Distributed attenuators

[Phil Hobbs]

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Jamie M]

On 2019-07-10 12:58 p.m., Phil Hobbs wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes.  It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string.   Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA.  It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz.  For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
     |          |         |          |          |
     *--Cpar1---*         *--CparN---*        Cload
                |                    |          |
                *-----*              *-----*   GND
                |     |              |     |
              Rsh1   Csh1           RshN  CshN
                |     |              |     |
                |     |              |     |
                *-----*              *-----*
                |     |              |     |
              SWITCH Csw           SWITCH Csw
                |     |              |     |
               Rsw    |             Rsw    |
                |     |              |     |
                *-----*              *-----*
                |                    |
               GND                  GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range.  (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)

Hi,

Is this circuit replacing the PGA itself? Seems a bit like a DAC,
but instead of a +5V rail powering it, you are feeding it a signal
maybe, and thus need to compensate for non linear output. I guess
only 2 of 4 switches are shown.

cheers,
Jamie

 

[Phil Hobbs]

On 7/10/19 4:26 PM, George Herold wrote:

On Wednesday, July 10, 2019 at 3:58:54 PM UTC-4, Phil Hobbs wrote:
Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

That's interesting Phil, Can I ask how you figure out what capacitor values
to put in parallel with each resistor?

It starts with some given guess, generates random guesses with a
standard deviation of 20% or so, and runs the optimizer. Nelder-Mead is
an unconstrained optimizer, so to prevent it converging on unphysical
values, I use a mirroring technique.

If C < Cmin, I replace it with Cmin + |C-Cmin|.

Cheers

Phil Hobbs

George H.

(If anybody has a similar problem, I'll happily share the code.)


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Phil Hobbs]

On 7/10/19 4:31 PM, Jamie M wrote:

On 2019-07-10 12:58 p.m., Phil Hobbs wrote:
Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes.  It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string.   Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA.  It has a calibration loop that executes in a second or
so at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and
depends on the dpot setting, so there's no straightforward way of
compensating. Thus there's no way it's ever getting to 40 MHz.  For
this one, I wanted to use a distributed attenuator--an RC ladder
network with switches in the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
      |          |         |          |          |
      *--Cpar1---*         *--CparN---*        Cload
                 |                    |          |
                 *-----*              *-----*   GND
                 |     |              |     |
               Rsh1   Csh1           RshN  CshN
                 |     |              |     |
                 |     |              |     |
                 *-----*              *-----*
                 |     |              |     |
               SWITCH Csw           SWITCH Csw
                 |     |              |     |
                Rsw    |             Rsw    |
                 |     |              |     |
                 *-----*              *-----*
                 |                    |
                GND                  GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba
in Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff,
with an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms,
3.5 pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS
error of a couple of tenths of a percent over the whole range.  (There
are better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)




Hi,

Is this circuit replacing the PGA itself?  Seems a bit like a DAC,
but instead of a +5V rail powering it, you are feeding it a signal
maybe, and thus need to compensate for non linear output.  I guess
only 2 of 4 switches are shown.

cheers,
Jamie

The program will work for any number of sections. There's a dot dot dot
in the middle of the ASCII art.

It's a programmable attenuator rather than a DAC--the signal input is at
left. The switches have no significant nonlinearity.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[George Herold]

On Wednesday, July 10, 2019 at 3:58:54 PM UTC-4, Phil Hobbs wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

That's interesting Phil, Can I ask how you figure out what capacitor values
to put in parallel with each resistor?

George H.

(If anybody has a similar problem, I'll happily share the code.)


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Phil Hobbs]

On 7/10/19 6:11 PM, whit3rd wrote:

On Wednesday, July 10, 2019 at 2:46:32 PM UTC-7, John Larkin wrote:
On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range.

You could also maybe use an analog multiplier and a DAC. AD835 is
nice.

The easy multiplier for 40 Mhz is probably a Gilbert cell; all you need is a
controllable current source for the emitters. That's easy for signal bandwidth,
but slightly harder for attenuator-level bandwidth, but you can get free gain
and differential outputs.

And horrible, horrible noise at low gains.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[whit3rd]

On Wednesday, July 10, 2019 at 2:46:32 PM UTC-7, John Larkin wrote:

On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range.

You could also maybe use an analog multiplier and a DAC. AD835 is
nice.

The easy multiplier for 40 Mhz is probably a Gilbert cell; all you need is a
controllable current source for the emitters. That's easy for signal bandwidth,
but slightly harder for attenuator-level bandwidth, but you can get free gain
and differential outputs.

 

[Phil Hobbs]

On 7/10/19 5:46 PM, John Larkin wrote:

On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)

Lots of people make logic-programmed RF step attenuator chips. Can you
work at 50 ohms?

Not easily. Also none of those I know of go in such small steps--6
dB/16 = 0.375 dB. The idea is to make a tolerable mimic of a continuous
control, without trashing the noise performance. A 6-section attenuator
would be down below 0.1 dB/step. It would be a lot easier to do with
relays, but that would take a lot of power, space, and cost. This gizmo
will come in way below $1 BOM cost, counting just the attenuator and
switches.

You could also maybe use an analog multiplier and a DAC. AD835 is
nice. We're using that in our simulator of an eddy-current blade tip > sensor.

Transconductance-based devices are super noisy at low gains. Your
average analog multiplier is 60 dB noisier than a good op amp. The
AD835 superficially appears better (1-Hz noise of 50 nV vs. 1-2 uV for a
MPY634), but its noise is only specified at zero gain in both arms! (Vx=
Vy = 0)

CMOS bus switches are great analog multiplexers, but priced about 1/20
of an official analog mux. FSA3157 costs 6 cents.

Right, that's a similar part to the one I'm thinking of using. 5 ohms,
3.5 pF. (I found it in AoE.)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[John Larkin]

On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)

Lots of people make logic-programmed RF step attenuator chips. Can you
work at 50 ohms?

You could also maybe use an analog multiplier and a DAC. AD835 is
nice. We're using that in our simulator of an eddy-current blade tip
sensor.

CMOS bus switches are great analog multiplexers, but priced about 1/20
of an official analog mux. FSA3157 costs 6 cents.






--

John Larkin Highland Technology, Inc
picosecond timing precision measurement

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com

 

[Phil Hobbs]

On 7/10/19 9:02 PM, George Herold wrote:

On Wednesday, July 10, 2019 at 4:34:40 PM UTC-4, Phil Hobbs wrote:
On 7/10/19 4:26 PM, George Herold wrote:
On Wednesday, July 10, 2019 at 3:58:54 PM UTC-4, Phil Hobbs
wrote:
Hi, All.

So I have this gig building a cathodoluminescence system for
use in electron microscopes. It needs a programmable-gain amp
with about 0.2 dB steps, low noise, and a bandwidth of > 40
MHz.

A previous voltage-controlled amp board for a biomed customer
used a 256-step dpot and a power-of-two PGA made from a
74HC4051 MUX and a resistor string. Except at the very lower
limit, the dpot's attenuation is never more than 6 dB, which
helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and
sets the dpot and PGA. It has a calibration loop that executes
in a second or so at boot-up, so everything is kept relatively
copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and
depends on the dpot setting, so there's no straightforward way
of compensating. Thus there's no way it's ever getting to 40
MHz. For this one, I wanted to use a distributed
attenuator--an RC ladder network with switches in the shunt
legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out |
| | | | *--Cpar1---*
*--CparN---* Cload | | |
*-----* *-----* GND | | |
| Rsh1 Csh1 RshN CshN | | |
| | | | | *-----* *-----* |
| | | SWITCH Csw SWITCH Csw | |
| | Rsw | Rsw | | | |
| *-----* *-----* | | GND
GND

The math for this is fairly ugly, so I coded up a smallish C++
program to optimize it, using the Nelder-Mead downhill simplex
method (amoeba in Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination
of the accuracy of the steps (mean error over frequency) and
the rolloff, with an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5
ohms, 3.5 pF Coff) I can do a 4-bit distributed 0-6 dB
attenuator with RMS error of a couple of tenths of a percent
over the whole range. (There are better ones, but few I know
of work above 3.6 V.)

I made some effort to include realistic strays in the analysis,
so I expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

That's interesting Phil, Can I ask how you figure out what
capacitor values to put in parallel with each resistor?

It starts with some given guess, generates random guesses with a
standard deviation of 20% or so, and runs the optimizer.
Nelder-Mead is an unconstrained optimizer, so to prevent it
converging on unphysical values, I use a mirroring technique.

If C < Cmin, I replace it with Cmin + |C-Cmin|.
Huh, OK, so getting the C's right is the hard part. I'm sure you know
the nice RF attenuator strips, blue with funky knobs on the toggle
switches... at least that's mine, great on the output of my sig gen.

So how do you make your initial guess? Equal time constants every
where?

I started with a 1-section, 0.4 dB switchable attenuator, then made four
identical sections in a row for one guess, and just randomized the other
vectors in the simplex. Something like

Csh = Csh[0]*(1.+0.2*(rand()/double(RND_MAX) - 0.5));
// it was a bit more intelligent than that, but that's the gist.

The capacitors on the series legs turned out to be right near the
minimum of 0.05 pF that I put in manually (that's approximately the
parallel capacitance of an 0603 or 0805 resistor). The shunt legs
wanted something up around 1.5 pF.

My initial idea was to allow the attenuation values to be all over the
place in the code space. That is, changing from -3.0 to -3.4 dB
wouldn't necessarily involve toggling the LSB. That was implemented by
computing all the gain values and then sorting them before applying the
penalty function. Turned out that the small gain wasn't worth the agita.

I'll let everybody know how it works.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[George Herold]

On Wednesday, July 10, 2019 at 4:34:40 PM UTC-4, Phil Hobbs wrote:

On 7/10/19 4:26 PM, George Herold wrote:
On Wednesday, July 10, 2019 at 3:58:54 PM UTC-4, Phil Hobbs wrote:
Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

That's interesting Phil, Can I ask how you figure out what capacitor values
to put in parallel with each resistor?

It starts with some given guess, generates random guesses with a
standard deviation of 20% or so, and runs the optimizer. Nelder-Mead is
an unconstrained optimizer, so to prevent it converging on unphysical
values, I use a mirroring technique.

If C < Cmin, I replace it with Cmin + |C-Cmin|.

Huh, OK, so getting the C's right is the hard part.
I'm sure you know the nice RF attenuator strips,
blue with funky knobs on the toggle switches...
at least that's mine, great on the output of my sig gen.

So how do you make your initial guess?
Equal time constants every where?

George H.

Cheers

Phil Hobbs



George H.

(If anybody has a similar problem, I'll happily share the code.)


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com



--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Chris Jones]

On 11/07/2019 08:06, Phil Hobbs wrote:

On 7/10/19 5:46 PM, John Larkin wrote:
On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes.  It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string.   Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA.  It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz.  For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
      |          |         |          |          |
      *--Cpar1---*         *--CparN---*        Cload
                 |                    |          |
                 *-----*              *-----*   GND
                 |     |              |     |
               Rsh1   Csh1           RshN  CshN
                 |     |              |     |
                 |     |              |     |
                 *-----*              *-----*
                 |     |              |     |
               SWITCH Csw           SWITCH Csw
                 |     |              |     |
                Rsw    |             Rsw    |
                 |     |              |     |
                 *-----*              *-----*
                 |                    |
                GND                  GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range.  (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)

Lots of people make logic-programmed RF step attenuator chips. Can you
work at 50 ohms?

Not easily.  Also none of those I know of go in such small steps--6
dB/16 = 0.375 dB.  The idea is to make a tolerable mimic of a continuous
control, without trashing the noise performance.  A 6-section attenuator
would be down below 0.1 dB/step.  It would be a lot easier to do with
relays, but that would take a lot of power, space, and cost.  This gizmo
will come in way below $1 BOM cost, counting just the attenuator and
switches.

I'm curious: if you can tell me, what is the signal source, i.e. is it a
current or voltage, what sort of source impedance, amplitude? And what
is the load? Do you only need 6dB range?

I did a few PGAs for cellphone transmitters, both at baseband and at RF
and also a thing that pretended to be an analogue VGA but really used a
1dB stepped attenuator and a VGA stage to fill in between these steps,
with some hysteresis on the stepped attenuator.

One of my preferred techniques for a baseband PGA was to convert the
input signal to a current and feed it into a digitally-chosen tap on a
resistive ladder - you can use R:2R for ~6dB steps and R:75R (or
R/5:15R) gives 1dB steps. With the input signal being a current, the
resistance and nonlinearity of the switches didn't matter much so they
could be small. I forget how I did the 1/32dB steps, maybe just a linear
scaling of the gm of the stage that fed the signal current to the
ladder, as linear is a reasonable approximation over 1dB range. Those
things are fun on a chip, with well matched resistors being very cheap.

You could also add 0.2dB steps by making the terminating resistor at one
end of the ladder have some taps, and select one of those taps to your
output, but then switch resistance for those taps would matter.

If you are filling in between 1dB steps using a VGA, that can be done in
a reasonably low-noise way because you can have two signal paths, one
path that is always there with a gain of 1, and a path that goes through
a VGA, with a gain of between 0 and 0.122 - since you can always
attenuate the signal that has been through the VGA part, its noise
voltage should also get attenuated, making it not terrible anymore.

 

[George Herold]

On Wednesday, July 10, 2019 at 9:17:00 PM UTC-4, Phil Hobbs wrote:

On 7/10/19 9:02 PM, George Herold wrote:
On Wednesday, July 10, 2019 at 4:34:40 PM UTC-4, Phil Hobbs wrote:
On 7/10/19 4:26 PM, George Herold wrote:
On Wednesday, July 10, 2019 at 3:58:54 PM UTC-4, Phil Hobbs
wrote:
Hi, All.

So I have this gig building a cathodoluminescence system for
use in electron microscopes. It needs a programmable-gain amp
with about 0.2 dB steps, low noise, and a bandwidth of > 40
MHz.

A previous voltage-controlled amp board for a biomed customer
used a 256-step dpot and a power-of-two PGA made from a
74HC4051 MUX and a resistor string. Except at the very lower
limit, the dpot's attenuation is never more than 6 dB, which
helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and
sets the dpot and PGA. It has a calibration loop that executes
in a second or so at boot-up, so everything is kept relatively
copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and
depends on the dpot setting, so there's no straightforward way
of compensating. Thus there's no way it's ever getting to 40
MHz. For this one, I wanted to use a distributed
attenuator--an RC ladder network with switches in the shunt
legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out |
| | | | *--Cpar1---*
*--CparN---* Cload | | |
*-----* *-----* GND | | |
| Rsh1 Csh1 RshN CshN | | |
| | | | | *-----* *-----* |
| | | SWITCH Csw SWITCH Csw | |
| | Rsw | Rsw | | | |
| *-----* *-----* | | GND
GND

The math for this is fairly ugly, so I coded up a smallish C++
program to optimize it, using the Nelder-Mead downhill simplex
method (amoeba in Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination
of the accuracy of the steps (mean error over frequency) and
the rolloff, with an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5
ohms, 3.5 pF Coff) I can do a 4-bit distributed 0-6 dB
attenuator with RMS error of a couple of tenths of a percent
over the whole range. (There are better ones, but few I know
of work above 3.6 V.)

I made some effort to include realistic strays in the analysis,
so I expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

That's interesting Phil, Can I ask how you figure out what
capacitor values to put in parallel with each resistor?

It starts with some given guess, generates random guesses with a
standard deviation of 20% or so, and runs the optimizer.
Nelder-Mead is an unconstrained optimizer, so to prevent it
converging on unphysical values, I use a mirroring technique.

If C < Cmin, I replace it with Cmin + |C-Cmin|.
Huh, OK, so getting the C's right is the hard part. I'm sure you know
the nice RF attenuator strips, blue with funky knobs on the toggle
switches... at least that's mine, great on the output of my sig gen.

So how do you make your initial guess? Equal time constants every
where?

I started with a 1-section, 0.4 dB switchable attenuator, then made four
identical sections in a row for one guess, and just randomized the other
vectors in the simplex. Something like

Csh = Csh[0]*(1.+0.2*(rand()/double(RND_MAX) - 0.5));
// it was a bit more intelligent than that, but that's the gist.

The capacitors on the series legs turned out to be right near the
minimum of 0.05 pF that I put in manually (that's approximately the
parallel capacitance of an 0603 or 0805 resistor). The shunt legs
wanted something up around 1.5 pF.

My initial idea was to allow the attenuation values to be all over the
place in the code space. That is, changing from -3.0 to -3.4 dB
wouldn't necessarily involve toggling the LSB. That was implemented by
computing all the gain values and then sorting them before applying the
penalty function. Turned out that the small gain wasn't worth the agita.

I'll let everybody know how it works.

Fun, thanks for sharing! And do let us know how it works.
You'll probably learn more about stray capacitance. :^)

George H.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Phil Hobbs]

On 7/11/19 9:12 AM, Chris Jones wrote:

On 11/07/2019 08:06, Phil Hobbs wrote:
On 7/10/19 5:46 PM, John Larkin wrote:
On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes.  It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string.   Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA.  It has a calibration loop that executes in a second
or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz.  For this one, I
wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
      |          |         |          |          |
      *--Cpar1---*         *--CparN---*        Cload
                 |                    |          |
                 *-----*              *-----*   GND
                 |     |              |     |
               Rsh1   Csh1           RshN  CshN
                 |     |              |     |
                 |     |              |     |
                 *-----*              *-----*
                 |     |              |     |
               SWITCH Csw           SWITCH Csw
                 |     |              |     |
                Rsw    |             Rsw    |
                 |     |              |     |
                 *-----*              *-----*
                 |                    |
                GND                  GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method
(amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms,
3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range.  (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)

Lots of people make logic-programmed RF step attenuator chips. Can you
work at 50 ohms?

Not easily.  Also none of those I know of go in such small steps--6
dB/16 = 0.375 dB.  The idea is to make a tolerable mimic of a
continuous control, without trashing the noise performance.  A
6-section attenuator would be down below 0.1 dB/step.  It would be a
lot easier to do with relays, but that would take a lot of power,
space, and cost.  This gizmo will come in way below $1 BOM cost,
counting just the attenuator and switches.

I'm curious: if you can tell me, what is the signal source, i.e. is it a
current or voltage, what sort of source impedance, amplitude? And what
is the load? Do you only need 6dB range?

It's coming from the front end, and will probably be a CFA.

The following stage is a noninverting amp built from an HC4051 and a
string of resistors, wrapped round something like an OPA695, with gains
from 1 to 32. There's a micro on the board, so we use that to get rid
of the offsets.

I did a few PGAs for cellphone transmitters, both at baseband and at RF
and also a thing that pretended to be an analogue VGA but really used a
1dB stepped attenuator and a VGA stage to fill in between these steps,
with some hysteresis on the stepped attenuator.

Right, that's the idea. The problem with transconductance devices is
that you have to divide the signal down to something the transconductor
can cope with, e.g. +- 60 mV, and that trashes the SNR. They're great
at high gain.

The application here is photomultiplier replacement, and one of the
things people like about PMTs is that you can vary the gain continuously.

One of my preferred techniques for a baseband PGA was to convert the
input signal to a current and feed it into a digitally-chosen tap on a
resistive ladder - you can use R:2R for ~6dB steps and R:75R (or
R/5:15R) gives 1dB steps. With the input signal being a current, the
resistance and nonlinearity of the switches didn't matter much so they
could be small. I forget how I did the 1/32dB steps, maybe just a linear
scaling of the gm of the stage that fed the signal current to the
ladder, as linear is a reasonable approximation over 1dB range. Those
things are fun on a chip, with well matched resistors being very cheap.

As long as you only care about the ratios, of course.

You could also add 0.2dB steps by making the terminating resistor at one
end of the ladder have some taps, and select one of those taps to your
output, but then switch resistance for those taps would matter.

If you are filling in between 1dB steps using a VGA, that can be done in
a reasonably low-noise way because you can have two signal paths, one
path that is always there with a gain of 1, and a path that goes through
a VGA, with a gain of between 0 and 0.122 - since you can always
attenuate the signal that has been through the VGA part, its noise
voltage should also get attenuated, making it not terrible anymore.

Interesting idea, thanks.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[John Larkin]

On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)

You can't do it with just resistors and switches? 40 MHz isn't very
scary.

We sometimes use a trimpot to calibrate the gain of o/e converters.
Some of the smaller pots are good to about 2 GHz.

Some people and organizations are adamantly opposed to trimpots.
Sometimes they are just what you want. They don't need a lot of code
support.



--

John Larkin Highland Technology, Inc

lunatic fringe electronics

 

[Phil Hobbs]

On 7/11/19 11:35 AM, John Larkin wrote:

On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)


You can't do it with just resistors and switches? 40 MHz isn't very
scary.

Trying to keep the bandwidth constant is one of the goals, as well as
maintaining a reasonable input impedance. I could use pHEMTs or relays
to do the switching, which would be about a factor of 10 easier, but as
you say, those bus switches are pretty attractive.

And besides, my ideal project is building a computer from sand.

We sometimes use a trimpot to calibrate the gain of o/e converters.
Some of the smaller pots are good to about 2 GHz.

Some people and organizations are adamantly opposed to trimpots.
Sometimes they are just what you want. They don't need a lot of code
support.

Like any time you want to go faster than a few hundred kilohertz.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Jamie M]

On 2019-07-11 8:47 a.m., Phil Hobbs wrote:

On 7/11/19 11:35 AM, John Larkin wrote:
On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes.  It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string.   Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA.  It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz.  For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
      |          |         |          |          |
      *--Cpar1---*         *--CparN---*        Cload
                 |                    |          |
                 *-----*              *-----*   GND
                 |     |              |     |
               Rsh1   Csh1           RshN  CshN
                 |     |              |     |
                 |     |              |     |
                 *-----*              *-----*
                 |     |              |     |
               SWITCH Csw           SWITCH Csw
                 |     |              |     |
                Rsw    |             Rsw    |
                 |     |              |     |
                 *-----*              *-----*
                 |                    |
                GND                  GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range.  (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)


You can't do it with just resistors and switches? 40 MHz isn't very
scary.

Trying to keep the bandwidth constant is one of the goals, as well as
maintaining a reasonable input impedance.  I could use pHEMTs or relays
to do the switching, which would be about a factor of 10 easier, but as
you say, those bus switches are pretty attractive.

And besides, my ideal project is building a computer from sand.

Hi,

To build a computer from sand: first idea: melt some sand into an
hourglass and fill it with sand, then that is the system clock.

More serious idea:

use nuclear reactor type doping of pure silicon crystals (from sand of
course). However to avoid lithography, use a nuclear decay source which
can precisely dope the silicon crystal in 3D. So this way the doping
can be done to form internal transistors/fets within the 3D crystal
by using a precision decay source. Perhaps one of the sunken Russian
nuclear subs could be used however since they are sunk in peacetime they
probably don't have very precise anything.

cheers,
Jamie

We sometimes use a trimpot to calibrate the gain of o/e converters.
Some of the smaller pots are good to about 2 GHz.

Some people and organizations are adamantly opposed to trimpots.
Sometimes they are just what you want. They don't need a lot of code
support.

Like any time you want to go faster than a few hundred kilohertz.

Cheers

Phil Hobbs

 

[John Larkin]

On Thu, 11 Jul 2019 11:47:34 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

On 7/11/19 11:35 AM, John Larkin wrote:
On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)


You can't do it with just resistors and switches? 40 MHz isn't very
scary.

Trying to keep the bandwidth constant is one of the goals, as well as
maintaining a reasonable input impedance. I could use pHEMTs or relays
to do the switching, which would be about a factor of 10 easier, but as
you say, those bus switches are pretty attractive.

And besides, my ideal project is building a computer from sand.


We sometimes use a trimpot to calibrate the gain of o/e converters.
Some of the smaller pots are good to about 2 GHz.

Some people and organizations are adamantly opposed to trimpots.
Sometimes they are just what you want. They don't need a lot of code
support.

Like any time you want to go faster than a few hundred kilohertz.

Cheers

Phil Hobbs

No, really, some are usable to 2 GHz.

Some have weird convoluted internal structures, lots of distributed L
and C.


--

John Larkin Highland Technology, Inc
picosecond timing precision measurement

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com

 

[Phil Hobbs]

On 7/11/19 8:21 PM, John Larkin wrote:

On Thu, 11 Jul 2019 11:47:34 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

On 7/11/19 11:35 AM, John Larkin wrote:
On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes. It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string. Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA. It has a calibration loop that executes in a second or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and depends
on the dpot setting, so there's no straightforward way of compensating.
Thus there's no way it's ever getting to 40 MHz. For this one, I wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
| | | | |
*--Cpar1---* *--CparN---* Cload
| | |
*-----* *-----* GND
| | | |
Rsh1 Csh1 RshN CshN
| | | |
| | | |
*-----* *-----*
| | | |
SWITCH Csw SWITCH Csw
| | | |
Rsw | Rsw |
| | | |
*-----* *-----*
| |
GND GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method (amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff, with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5 ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range. (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)


You can't do it with just resistors and switches? 40 MHz isn't very
scary.

Trying to keep the bandwidth constant is one of the goals, as well as
maintaining a reasonable input impedance. I could use pHEMTs or relays
to do the switching, which would be about a factor of 10 easier, but as
you say, those bus switches are pretty attractive.

And besides, my ideal project is building a computer from sand.


We sometimes use a trimpot to calibrate the gain of o/e converters.
Some of the smaller pots are good to about 2 GHz.

Some people and organizations are adamantly opposed to trimpots.
Sometimes they are just what you want. They don't need a lot of code
support.

Like any time you want to go faster than a few hundred kilohertz.

Cheers

Phil Hobbs

No, really, some are usable to 2 GHz.

Some have weird convoluted internal structures, lots of distributed L
and C.

I agree that screwdriver pots can work at UHF--it's the digital ones
that crap out early. MDACs are about as bad.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Chris Jones]

On 12/07/2019 00:22, Phil Hobbs wrote:

On 7/11/19 9:12 AM, Chris Jones wrote:
On 11/07/2019 08:06, Phil Hobbs wrote:
On 7/10/19 5:46 PM, John Larkin wrote:
On Wed, 10 Jul 2019 15:58:43 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

Hi, All.

So I have this gig building a cathodoluminescence system for use in
electron microscopes.  It needs a programmable-gain amp with about 0.2
dB steps, low noise, and a bandwidth of > 40 MHz.

A previous voltage-controlled amp board for a biomed customer used a
256-step dpot and a power-of-two PGA made from a 74HC4051 MUX and a
resistor string.   Except at the very lower limit, the dpot's
attenuation is never more than 6 dB, which helps the noise a lot.

A little Cortex M0+ (LPC804) measures the control voltage and sets the
dpot and PGA.  It has a calibration loop that executes in a second
or so
at boot-up, so everything is kept relatively copacetic and accurate.

Thing is, its BW is limited to less than 1 MHz by the dpot, and
depends
on the dpot setting, so there's no straightforward way of
compensating.
Thus there's no way it's ever getting to 40 MHz.  For this one, I
wanted
to use a distributed attenuator--an RC ladder network with switches in
the shunt legs, like this:

In 0-*--Rser1---*---...---*--RserN---* ---------*---0 Out
      |          |         |          |          |
      *--Cpar1---*         *--CparN---*        Cload
                 |                    |          |
                 *-----*              *-----*   GND
                 |     |              |     |
               Rsh1   Csh1           RshN  CshN
                 |     |              |     |
                 |     |              |     |
                 *-----*              *-----*
                 |     |              |     |
               SWITCH Csw           SWITCH Csw
                 |     |              |     |
                Rsw    |             Rsw    |
                 |     |              |     |
                 *-----*              *-----*
                 |                    |
                GND                  GND

The math for this is fairly ugly, so I coded up a smallish C++ program
to optimize it, using the Nelder-Mead downhill simplex method
(amoeba in
Numerical Recipes, 2nd Ed.).

The penalty function for the optimizer is a linear combination of the
accuracy of the steps (mean error over frequency) and the rolloff,
with
an adjustable constant setting the balance.

Turns out that with fairly garden-variety CMOS bus switches (5
ohms, 3.5
pF Coff) I can do a 4-bit distributed 0-6 dB attenuator with RMS error
of a couple of tenths of a percent over the whole range.  (There are
better ones, but few I know of work above 3.6 V.)

I made some effort to include realistic strays in the analysis, so I
expect it to work pretty well.

Fun.

Cheers

Phil Hobbs

(If anybody has a similar problem, I'll happily share the code.)

Lots of people make logic-programmed RF step attenuator chips. Can you
work at 50 ohms?

Not easily.  Also none of those I know of go in such small steps--6
dB/16 = 0.375 dB.  The idea is to make a tolerable mimic of a
continuous control, without trashing the noise performance.  A
6-section attenuator would be down below 0.1 dB/step.  It would be a
lot easier to do with relays, but that would take a lot of power,
space, and cost.  This gizmo will come in way below $1 BOM cost,
counting just the attenuator and switches.

I'm curious: if you can tell me, what is the signal source, i.e. is it
a current or voltage, what sort of source impedance, amplitude? And
what is the load? Do you only need 6dB range?

It's coming from the front end, and will probably be a CFA.

Thanks. Is the CFA stage in turn taking its input from a TIA with
photodiode? (only if you are comfortable discussing this)

If so, do you do some gain control by changing the feedback resistor? (I
imagine that this would give the lowest noise but I can't think of a way
to do it without the parasitic capacitaince being annoying.)

The following stage is a noninverting amp built from an HC4051 and a
string of resistors, wrapped round something like an OPA695, with gains
from 1 to 32.  There's a micro on the board, so we use that to get rid
of the offsets.
Thanks.
I did a few PGAs for cellphone transmitters, both at baseband and at
RF and also a thing that pretended to be an analogue VGA but really
used a 1dB stepped attenuator and a VGA stage to fill in between these
steps, with some hysteresis on the stepped attenuator.

Right, that's the idea.  The problem with transconductance devices is
that you have to divide the signal down to something the transconductor
can cope with, e.g. +- 60 mV, and that trashes the SNR.  They're great
at high gain.
Yes fair enough.

The one transmitter IF stage that I did with an analog VGA stage used
two MOSFETs as the input devices. Two, because like most circuits on
chips it was differential. The MOSFETs were operating in the triode
region so that the AC input signal on the gates could be fairly large.
The sources of those MOSFETs were grounded directly, and the drains were
each cascoded with an NPN bipolar transistor. We did the gain control by
adjusting the base voltage of the bipolar devices, which adjusted the
D-S voltage of the MOSFETs. It was only practical because we could make
a bias circuit using devices that matched to the ones in the signal
path, but for discrete devices that would be hard, and small enough
MOSFETs to get a low enough gm are not readily available as discretes.
It wasn't especially low-noise, but probably a bit better than the usual
multiplier circuits, above the 1/f region.

The application here is photomultiplier replacement, and one of the
things people like about PMTs is that you can vary the gain continuously.


One of my preferred techniques for a baseband PGA was to convert the
input signal to a current and feed it into a digitally-chosen tap on a
resistive ladder - you can use R:2R for ~6dB steps and R:75R (or
R/5:15R) gives 1dB steps. With the input signal being a current, the
resistance and nonlinearity of the switches didn't matter much so they
could be small. I forget how I did the 1/32dB steps, maybe just a
linear scaling of the gm of the stage that fed the signal current to
the ladder, as linear is a reasonable approximation over 1dB range.
Those things are fun on a chip, with well matched resistors being very
cheap.

As long as you only care about the ratios, of course.

Yes, it was important to use the same resistor material in the gm stage
that drove the attenuator. I generally used unit resistors where I
needed matching. I didn't have a good feel for what would happen to the
matching if I didn't, and it was a nice challenge, and an excuse to
write some scripts to figure out the best configurations of unit resistors.

You could also add 0.2dB steps by making the terminating resistor at
one end of the ladder have some taps, and select one of those taps to
your output, but then switch resistance for those taps would matter.

I now remember that to make the fine steps over a <1dB range, I switched
in shunt resistors across the termination at the end of my R-75R ladder,
similar to what you did except that all of my shunt resistors were
switched across the same point. I think this is better than what I
suggested above because switches at ground have better and more constant
on-resistance than if they are in the signal path, if you're using those
nice NMOS only bus switches.

Anyway thanks for sharing.