The continuing saga of the hyperbolic tangent

May 21, 2005 30 Replies

Rodger Rosenbaum has been feeding me papers by Barrie Gilbert about using differential pairs to produce various and wondrous nonlinear transfer functions. Based on this inspiration, I have decided to try to fit a sum of my two temperature controlled tanh functions contained in one LM13700 and a linear gain to generate an arbitrary transfer function that serves my purposes.



My aim is to have a high gain for signals near zero volts but roll the gain off as the signal amplitude rises so that my 10 bit +-10 volt A/D converter has a fixed relative resolution over the widest possible range.



I have chosen the peak gain to be 8 (to increase the effective resolution to 13 bits for signals between +-.1 volts and roll the incremental gain off so that above the lowest possible voltage (about



+-.3 volts) each 1% increase in amplitude moves the output 1 A/D count up to the full signal range of +-10 volts. And I want a 10 volt input to produce a 10 volt output. I put all these requirements into a Mathcad worksheet and produced the following function:

a*tanh(b*input)+c*tanh(d*input)+f*input with a=3.582, b=1.80, c=3.943, d=0.331, f=.248



I will post graphs of the results under this title on A.B.S.E.


The LM13700's unused "buffer output" transistors could be used for heating in a chip-temperature-control scheme.

Thanks, - Win

Snip:

Have a look at John's schematic posted 5/13.

Don't know if is useful but you can use one side of a dual OTA to temperature-compensate the other side. C +-----||-----+---+---[R4]----->Iabc2 | 0v-|+_/ | | [R3] | | Iout1 = Iref +----------------- +------|+ \\ | | [R2] |OTA1>OO--------+ Vref--> +------|-__/ | [R1] Iabc1 = 2kT/q(Iref/Vref). | \\|/Iref Iabc2 = Iabc1(R3/R4). | --+-- -Vcc Vref = 25mV or so.

Choose Iref and Vref, which gets R1+R2, then calc R3+R4 on the assumption that V1= 0v at T= (273+25)K.

Tony Williams.

I am controlling the actual temperature of my OTA chip, but I want to make sure I understand your concept.

I assume that Vref is created by Iref passing through R2 (not sure why R1 is needed unless Iref is just the current through R1 because it is connected to a large voltage). Then th integrator adjusts the current to both OTAs to whatever holds the current out of OTA1 equal to Iref.

This would force a fixed transconductance at the given Vref, but I don't see how it forces a temperature compensated tanh function. The function is essentially A*tanh(B*Vin) Temperature changes primarily alter B but you are correcting at a single input voltage by changing A.

Or have I got it all wrong?

Simple temperature compensation (with a PTAT) ONLY forces the same slope (at zero) over temperature. The full-scale varies. The full TANH compensation CAN be done on-chip, but it's a bitch to do with off-the-shelf components.

Temperature control is probably the simplest solution, although I can envision a possibility using thermistors.

I've just been commissioned to do a log IF (at 600MHz)... maybe that task will provide the impetus to develop some methodology to flatten the FS portion.

...Jim Thompson

| James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC\'s and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | | http://www.analog-innovations.com | 1962 | I love to cook with wine. Sometimes I even put it in the food.

Simple temperature compensation (with a PTAT) ONLY forces the same slope (at zero) over temperature. The full-scale varies. The full TANH compensation CAN be done on-chip, but it's a bitch to do with off-the-shelf components.

Temperature control is probably the simplest solution, although I can envision a possibility using thermistors.

I've just been commissioned to do a log IF (at 600MHz)... maybe that task will provide the impetus to develop some methodology to flatten the FS portion.

...Jim Thompson

| James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC\'s and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | | http://www.analog-innovations.com | 1962 | I love to cook with wine. Sometimes I even put it in the food.

I will be watching if you come up with anything to share.

[...]

John, I looked at those graphs, and have a question. Suppose you have a small amplitude signal riding on a larger amplitude one. If you reduce the gain at high amplitude, won't you lose the small signal? And once the output of the circuit is digitized, is there is any way to get the small signal back again?

I saw your argument that the least significant bits in an a/d are not useful at high signal amplitudes. But aren't these the bits that allow you to capture a small amplitude signal in the presence of a much larger one?

Mike Monett

In article , John Popelish wrote: [snip]

Apologies. I have an erratic download/reader atm, so don't see the whole of threads. In this case I saw the reference to LM13700, (without really understanding what had gone on before), and jumped in with both feet.

Tony Williams.

No.

Yes they are. But I am looking for the arrival of one event at a time (earthquakes), especially the arrival of the P and S wave signatures. The actual quality of the event is not so important as just identifying its arrival time. Two overlapping earthquakes will be a pig's breakfast (as far as my ability to interpret the recording), anyway. Retaining 1% relative resolution for the stronger signals is plenty, because there are other part of the seismometer that are no more accurate or linear than that. Most A/D systems use 16 bit converters, but only use all that resolution for the stuff within 1% of span near (middle) zero.

This lossy compression is somewhat analogous to how the nonlinear ear response causes a louder sound to mask the presence of somewhat softer sounds, but in a frequency dependent way. This masking effect is what makes one of the compression levels in MPEG level 3 possible. It calculates what soft spectral components of the sound are inaudible at the moment because of ear masking, and simply discards those soft sounds, since you can't hear them at that moment, anyway. This also saves a lot of bits.

Monitoring atomic explosions in Korea, by chance?

That's lossy compression, similar to jpeg. It is fine for photos and sound, but it can create artifacts on some types of data. For example, using jpg for engineering graphs where gif, tif and png are better suited.

All the commercial seismometers seem to be 18 or 24 bits. Storage is cheap

- why worry about saving bits? Why not use 16?

Mike Monett

With 24-bit converters becoming commonplace, and selling for under $10 to the big boys, why fool around with 16 bits, let alone 10?

Thanks, - Win

No. Just garden variety seismic events.

For now, the seismometer application is an excuse for me to explore the world of nonlinear transfer functions and their uses. I have built a seismometer mechanism, and am in the process of building the amplifier and filter electronics. I happen to already have a 10 bit A/D serial interface for a PC.

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So I am trying to come up with a way to make best use of a limited resolution converter, as a learning experience. I may well throw the whole thing over after a bit of play and use a 16 bit converter.

To see what it can accomplish. The lessons apply to any digital resolution.

[...]

LOL! I really have to admire your persistence. After going to the trouble of winding 4 miles of 44 gauge for the coils, I'd be inclined start with the best a/d I could get:)

Anyway, thanks for the replies. I enjoyed exploring the topic, and found quite a few references in google. One looks really interesting - a "$2 Diamagnetic Suspension Seismometer", by James Spottiswoode. He shows the tilt caused by cars entering and leaving a garage, and the effect of wind noise:

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It seems like it would be simple to automatically adjust the zero by adding some tilt. But his drum plots seem to be quite stable, so maybe it's not needed.

Mike Monett

The AD7791 claims 22 effective bits for $3.83/1k, with a very simple serial interface. They allow two free samples:

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The TI ADS1271 is $5.90/1k, offers high sample rate, three operating modes, and a serial interface that can be daisy-chained. Also free samples:

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Mike Monett

Thanks for this link. I am also interested in making a differential photo diode tilt meter using cheap and simple parts (compared to 4 miles of wire and 50$ worth of neodymium iron magnets in a $100 pole structure.

You guys are trying to take all the fun out of this project.

It seems that the Earth provides a 6 hertz rumble that is fairly independent of any earthquakes (a sort of crustal resonance). Picking up this so called "microseism" is the test that any seismometer is functioning. But I agree that if I can digitize faster than the 20 or so samples needed to record the arriving waves, then I can use multiple samples to increase my net A/D resolution.

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