How to adjust passive peaking filter Q?

[Svart]

I'm going to drop a hodgepodged passive EQ on the forum in the next few days but I am uncertain of how to change a peaking filter's Q. I've been peeping examples and some have series resistors before the inductors. what is the equation for figuring this out?

 

[NewYorkDave]

Q of an inductor= (2pi * F * L )/ R
Q of a capacitor= 1/(R*Xc)

The term "R" in both cases is a parasitic, DCR for the inductor and ESR for the capacitor.

How this all relates to bandwidth in a filter: http://fourier.eng.hmc.edu/e84/lectures/ch3/node9.html

 

[Svart]

excellent, thanks

 

[Svart]

www.theopiumdenproductions.com/EQ.JPG

the framework so far.

After thinking about it and coming up with an idea I later found that it had a remarkable similarity to something that Mr. Fred Forssell had posted that I only recently discovered. At least I can say that I must be on the right track.

No values are posted, I have yet to put this in a proper schematic and figure out my values. Going with the feedback resistor needed for the FETbloke, I figure that the pots will be around 10k and the input series resistor will be around 5k-10k. I'm not sure how this will affect the values of the L and C components yet.

Any and all suggestions welcome.

Personally I will be using this for a mastering EQ.

Now for the legal mumbo-jumbo:

I intend this to be a group project, maybe someone will offer boards, I might lay it out as well but any work on my part will be offered as free for NON COMMERCIAL use only and any similarity to any other person's work is strictly coincidental as I have pulled influences from many sources. I do not consider myself the author of this design, I am simply organizing readily available information into a usable form.

 

[Svart]

After thoroughly reading Fred's whitepaper on EQ design a few minutes ago I see that although I was on the right track, I screwed up my thought process. He states that the series R should be between the L and C to adjust the Q of the filter, not in front of the filter. Any comments?

Another observation that I wonder about now is which component should come first in the filter, the C or the L? Fred shows the C first but I have the notion that the L should come first right? If you have a series C first you filter all your lower freqs out before you get to the inductor thus creating a non working filter. Am I not thinking about this correctly?

 

[NewYorkDave]

That's not a passive EQ, that's a classic "swinging input" active EQ. It's a topology that's been used quite successfully. Here's just one of many examples:

Opamp Labs Model 109 EQ

(Note that the input series resistor is internal to the amp, but it's there).

As for the R, L and C: hook 'em up in any order you like. In your last paragraph, you're misunderstanding how the filter works. Study the workings of L-C resonance more closely.

 

[Svart]

This also creates a problem in the fact that now you have to encase the Q resistors within the switching for the frequency and your switching requirements start to become very complicated with multiple decks.

Another question I have pertains to having an inductor connected to a circuit via one leg only. Other than a small capacitence and an RF antenna what other problems would this cause. If we could leave one side of the L and one side of the C connected to a common bus, then we could simplify this to a ganged rotary switch for frequency and a single deck switch for Q.

any thoughts?

 

[Svart]

Ok, maybe I'm misunderstanding the definition of passive EQ. I was under the impression that a passive EQ was any EQ that does not use an active device in the filter itself. I have not considered the gain element as part of the filter as it only uses positive and negative feedback to "boost/cut" and not modify the actual filter attributes such as frequency and bandwidth.


In some other filters I have seen, I noticed that their "cut" is referenced to ground and that their "boost" is refernced to the input signal in relation to a midpoint and that the attenuation or lack thereof is what drives the following filters and gain stage.

So what makes a passive EQ a "passive EQ" is the fact that there is no feedback in the system at all regardless of the filter topology?

So I could make a gyrator circuit but include no feedback for the gain stage and what would we call it?

 

[NewYorkDave]

As you say, there's a potential problem with capacitance. This can cause instability if that inductor (with its capacitance to circuit ground) is hanging off an amp's inverting input.

The main purpose of the series resistor in the swinging-input arrangement is to set the limit on amount of boost and cut. Your HF and LF shelving controls should have series resistors added, otherwise your boost/cut is limited only by inductor DCR or capacitor ESR. At full boost, the opamp will saturate.

So, as drawn, your "Q" control is really a "max boost/cut" control. The series resistance does of course have an effect on bandwidth but that's not the main criterion in selecting its value. Remember also to take into account the DCR of the inductor and ESR of the cap; deduct these from the value of resistance needed for a given amount of boost or cut. In practice, ESR is usually low enough to ignore.

In this circuit, a better way to vary bandwidth is to change L/C ratio --which is admittedly cumbersome and requires a lot of parts.

Another, more stripped down swinging-input EQ using a regular opamp:

425 Opamp used in tone control ckt

 

[NewYorkDave]

As for definition: if the gain of an amplifier is being varied at a given frequency, it's an active EQ. "Passive" applies to a frequency-selective lossy network (R-C, L-C-R or whatever) which may or may not be followed by an amplifier to make up the loss.

To be really specific about it, you could say the swinging-input EQ is "active boost, passive cut."

 

[TomWaterman]

This is like the API553 and the Sphere's...

I was working on a version very similar but a 7-band design based upon the Motown mastering EQs....IIRC simulation shows that the 'Q' resistor limits maximum available boost and cut too...

-Tom

 

[NewYorkDave]

Motown mastering EQs

I must've missed that one. Got a link?

 

[Svart]

I have to say that this is most enlightening.

Do you think that the effect of the neg/pos feedback affects the filter attributes differently than a totally passive design?

EDIT:

Of course I believe it would, actually I am more interested in the magnitude of the change. I would be interested in how different opamps with different input structures would change our outcomes.

I also realized that a FETbloke is not the optimum device to use here due to it's INV input. Something else like Fred's opamp would need to be used I believe.

I also suppose that since this will be the last EQ in the mastering chain, it will not need variable Q even though it would be nice.

EDIT EDIT:

Of course I am stupid. I am not thinking things through, just trying to get them on paper. The easiest way to get variable Q would be a series rheostat between the L and C bypassed with a switch. It's not totally recallable but who can really tell the difference between .5 and .6 Q?

 

[SSLtech]

[quote author="NewYorkDave"]

Motown mastering EQs

I must've missed that one. Got a link?[/quote]
Search on prosoundweb... someone (I can't remember who) posted pictures and info...

[edit] here it is:

http://recforums.prosoundweb.com/index.php/m/184949/2172

Keith

 

[NewYorkDave]

Thanx for the link. It's described in that thread by Bob Olhsson (who would know) as a copy of the Langevin passive graphic--which, IIRC, used constant-impedance bridged-T circuits--followed by Opamp Labs makeup gain. That means it really doesn't bear any resemblance to the sort of "swinging input" active circuit we've been discussing here.

 

[TomWaterman]

Yeah - perhaps I shouldn't have said based upon....Bob O's posts were quite informative - I decided to take the swinging input idea in Forssells paper and do a 7-band EQ that is set to the same frequency spacing as the Motown EQ.

Use 990 opamps or QuadEight AM10s to get a Sphere type EQ with an interface based upon the Motown EQs.

Sorry Dave.

Tom

 

[Svart]

That's cool. Do you have any more information on the values of C and L that you used?

 

[Svart]

In case anyone is wondering, the formula that I find most easily used for resonant freq of an LC circuit is:

(get your calculators warmed up..)

Fo=frequency in hertz(Hz)

Fo=1/(2pi)sqrt(LC)

So to prove a frequency that was previously solved for 260hz:

We know that the chosen L was 390mH or .39H

The C was chosen as 1uF or .000001F

Fo=1/(2pi)sqrt(.39*.000001)

Fo=1/(2pi)sqrt(0.00000039)

Fo=1/(2*3.14)sqrt(0.00000039)

Fo=1/(6.28)sqrt(0.00000039)

Fo=1/6.28*6.2449979983983982058468931209398e-4

Fo=1/0.0039218587429941940732718488799502

Fo=254.98113663230435268034023854536

Round up for 255hz. probably close enough to 260hz you can get with standard values.

I have yet to figure out how the impedence of the system ties into the equation. It might be small enough to not care though.

any comments?

 

[bigugly]

svart,

that excel spreadsheet that you hosted for me was designed for this type of circuit. oh, wait, it is for calculating the values for the first cap and the gyrators cap, so it would need to be changed slightly for inductors.

here's the link to that thread:
http://www.groupdiy.com/index.php?topic=19234&highlight=

 

[Svart]

cool I figured that someone could learn something by posting how to do it. We don't get into that enough around here. We tell folks to go read about it but there are many ways of doing things and when someone doesn't have enough background to tell one formula from another it can be completely confusing not to mention embarrassing. This could keep folks from actually trying something new on their own from that point on. The least we can do is try to be open and educational as well as have fun. This will compel interested parties to contribute and themselves educate others when the time comes.

Back to the circuit.

I suppose that the mid bands don't need to have adjustable Q if we choose the right static Q but a 4 gang rotary switch should allow us to have variable Q on the bands when coupled with another 2 gang rotary switch.

Now I just have to find a place to order Wilco inductors on a large scale.

Also, those of you who have worked with inductors in this way before(not me) do you find the DC specs of the inductor to be important? lets say we have a 820000uh inductor and can get it in a small version as well as a larger version, each with very different DC resistance...