 10 log(P1/P2)

dB = 10 log(8/1)

dB = 10 log 8

dB = 10 times 0.903089 = 9.0308dB

example 4

now for the situation when P1 is 16 times P2

dB = 10 log(P1/P2)

dB = 10 log(16/1)

dB = 10 log 16

dB = 10 times 1.204119 = 12.04119 dB

so 3db + 3db + 3db + 3db = 12dB

= 2 times 2 times 2 times 2 = 16:1 increase

so knowing this

and without involving any further maths

3dB + 3dB + 3dB + 3dB + 3dB = 15dB

= 2 times 2 times 2 times 2 times 2 = 32:1 (amplification)increase

checking using logs

10 log(P1/P2)

10 log(32/1)

10 times 1.505149 = 15dB to 2 decimal places

dB gains that are only fractional are preceeded by a minus sign

see the following

dB gain = 10 log (Pout/Pin) where Pout is Power Out and Pin is Power in

dB gain = 10 log (1/2)

dB gain = 10 log 0.5

dB gain = 10 times -0.301029

dB gain = -3.010dB = 3dB to 2 decimal places

and

-3dB + -3dB + -3dB + -3dB + -3dB = - 15dB

= 1/2 times 1/2 times 1/2 times 1/2 times 1/2 = 1/32 = 1:32

------------------------------------------part 3 is correct---------------------------------------------

##
##### Re: some leftover maths

##### Re: some leftover maths

28-11-2010 7:03 PM

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##
##### Re: some leftover maths

##### Re: some leftover maths

28-11-2010 7:06 PM

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i'm near but still quite far

##
##### Re: some leftover maths

##### Re: some leftover maths

28-11-2010 9:06 PM

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**Remember you are unique - just like everyone else**##
##### Re: some leftover maths

##### Re: some leftover maths

29-11-2010 4:17 PM

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i've totaled the line attenuation dB figure and the SNR margin dB figure by adding both together (attenuation (dB) + SNR Margin(dB)

then placed its total as Downstream Attenuation in the Kitz max speed calculator

notewith a SNR margin it makes my line longer it places me a little further from the exchange )

and got ~my real download speed

coolio

##
##### Re: some leftover maths

##### Re: some leftover maths

30-11-2010 1:58 PM

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a first attempt at an

estimated download speed formula using max bins and tones

and using graph to account for loss of bits from signal attenuation

[4000 times 15 times 256] -[2000000 times signal attenuation /10]

that needs testing

?

##
##### Re: some leftover maths

##### Re: some leftover maths

30-11-2010 2:02 PM

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##### Re: some leftover maths

##### Re: some leftover maths

02-12-2010 7:09 PM

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##### Re: some leftover maths

##### Re: some leftover maths

02-12-2010 8:26 PM

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There are a number of factors to take into account. No line is perfect.

http://en.wikipedia.org/wiki/ITU_G.992.1

When POTS is present (as in the UK), we start at bin 6, bin 0 exists and 255 bins includes upstream as well (256 I presume includes bin 0, which cannot be used).

There are a number on bins between downstream and upstream which are typically not used anyway.

In the UK, AM radio accounts for a number of bins not being able to load up all the symbols in some bins.

One example is in the Ipswitch area. There are significantly more bins put to waste due to AM radio from the continent.

Oooh, don't forgot lone cross talk. Time to everybody else off in town, for the sake of your additional speed

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