J
Jim Thompson
- Jan 1, 1970
- 0
[snip]
Probably there's an Analog Devices chip that has everything in it.
...Jim Thompson
Probably there's an Analog Devices chip that has everything in it.
...Jim Thompson
Circuit to calculate square root of voltage?
M
Max Hauser
- Jan 1, 1970
- 0
Jeez Louise. All these replies and nobody (that I spotted anyway) mentioned
Translinear circuits? Are there no analog experts here at all? (Those
suggesting microprocessors for getting an analog square root function have
been noted down and are permanently disbarred.
Who knows if any of this shows up online, but there is plenty in print,
familiar to specialists. Try searching under "Translinear circuits" or
"Barrie Gilbert" or possibly the latter's seminal pair of papers in the
December 1968 _IEEE Journal of Solid-State Circuits_ of which the truly
relevant one is not the "Precise four-quadrant multiplier with subnanosecond
response" but rather "A new wide-band amplifier technique" which contains
the insightful and prophetic phrase "The number of circuits that can be
devised to perform functions of this kind is legion."
This is from memory, I am pressed for time. You can even do it all directly
with FETs if you really want. Klumperink and Meyer and Mack and I wrote a
broad survey paper in 96 though it does not mention square roots
specifically. Evert Seevinck wrote a good thesis on the subject in 81 or
82, I wrote something back then that touched on the FET versions, many
others did too. (Analog multipliers in feedback loops. Hmmph.)
-- Max
"Chaos Master" in news:[email protected]...
Translinear circuits? Are there no analog experts here at all? (Those
suggesting microprocessors for getting an analog square root function have
been noted down and are permanently disbarred.
Who knows if any of this shows up online, but there is plenty in print,
familiar to specialists. Try searching under "Translinear circuits" or
"Barrie Gilbert" or possibly the latter's seminal pair of papers in the
December 1968 _IEEE Journal of Solid-State Circuits_ of which the truly
relevant one is not the "Precise four-quadrant multiplier with subnanosecond
response" but rather "A new wide-band amplifier technique" which contains
the insightful and prophetic phrase "The number of circuits that can be
devised to perform functions of this kind is legion."
This is from memory, I am pressed for time. You can even do it all directly
with FETs if you really want. Klumperink and Meyer and Mack and I wrote a
broad survey paper in 96 though it does not mention square roots
specifically. Evert Seevinck wrote a good thesis on the subject in 81 or
82, I wrote something back then that touched on the FET versions, many
others did too. (Analog multipliers in feedback loops. Hmmph.)
-- Max
"Chaos Master" in news:[email protected]...
W
Winfield Hill
- Jan 1, 1970
- 0
Max Hauser wrote...
The classic translinear circuit is the Gilbert cell, which is the
prime component in most analog multipliers, which were recommended
several times in this thread. There's your mention of translinear
circuits. :>) I prefer the AD734, and have often suggested it for
tasks like this. The datasheet fig 9 shows a square root circuit.
The classic translinear circuit is the Gilbert cell, which is the
prime component in most analog multipliers, which were recommended
several times in this thread. There's your mention of translinear
circuits. :>) I prefer the AD734, and have often suggested it for
tasks like this. The datasheet fig 9 shows a square root circuit.
R
Rick
- Jan 1, 1970
- 0
Winfield Hill said:
Barry Gilbert himself freely admits in his publications that a
certain Mr H.E. Jones has prior art on the "Gilbert Cell".
W
Winfield Hill
- Jan 1, 1970
- 0
Rick wrote...
Barry is a quiet type of guy. He explained, improved, promolgated
and popularized this circuit, so we insisted on naming it after him.
He doesn't (didn't back then) use the name Gilbert Cell, hence his
proposed name (IIRC), translinear. We liked Gilbert Cell better.
Barry is a quiet type of guy. He explained, improved, promolgated
and popularized this circuit, so we insisted on naming it after him.
He doesn't (didn't back then) use the name Gilbert Cell, hence his
proposed name (IIRC), translinear. We liked Gilbert Cell better.
M
Max Hauser
- Jan 1, 1970
- 0
"Winfield Hill" in news:[email protected]...
Come ON. (A "textbook" explanation, facile, unrelated to the established
art that I referred to, and just what I was complaining about.)
I'll explain. Here are some things that emerge when you delve into
translinear circuits, or even just their literature. This includes an
explanation of them. (The following is supported in much more depth than I
cite here.)
(a) The prototype translinear circuit, if the subject is viewed from a long
focus, is the bipolar-transistor current mirror. (It's useful also in
explaining.) It is both the simplest embodiment of the principle, and also
is very obviously a current-input current-output function, underscoring the
point that translinear circuits basically perform arithmetic operations on
currents.
(b) In the current mirror, two junction devices (BJTs) share the same Vbe
voltage. At the same time, these devices each have a nonlinear relation of
Vbe to collector current (Ic) that is (to remarkable potential accuracy)
exponential [1]. The connection of their Vbe voltages, and the exponential
large-signal Vbe-Ic law, lead to a relation between the two collector
currents, which prevails as long as the two transistors are happy (i.e.,
forward-active). In this very simple case, the two collector currents will
tend to track, whatever else is happening, and this is useful. Notably, the
two collector currents stay equal regardless of transistor construction (the
notorious Js current-density parameter) or temperature (which shows up in
kT/q, and even more so, implicitly, in Js). Of course, you must use matched
(or deliberately area-ratioed) devices -- these designs are most often
monolithic. Commercial monolithic dual or quad transistors or monolithic
"kit parts" serve this need in a discrete design.
(c) Generalizing, if you put four Vbe voltages into a loop (two in series,
equaling the voltage across another two in series), these voltages will sum
algebraically to zero (KVL) and this again will impose a relation among
collector currents. Depending on what you do with the collector currents,
you can get explicit algebraic relationships among these currents, such as
I1 I2 = I3 I4
-- which, if I1and I2 are arranged to be identical and to equal the output
current, and I3 is a fixed current and I4 an input current, will give a DC,
large-signal, fundamentally accurate square-root relation between input and
output currents. (Embed it with an op amp and resistors and you can get and
give voltages.) Various simple, four-transistor square-root-law circuit
cores pervade the "translinear" literature. Broader versions of the
principle apply to general voltage loops of BJTs. Obvious further
generalizations apply to other semiconductor devices (even with
generalizations beyond voltage loops).
(d) The chief origin and exploration of these circuits in print is, as I
already cited in the earlier posting, Barrie Gilbert's December-1968 JSSC
"Amplifier" paper, not the companion "Multiplier" paper, which employed
some of the results. I _strongly_ recommend reading them, they disabuse
some notions cultivated elsewhere in print. The first is where the "legion"
remark appeared. In 1975, BG coined the nickname "translinear" (because
they rely on exponential I-V devices, which have TRANSconductance LINEAR in
collector current) for this pervasive class of circuits [2]. Note well
that --
(e) -- one of the basic four-junction translinear blocks is often called a
"gain cell," focus of the 1968 "Amplifier" paper, and pretty clearly
associated with Gilbert. I am using the language here carefully, read on.
This cell contains two transistors at one DC current level, whose Vbe
difference is then imposed easily onto a second pair at another DC current
level. Current differences within the two pairs are input and output
signals, and can have either polarity. Changing the relative DC currents,
or "tail" currents, controls the _current_ gain in the signal path. If then
you take two different output pairs and a single input pair, and drive the
input pair with one differential current, and the "tail" currents of the two
output pairs with a second differential current, you achieve an accurate
four-quadrant (either polarity on either input) multiplication ("with
subnanosecond response" even in 1967). Note carefully that the accurate
relation is among currents (as always with classic translinear circuits).
This is the true six-transistor multiplier core or "six-pack" as it was
often called in the 1970s by IC designers. It and other variations are the
upshots of the 1968 "Multiplier" paper that I cited.
(f) Some later authors, despite this black-and-white origin, took to calling
a different set of six transistors (the two output pairs above, and the
differential tail current source that drives them) a "Gilbert six-transistor
multiplier" even though it is neither Gilbert's, nor a multiplier. The
original "six-pack" is a true self-contained, current-mode four-quadrant
analog multiplier and is the core of many monolithic bipolar-transistor
multiplier products.
(g) Though the translinear idea was first explored in depth in Gilbert's
1968 "Amplifier" paper, analog circuits embodying the principle can be found
earlier, even beyond the trivial example of a current mirror and its
variations. Grasselli and Stefanelli's 1966 BJT current-gain cell is
"almost" translinear. Certain JFET circuits falling outside Gilbert's
original definition embodied useful generalizations of the idea as early as
1965, I've cited them in print in the past.
(h) Some of the oldest cases of what are called generalizations of
translinearity (early to middle 1960s) employ the "square-law" relationships
found in FET devices. An aspect of translinearity that carries over to its
generalizations is that unpredictable device parameters can be cancelled out
inherently. Temperature- and manufacturing-independent square-root
functions have been designed using FETs cleverly, though the FET square laws
have not the fundamental accuracy of the BJT exponential.
(i) Please note finally that translinear circuits are _not_ "log-antilog"
analog circuits as found in classic analog-computer texts of Jackson or Korn
and Korn or in the App Notes of makers of temperature-compensated log
amplifiers (or classic discrete log-amp app circuits with Tel-Labs Q81
thermistors). They are compact, specialized circuits that directly
implement large-signal, temperature-independent linear or nonlinear
input-output relations, such as square roots.
I did not mean to claim that one of the simple four-transistor dedicated BJT
square-rooting circuits, or the various FET square-rooting circuits, was
always the best or simplest solution, but rather that they should be
suggested, and considered, for this task.
Your servant -- MH
[1] Gibbons and Horn popularized this point in an ISSCC 1963 paper, still
cited, demonstrating ten decades of current range, with attention to
second-order effects.
[2] _Electronics Letters_ vol. 11 no. 1 pp. 14-16, January 1975.
Come ON. (A "textbook" explanation, facile, unrelated to the established
art that I referred to, and just what I was complaining about.)
I'll explain. Here are some things that emerge when you delve into
translinear circuits, or even just their literature. This includes an
explanation of them. (The following is supported in much more depth than I
cite here.)
(a) The prototype translinear circuit, if the subject is viewed from a long
focus, is the bipolar-transistor current mirror. (It's useful also in
explaining.) It is both the simplest embodiment of the principle, and also
is very obviously a current-input current-output function, underscoring the
point that translinear circuits basically perform arithmetic operations on
currents.
(b) In the current mirror, two junction devices (BJTs) share the same Vbe
voltage. At the same time, these devices each have a nonlinear relation of
Vbe to collector current (Ic) that is (to remarkable potential accuracy)
exponential [1]. The connection of their Vbe voltages, and the exponential
large-signal Vbe-Ic law, lead to a relation between the two collector
currents, which prevails as long as the two transistors are happy (i.e.,
forward-active). In this very simple case, the two collector currents will
tend to track, whatever else is happening, and this is useful. Notably, the
two collector currents stay equal regardless of transistor construction (the
notorious Js current-density parameter) or temperature (which shows up in
kT/q, and even more so, implicitly, in Js). Of course, you must use matched
(or deliberately area-ratioed) devices -- these designs are most often
monolithic. Commercial monolithic dual or quad transistors or monolithic
"kit parts" serve this need in a discrete design.
(c) Generalizing, if you put four Vbe voltages into a loop (two in series,
equaling the voltage across another two in series), these voltages will sum
algebraically to zero (KVL) and this again will impose a relation among
collector currents. Depending on what you do with the collector currents,
you can get explicit algebraic relationships among these currents, such as
I1 I2 = I3 I4
-- which, if I1and I2 are arranged to be identical and to equal the output
current, and I3 is a fixed current and I4 an input current, will give a DC,
large-signal, fundamentally accurate square-root relation between input and
output currents. (Embed it with an op amp and resistors and you can get and
give voltages.) Various simple, four-transistor square-root-law circuit
cores pervade the "translinear" literature. Broader versions of the
principle apply to general voltage loops of BJTs. Obvious further
generalizations apply to other semiconductor devices (even with
generalizations beyond voltage loops).
(d) The chief origin and exploration of these circuits in print is, as I
already cited in the earlier posting, Barrie Gilbert's December-1968 JSSC
"Amplifier" paper, not the companion "Multiplier" paper, which employed
some of the results. I _strongly_ recommend reading them, they disabuse
some notions cultivated elsewhere in print. The first is where the "legion"
remark appeared. In 1975, BG coined the nickname "translinear" (because
they rely on exponential I-V devices, which have TRANSconductance LINEAR in
collector current) for this pervasive class of circuits [2]. Note well
that --
(e) -- one of the basic four-junction translinear blocks is often called a
"gain cell," focus of the 1968 "Amplifier" paper, and pretty clearly
associated with Gilbert. I am using the language here carefully, read on.
This cell contains two transistors at one DC current level, whose Vbe
difference is then imposed easily onto a second pair at another DC current
level. Current differences within the two pairs are input and output
signals, and can have either polarity. Changing the relative DC currents,
or "tail" currents, controls the _current_ gain in the signal path. If then
you take two different output pairs and a single input pair, and drive the
input pair with one differential current, and the "tail" currents of the two
output pairs with a second differential current, you achieve an accurate
four-quadrant (either polarity on either input) multiplication ("with
subnanosecond response" even in 1967). Note carefully that the accurate
relation is among currents (as always with classic translinear circuits).
This is the true six-transistor multiplier core or "six-pack" as it was
often called in the 1970s by IC designers. It and other variations are the
upshots of the 1968 "Multiplier" paper that I cited.
(f) Some later authors, despite this black-and-white origin, took to calling
a different set of six transistors (the two output pairs above, and the
differential tail current source that drives them) a "Gilbert six-transistor
multiplier" even though it is neither Gilbert's, nor a multiplier. The
original "six-pack" is a true self-contained, current-mode four-quadrant
analog multiplier and is the core of many monolithic bipolar-transistor
multiplier products.
(g) Though the translinear idea was first explored in depth in Gilbert's
1968 "Amplifier" paper, analog circuits embodying the principle can be found
earlier, even beyond the trivial example of a current mirror and its
variations. Grasselli and Stefanelli's 1966 BJT current-gain cell is
"almost" translinear. Certain JFET circuits falling outside Gilbert's
original definition embodied useful generalizations of the idea as early as
1965, I've cited them in print in the past.
(h) Some of the oldest cases of what are called generalizations of
translinearity (early to middle 1960s) employ the "square-law" relationships
found in FET devices. An aspect of translinearity that carries over to its
generalizations is that unpredictable device parameters can be cancelled out
inherently. Temperature- and manufacturing-independent square-root
functions have been designed using FETs cleverly, though the FET square laws
have not the fundamental accuracy of the BJT exponential.
(i) Please note finally that translinear circuits are _not_ "log-antilog"
analog circuits as found in classic analog-computer texts of Jackson or Korn
and Korn or in the App Notes of makers of temperature-compensated log
amplifiers (or classic discrete log-amp app circuits with Tel-Labs Q81
thermistors). They are compact, specialized circuits that directly
implement large-signal, temperature-independent linear or nonlinear
input-output relations, such as square roots.
I did not mean to claim that one of the simple four-transistor dedicated BJT
square-rooting circuits, or the various FET square-rooting circuits, was
always the best or simplest solution, but rather that they should be
suggested, and considered, for this task.
Your servant -- MH
[1] Gibbons and Horn popularized this point in an ISSCC 1963 paper, still
cited, demonstrating ten decades of current range, with attention to
second-order effects.
[2] _Electronics Letters_ vol. 11 no. 1 pp. 14-16, January 1975.
T
Tony Williams
- Jan 1, 1970
- 0
Winfield Hill said:
For powers and roots I used to be a fan of a circuit
taken from an Analog Devices publication, called the
Multifunction Circuit. Two pairs of transistors and
a few opamps.
That was in the days when packaged multiplier/dividers
were a fearsome price........
C
Chaos Master
- Jan 1, 1970
- 0
In me, the Tony Williams:
Do you have the schematic of this circuit? I wish to see it.
[]s
--
Chaos Master®, posting from Canoas, Brazil - 29.55° S / 51.11° W
"Now: the 2-bit processor, with instructions:
1. NOP - does nothing, increase PC.
2. HLT - does nothing, doesn't increase PC
3. MMX - enter Pentium(r) emulation mode; increase PC
4. LCK - before MMX: NOP ; after MMX: executes F0 0F C7 C8 "
Do you have the schematic of this circuit? I wish to see it.
[]s
--
Chaos Master®, posting from Canoas, Brazil - 29.55° S / 51.11° W
"Now: the 2-bit processor, with instructions:
1. NOP - does nothing, increase PC.
2. HLT - does nothing, doesn't increase PC
3. MMX - enter Pentium(r) emulation mode; increase PC
4. LCK - before MMX: NOP ; after MMX: executes F0 0F C7 C8 "
T
Tony Williams
- Jan 1, 1970
- 0
Chaos Master said:
Analog Devices Model 433. It was essentially a log-antilog
multiplier/divider with a 4-element resistor bridge between
the log-antilog sections. It would take powers/roots over an
exponent range of 5/1 to 1/5. I used the circuit extensively
after realising the curves of many of the exotic thermocouples
could be simply described just by raising to a specific power.
Copied below, all opamps were inverters with their +ve inputs
connected to 0v.
+---||--+ +----[R3]--+-Vout
| |\ | | |\ |
Vx--[R1]-+--|->--+---[R?]----+ +--|->-----+
| |/ | | |/
| | |
+----+ | |
| +---+---+ |
+----|---+ | B | | +----+
| | | [Ra] [Rc] | | |
| |/ \| | | |/ \| |
0v---|--| Q1a/b |----+A C+----| Q2a/b |--|---0v
| |\e e/| | | |\e e/| |
| | | [Rb] [Rb] | | |
| +-+-+ | | +-+-+ |
| | +---+---+ | |
| [Rt1] | [Rt2] |
| | -+-0v | |
+---||-+ +-||---+
| |\ | | /| |
Vz--[R2]-+--|->-+ +-<-|--+-[R4]--Vy
|/ \|
m
R3 ( Vx ) Rb + Ra
Vout= --.Vy.( -- ) where m = -------
R4 ( Vz ) Rb + Rc
For raising to a power (m= >1), B-C would be shorted and
m = (Rb + Ra)/Rb.
For roots, B-A would be shorted and m = Rb/(Rb +Rc).
For a straightforward XY/Z multiplier/divider, short ABC.
The Model 433 had an internal 9v Vref and in manufacture
the ratio R4/R3 was adjusted to equal the value of Vref/10.
T
Tony Williams
- Jan 1, 1970
- 0
About 100mS after upload you see the typo, ambiguity,
whatever.
Rt1/2 are not temperature senstive resistors. They are
simply Rtail-1 and Rtail-2 (of the long-tailed pairs).
AFAIR I ran I-tail at about 125uA full scale using the
RCA 5-transistor array.
W
Winfield Hill
- Jan 1, 1970
- 0
Tony Williams wrote...
Did you cancel that? Could you repost it? It didn't appear.
Did you cancel that? Could you repost it? It didn't appear.
T
Tony Williams
- Jan 1, 1970
- 0
Winfield Hill said:
No I didn't cancel it and it did appear back here.
Text of the original article reposted below........
Analog Devices Model 433. It was essentially a log-antilog
multiplier/divider with a 4-element resistor bridge between
the log-antilog sections. It would take powers/roots over an
exponent range of 5/1 to 1/5. I used the circuit extensively
after realising the curves of many of the exotic thermocouples
could be simply described just by raising to a specific power.
Copied below, all opamps were inverters with their +ve inputs
connected to 0v.
+---||--+ +----[R3]--+-Vout
| |\ | | |\ |
Vx--[R1]-+--|->--+---[R?]----+ +--|->-----+
| |/ | | |/
| | |
+----+ | |
| +---+---+ |
+----|---+ | B | | +----+
| | | [Ra] [Rc] | | |
| |/ \| | | |/ \| |
0v---|--| Q1a/b |----+A C+----| Q2a/b |--|---0v
| |\e e/| | | |\e e/| |
| | | [Rb] [Rb] | | |
| +-+-+ | | +-+-+ |
| | +---+---+ | |
| [Rt1] | [Rt2] |
| | -+-0v | |
+---||-+ +-||---+
| |\ | | /| |
Vz--[R2]-+--|->-+ +-<-|--+-[R4]--Vy
|/ \|
m
R3 ( Vx ) Rb + Ra
Vout= --.Vy.( -- ) where m = -------
R4 ( Vz ) Rb + Rc
For raising to a power (m= >1), B-C would be shorted and
m = (Rb + Ra)/Rb.
For roots, B-A would be shorted and m = Rb/(Rb +Rc).
For a straightforward XY/Z multiplier/divider, short ABC.
The Model 433 had an internal 9v Vref and in manufacture
the ratio R4/R3 was adjusted to equal the value of Vref/10.
S
Stephan Goldstein
- Jan 1, 1970
- 0
This circuit is described at some length (about 9 pages as I recall)
in the Nonlinear Circuits Handbook, published by Analog Devices
and edited by Dan Sheingold. There's a lot of old-time circuits
wisdom contained therein. I don't know if it's still in print, or available
on the web - I keep a copy on my desk. Tony's quick description
appears to cover most of the important bits.
Steve
T
Tony Williams
- Jan 1, 1970
- 0
Stephan Goldstein said:
A totally valuable book to analogue designers. I lost mine
for about 15 years but recovered it earlier this year (from
a customer's bookshelf of all places). The spine is broken
and there appears to be a chunk missing, but what is left
is still worth keeping for reference. Those 9 pages of
the Multifunction Converter are still there and the posted
sketch was copied directly from them.
Resistor [R?] was not in the A-D circuit. It is neccessary
to avoid oscillations in the log-ratio circuit and to limit
the voltage excursions on the Q1,Q2 bases. I arbitrarily
sized [R?] so that, at full opamp output swing, the voltage
at point B did not exceed about 1V.
C
Chaos Master
- Jan 1, 1970
- 0
Tony said:
Good! Thanks, I will check this circuit and maybe simulate it.
[]s
--
Chaos Master®, posting from Canoas, Brazil - 29.55° S / 51.11° W
"Now: the 2-bit processor, with instructions:
1. NOP - does nothing, increase PC.
2. HLT - does nothing, doesn't increase PC
3. MMX - enter Pentium(r) emulation mode; increase PC
4. LCK - before MMX: NOP ; after MMX: executes F0 0F C7 C8 "
T
Tony Williams
- Jan 1, 1970
- 0
When m=1 the 433 circuit does Vout= X*Y/Z. If Z is
connected back to Vout then X*Y = Vout-squared.
If X is the input and Y is a fixed Vref then it
functions as a square rooter.
However, (AFAIR) Win's suggested AD734 (and say the
B-B MPY600) can function as a direct square-rooter,
without the need for an extra Vref.
This is because this type of multiplier has a high
gain internal opamp, which has X*Y on one input and
Z on the other. Connections are always made so the
the negative feedback forces (X*Y - Z) = 0.
If Z is made the input and Vout connected back to both
X and Y then circuit is forced to do Vout= sq-rt(Z).
No Vref needed.
S
Spehro Pefhany
- Jan 1, 1970
- 0
Speaking of square root circuits and design methodology (another
thread), here's an interesting paper:
http://www.genetic-programming.com/jkpdf/icec1997.pdf
Best regards,
Spehro Pefhany
T
Tony Williams
- Jan 1, 1970
- 0
Spehro Pefhany said:
Page 6, Figure 8. Q123 looks a little suspicious.
M
Mike Monett
- Jan 1, 1970
- 0
Tony said:
Nice. Also QPC19, Q77, Q184 and Q258.
Mike Monett
J
Jim Thompson
- Jan 1, 1970
- 0
What weed were those guys smoking ?
...Jim Thompson
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