LM13700 and Adjustable gm via Iabc

[DanDaManJC]

Hi all -- I posted this in off topic, but the thread would be better suited here.

http://forums.anandtech.com/showthread.php?t=2119821


mods.. could you combine threads etc?

 

[William Gaatjes]

Circuit question for you folks out there...

I'm considering using a set of LM13700 to make an adjustable, 5th-7th-ish order, low pass filiter whose f0 should vary between 10khz and 20khz. Anyways... all that said, I was looking into using OTAs since varying the gm of the amplifiers yields an adjustable cutoff frequency with a single control voltage/current. Compared to a cutoff frequency change of something like a sallen key topology on a typical vcvs setup, the gm-c approach seems a bit simpler.

Anyways, while running my simulations, it seems like the gm is quite variable. That is, by definition the output of an OTA is:

Io = gm(V+-V-)

where gm = 1/(2Vt)*Ibias. Ibias is the input current, Vt=the thermal voltage (physics constant).

Now say the cutoff frequency, for a 2nd order lpf, is:
fc=gm/(2pi*sqrt(C1*C2)=X*Ibias/(2pi*sqrt(C1*C2)

(diagram can be found here: http://129.105.69.13/datasheets/Opam...p_Tutorial.PDF Fig 7a)

simulating, with C1,C2 constant...changing Ibias, finding the -3dB point in simulation and solving for "X" yields the constant factor 1/(2Vt). However, this constant varies significantly from Ibias = 1mA to 2mA with the 2nd order lpf.

Sooooo... with all that said... it seems to me like this "X" variable should be pretty consistent. Has anyone here played around with OTAs before and have some experience with 'em?

Obviously by changing the bias current, the gm still is the only thing changing in my equation -- so my cutoff freq is only being affected by the gm, but there seems to be this non linear relationship between the bias current and the multiplicative factor in front of it that yields gm.

I understand the idea : To control the charge current of the capacitor by controlling the output current of the ota. Thereby changing the time the capacitor needs to charge and discharge. And since time and frequency are related. It is similar as changing the resistor with a certain value for a resistor with a higher or lower value. Causing a lower cut off frequency or a higher.

I understand that you take the formula for a low pass rc filter and replace the r for the characteristics of an ota ?

A low pass rc filter is basically an integrator.

Just a question, what happens when you simulate a 1st order filter ?
And when you compared the results with a second order filter what do you see ?

But most of all, is the ibias input for the ota linear or is it shaped like the transfer function of a transistor or a diode ? If that is not a straight line, choose a part of that line that is almost straight.


I may be wrong, but is this gm - ibias graph not logarithmic ?
When looking at page 5, top right graph of the datasheet ?

http://www.national.com/profile/snip.cgi/openDS=LM13700

The lowest right graph on page 5 is also logarithmic, if i am not making a mistake...

 

[DanDaManJC]

I understand the idea : To control the charge current of the capacitor by controlling the output current of the ota. Thereby changing the time the capacitor needs to charge and discharge. And since time and frequency are related. It is similar as changing the resistor with a certain value for a resistor with a higher or lower value. Causing a lower cut off frequency or a higher.

I understand that you take the formula for a low pass rc filter and replace the r for the characteristics of an ota ?

Sure. I think the overall transfer function was basically derived from scratch using the usual, brute force, math (likely proper use of KCL and whatnot). But that's a good intuitive explanation.

Basically, with these OTA amps I'd be able to control the cutoff frequency by simply changing gm, and gm is directly proportional to Ibias (or Iabc in the datasheet).

A low pass rc filter is basically an integrator.

Just a question, what happens when you simulate a 1st order filter ?
And when you compared the results with a second order filter what do you see ?

The 1st order filter behaves as I would expect it. The datasheet mentions gm = 19.2*Iabc, and when I experimentally calculate for that "19.2" factor, I get a number on the order of 18.3. Which is pretty close. Changing my bias current, I do get the variable cutoff frequency I expect.

But most of all, is the ibias input for the ota linear or is it shaped like the transfer function of a transistor or a diode ? If that is not a straight line, choose a part of that line that is almost straight.


I may be wrong, but is this gm - ibias graph not logarithmic ?
When looking at page 5, top right graph of the datasheet ?

http://www.national.com/profile/snip.cgi/openDS=LM13700

The lowest right graph on page 5 is also logarithmic, if i am not making a mistake...

Hehe.. well if that's the case, then there we have it

So looks like I need to make use of the linearizing diodes or really limit my input voltage swing so I don't see the non linear aspects of the amp. Thanks for the input... ill see what happens with this knowledge.

 

[William Gaatjes]

Hehe.. well if that's the case, then there we have it

So looks like I need to make use of the linearizing diodes or really limit my input voltage swing so I don't see the non linear aspects of the amp. Thanks for the input... ill see what happens with this knowledge.

I read that part too, that the input of the amp is only linear with small signals.
But i have difficulty understanding how it relates to the linearity of the IABC input and the resulting behaviour of the low pass filter. When you have figured it out, i am interested to find out the conclusion.

For some reason, i have to think more of distortion of the output signal when thinking of those small signal inputs. However, i do think distortion of the output signal influences the output signal and as such the output voltage/frequency graph of the filter. But it is a guess...

 

[uclabachelor]

I read that part too, that the input of the amp is only linear with small signals.
But i have difficulty understanding how it relates to the linearity of the IABC input and the resulting behaviour of the low pass filter. When you have figured it out, i am interested to find out the conclusion.

For some reason, i have to think more of distortion of the output signal when thinking of those small signal inputs. However, i do think distortion of the output signal influences the output signal and as such the output voltage/frequency graph of the filter. But it is a guess...

a delta of 1mA for Ibias isn't really "small" per say. Using a current mirror techniques you can get very stable Ibias that are adjustable between 1 - 2mA.

Or get a gang pot designed specifically for audio and use that to adjust your cutoff frequency. Then it would be a matter of a few simple op-amp filter circuits cascaded.

 

[DanDaManJC]

a delta of 1mA for Ibias isn't really "small" per say. Using a current mirror techniques you can get very stable Ibias that are adjustable between 1 - 2mA.

Or get a gang pot designed specifically for audio and use that to adjust your cutoff frequency. Then it would be a matter of a few simple op-amp filter circuits cascaded.

Hmm ok. So im building up a couple of the cascaded stages right now, and finding that using the diode input ends up drastically changing my frequency response. To some degree, it is all a matter of tuning and getting things "just right".

So for my bias currents, im simply running a resistor from +Vcc to the input.. simply using ohms law. Using a multimeter, I saw that this provided a pretty stable current supply. That said, do you think this would be providing stability issues?

Do you have much experience working with otas too? specifically, any tips and tricks that i might be missing from a practical standpoint? also.. do you think it matters, if not using the darlington buffers on the chip, that i leave them floating?

 

[William Gaatjes]

Hmm ok. So im building up a couple of the cascaded stages right now, and finding that using the diode input ends up drastically changing my frequency response. To some degree, it is all a matter of tuning and getting things "just right".

So for my bias currents, im simply running a resistor from +Vcc to the input.. simply using ohms law. Using a multimeter, I saw that this provided a pretty stable current supply. That said, do you think this would be providing stability issues?

Do you have much experience working with otas too? specifically, any tips and tricks that i might be missing from a practical standpoint? also.. do you think it matters, if not using the darlington buffers on the chip, that i leave them floating?

Did you get any further ?

The current mirror(might need an opamp as well) idea from uclabachelor is a good one. It will allow you to shift the voltage range and increase the range if needed. For example from 6,5 to 8 volts shifting to 0 to 3 Volts.

When the ota is distorting the signal, you add different sinusoidal waves as Fourier figured out. These are of different frequency and amplitude but add up to your amplified original signal. I think the explanation of the changing output frequency range is because of this. The diodes themselves also cause a distortion where the constant e has something to with as well. But it is shards of memories and ideas.

With electronics, sometimes it is easier to calculate backwards.
Best way is to start with what you want as output. Then calculate in reverse.
In the datasheet are some examples of ota's used as filter. Maybe you could model those examples to see how these examples respond and then calculate back.

 

[DanDaManJC]

Did you get any further ?

The current mirror(might need an opamp as well) idea from uclabachelor is a good one. It will allow you to shift the voltage range and increase the range if needed. For example from 6,5 to 8 volts shifting to 0 to 3 Volts.

When the ota is distorting the signal, you add different sinusoidal waves as Fourier figured out. These are of different frequency and amplitude but add up to your amplified original signal. I think the explanation of the changing output frequency range is because of this. The diodes themselves also cause a distortion where the constant e has something to with as well. But it is shards of memories and ideas.

With electronics, sometimes it is easier to calculate backwards.
Best way is to start with what you want as output. Then calculate in reverse.
In the datasheet are some examples of ota's used as filter. Maybe you could model those examples to see how these examples respond and then calculate back.

Well, my lab partners and I ended up keeping out input signal just small enough. Also adjusted the supply voltage and bias currents such that we met the assignment spec. We ended up figuring out that the high Q in our stages was making the input signal too large (thus entering the nonlinear regions), also fiddled around with the supply voltage and bias currents. Basically, we figured out that we had these nonlinearities in the operation of these chips... and worked our best to try and keep in the linear region.

In our discussion here (AT), we came to this same conclusion. So the next steps we took were experimentally focused based on this insight.

on the current mirror idea -- yeah, that's basically why we wanted to use the otas, makes the filter very easy to adjust by choosing the right topology.

so really, my question was on how to either better linearize these OTAs or else how to better model their transfer characteristics. After doing some googling, it looked like TI has some good material on the subject. Or at least they take a different approach to analyzing OTAs in their datasheets.

http://focus.ti.com/docs/prod/folders/print/opa860.html#technicaldocuments

after writing all this, another approach that could be taken would be to model the circuit with its own small signal model. of course, that's already done in the simulation program, but that exercise would probably give a lot more analytical insight.

 

[uclabachelor]

Well, my lab partners and I ended up keeping out input signal just small enough. Also adjusted the supply voltage and bias currents such that we met the assignment spec. We ended up figuring out that the high Q in our stages was making the input signal too large (thus entering the nonlinear regions), also fiddled around with the supply voltage and bias currents. Basically, we figured out that we had these nonlinearities in the operation of these chips... and worked our best to try and keep in the linear region.

In our discussion here (AT), we came to this same conclusion. So the next steps we took were experimentally focused based on this insight.

on the current mirror idea -- yeah, that's basically why we wanted to use the otas, makes the filter very easy to adjust by choosing the right topology.

so really, my question was on how to either better linearize these OTAs or else how to better model their transfer characteristics. After doing some googling, it looked like TI has some good material on the subject. Or at least they take a different approach to analyzing OTAs in their datasheets.

http://focus.ti.com/docs/prod/folders/print/opa860.html#technicaldocuments

after writing all this, another approach that could be taken would be to model the circuit with its own small signal model. of course, that's already done in the simulation program, but that exercise would probably give a lot more analytical insight.

Do you have a transfer function of required filter? I'm curious as to see how I would implement it.

 

[DanDaManJC]

Oh yeah that's the easy part...

just need to create a LPF, >1.2db ripple in pass band, and 50db/1 octave attenuation. Then we'd need to auto-tune the circuit to go between 10khz and 20khz

in short, i could use a 7th order chebysev with .1db ripple and just use the table + w0 + q equations from the transfer function. i linked a tutorial on otas that included derived transfer functions for the 2nd order ota that i used.

ran into a couple issues though... i wasnt sure how to deal with using the linearizing diodes. you can assume gm~Iabc/(2Vt) for small inputs... but once you use the diodes gm also changes. so we just decided to keep vin small (within 20mv or so). also, high q => you'll easily get out of the linear region and have a distorted signal. so rather than use a straight 7th order cheby, we cascaded two 4th orders. that is kinda klunky... and probably not mathematically optimal, but it still worked and avoided the high q issue.