Hyperbolic tangent transfer function

[The Phantom]

On Tue, 10 May 2005 13:05:57 -0400, John Popelish <jpopelish@rica.net> wrote:

Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of Barrie
Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep running
into IEEE requests for my membership number (which I don't have).

It is now known that the tanh function isn't quite the right function.

See: http://www.adeptscience.co.uk/maplearticles/f969.html

 

[Kevin Aylward]

The Phantom wrote:

On Tue, 10 May 2005 13:05:57 -0400, John Popelish
jpopelish@rica.net> wrote:

Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of Barrie
Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep running
into IEEE requests for my membership number (which I don't have).

It is now known that the tanh function isn't quite the right function.

No it isnt. The tanh function is the correct one.

See: http://www.adeptscience.co.uk/maplearticles/f969.html

This has nothing to do with the diff pair having a tanh function.

Secondly, I already have prior priority to using the Lambert function to
solve this problem.

http://www.anasoft.co.uk/EE/widlarlambert/widlarlambert.html

In fact, if this TC Banwell is claiming the first credit by his IEEE
paper (Nov 2000), it pisses me off no end

I obtained this result in Jan 2000, to wit:

http://groups-beta.google.com/group/sci.math/browse_thread/thread/cb85a17bbe6bfd01/e2ad1bb564201bf1?q=aylward+%22Lambert+%22&rnum=20&hl=en#e2ad1bb564201bf1

So, sure, I cheated to get the actual solution of x=y.exp in closed
form, but it would seem that I beat everyone to the punch in its
application to transister circuits.

Kevin Aylward
informationEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[analog]

Kevin Aylward wrote:

The Phantom wrote:
John Popelish wrote:
Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of
Barrie Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep
running into IEEE requests for my membership number (which I
don't have).

It is now known that the tanh function isn't quite the right
function.

No it isnt. The tanh function is the correct one.

See: http://www.adeptscience.co.uk/maplearticles/f969.html

This has nothing to do with the diff pair having a tanh function.

Secondly, I already have prior priority to using the Lambert
function to solve this problem.

http://www.anasoft.co.uk/EE/widlarlambert/widlarlambert.html

In fact, if this TC Banwell is claiming the first credit by his
IEEE paper (Nov 2000), it pisses me off no end

I obtained this result in Jan 2000, to wit:

http://groups-beta.google.com/group/sci.math/browse_thread/thread/cb85a17bbe6bfd01/e2ad1bb564201bf1?q=aylward+%22Lambert+%22&rnum=20&hl=en#e2ad1bb564201bf1

So, sure, I cheated to get the actual solution of x=y.exp in
closed form, but it would seem that I beat everyone to the punch
in its application to transister circuits.

"Exact analytical solution for current flow through diode with
series resistance" by Banwell, T.C. and Jayakumar, A.

This paper appears in Electronics Letters, 17 Feb 2000, Volume 36,
Issue 4 on pages 291-292.

Abstract: A simple analytical expression is presented for the
current flow in a diode driven by a voltage source through a
series resistance. The proposed solution is based on the Lambert
W-function. The new expression leads to an efficient method for
extracting series resistance from measured current-voltage data.
Experimental results are presented which validate the proposed
solution and extraction method

This paper was published nearly at the time of the thread you
referenced, but it must have been submitted at least several
months prior to that date. Still, since it is the earliest
reference to the subject I found via the IEEE, I am impressed
that you were looking at this back then.

What led you to consider the Lambert W function and what did you
mean by, "So, sure, I cheated to get the actual solution [...]?"

Regards -- analogspiceman

 

[The Phantom]

On Sat, 14 May 2005 07:18:22 GMT, "Kevin Aylward" <see_website@anasoft.co.uk> wrote:

The Phantom wrote:
On Tue, 10 May 2005 13:05:57 -0400, John Popelish
jpopelish@rica.net> wrote:

Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of Barrie
Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep running
into IEEE requests for my membership number (which I don't have).

It is now known that the tanh function isn't quite the right function.

No it isnt. The tanh function is the correct one.


See: http://www.adeptscience.co.uk/maplearticles/f969.html

This has nothing to do with the diff pair having a tanh function.

Secondly, I already have prior priority to using the Lambert function to
solve this problem.

http://www.anasoft.co.uk/EE/widlarlambert/widlarlambert.html

In fact, if this TC Banwell is claiming the first credit by his IEEE
paper (Nov 2000), it pisses me off no end

I don't see anything in his paper about *claims* one way or another. But at the bottom
of the first page of the paper it says that the IEEE received his manuscript on July 15,
1998. I posted the first page over on alt.binaries.schematics.electronic FYI.

I obtained this result in Jan 2000, to wit:

http://groups-beta.google.com/group/sci.math/browse_thread/thread/cb85a17bbe6bfd01/e2ad1bb564201bf1?q=aylward+%22Lambert+%22&rnum=20&hl=en#e2ad1bb564201bf1

So, sure, I cheated to get the actual solution of x=y.exp in closed
form, but it would seem that I beat everyone to the punch in its
application to transister circuits.

Kevin Aylward
informationEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Kevin Aylward]

analog wrote:

Kevin Aylward wrote:
The Phantom wrote:
John Popelish wrote:
Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of
Barrie Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep
running into IEEE requests for my membership number (which I
don't have).

It is now known that the tanh function isn't quite the right
function.

No it isnt. The tanh function is the correct one.

See: http://www.adeptscience.co.uk/maplearticles/f969.html

This has nothing to do with the diff pair having a tanh function.

Secondly, I already have prior priority to using the Lambert
function to solve this problem.

http://www.anasoft.co.uk/EE/widlarlambert/widlarlambert.html

In fact, if this TC Banwell is claiming the first credit by his
IEEE paper (Nov 2000), it pisses me off no end

I obtained this result in Jan 2000, to wit:

http://groups-beta.google.com/group/sci.math/browse_thread/thread/cb85a17bbe6bfd01/e2ad1bb564201bf1?q=aylward+%22Lambert+%22&rnum=20&hl=en#e2ad1bb564201bf1

So, sure, I cheated to get the actual solution of x=y.exp in
closed form, but it would seem that I beat everyone to the punch
in its application to transister circuits.

"Exact analytical solution for current flow through diode with
series resistance" by Banwell, T.C. and Jayakumar, A.

This paper appears in Electronics Letters, 17 Feb 2000, Volume 36,
Issue 4 on pages 291-292.

Abstract: A simple analytical expression is presented for the
current flow in a diode driven by a voltage source through a
series resistance. The proposed solution is based on the Lambert
W-function. The new expression leads to an efficient method for
extracting series resistance from measured current-voltage data.
Experimental results are presented which validate the proposed
solution and extraction method

This paper was published nearly at the time of the thread you
referenced, but it must have been submitted at least several
months prior to that date. Still, since it is the earliest
reference to the subject I found via the IEEE, I am impressed
that you were looking at this back then.

What led you to consider the Lambert W function and what did you
mean by, "So, sure, I cheated to get the actual solution [...]?"

If you went to the NG link I posted you will see that I posted to the
maths NG.

I asked for the *derivation* of the power series solution to x=y.exp,
as I was using it to solve said electronics problems, around the 80's,
prior to the internet.

I got the answer that it was the Lambert W function. So I cheated in
knowing it was named the Lambert W function. However, I was using the
function, as is by the PS solution. So, the cheat was in name only.

I first studied this equation around 1983. It was in the shumms advanced
calculus book. One of the questions was, show that the solution to that
equation was the power series I referenced in my paper. So, I had the PS
solution, but I never manged to derive it myself.

I realised later, that the solution was relevant to diode equation
circuits. I didn't know until the maths posting that it was already
considered as a standard function, and had a name. The schumms book
didn't mention that fact.

Kevin Aylward
informationEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[The Phantom]

On Sat, 14 May 2005 07:18:22 GMT, "Kevin Aylward" <see_website@anasoft.co.uk> wrote:

The Phantom wrote:
On Tue, 10 May 2005 13:05:57 -0400, John Popelish
jpopelish@rica.net> wrote:

Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of Barrie
Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep running
into IEEE requests for my membership number (which I don't have).

It is now known that the tanh function isn't quite the right function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base spreading resistance,
various extrinsic resistances). For example, using a pair of 2N2102 silicon transistors,
with the current source in the emitters set to 10 mA, the transfer function looks pretty
close to a tanh curve. But, just raise the current source to 100 mA and the curve is
plainly no longer a tanh curve. At these higher currents the curve almost becomes a
straight line between limits. At 10 mA the same effect can be achieved with 50 ohm
resistors in series with the emitters. So, the Lambert W function could be used to
provide a better analytical description of the behavior of this circuit when resistances
are present, since the tanh function is only an approximation, failing as the voltages
across resistances rise past a few tens of millivolts. Fifty millivolts across emitter
resistances is enough to cause substantial deviation from a true tanh curve.

See: http://www.adeptscience.co.uk/maplearticles/f969.html

This has nothing to do with the diff pair having a tanh function.

Secondly, I already have prior priority to using the Lambert function to
solve this problem.

http://www.anasoft.co.uk/EE/widlarlambert/widlarlambert.html

In fact, if this TC Banwell is claiming the first credit by his IEEE
paper (Nov 2000), it pisses me off no end

I obtained this result in Jan 2000, to wit:

http://groups-beta.google.com/group/sci.math/browse_thread/thread/cb85a17bbe6bfd01/e2ad1bb564201bf1?q=aylward+%22Lambert+%22&rnum=20&hl=en#e2ad1bb564201bf1

So, sure, I cheated to get the actual solution of x=y.exp in closed
form, but it would seem that I beat everyone to the punch in its
application to transister circuits.

Kevin Aylward
informationEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Kevin Aylward]

The Phantom wrote:

On Sat, 14 May 2005 07:18:22 GMT, "Kevin Aylward"
see_website@anasoft.co.uk> wrote:

The Phantom wrote:
On Tue, 10 May 2005 13:05:57 -0400, John Popelish
jpopelish@rica.net> wrote:

Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of
Barrie Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep running
into IEEE requests for my membership number (which I don't have).

It is now known that the tanh function isn't quite the right
function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base
spreading resistance, various extrinsic resistances).

The statement was in the context of using the Lambert W function. Such a
function is not required for the 1st order model.

For example,
using a pair of 2N2102 silicon transistors, with the current source
in the emitters set to 10 mA, the transfer function looks pretty
close to a tanh curve. But, just raise the current source to 100 mA
and the curve is plainly no longer a tanh curve.

Ho humm....yes, yes, yes... Ho humm....we all know...but beyond the
scope of the discussion as far as I am concerned.

Kevin Aylward
informationEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Jim Thompson]

On Thu, 19 May 2005 03:00:33 -0700, The Phantom <phantom@aol.com>
wrote:

On Sat, 14 May 2005 07:18:22 GMT, "Kevin Aylward" <see_website@anasoft.co.uk> wrote:

The Phantom wrote:
[snip]
It is now known that the tanh function isn't quite the right function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base spreading resistance,
various extrinsic resistances). For example, using a pair of 2N2102 silicon transistors,
with the current source in the emitters set to 10 mA, the transfer function looks pretty
close to a tanh curve. But, just raise the current source to 100 mA and the curve is
plainly no longer a tanh curve. At these higher currents the curve almost becomes a
straight line between limits. At 10 mA the same effect can be achieved with 50 ohm
resistors in series with the emitters. So, the Lambert W function could be used to
provide a better analytical description of the behavior of this circuit when resistances
are present, since the tanh function is only an approximation, failing as the voltages
across resistances rise past a few tens of millivolts. Fifty millivolts across emitter
resistances is enough to cause substantial deviation from a true tanh curve.

[snip]

Well DUH!

Large devices run at small currents come close enough to TANH for
government work ;-)

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

 

[The Phantom]

On Thu, 19 May 2005 12:24:46 GMT, "Kevin Aylward" <see_website@anasoft.co.uk> wrote:

The Phantom wrote:
On Sat, 14 May 2005 07:18:22 GMT, "Kevin Aylward"
see_website@anasoft.co.uk> wrote:

The Phantom wrote:
On Tue, 10 May 2005 13:05:57 -0400, John Popelish
jpopelish@rica.net> wrote:

Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of
Barrie Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep running
into IEEE requests for my membership number (which I don't have).

It is now known that the tanh function isn't quite the right
function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base
spreading resistance, various extrinsic resistances).

The statement was in the context of using the Lambert W function. Such a
function is not required for the 1st order model.

Where did you get the impression that I was referring to a first order model? Your own
web site plainly shows that when resistances are taken into account, the Lambert function
is appropriate to use. What does Jim say above? "Pretty small range, but can be built
out." Then I said "...the tanh function isn't *quite* the right function." The first
order model is only approximate, since it *is* just a "first order model". I simply
pointed out that if one wants an analysis that goes beyond a first order model, the
Lambert W function is an appropriate tool.

For example,
using a pair of 2N2102 silicon transistors, with the current source
in the emitters set to 10 mA, the transfer function looks pretty
close to a tanh curve. But, just raise the current source to 100 mA
and the curve is plainly no longer a tanh curve.

Ho humm....yes, yes, yes... Ho humm....we all know...but beyond the
scope of the discussion as far as I am concerned.

Kevin Aylward
informationEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[The Phantom]

On Thu, 19 May 2005 08:23:27 -0700, Jim Thompson <thegreatone@example.com> wrote:

On Thu, 19 May 2005 03:00:33 -0700, The Phantom <phantom@aol.com
wrote:

On Sat, 14 May 2005 07:18:22 GMT, "Kevin Aylward" <see_website@anasoft.co.uk> wrote:

The Phantom wrote:
[snip]
It is now known that the tanh function isn't quite the right function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base spreading resistance,
various extrinsic resistances). For example, using a pair of 2N2102 silicon transistors,
with the current source in the emitters set to 10 mA, the transfer function looks pretty
close to a tanh curve. But, just raise the current source to 100 mA and the curve is
plainly no longer a tanh curve. At these higher currents the curve almost becomes a
straight line between limits. At 10 mA the same effect can be achieved with 50 ohm
resistors in series with the emitters. So, the Lambert W function could be used to
provide a better analytical description of the behavior of this circuit when resistances
are present, since the tanh function is only an approximation, failing as the voltages
across resistances rise past a few tens of millivolts. Fifty millivolts across emitter
resistances is enough to cause substantial deviation from a true tanh curve.

[snip]

Well DUH!

Large devices run at small currents come close enough to TANH for
government work ;-)

Do you get the impression that I'm saying something contrary to this? Don't I say
above "...with the current source in the emitters set to 10 ma, the transfer function
looks pretty close to a tanh curve." I'm discussing what one should do when the currents
are large enough that this approximation fails. Is it not permissible to raise this
issue? Duh, indeed.

...Jim Thompson

 

[The Phantom]

On Thu, 19 May 2005 12:24:46 GMT, "Kevin Aylward" <see_website@anasoft.co.uk> wrote:

Only for an ideal transistor having no parasitic resistances (base
spreading resistance, various extrinsic resistances).

The statement was in the context of using the Lambert W function. Such a
function is not required for the 1st order model.

In the context of using the Lambert W function, don't you think it would be interesting to
develop an expression for a 2nd order model, possibly using the Lambert W? I've been
giving it some effort and the it looks to me like it may not be possible to whip it into a
closed form expression, even with the Lambert function. I haven't given up yet, though.

A Lambert W formulation would be making the assumption that the resistances involved are
constant, which isn't *quite* true due to conductivity modulation. But I think it would
be interesting to see just how close such an analysis could come at moderate to high
currents, compared to the straight tanh analysis.

 

[Jim Thompson]

On Thu, 19 May 2005 09:54:42 -0700, The Phantom <phantom@aol.com>
wrote:

On Thu, 19 May 2005 08:23:27 -0700, Jim Thompson <thegreatone@example.com> wrote:

On Thu, 19 May 2005 03:00:33 -0700, The Phantom <phantom@aol.com
wrote:

On Sat, 14 May 2005 07:18:22 GMT, "Kevin Aylward" <see_website@anasoft.co.uk> wrote:

The Phantom wrote:
[snip]
It is now known that the tanh function isn't quite the right function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base spreading resistance,
various extrinsic resistances). For example, using a pair of 2N2102 silicon transistors,
with the current source in the emitters set to 10 mA, the transfer function looks pretty
close to a tanh curve. But, just raise the current source to 100 mA and the curve is
plainly no longer a tanh curve. At these higher currents the curve almost becomes a
straight line between limits. At 10 mA the same effect can be achieved with 50 ohm
resistors in series with the emitters. So, the Lambert W function could be used to
provide a better analytical description of the behavior of this circuit when resistances
are present, since the tanh function is only an approximation, failing as the voltages
across resistances rise past a few tens of millivolts. Fifty millivolts across emitter
resistances is enough to cause substantial deviation from a true tanh curve.

[snip]

Well DUH!

Large devices run at small currents come close enough to TANH for
government work ;-)

Do you get the impression that I'm saying something contrary to this? Don't I say
above "...with the current source in the emitters set to 10 ma, the transfer function
looks pretty close to a tanh curve." I'm discussing what one should do when the currents
are large enough that this approximation fails. Is it not permissible to raise this
issue? Duh, indeed.

I think it's unlikely that the typical user would be running a device
at such a high current that bulk resistances matter.

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

 

[Kevin Aylward]

The Phantom wrote:

On Thu, 19 May 2005 12:24:46 GMT, "Kevin Aylward"
see_website@anasoft.co.uk> wrote:

The Phantom wrote:
On Sat, 14 May 2005 07:18:22 GMT, "Kevin Aylward"
see_website@anasoft.co.uk> wrote:

The Phantom wrote:
On Tue, 10 May 2005 13:05:57 -0400, John Popelish
jpopelish@rica.net> wrote:

Jim Thompson wrote:

Without checking my math, I do believe that an ordinary bipolar
differential pair has TANH for a transfer function.

Pretty small range, but can be built out. Look into some of
Barrie Gilbert's paper's.

I would like very much to read Gilbert's papers, but I keep
running into IEEE requests for my membership number (which I
don't have).

It is now known that the tanh function isn't quite the right
function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base
spreading resistance, various extrinsic resistances).

The statement was in the context of using the Lambert W function.
Such a function is not required for the 1st order model.

Where did you get the impression that I was referring to a first
order model? Your own web site plainly shows that when resistances
are taken into account, the Lambert function is appropriate to use.
What does Jim say above? "Pretty small range, but can be built out."
Then I said "...the tanh function isn't *quite* the right function."
The first order model is only approximate, since it *is* just a
"first order model". I simply pointed out that if one wants an
analysis that goes beyond a first order model, the Lambert W function
is an appropriate tool.

I suspect there was simply a miscommunication problem on what was being
addressed.


Kevin Aylward
informationEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Ban]

Jim Thompson wrote:

The Phantom wrote:
[snip]
It is now known that the tanh function isn't quite the right
function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base
spreading resistance, various extrinsic resistances). For
example, using a pair of 2N2102 silicon transistors, with the
current source in the emitters set to 10 mA, the transfer function
looks pretty close to a tanh curve. But, just raise the current
source to 100 mA and the curve is plainly no longer a tanh curve.
At these higher currents the curve almost becomes a straight line
between limits. At 10 mA the same effect can be achieved with 50
ohm resistors in series with the emitters. So, the Lambert W
function could be used to provide a better analytical description
of the behavior of this circuit when resistances are present,
since the tanh function is only an approximation, failing as the
voltages across resistances rise past a few tens of millivolts.
Fifty millivolts across emitter resistances is enough to cause
substantial deviation from a true tanh curve.

[snip]

Well DUH!

Large devices run at small currents come close enough to TANH for
government work ;-)

Do you get the impression that I'm saying something contrary to
this? Don't I say above "...with the current source in the emitters
set to 10 ma, the transfer function looks pretty close to a tanh
curve." I'm discussing what one should do when the currents are
large enough that this approximation fails. Is it not permissible
to raise this issue? Duh, indeed.


I think it's unlikely that the typical user would be running a device
at such a high current that bulk resistances matter.

I have been running a short simulation with a 100uA current source in the
emitter of 2N2222 and 1k resistors on the opamp.
all values are in mV
0000 0000
0020 0036.7
0040 0064.12
0060 0081.1
0080 0090.4
0100 0094.9
0200 0099.31
0500 0099.36
1000 0099.42
There is a certain tolerance as I measured the values with the curser

--
ciao Ban
Bordighera, Italy

 

[Jim Thompson]

On Thu, 19 May 2005 18:07:33 GMT, "Ban" <bansuri@web.de> wrote:

Jim Thompson wrote:
The Phantom wrote:
[snip]
It is now known that the tanh function isn't quite the right
function.

No it isnt. The tanh function is the correct one.

Only for an ideal transistor having no parasitic resistances (base
spreading resistance, various extrinsic resistances). For
example, using a pair of 2N2102 silicon transistors, with the
current source in the emitters set to 10 mA, the transfer function
looks pretty close to a tanh curve. But, just raise the current
source to 100 mA and the curve is plainly no longer a tanh curve.
At these higher currents the curve almost becomes a straight line
between limits. At 10 mA the same effect can be achieved with 50
ohm resistors in series with the emitters. So, the Lambert W
function could be used to provide a better analytical description
of the behavior of this circuit when resistances are present,
since the tanh function is only an approximation, failing as the
voltages across resistances rise past a few tens of millivolts.
Fifty millivolts across emitter resistances is enough to cause
substantial deviation from a true tanh curve.

[snip]

Well DUH!

Large devices run at small currents come close enough to TANH for
government work ;-)

Do you get the impression that I'm saying something contrary to
this? Don't I say above "...with the current source in the emitters
set to 10 ma, the transfer function looks pretty close to a tanh
curve." I'm discussing what one should do when the currents are
large enough that this approximation fails. Is it not permissible
to raise this issue? Duh, indeed.


I think it's unlikely that the typical user would be running a device
at such a high current that bulk resistances matter.


I have been running a short simulation with a 100uA current source in the
emitter of 2N2222 and 1k resistors on the opamp.
all values are in mV
0000 0000
0020 0036.7
0040 0064.12
0060 0081.1
0080 0090.4
0100 0094.9
0200 0099.31
0500 0099.36
1000 0099.42
There is a certain tolerance as I measured the values with the curser

Needs to be differential (2x 2N2222), to get TANH.

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

 

[Ban]

Jim Thompson wrote:

Needs to be differential (2x 2N2222), to get TANH.

...Jim Thompson

Of course it is a differential amp
+-----+---o
| | +Vcc
.-. .-.
| | | | 1k_
| |10k| | +--|___|--+
'-' '-' | |
| | | |\ |
| +------------+----|-\ |
| | | >-+---o
+-----)------------+----|+/ Vout
| | | |/
Vin |/ \| .-.
o------| 2222 |--+ | |1k
|> <| | | |
| | | '-'
+--+--+ | |
| === ===
| GND GND
|
|
.-.
( I )100uA
'-'
|
o -Vee
(created by AACircuit v1.28 beta 10/06/04 www.tech-chat.de)

--
ciao Ban
Bordighera, Italy

 

[Tony Williams]

In article <fYdje.1412714$35.52718843@news4.tin.it>,
Ban <bansuri@web.de> wrote:

Of course it is a differential amp
+-----+---o
| | +Vcc
.-. .-.
| | | | 1k_
| |10k| | +--|___|--+
'-' '-' | |
| | | |\ |
| +------------+----|-\ |
| | | >-+---o
+-----)------------+----|+/ Vout
| | | |/
Vin |/ \| .-.
o------| 2222 |--+ | |1k
|> <| | | |
| | | '-'
+--+--+ | |
| === ===
| GND GND
|
|
.-.
( I )100uA
'-'
|
o -Vee
(created by AACircuit v1.28 beta 10/06/04 www.tech-chat.de)

Or perhaps an OTA, LM3080 or LM13700?

--
Tony Williams.

 

[Rich Grise]

On Fri, 20 May 2005 01:54:10 -0700, Winfield Hill wrote:

Tony Williams wrote...

In article <fYdje.1412714$35.52718843@news4.tin.it>,
Ban <bansuri@web.de> wrote:

Of course it is a differential amp

+-----+---o
| | +Vcc
.-. .-.
| | | | 1k_
| |10k| | +--|___|--+
'-' '-' | |
| | | |\ |
| +------------+----|-\ |
| | | >-+---o
+-----)------------+----|+/ Vout
| | | |/
|/ \| .-.
o------| 2222 |--+ | |1k
|> <| | | |
Vin +--+--+ | '-'
| | |
o---------- | ------' ===
| GND
.-.
( I )100uA
'-'
|
o -Vee

Or perhaps an OTA, LM3080 or LM13700?

In Ban's drawing, one must take care with Vcc not to saturate the
transistors. A fully-differential input is best (I've edited the
drawing to show this), with a common-mode voltage well below Vout.
Properly done, the 10k pullup resistors may not be necessary.

When I was in the USAF (1968 - 1976) there were differential pairs
in one TO-5 sized package, but with 6 leads. I'd think they'd temperature-
track fairly well, but a very quick web search on "differential
transistor pair" didn't seem to turn up much, and I don't really
know who has a website where I could look up something like that.

Anybody remember them, and if they're still available? Albeit,
I've just looked up LM3080, and it does put more stuff into one
package.

Thanks,
Rich

 

[Ban]

Rich Grise wrote:

On Fri, 20 May 2005 01:54:10 -0700, Winfield Hill wrote:

Tony Williams wrote...

In article <fYdje.1412714$35.52718843@news4.tin.it>,
Ban <bansuri@web.de> wrote:

Of course it is a differential amp

+-----+---o
| | +Vcc
.-. .-.
| | | | 1k_
| |10k| | +--|___|--+
'-' '-' | |
| | | |\ |
| +------------+----|-\ |
| | | >-+---o
+-----)------------+----|+/ Vout
| | | |/
|/ \| .-.
o------| 2222 |--+ | |1k
|> <| | | |
Vin +--+--+ | '-'
| | |
o---------- | ------' ===
| GND
.-.
( I )100uA
'-'
|
o -Vee

Or perhaps an OTA, LM3080 or LM13700?

In Ban's drawing, one must take care with Vcc not to saturate the
transistors. A fully-differential input is best (I've edited the
drawing to show this), with a common-mode voltage well below Vout.
Properly done, the 10k pullup resistors may not be necessary.

When I was in the USAF (1968 - 1976) there were differential pairs
in one TO-5 sized package, but with 6 leads. I'd think they'd
temperature- track fairly well, but a very quick web search on
"differential transistor pair" didn't seem to turn up much, and I
don't really
know who has a website where I could look up something like that.

Anybody remember them, and if they're still available? Albeit,
I've just looked up LM3080, and it does put more stuff into one
package.

I answered somewhere else in this thread, the LM194 would be one of these
dual NPN, with a very low rbb, high beta and very low offset. It would
certainly make a very close approximation of the TANH function at the
proposed 100uA current through the long tailed pair. The differential input
Win proposed will IMHO not improve the curve, but allow for a higher input
voltage. Since for values over 10Vt the output is 0.99991, we can put a
limiter in front to allow for higher input voltages.
--
ciao Ban
Bordighera, Italy

 

[Tony Williams]

In article <NKoje.1416023$35.52808274@news4.tin.it>,
Ban <bansuri@web.de> wrote:
[snip]

.............. The differential input Win proposed will IMHO not
improve the curve, but allow for a higher input voltage. Since
for values over 10Vt the output is 0.99991, we can put a limiter
in front to allow for higher input voltages.

You can make the collector voltages more favourable
by swapping the collector-opamp connections. As below.

+-----+---o
| | +Vcc
.-. .-.
| | | | 1k_
| |10k| | +--|___|--+
'-' '-' | |
| | | |\ |
+-----)------------+----|-\ |
| | | >-+---o
| +------------+----|+/ Vout
| | | |/
Vin |/ \| .-.
o------|Q1 Q2|--+ | |1k
|> <| | | |
| | | '-'
+--+--+ | |
| === ===
| GND GND
|
|
.-.
( I )100uA
'-'
|
o -Vee

As Q1 takes more current, Q2 takes less current,
which raises Q2's collector voltage.

--
Tony Williams.