LM13700 - new discovery (at least for me)

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alphabetter
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LM13700 - new discovery (at least for me)

Post by alphabetter » Wed Aug 15, 2012 4:41 am

Hi Folks,

Designing a new module for my LushOne synth recently I discovered that the LM13700 in the circuit was providing a significantly different gain from what I thought it theoretically should. This triggered a lot of investigation, measurement and simulation which finally lead to a new understanding of this component and the conclusion that the common magazine articles about it are not quite correct.

The whole thing got under my skin so much that I made a write-up here:
http://lushprojects.com/blog/2012/08/lm13700-missing-forumla/

I suspect only about 20 people in the world still care to underand this level of detail about the LM13700 and 18.5 of those already know what I've written but in case you are the missing 1.5 then you might find it interesting and at least there is a record on the web so my efforts might be useful to others!

Comments/corrections/better analysis are welcome!
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Post by frequencycentral » Wed Aug 15, 2012 4:44 am

As the 0.5 I'm very grateful for your efforts. :hihi:

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Post by Dr. Sketch-n-Etch » Wed Aug 15, 2012 8:07 am

Nice work, alphabetter! I stopped using the LM13700 a couple of years ago in favour of the SSM2164, mostly because I didn't like having to voltage-divide the inputs by a factor of several hundred to maintain linearity, and the fact that the control pin is a current referenced to the negative rail. The SSM2164 has its own special challenges (not the least of which being that there is no SPICE model for it, and its datasheet has to be one of the worst I've seen for any chip), but once you figure out its idiosyncracies, it's probably the single most useful (non-opamp) chip out there. However, if I ever feel the need to return to OTAs, I'll definitely keep your analysis in mind.
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Post by alphabetter » Wed Aug 15, 2012 9:14 am

Dr. Sketch-n-Etch wrote:Nice work, alphabetter! I stopped using the LM13700 a couple of years ago in favour of the SSM2164, mostly because I didn't like having to voltage-divide the inputs by a factor of several hundred to maintain linearity, and the fact that the control pin is a current referenced to the negative rail.
Thanks! I agree both these attributes of the LM13700 are somewhat annoying.
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Post by J3RK » Wed Aug 15, 2012 11:57 am

I'm still quite happily using this chip, and will definitely check out your write-up! Thanks for putting it together!

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Post by Tim Stinchcombe » Wed Aug 15, 2012 1:28 pm

I went through that same pain about 7 years ago when I was writing up my HNC project report, and ended up doing pretty much the same thing - start from scratch in order to work out what is what. I concluded in the end that the confusion arises because the equation is couched around having resistive dividers on both sides of the differential pair, but the figure then shows only a resistor on one side only. Here was my equivalent diagram for working everything out:
Image
If you look at the overall picture of the input being Va-Vb, then you can assume that Va' is approximately Vb' at the inputs to the diff pair, and so then the current flowing from Va to Vb is just (Va-Vb)/(2*Rin) = Vin/(2*Rin), and this is current 'Is', and so there we get the '2' back which appears in the datasheet equation!

In my report I noted that this had been remarked upon in old issues of Electronotes back when the device first became available, and also that (at the time of my report writing), there had been a recent thread on Synth DIY about the exact same thing. Just think of all that needless suffering that could have been saved if the datasheet author had actually made sure his/her diagrams properly matched the equations. :eek:

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Post by alphabetter » Wed Aug 15, 2012 4:15 pm

Tim Stinchcombe wrote: I concluded in the end that the confusion arises because the equation is couched around having resistive dividers on both sides of the differential pair, but the figure then shows only a resistor on one side only.
Yes - this is another possible explanation!

BTW Tim - your analysis of the MS-20 filter became a bit of a reference point and obsession when I was messing around with filter prototypes recently!
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Re: LM13700 - new discovery (at least for me)

Post by frijitz » Wed Aug 15, 2012 5:51 pm

alphabetter wrote:Comments/corrections/better analysis are welcome!
To expand just a bit on what Tim said. Bernie Hutchins reported on the apparent factor-of-two discrepancy in EN #107 (Nov 1979). Subsequently, in EN #113, Serge T. explained the discrepancy by noting that in the actual VCA circuit (with resistors) it only takes I_S = I_D / 2 to shut one leg of the input diode pair off. An elegnt way of explaining the factor of two, but not as detailed as yours and Tim's analyses. In the same issue, I reported that I had come to the same conclusion by a careful analysis of the equations, but I didn't go through the details.

I think where the data sheet is misleading is where they say the VCA circuit works the same as the current-based circuit that the analysis was done on.

Ian

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Post by frijitz » Wed Aug 15, 2012 5:54 pm

Dr. Sketch-n-Etch wrote: ... I didn't like having to voltage-divide the inputs by a factor of several hundred to maintain linearity...
Ummm ... That's why the chip has linearizing diodes on the input. Did you forget to use them? :grin:

Ian

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Post by Dr. Sketch-n-Etch » Thu Aug 16, 2012 1:57 am

frijitz wrote:
Dr. Sketch-n-Etch wrote: ... I didn't like having to voltage-divide the inputs by a factor of several hundred to maintain linearity...
Ummm ... That's why the chip has linearizing diodes on the input. Did you forget to use them? :grin:

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Re: LM13700 - new discovery (at least for me)

Post by alphabetter » Thu Aug 16, 2012 3:16 am

To expand just a bit on what Tim said. Bernie Hutchins reported on the apparent factor-of-two discrepancy in EN #107 (Nov 1979). Subsequently, in EN #113, Serge T. explained the discrepancy by noting that in the actual VCA circuit (with resistors) it only takes I_S = I_D / 2 to shut one leg of the input diode pair off. An elegnt way of explaining the factor of two, but not as detailed as yours and Tim's analyses. In the same issue, I reported that I had come to the same conclusion by a careful analysis of the equations, but I didn't go through the details.
[/quote]

Thanks for the additional information. It was sure that other people had already figured this out, but I couldn't find anything on the web.

I was 9 years old in 1979 so I missed this discussion at the time :)
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Re: LM13700 - new discovery (at least for me)

Post by frijitz » Thu Aug 16, 2012 2:53 pm

FWIW, here's a doodle showing my derivation of the infamous factor of 2:

A useful trick is to replace the input V and R by their Thevenin-equivalent current, indicated by I_S in the doodle. Then most of the analysis can be done in terms of currents.

I_S gets split at the diode-resistor junction, but we don't yet know how. In fact, this is what we are trying to determine. So assume a fraction "a" goes downward into the resistor and (1-a) into the diode. The left-branch currents are indicated by the expressions on the left side of the figure.

Since the diodes are assumed to be ideal, the voltages across the two resistors are equal, and so are their currents, as indicated by the lower-right expression. Finally, remembering that the sum of the diode currents is I_D, the expression for the right-side diode current is immediately obvious as written in the upper right.

Now note that we have two different expressions for the current in the right-side branch. Since these must be equal we see that "a" is determined as a = (1-a) = 1/2. Poof! There's your factor of two!

So the input current is split in two, with only 1/2 going into the diodes to produce the transconductance action. In the data sheet derivation, the I_D/2 current sink forces all of I_S to go into the diode. So there's twice as much action.

The factor of two carries into the derivation of the final transconductane in the usual manner.

Ian
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Post by DannySebahar » Sat Apr 29, 2017 2:34 am

No idea what y'all are saying but I'm making SynthRoteks MST Low Pass Filter and not only did I install the female pin sockets for both LM13700 receiving 16 pin connectors but one only one of the 14 pin connectors. Do the connectors have polarity at all. I order two new LM13700s and two new TL074s because they were all oppositely placed when put in but I am not sure if that matters however they have diodes in them which do have polarity. Anyway, the kit didn't work but I took a multimeter to everything and everything was goo but those ICs were the wrong direction.

I ordered Erica Synths Bundle and one more 6-1 Output from Synthrotek so this was my first experience and it generally went well. I hope replacing the 14 pin and 16 pin connectors and 2xLM13700s and 2xTL074s will make it work.

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Post by Sandrine » Mon May 01, 2017 2:22 pm

poof!!

I ended up not using the darlington pair in my last design...biasing, non-linearity, too variant.. what were they thinking with that anyway?

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Post by J3RK » Mon May 01, 2017 2:36 pm

Sandrine wrote:poof!!

I ended up not using the darlington pair in my last design...biasing, non-linearity, too variant.. what were they thinking with that anyway?
I've never even attempted to use it. Just never seemed like a great idea. I have used the linearization diodes a bit, so not all of the extra features were a waste. :hihi: Everything I've wanted to build with this IC I felt should be buffered, integrated, etc. etc. with op amps though.
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Post by jorg » Tue May 02, 2017 3:48 pm

Thanks for an excellent analysis! That will save me some time on my next design. I simulate everything so hopefully TI's model for the LM13700 is reasonably correct.

I did use the Darlingtons in my most recent design: as inputs! They are very handy input buffers. I did a saw-to-variable-ramp processor. One Darlington is used on the saw signal; the other is used on the CV. The whole thing uses one LM13700, a TL074, and a couple of dual transistors (probably could get away with singles).

We are all familiar with the very small input signal range, but it's also important to note the very small output swing. In my design, the OTA is providing feedback to the (-) input of an op amp, so there is basically no voltage swing. Tip: in this configuration, you want to put the compensating capacitor at the OTA input; that way more OTA feedback (less op amp gain) automatically makes more compensation and it all stays nice and clean.

I'll post the schematic when I get a chance.

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Post by windspirit » Wed May 03, 2017 1:35 pm

Just double checking, do people just use a simple op amp buffer instead of the darlington pair or is it more case dependent? I usually just use the schematics from the data sheet so I never thought to try a different output buffer method.

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Post by J3RK » Wed May 03, 2017 1:55 pm

I always use an op amp and skip the darlington pair for the output. However, I do like the idea above using them on the inputs in some cases. Never tried that, or even thought about it, but could be handy for some things.
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Post by jorg » Thu May 04, 2017 8:20 am

Using the Darlingtons on inputs saved me a couple of op amps. The main reason Darlingtons aren't great for OTA output buffers is that the Darlington is only a voltage buffer. What an OTA really needs is a current to voltage converter, so its output voltage swing can be very small. Using an op amp C to V converter lets the OTA have near zero output voltage swing.

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Post by Sandrine » Thu May 04, 2017 8:39 pm

jorg wrote:Using the Darlingtons on inputs saved me a couple of op amps. The main reason Darlingtons aren't great for OTA output buffers is that the Darlington is only a voltage buffer. What an OTA really needs is a current to voltage converter, so its output voltage swing can be very small. Using an op amp C to V converter lets the OTA have near zero output voltage swing.
Exactly, and DC V noise bummer

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