Convert Bits/sec to Hz

[Daku]

I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

 

[Tim Wescott]

On 08/05/2010 08:04 AM, Daku wrote:

I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

Without knowing more, one can't. In general, for a given modulation
scheme, increasing the data rate involves scaling everything down
equally in time, which scales everything up equally in frequency.

But there are so many different ways to encode data onto a signal that
the bandwidth vs. data rate spread is pretty wide. There are practical
systems that have 16-point constellations (four bits/symbol) that can
pack in four bits/Hz; there may be practical (or at least fitfully
practical) systems that can do six bits/Hz. On the other hand, there
are systems that are vastly spectrally inefficient; with those the sky's
the limit as far as wasted bandwidth.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

[Tom Biasi]

"Daku" <dakupoto@gmail.com> wrote in message
news:1f08b0d9-9d6a-4cf3-93cc-19803e81b278@y32g2000prc.googlegroups.com...

I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

Hi,
Tim is quite knowledgeable on these subjects and gave some usefull info but
maybe your question is not quite so deep.
Hertz is used to describe cycles/second (cycles per second). If you allow it
to mean events per second then a bit can be an event.
So 1Gb/sec is 10^9bits / sec or 1 Ghz.
This is for mental clarity and the actual units may vary.

Tom

 

[Grant]

On Thu, 5 Aug 2010 16:19:00 -0400, "Tom Biasi" <tombiasi@optonline.net> wrote:

"Daku" <dakupoto@gmail.com> wrote in message
news:1f08b0d9-9d6a-4cf3-93cc-19803e81b278@y32g2000prc.googlegroups.com...
I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

Hi,
Tim is quite knowledgeable on these subjects and gave some usefull info but
maybe your question is not quite so deep.
Hertz is used to describe cycles/second (cycles per second). If you allow it
to mean events per second then a bit can be an event.
So 1Gb/sec is 10^9bits / sec or 1 Ghz.
This is for mental clarity and the actual units may vary.

Yes, Tim touches on the old baud rate (symbol rate) vs frequency that
you're suggesting as the simple answer.

Both are not incorrect (double negative only to show grey area).

For example 100Mbps network link bangs four symbols on each of 1/25MHz
to get the speed, and Gbps copper network links don't run at 1GHz, they
run slower speed, using a couple pairs in each direction.

So, in this case, context matters.

Where I said symbols, Tim said constellation, Tim is more accurate

Grant.

 

[krw@att.bizzzzzzzzzzzz]

On Fri, 06 Aug 2010 06:49:33 +1000, Grant <omg@grrr.id.au> wrote:

On Thu, 5 Aug 2010 16:19:00 -0400, "Tom Biasi" <tombiasi@optonline.net> wrote:


"Daku" <dakupoto@gmail.com> wrote in message
news:1f08b0d9-9d6a-4cf3-93cc-19803e81b278@y32g2000prc.googlegroups.com...
I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

Hi,
Tim is quite knowledgeable on these subjects and gave some usefull info but
maybe your question is not quite so deep.
Hertz is used to describe cycles/second (cycles per second). If you allow it
to mean events per second then a bit can be an event.
So 1Gb/sec is 10^9bits / sec or 1 Ghz.
This is for mental clarity and the actual units may vary.

Yes, Tim touches on the old baud rate (symbol rate) vs frequency that
you're suggesting as the simple answer.

Both are not incorrect (double negative only to show grey area).

For example 100Mbps network link bangs four symbols on each of 1/25MHz
to get the speed, and Gbps copper network links don't run at 1GHz, they
run slower speed, using a couple pairs in each direction.

So, in this case, context matters.

Where I said symbols, Tim said constellation, Tim is more accurate

Not really. Symbols are the stars in a constellation of stars. The symbol is
the basic unit of information transferred. A constellation is a
representation of the possible physical values (voltage, frequency, phase,
whatever).

A little more specifically, a symbol may be a specific value in the
constellation or a transition from the current point to another.

 

[Daku]

Thanks to all for your feedback. I had thought
about the baud rate idea that Tim elaborated
on, but the context in which I asked this question
was Ethernet bits going from the MAC layer
to the PHY layer at say 1 Gb/s or more (for the
newer standards).



On Aug 6, 3:25 am, "k...@att.bizzzzzzzzzzzz" <k...@att.bizzzzzzzzzzzz>
wrote:

On Fri, 06 Aug 2010 06:49:33 +1000, Grant <o...@grrr.id.au> wrote:
On Thu, 5 Aug 2010 16:19:00 -0400, "Tom Biasi" <tombi...@optonline.net> wrote:

"Daku" <dakup...@gmail.com> wrote in message
news:1f08b0d9-9d6a-4cf3-93cc-19803e81b278@y32g2000prc.googlegroups.com...
I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

Hi,
Tim is quite knowledgeable on these subjects and gave some usefull info but
maybe your question is not quite so deep.
Hertz is used to describe cycles/second (cycles per second). If you allow it
to mean events per second then a bit can be an event.
So 1Gb/sec is 10^9bits / sec or 1 Ghz.
This is for mental clarity and the actual units may vary.

Yes, Tim touches on the old baud rate (symbol rate) vs frequency that
you're suggesting as the simple answer.

Both are not incorrect (double negative only to show grey area).

For example 100Mbps network link bangs four symbols on each of 1/25MHz
to get the speed, and Gbps copper network links don't run at 1GHz, they
run slower speed, using a couple pairs in each direction.

So, in this case, context matters.

Where I said symbols, Tim said constellation, Tim is more accurate

Not really. Symbols are the stars in a constellation of stars. The symbol is
the basic unit of information transferred. A constellation is a
representation of the possible physical values (voltage, frequency, phase,
whatever).

A little more specifically, a symbol may be a specific value in the
constellation or a transition from the current point to another.

 

[Cydrome Leader]

Tim Wescott <tim@seemywebsite.com> wrote:

On 08/05/2010 08:04 AM, Daku wrote:
I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

Without knowing more, one can't. In general, for a given modulation
scheme, increasing the data rate involves scaling everything down
equally in time, which scales everything up equally in frequency.

But there are so many different ways to encode data onto a signal that
the bandwidth vs. data rate spread is pretty wide. There are practical
systems that have 16-point constellations (four bits/symbol) that can
pack in four bits/Hz; there may be practical (or at least fitfully
practical) systems that can do six bits/Hz. On the other hand, there
are systems that are vastly spectrally inefficient; with those the sky's
the limit as far as wasted bandwidth.

MIME encoded XML is one serious contender for wasted bandwidth.

 

[krw@att.bizzzzzzzzzzzz]

On Fri, 6 Aug 2010 03:42:15 -0700 (PDT), Daku <dakupoto@gmail.com> wrote:

Thanks to all for your feedback. I had thought
about the baud rate idea that Tim elaborated
on, but the context in which I asked this question
was Ethernet bits going from the MAC layer
to the PHY layer at say 1 Gb/s or more (for the
newer standards).

Again, you need to know how many bits per symbol are used. IIRC GBE is four
bits (4-pairs in use).

 

[Grant]

On Fri, 06 Aug 2010 19:30:03 -0500, "krw@att.bizzzzzzzzzzzz" <krw@att.bizzzzzzzzzzzz> wrote:

On Fri, 6 Aug 2010 03:42:15 -0700 (PDT), Daku <dakupoto@gmail.com> wrote:

Thanks to all for your feedback. I had thought
about the baud rate idea that Tim elaborated
on, but the context in which I asked this question
was Ethernet bits going from the MAC layer
to the PHY layer at say 1 Gb/s or more (for the
newer standards).

Again, you need to know how many bits per symbol are used. IIRC GBE is four
bits (4-pairs in use).

I think 100Mbps symbol rate is 25Mhz, 4 bits/symbol, 1 pair each
direction, but no idea what magic's done for 1Gbps over the 4 pairs.

Grant.

 

[Gareth]

On 05/08/2010 16:04, Daku wrote:

I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

According to the Shannon-Hartley theorem, the highest possible data rate is:

C = B*log2(1 + S/N)

Where C is the channel capacity in bits per second

B is the channel bandwidth in Hz

Log2 is base 2 logarithm

and S/N is the signal to noise power ratio (as a linear ratio not in dB)

In practice you will always get less than this, though some modulation
schemes can get quite close.

--
-----------------------------------------------------------------------
To reply to me directly:

Replace privacy.net with: totalise DOT co DOT uk and replace me with
gareth.harris

 

[Grant]

On Sat, 7 Aug 2010 20:57:07 -0700 (PDT), Daku <dakupoto@gmail.com> wrote:

Thanks to all for your answers. However, I am a bit confused. In a
very simple situation where e.g., a
clock (1 - 0 - 1 - 0 ....) may I know where the bits/
symbol concept is coming in - I am transferring
some bits. Thanks in advance.

depends how you do the data framing too, how do you tell if a bit is a
one or zero?

Grant.

 

[Daku]

Thanks to all for your answers. However, I am a bit confused. In a
very simple situation where e.g., a
clock (1 - 0 - 1 - 0 ....) may I know where the bits/
symbol concept is coming in - I am transferring
some bits. Thanks in advance.

On Aug 7, 10:30 pm, Gareth <m...@privacy.net> wrote:

On 05/08/2010 16:04, Daku wrote:

I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

According to the Shannon-Hartley theorem, the highest possible data rate is:

C = B*log2(1 + S/N)

Where C is the channel capacity in bits per second

B is the channel bandwidth in Hz

Log2 is base 2 logarithm

and S/N is the signal to noise power ratio (as a linear ratio not in dB)

In practice you will always get less than this, though some modulation
schemes can get quite close.

--
-----------------------------------------------------------------------
To reply to me directly:

Replace privacy.net with: totalise DOT co DOT uk and replace me with
gareth.harris

 

[Gareth]

On 08/08/2010 17:00, Daku wrote:

Bit values may be inferred from the specified voltage levels,
as in stabdard CMOS - analogous to a timing diagram.

What exactly are you trying to do here? a bit of background may help
answer your question. E.g. are you trying to send data down a cable? if
so will it be synchronous or asynchronous? Is it just one way
communication between two devices?

Gareth.

PS top posting, that's posting your reply above the relevant text, can
make threads difficult to follow. it is usually clearer to put your
reply below the relevant text in the post you are replying to.

 

[Tim Wescott]

On 08/06/2010 03:42 AM, Daku wrote:
(top posting fixed)

On Aug 6, 3:25 am, "k...@att.bizzzzzzzzzzzz"<k...@att.bizzzzzzzzzzzz
wrote:
On Fri, 06 Aug 2010 06:49:33 +1000, Grant<o...@grrr.id.au> wrote:
On Thu, 5 Aug 2010 16:19:00 -0400, "Tom Biasi"<tombi...@optonline.net> wrote:

"Daku"<dakup...@gmail.com> wrote in message
news:1f08b0d9-9d6a-4cf3-93cc-19803e81b278@y32g2000prc.googlegroups.com...
I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

Hi,
Tim is quite knowledgeable on these subjects and gave some usefull info but
maybe your question is not quite so deep.
Hertz is used to describe cycles/second (cycles per second). If you allow it
to mean events per second then a bit can be an event.
So 1Gb/sec is 10^9bits / sec or 1 Ghz.
This is for mental clarity and the actual units may vary.

Yes, Tim touches on the old baud rate (symbol rate) vs frequency that
you're suggesting as the simple answer.

Both are not incorrect (double negative only to show grey area).

For example 100Mbps network link bangs four symbols on each of 1/25MHz
to get the speed, and Gbps copper network links don't run at 1GHz, they
run slower speed, using a couple pairs in each direction.

So, in this case, context matters.

Where I said symbols, Tim said constellation, Tim is more accurate

Not really. Symbols are the stars in a constellation of stars. The symbol is
the basic unit of information transferred. A constellation is a
representation of the possible physical values (voltage, frequency, phase,
whatever).

A little more specifically, a symbol may be a specific value in the
constellation or a transition from the current point to another.

Thanks to all for your feedback. I had thought
about the baud rate idea that Tim elaborated
on, but the context in which I asked this question
was Ethernet bits going from the MAC layer
to the PHY layer at say 1 Gb/s or more (for the
newer standards).

GB Ethernet uses 5-level signaling on four pairs of wires. I can't find
a reference that gives the symbol rate; without forward error correction
(FEC) it could be as low as 110MBaud. I don't believe this at all-- I'm
sure there's at least some coding to keep the average voltage at 0 for
transformer coupling, for error detection, and maybe even for error
correction.

But surfing on Wikipedia for a few moments didn't tell me -- you'll have
to dig up the appropriate standard and take a look for yourself!

http://en.wikipedia.org/wiki/Ethernet_over_twisted_pair has a
discussion, and a link to IEEE 803.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

[Tim Wescott]

On 08/06/2010 03:42 AM, Daku wrote:

Thanks to all for your feedback. I had thought
about the baud rate idea that Tim elaborated
on, but the context in which I asked this question
was Ethernet bits going from the MAC layer
to the PHY layer at say 1 Gb/s or more (for the
newer standards).

OOps -- http://en.wikipedia.org/wiki/Ethernet_over_twisted_pair has a

link to IEEE 802.3.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

[Daku]

Bit values may be inferred from the specified voltage levels,
as in stabdard CMOS - analogous to a timing diagram.

On Aug 8, 9:29 am, Grant <o...@grrr.id.au> wrote:

depends how you do the data framing too, how do you tell if a bit is a
one or zero?

Grant.

 

[Grant]

On Sun, 8 Aug 2010 09:00:08 -0700 (PDT), Daku <dakupoto@gmail.com> wrote:

Bit values may be inferred from the specified voltage levels,
as in stabdard CMOS - analogous to a timing diagram.

And data framing? Bit and byte/word separation? A square wave conveys
no information until you agree on how to interpret it, frequency? So
you need to modulate the pulse train in some fashion, agreed beforehand
at both ends before you can convey information.

Basic information theory: sender and receiver must first agree on a
dictionary

Grant.

On Aug 8, 9:29 am, Grant <o...@grrr.id.au> wrote:

depends how you do the data framing too, how do you tell if a bit is a
one or zero?

Grant.

 

[Grant]

On Sun, 08 Aug 2010 10:17:50 -0700, Tim Wescott <tim@seemywebsite.com> wrote:

On 08/06/2010 03:42 AM, Daku wrote:
(top posting fixed)
On Aug 6, 3:25 am, "k...@att.bizzzzzzzzzzzz"<k...@att.bizzzzzzzzzzzz
wrote:
On Fri, 06 Aug 2010 06:49:33 +1000, Grant<o...@grrr.id.au> wrote:
On Thu, 5 Aug 2010 16:19:00 -0400, "Tom Biasi"<tombi...@optonline.net> wrote:

"Daku"<dakup...@gmail.com> wrote in message
news:1f08b0d9-9d6a-4cf3-93cc-19803e81b278@y32g2000prc.googlegroups.com...
I understand that they are different domains (Hz - analog and bits/sec
- digital), how would one
convert e.g., 1Gbit/s to corresponding Hertz
frequency ?

Hi,
Tim is quite knowledgeable on these subjects and gave some usefull info but
maybe your question is not quite so deep.
Hertz is used to describe cycles/second (cycles per second). If you allow it
to mean events per second then a bit can be an event.
So 1Gb/sec is 10^9bits / sec or 1 Ghz.
This is for mental clarity and the actual units may vary.

Yes, Tim touches on the old baud rate (symbol rate) vs frequency that
you're suggesting as the simple answer.

Both are not incorrect (double negative only to show grey area).

For example 100Mbps network link bangs four symbols on each of 1/25MHz
to get the speed, and Gbps copper network links don't run at 1GHz, they
run slower speed, using a couple pairs in each direction.

So, in this case, context matters.

Where I said symbols, Tim said constellation, Tim is more accurate

Not really. Symbols are the stars in a constellation of stars. The symbol is
the basic unit of information transferred. A constellation is a
representation of the possible physical values (voltage, frequency, phase,
whatever).

A little more specifically, a symbol may be a specific value in the
constellation or a transition from the current point to another.

Thanks to all for your feedback. I had thought
about the baud rate idea that Tim elaborated
on, but the context in which I asked this question
was Ethernet bits going from the MAC layer
to the PHY layer at say 1 Gb/s or more (for the
newer standards).

GB Ethernet uses 5-level signaling on four pairs of wires. I can't find
a reference that gives the symbol rate; without forward error correction
(FEC) it could be as low as 110MBaud. I don't believe this at all-- I'm
sure there's at least some coding to keep the average voltage at 0 for
transformer coupling, for error detection, and maybe even for error
correction.

Rather magical, part of the training sequence (on copper) determines
cable length

Grant.

But surfing on Wikipedia for a few moments didn't tell me -- you'll have
to dig up the appropriate standard and take a look for yourself!

http://en.wikipedia.org/wiki/Ethernet_over_twisted_pair has a
discussion, and a link to IEEE 803.

 

[Daku]

On Aug 8, 9:27 pm, Gareth <m...@privacy.net> wrote:

What exactly are you trying to do here? a bit of background may help
answer your question. E.g. are you trying to send data down a cable? if
so will it be synchronous or asynchronous? Is it just one way
communication between two devices?
I am creating Verilog models of high-speed Ethernet protocols (e.g.,
= 1Gbit/sec). All data movement is in between the sub-circuits of
an integrated circuit. However, some of the IEEE specification

documents that I have read do not mention any of the coding
schemes etc.

Gareth.

PS top posting, that's posting your reply above the relevant text, can
make threads difficult to follow. it is usually clearer to put your
reply below the relevant text in the post you are replying to.