Gyrator Calculations..Right idea?

[jeth]

Been working out some values for Gyrator circuits to build up some EQ sections. The Gyrators are to be used in a single buffer eq, as seen on the Forsell tech. website. The configuration has the gyrators acting as freq. dependant input attenuators (for cut) and freq. dependant ground shunt in the feedback network (for boost). I'm hoping that this topology is common enough for folks to know what I'm on about...
I found some other formulas for the same gyrator circuits, and played with them along with forsells basic formulae. It wasn't to simple at first to get desirable figures, as the gyrators must use same R value for every band to keep boost/cut constant. This made picking caps tricky...I came up with the following method for picking my values. (bearing in mind easy component choice is more important to me here than precision of Q or Fo)

I took this formula.. 1/ (4x C1 x Q x Pi x Fo)=R

As R is fixed I rearrange for this.. 1/ (4 x R x Q x Pi x Fo)=C1

I put in my target Q and Fo to get C1,
e.g. 1/ (4 x 3k x 2 x Pi x 33)= 0.4uF

I then make C1 the closest available value, 0.39uF, and substitute it back into the formula to find the adjusted Q...
e.g. 1/ 4 x 3k x 0.39uF x Pi x 33=2.061058.....=Q

I then use this formula to find C2.... C2=4 x Qsqrd x C1= 6.626uF

Then put C1 and C2 into this formula to get my final Fo....

Fo= 1/ (2 x Pi x R x Sq.Rt (C1 x C2)) = 32.577...

Finally I put my final C1, C2 and Fo values back to the original formula to find Q... In this case 2.0878....

My question is...Am i on the right track? I know this seems long winded but it lets me use available C values. My main concern was that the ratio of C1 and C2 I end up with is not the same as the original found values. But I've run the final figures through every formula and the math works.. even using a different formula for Q...
Q= 1/2 x Sq.Rt (C2/C1)

Also, anyone have any info on general guidelines for this configuration... min/max R/C values or anything like that would be useful. A good search came upwith only the info to get as far as this so some confirmation would be handy.

 

[bcarso]

A schematic would be helpful.

 

[jeth]

Sorry... I wanted to post the schematic links, but only have brief online access at work at the moment. I hoped someone might be familiar with the topology. I´ll try to post some links asap...

 

[tv]

do your equations work only with opamp gyrators (LRC equivalent) or are they applicable to simple one-transistor/fet gyrators as well?

 

[jeth]

Actually TV, I have no idea
The article they came from mentions only opamp gyrators.. I'll be trying to post the links shortly.

 

[jeth]

OK.. Some links, finally..

Forssells article, including the Eq and Gyrator schematics...

http://www.forsselltech.com/Evolution of an EQ Design2.pdf

The Gyrator details...

http://www.forsselltech.com/schematics/Gyrator1.htm

The EQ schematic.

http://www.forsselltech.com/schematics/EQ1A.PDF

 

[jeth]

Anyone??? Really i just want to know if my cap selection will work ok. The sums work every which way...but do the caps need to be in a certain ratio(ie as they come out in the first calculations before changing value and adjusting the other parameters to suit) for the circuit to behave?

 

[alk509]

I'm not sure I understand exactly what the problem is... Are you asking if your math is right? Is there any reason why you haven't breadboarded this to figure out the answer yourself? Or did you already try it and it didn't work? I totally don't mean this as an attack on you, but it seems you've been waiting for a week for an answer that you could've found yourself in 15 minutes...

Peace,
Al.

 

[PRR]

> do the caps need to be in a certain ratio

It seems they need to be in ratio 4*Qsqrd. Which is how you are calculating. It looks fine to me.

> are they applicable to simple one-transistor/fet gyrators as well?

Since the scheme uses a unity-gain opamp, it will "work" with a transistor, with the limitation being that a transistor may have non-negligible input and output impedance. I think the practical fact is that low-Q is easy and high-Q is hard (even for an opamp).

I suspect that if you aim for Q=2, you'll get Q=1.8, 1.5, at a slightly different frequency. For many audio purposes, this is no big deal.

 

[bcarso]

The Forsell-preferred topology does have some benefits, but also requires some large C ratios for moderately high Q's. These Q's are unlikely to have much audio EQ use, so his preferences are well-supported.

One thing I noticed: the precise match of the two equal resistor values is not critical, unlike a lot of circuits. (EDIT) I misconstrued effects of finite output R of the follower at first blush. What it does do is make this resonator have the effect of a parasitic R across the inductor---I thought at first that it would just have detuning effect that could be compensated. Also haven't looked at the effect of the less-than-unity gain error effect yet though---my guess is that may be significant but not fatal for normal audio use. (EDIT 2) It turns out the effect of less-than-unity gain is also fairly pronounced, and very similar to the effect of finite output Z.

This stuff is suitable only for fixed parametric EQs---even just changing the frequency while maintaining the amount of boost or cut requires changing 3 resistors together while keeping the ratio constant. And forget changing the Q with the rest constant.

For topologies that are more adjustment-friendly but burn opamps, Fred mentions the Steve Dove-described first-order allpass version of the state-variable filter. Among filter scholars this has a specific name and ancestry, and is described as the Tarmy-Ghausi circuit (from 1970), modified for nondifferential output opamps by Moschytz (in 1972; see pg. 2407, The Circuits and Filters Handbook, ed. Chen, CRC Press, 1995*). This is probably another case of a circuit that Steve invented, but where unfortunately someone stole his idea some years before. Happens to the best of us---you spend your time thinking things up, or reading everything that is written, but it's hard to do both at once.

I still miss my encounters with Steve in the hallways at Harman, when we would set to strangling each other periodically. All in good fun of course.



*this tome of Professor Wai-Kai Chen's, Ed., which runs to almost 2900 pages, should be shelved in the lowest row of your bookshelf if you live in earthquake country. It could also be used as a pretty good doorstop, except that the covers are too slick. It's full of typos but whaddaya want for that much stuff? It's printed on that thin paper usually found in King James bibles.

 

[jeth]

I'm not sure I understand exactly what the problem is... Are you asking if your math is right? Is there any reason why you haven't breadboarded this to figure out the answer yourself? Or did you already try it and it didn't work? I totally don't mean this as an attack on you, but it seems you've been waiting for a week for an answer that you could've found yourself in 15 minutes...

Al, My query was regarding my math. I was concerned that the ratio of C1/C2 is being changed by my adjustment of C1 to the nearest available value to the one found with my first calculation. As I noted the math still appears to work with the adjusted values, albeit with a small change to the Q and the Fo. This is far less a problem for me than difficult component values. My concern was that this may have some other effect, perhaps on the response curve of the gyrators peak/notch.
The reason I did not experiment to get my answer is that I'm stuck out in deepest mexico with few parts available and little cash to spare on my hobby at this time. So for now I'm just occupying myself with attempts to learn from studying circuits and theory...not ideal I know but better to keep my interest and knowledge alive, besides I have little else to do!
As for the search, a thorough dig around the forum came up with little info about this area of design.

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> do the caps need to be in a certain ratio

It seems they need to be in ratio 4*Qsqrd. Which is how you are calculating. It looks fine to me.

PRR..but they don't stay in exactly that ratio once I've substituted C1 for an available value. Will this have other effects than just adjusting the Q..?

 

[PRR]

> As R is fixed I rearrange ... ... to get C1.....= 0.4uF ... I then make C1 the closest available value, 0.39uF

The "problem" is that now "R" is wrong.

In the boost-cut EQ, the boost or dip amount is wrong.

In the topology Forssell uses, the "wrong R" is totally swamped by pot resistance, except at the extremes, where the pot wiper hits the end-stop.

So you fiddle your added R to meet the boost/cut spec, +/-12dB instead of +/-11.5dB or whatever the "wrong R" result is.

That changes Q from 1.0000 to maybe 1.1.

Can you hear the difference? Either a part-dB error in boost/cut, or a tenth-error in Q? No.

I'm too lazy to do the math. I do think that if the "right" answer is 4.0uFd, a 3.9uFd part is all the same for audio. Error is either 4.0/3.9= 2.5%, or (4.0/3.9)^2= 5%. I'm not going to figure which function is right, because we don't hear amplitude errors of 5%.

 

[bcarso]

I think you (jeth) have it within your power to calculate the shifts you are concerned about from the equations you've already used and/or posted links to. Don't be afraid of the algebra---dive in and realize that you may make mistakes but will get the right answers eventually. You'll know when they are consistent with the original formulas.