Question on the "super gain" op-amp

[Adam. S]

For an impedance measurement circuit I want to convert a 100kHz (40mA
pk-pk) current into a voltage using the op-amp configuration below. The
catch is that the virtual ground point must have an impedance of only a
few milliohms at 100kHz.

50
,-----/\/\--,
| __ |
Iin >--+-|- \ |
| >-----+----
gnd --|+_/


The above op-amp will require a gain of about 50ohm/0.002ohm= 88dB at
100kHz. Ok, this is pretty high gain-bandwidth demand for an op-amp.
But, Linear Technology Magazine issue Feb, 1994 describes a "super gain
block" using composite op-amps to achieve 180dB gain at 10kHz and is
unity gain stable, equivalent GBW product = 10THz! ( see page 26
http://www.linear.com/pdf/ltm9402.pdf )

How do I go about designing my own composite op-amp for a very high GBW
block ? Reading Dale Eagar's article, he modifies the 2nd stage so it
has close to zero phase shift at same frequency the first stage has
unity gain (5MHz for the LT1007). 100MHz GBW op-amps are dirt cheap
these days, such as LMH6642's. So say I select a LMH6643 for the 1st
stage which has been slowed down to give a GBW of 20MHz, then I design
the feedback of the 2nd stage so it has relatively flat response around
20MHz, then C >= 1/(2pi*f*R) or 4.7pF. Calculating the first stage gain
as 1/(100kHz*2*pi*10pF*470ohm) = 50dB with 6dB/octave slope at
crossover. The second stage gain is 1/(100kHz*2*pi*4.7pF*2k) = 45dB with
only small phase shift at 20MHz because the high LMH6643's 130MHz GBW.
Total gain is 50+45 = 95dB at 100kHz.
Are my assumptions correct ? And will this circuit work ?


.------/\/\------------------.
| 50 |
|(LMH6643) 4.7p 2k |
| __ ,--||--/\/\--+
Iin >----+-|+ \ 2k | __ |
| >-+--/\/\-+--|- \ |
GND-/\/\-+-|-_/ | | >-----+----
470 | | GND ---|+_/
`--||---'
10p (LMH6643)



Adam

 

[Michael A. Covington]

Why do you have to have all the gain in one stage?

 

[Jim Thompson]

For an impedance measurement circuit I want to convert a 100kHz (40mA
pk-pk) current into a voltage using the op-amp configuration below. The
catch is that the virtual ground point must have an impedance of only a
few milliohms at 100kHz.

50
,-----/\/\--,
| __ |
Iin >--+-|- \ |
| >-----+----
gnd --|+_/


The above op-amp will require a gain of about 50ohm/0.002ohm= 88dB at
100kHz. Ok, this is pretty high gain-bandwidth demand for an op-amp.
But, Linear Technology Magazine issue Feb, 1994 describes a "super gain
block" using composite op-amps to achieve 180dB gain at 10kHz and is
unity gain stable, equivalent GBW product = 10THz! ( see page 26
http://www.linear.com/pdf/ltm9402.pdf )

[snip]

To gain some understanding of the compound OpAmp technique, look up:

"Integrator Design for High Frequency Active Filter Applications"
Randall L. Geiger and Glenn R. Bailey
IEEE Transactions on Circuits and Systems, Vol. CAS-29, No. 9,
September 1982, pp 595-603

I have a copy I could scan for you if necessary, but it's already a
copy, so the quality is not terribly wonderful. Let me know.

...Jim Thompson

 

[Winfield Hill]

Adam. S wrote...

For an impedance measurement circuit I want to convert a 100kHz (40mA
pk-pk) current into a voltage using the op-amp configuration below. The
catch is that the virtual ground point must have an impedance of only a
few milliohms at 100kHz.

50
,-----/\/\--,
| __ |
Iin >--+-|- \ |
| >-----+----
gnd --|+_/

The above op-amp will require a gain of about 50ohm/0.002ohm= 88dB at
100kHz. Ok, this is pretty high gain-bandwidth demand for an op-amp.
But, Linear Technology Magazine issue Feb, 1994 describes a "super gain
block" using composite op-amps to achieve 180dB gain at 10kHz and is
unity gain stable, equivalent GBW product = 10THz!

Dale Egar's circuit is overly complex and is not necessary to make an
effective composite opamp. 88dB gain at 100kHz is not difficult -
I've shown several circuits in times past here on s.e.d., which were
not too different from your circuit (which I haven't analyzed):

50
.------/\/\------------------.
| |
| (LMH6643) 4.7p 2k |
| __ ,--||--/\/\--+
Iin >----+-|+ \ 2k | __ |
| >-+--/\/\-+--|- \ |
GND-/\/\-+-|-_/ | | >-----+----
470 | | GND ---|+_/
`--||---'
10p (LMH6643)

But you should carefully consider the reasonableness of your spec:
0.002 ohms at 100kHz implies a total circuit series inductance of
under 3nH, which is clearly impossible or highly impractical. What
are you working on anyway?

 

[Martin Schönegg]

| But you should carefully consider the reasonableness of your spec:
| 0.002 ohms at 100kHz implies a total circuit series inductance of
| under 3nH, which is clearly impossible or highly impractical.

nice that is reached after 3 mm wire ;-)

MArtin

 

[Fred Bartoli]

"Martin Schönegg"

| But you should carefully consider the reasonableness of your spec:
| 0.002 ohms at 100kHz implies a total circuit series inductance of
| under 3nH, which is clearly impossible or highly impractical.

nice that is reached after 3 mm wire ;-)

Well, I could achieve that for a 1.2m(eter) power cable, including cables
connectors (heavy duty, "zero force", fast lock) to the backplane PCB, 2mm
connectors from the backplane to the PCB boards, main boards PCB, and
loadboard PCB.

Lots of interdigitated connector pins, paralleled specially made coax.
cables and customized connectors.

 

[Winfield Hill]

Fred Bartoli wrote...

Well, I could achieve that for a 1.2m(eter) power cable, including cables
connectors (heavy duty, "zero force", fast lock) to the backplane PCB, 2mm
connectors from the backplane to the PCB boards, main boards PCB, and
loadboard PCB.

Lots of interdigitated connector pins, paralleled specially made coax.
cables and customized connectors.

Fred, I can believe 0.002 ohms dc resistance, but sorry, not 3nH.

 

[Fred Bartoli]

Fred Bartoli wrote...

Fred, I can believe 0.002 ohms dc resistance, but sorry, not 3nH.

I know, it's amazing but you really should. It wasn't 2mR, maybe 5mR, but we
measured the 3nH, well, maybe 3.5nH.

We had a custom designed coax cable with ultra thin kapton isolation. Don't
remember it's loop inductance but I still have a sample in my office and
I'll measure it when I have time.
20 paralleled coaxs with custom made connector terminations (the coax where
wired on the connectors with an interdigitated pattern).

Someting like this :

F R F R F
R F R F R
F R F R F
R F R F R

(F = forward path, R = return path)

The 2mm connectors (from main PCB to the backplane) had almost 100 pins
(2x50) wired in a same pattern. The PCBs were of course designed
accordingly.

This inductance *had* to be pretty low : it was for a power supply I
designed in an ATE tester for testing the P4 (I guess it was this one) on
wafer (production and charaterization).
They wanted 200A sustained current, 100A current step capability, and IIRC
100A/ns (or was it 50A/ns ?) right at the wafer connections.
This was translated to about a small 1A/ns that the supply had to provide. I
designed the PSU for 7nH cable max, targetted the cable at 4nH and obtained
3.5.
This is about a 4V drop and is what was observed, confirming the cable
measurements.

A nice piece of work (and a huge amount of $) was what they call the "space
transformer", which supported more than a thousand springs to make contact
with the die bumps. It's a pyramid shape ***multi***layered ceramic device
with a lot of interdigitated vias whose purpose is to convert the external
world pin spacing to the die level spacing (springs). I don't know if I'm
clear.
The model I was given stated a few 10s of pH (yes pH) serial inductances.

 

[Winfield Hill]

Fred Bartoli wrote...

Winfield Hill said...

I know, it's amazing but you really should. It wasn't 2mR, maybe 5mR,
but we measured the 3nH, well, maybe 3.5nH.

We had a custom designed coax cable with ultra thin kapton isolation.
Don't remember it's loop inductance but I still have a sample in my
office and I'll measure it when I have time. 20 paralleled coaxes
with custom made connector terminations (the coax where wired on the
connectors with an interdigitated pattern). Something like this:

F R F R F
R F R F R
F R F R F
R F R F R

(F = forward path, R = return path)

The 2mm connectors (from main PCB to the backplane) had almost 100 pins
(2x50) wired in a same pattern. The PCBs were of course designed
accordingly.

This inductance *had* to be pretty low : it was for a power supply I
designed in an ATE tester for testing the P4 (I guess it was this one)
on wafer (production and charaterization).
They wanted 200A sustained current, 100A current step capability, and
IIRC 100A/ns (or was it 50A/ns ?) right at the wafer connections.
This was translated to about a small 1A/ns that the supply had to provide.
I designed the PSU for 7nH cable max, targetted the cable at 4nH and
obtained 3.5. This is about a 4V drop and is what was observed,
confirming the cable measurements.

A nice piece of work (and a huge amount of $) was what they call the
"space transformer", which supported more than a thousand springs to
make contact with the die bumps. It's a pyramid shape ***multi***layered
ceramic device with a lot of interdigitated vias whose purpose is to
convert the external world pin spacing to the die level spacing (springs).
I don't know if I'm clear.
The model I was given stated a few 10s of pH (yes pH) serial inductances.

OK, if it was to be done, that would be the way to do it alright. But
I must admit it does raise my eyebrows. :>)

However, I doubt Adam S. has such a wiring and connection scheme in mind
and available when he takes on his specification of 0.002 ohms at 100kHz.

 

[Adam. S]

Adam. S wrote...



Dale Egar's circuit is overly complex and is not necessary to make an
effective composite opamp. 88dB gain at 100kHz is not difficult -
I've shown several circuits in times past here on s.e.d., which were
not too different from your circuit (which I haven't analyzed):

Win,
I had previously found your postings in s.e.d on
composite amplifiers. This is where I originally stole the circuit idea
from. I have yet to test your circuit which uses an integrator as the
second stage. Dale Egar's circuit uses a T look alike thingy in addition
to some weired negative feedback on the 2nd op-amp. I analyzed his
circuit in SPICE using but with just one op-amp in the 2nd stage (Dale's
"A1" amplifier) and got similar matching bode plots. I am bit rusty on
my control loop theory to feel confident designing one of these
composite op-amps.

But you should carefully consider the reasonableness of your spec:
0.002 ohms at 100kHz implies a total circuit series inductance of
under 3nH, which is clearly impossible or highly impractical. What
are you working on anyway?

I was looking at building a microcontroller based LCR meter for a home
project. But I see what your saying about the realism of 0.002 ohms @
100kHz. Now having thought about it, even a 0.1 ohm impedance at 100kHz
at the virtual ground point could still probably work with most cases
such as ESR measurement of electrolytic. I just need to compensate out
this impedance during a "short circuit" calibration procedure.

Adam

 

[Roy McCammon]

Fred Bartoli wrote:

A nice piece of work (and a huge amount of $) was what they call the "space
transformer", which supported more than a thousand springs to make contact
with the die bumps. It's a pyramid shape ***multi***layered ceramic device
with a lot of interdigitated vias whose purpose is to convert the external
world pin spacing to the die level spacing (springs). I don't know if I'm
clear.
The model I was given stated a few 10s of pH (yes pH) serial inductances.

Hey Fred,
can you post a picture. It sounds fascinating.

 

[Fred Bartoli]

Fred Bartoli wrote:

inductances.

Hey Fred,
can you post a picture. It sounds fascinating.

Roy,

sure this kind of figures are fascinating, at least at the begining. Then
you become accustomed.

For the space transformer pictures, I have to say that I've never seen one
and that the pyramidal shape was what my imagination gave me when I was
described the device at this time (1999-2000). In fact, from the links
bellow, the pyramid seems to be "rather flat".
I've done a bit of googling with the names I can remember and found this :

http://www.swtest.org/swtw_library/1999proc/PDF/S01_JL.pdf
http://www.swtest.org/swtw_library/2000proc/PDF/S04_Chan.pdf

Lots of interesting papers here covering many aspects of wafer probing.

http://www.formfactor.com/FormFactor Online/technology.html and walk
through the menus
http://www.formfactor.com/FormFactor Online/downloadables/SWTW_MicroForce.pdf


You'll find a lot more links with "C4 bumps" and formfactor keywords.