GEOFEX Simple Easy Graphic Equaliser PCB Layout

[slotbot]

f = (2*pi*sqrt(Rq*R2*C1*C2))^(-1)

so

it means just R in ohms and C in Farad like 1 meg ohm = 1 000 000 ohms

1 uF  = .000 001 F  => .047uF = .000 000 047 F

u is a suffix meaning *10^-6 and M is *10^6

K is *10^3 so for exampke 6.8K is 6800 becasue 10^3 = 10*10*10 = 1000.

f I understand right its R1 X R2 X C1 x C2 divided by 2 X Pi divided by 1

not quite how i would phrase it.


an example. say c1 is .01 uf and c2 .02 uf, R1 = R2 = 22k

first calculate c1*c2*R1*R2 = 22K*22K*.01uF*.02uF = 96 nS^2 ( thats nano seconds^2)

now take the square root of that you get 311mS

result * 2 * pi = 1.95 mS

now the whole denominator is calculated so take 1 over that. ie 1/result = 1/1.95ms = 511.54 Hz



edit: sorry i didn't see you asked for the 60 Hz.

same steps....

c1*c2*R1*R2 = 6.8K*6.8K*.1uF*1uF = 4.624 uS^2

sqrt(4.624uS^2) = 2.150mS

2.150mS * 2 *pi = 13.51 mS

1/13.51mS = 74.0135 Hz

so its around 60 Hz.


and also for Q its a bit easier. it look s like the q chosen was ~ 1.58

for all the filters C2/C1 is 10
sqrt 10 = 3.162
and .5* 3.162 = 1.58

[PRR]

> Vref was low with a 12K bias resistor so I used 1K

Low? How low? Something's not wired right. Something goes to DC ground which shouldn't.

> 6KHZ and 15KHZ bands dont seem to be doing anything

No input, amp cranked, the 6KC should raise "hiss".

IMHO you do not want 15KHz on a gitar. You probably do want ~~6KC because the slope from 3KHz to the limit (usually of your speaker, ~~5KHz) adds the finish on the zzzing, tizzy or mellow.

In the same room with strong cymbals, or if you have worked around strong cymbals too much, you may not have much hearing left past 4KHz. (I'm losing mine; decades back I heard 17KHz easily.)

> translate the formulas so I can do them myself

_I_ can't read those formulae. Just scale both caps the same amount bigger to get a lower frequency. If 1nF gave 10KHz, then 2nF would give 5KHz, etc.

The "Q" formula seems clear; clearer than "what Q to use?" Q of 0.7 gives a good broad octave, Q of 1.4 gives a narrow octave which won't overlap well when placed at octave centers. Q of 3 gives third-octave, or "4 semi-tone range", and will be ringy. Q of 10 is very ringy, "does nothing" until you hit "that note", and probably can't happen with a simple one-transistor resonator. So use Q around 1 for broad shaping, 2 to 4 for spotlighting narrow bands. (The 4dq plan gives Q=1.6.)

[Brymus]

Well Slotbot I REALLY appreciate you taking the time to show me that ,but for the life of me I could not get my math to come out like yours,IDK why,except I am just not educated enough for these types of calculations.
I even asked my sister-in-law whos taking math in college to come help me and she couldnt get it either.
I was really about to give up on this after some 12 hours trying to figure it out,google read,google read,to no avail.
When I decided to try my method of look at the proven example adjust what I know controls the action I am after and A/B with my ears.
Once again this proved my best progress,I have it working very well with the input buffer and an output gain stage.
The voltages are weird but it works like I want,I just have no may to verify want F the bands actually are at this point.
I added some more bands and got rid of the 15Khz one,but may add it back as a hiss removal band,not that there is hardly any hiss now with the values scaled its a very clean EQ + boost now.
It probably still has mistakes that need fixing with my hacking abilties at the root (Im sure of it).
And I am going to try a single opamp w/o the buffered Vref to get the input buffer there and see how it sounds.
Maybe some one else can explain the formulas in a way I can get,maybe not,feeling pretty dumb at this point
But at least with the forums help this EQ is almost done.

[Brymus]

Hey Paul you posted while I was typing.
Somethings not wired right I need to go back over the wiring yet again,and look for mistakes,it is working now
With amp cranked you should hear hiss Yeah with th evolume up and th einput buffer working I can tell they are indeed working
You probly dont want 15K on guitar That seems to be the consensus ,so its out as of now,thanks
_I_ can't read those formulae. Just scale both caps the same amount bigger to get a lower frequency. If 1nF gave 10KHz, then 2nF would give 5KHz, etc Thats exactly what I ended up doing, which worked pretty well,I would like to be able to tell people what F band X actually is centered on though
So use Q around 1 for broad shaping, 2 to 4 for spotlighting narrow bands. (The 4dq plan gives Q=1.6.)
Cool that means this EQ is pretty decent,and Im not just hearing what I want,thanks
And really a sincere thank you for all your help Paul,please keep the useful info coming ,I couldnt do this with out the guys like you who share their knowledge with us hacks.
Bryan

[R.G.]

Here is the original scheamtic from www.4qd.co.uk if someone would PLEASE show me how to work the F and Q formulas ?

Sorry I got to this a bit late.
The bits of advice you're getting are good, so far.

Rs are in ohms, and Cs in farads. Pi = 3.14159..., but I often use it to only two decimal places, 3.14, and get acceptable accuracy. And we'll get to accuracy in a moment. That's what's getting you.

The equations to use are as stated. They're based on the fact that the frequency of resonance of an L-C pair is F = 1/(2*pi*SQRT(L*C)). You calculate SQRT(L*C), then calculate 2*pi times that (I use 6.28 for quick stuff), then invert to get the frequency.

The rub is that 4QD's frequencies are off, and I think it's because the writer simplified things too much. He/she probably did it because of an old, old problem with parts values.

Parts only come in certain isolated values. The preferred sequence of values is related to the precision. No need to have nominal values closer than 10% apart if your resistors are 10% tolerance. For example, a "1K" resistor with a 10% tolerance is anything between 900 and 1100 ohms. A 1K from the 5% tolerance is anything between 950 and 1050 ohms. So a set of standard values for 20%, 10%, 5% and 1% resistors was set up as being the most desirable values to cover all resistances and not overlap. This let you have a 1K resistor actually be different from, for example, a 1.1K. These are the EIA standard values and you can find them in a very usable form here: http://www.logwell.com/tech/components/resistor_values.html

This is a holdover from the days when 20% resistors were what everyone used, 10% was "precision" and used for better work, while 5% was rare and 1% was for military work with no monetary limitation.

Capacitors are worse. Caps should come in the standard values, and do, at least theoretically. However, unlike resistors, cap availability in the values you want is very chancy. Better to pick a very standard cap value and make the resistors do the tuning than to spend a fortune on precision caps. This persists to this day.

With that as background, q4d told you some mild untruths, based on the need to simplify, and a view to where things matter a lot and where they don't.

Here's the chart, reproduced:

As originally stated:         
R1, R2   C1   C2   F = 
6800   0.1   1   60
6800   0.047   0.47   150
6000   0.022   0.22   400
6800   0.0068   0.068   1000
6800   0.0033   0.033   2500
6800   0.001   0.01   6000
6800   0.00047   0.0047   15000

With actual frequencies calculated this becomes:
         
Actual Frequencies from calculation:         
R1, R2   C1        C2        F =
6800          0.1        1          74.01360973
6800    0.047   0.47      157.4757654
6000    0.022   0.22      381.2822319
6800    0.0068   0.068       1088.435437
6800    0.0033   0.033   2242.836658
6800    0.001   0.01      7401.360973
6800    0.00047   0.0047   15747.57654
         
Tuned with different 5% resistor values (EIA24):         
R1, R2   C1        C2        F =
7500      0.1       1          67.10567282
6800    0.047   0.47      157.4757654
6200    0.022   0.22      368.9828051
6800    0.0068   0.068     1088.435437
6800    0.0033   0.033   2242.836658
6800    0.001   0.01     7401.360973
6800    0.00047   0.0047   15747.57654
         
Tuned with different 1% resistor values (EIA96):         
R1, R2   C1           C2        F =
8250    0.1       1              61.005
7150    0.047   0.47       149.767
5760    0.022   0.22       397.168
7500    0.0068   0.068     986.848
6040    0.0033   0.033    2525.04
6650    0.001   0.01      7568.30
7150    0.00047   0.0047   14976.7

Try as I might with preformatted text and tinkering I can't make the columns come out even - sorry. But you get the idea.

What I did there was uncover that the stated values in the original chart are inconsistent. 6800, 0.1 an 1uF do not make a resonator with a frequency of 60Hz. Worse yet, when you take into account that the resistors are probably only within 5%, and the caps probably 10%, you only get a frequency near-ish to 60Hz. This sounds like an abomination, but is probably OK since the Q is so low (i.e. the bands are so wide).

In the following charts, I accept the capacitors as exact (which is obviously wrong!) and pick resistors from higher precision groups to tune in the frequencies. With 1% resistors, this gets pretty good. However, notice again that I've cheated on the cap values. You need hand-selected ideal cap values to get those frequencies. The real caps will be that close only if you hand select. 5% caps are available, but 1% caps are quite expensive if you can find them.

Q4d's untruths are actually something more like oversimplifications so that a novice can build the thing. The real truth is complex, and probably not necessary for a quick and dirty implementation. If this was lab equipment, it would be more precise.

This issue of component tolerance lurks underneath everything we do. Sometimes it matters, sometimes it can be ignored. Good design (as opposed to parts easter-egging) requires both an awareness of the issue, and a healthy dose of reality. Good designs will work in spite of the unavoidable tolerances, or at least minimize them to the extent that they can be ignored, but will put in trimming and adjustments where the necessary result justifies it.

[PRR]

Good reminder on tolerances, theory and practice.

If the contract SAYS "60Hz", then the 74Hz center is wrong.

In music we don't really know "exactly" where we want to act. And this is a broad-stroke tool. With 2/3rd-octave bump-widths, 74/60 is a mild error. And for guitar, 74Hz is probably more useful. (When you need a 60Hz wall-power filter, you do need to be close and you want a deep notch.... that's different from tone-shaping.)

> I can't make the columns come out even

Just so you don't waste more time trying: These boards do not handle fixed-width nor PRE correctly... the spaces always come out short.

The "right" way is TABLE:

Code Select Expand


[table]
[tr][td]R1, R2   [/td][td] C1      [/td][td]C2        [/td][td]F =        [/td][/tr]
[tr][td]6800  [/td][td]0.1         [/td][td]1      [/td][td]74.01360973[/td][/tr]
[tr][td]6800  [/td][td]0.047    [/td][td]0.47      [/td][td]157.4757654[/td][/tr]
[tr][td]6000  [/td][td]0.022    [/td][td]0.22      [/td][td]381.2822319[/td][/tr]
[tr][td]6800  [/td][td]0.0068   [/td][td]0.068     [/td][td]1088.435437[/td][/tr]
[tr][td]6800  [/td][td]0.0033   [/td][td]0.033     [/td][td]2242.836658[/td][/tr]
[tr][td]6800  [/td][td]0.001    [/td][td]0.01      [/td][td]7401.360973[/td][/tr]
[tr][td]6800  [/td][td]0.00047  [/td][td]0.0047    [/td][td]15747.57654[/td][/tr]
[/table]


This took me several minutes with a code-editor; hand-typing all that markup is too-too tedious.

And TABLE is missing several key attributes (padding, width, colspan).

Result:

Actual Frequencies from calculation:

R1, R2	C1	C2	F =
6800	0.1	1	74.01360973
6800	0.047	0.47	157.4757654
6000	0.022	0.22	381.2822319
6800	0.0068	0.068	1088.435437
6800	0.0033	0.033	2242.836658
6800	0.001	0.01	7401.360973
6800	0.00047	0.0047	15747.57654

[PRR]

OH! and Q is 1.6 only when the pot is full up/down. Q is less at any non-extreme setting. For gentle shaping, each knob gives small boost/cut extending more than an octave away. So the exact center frequencies are not very important. Sure it would be nice to know that "60" is really 74Hz. I'm not sure the correct 0.123uFd+1.23uFd caps would be musically different (except in this case where it hits power hum). And 1.23uFd is kinda an odd value.

[Brymus]

Thanks for all the info guys,my problem lies in my lack of math skills.
After reading online ,trying to educate myself,what they teach in Jr High these days was advanced back when I was in high school.
My job only required a limited amount of math=area and percentages so I could order supplies and figure out what to pay the help.
I have long since forgot anything more involved than that.

Back to the EQ I just finished trying with just one opamp  
It has more hiss than using two opamps the way PRR suggested,a volume knob helps but then your coming out belowe unity once you remove the hiss.
Still less than the original values give,so not a loss of effort.
As far as frequencies go I think even 6Khz is a little high if the scaled values I used are actually hitting close to the original.
I have since changed the scaled 33k = 3k resistors for 2k2 as this is more correct percentage wise with the 454R replacing the 6K8s
And now Im not getting as much/any color from the 2n5088s
My best guess on the bands by the values used I have added 700-800Hz and 4Khz and dropped the 6Khz and 15Khz
This seems to be better suited to my guitar /amp set up

[R.G.]

OH! and Q is 1.6 only when the pot is full up/down. Q is less at any non-extreme setting.

For the benefit of the readers, there's a graphic EQ with constant Q sections in the National Semi Audio Applications book, and Rane did a good sendup on constant Q equalizers on their site. The penalty for constant-Q is that you have to use an active filter per section, not a transistor set up as a gyrator.

I'm not sure the correct 0.123uFd+1.23uFd caps would be musically different (except in this case where it hits power hum).

That's the "practice" part. Probably no difference to the ear. And it makes it much easier to present to beginner hackers on a web page.

And 1.23uFd is kinda an odd value.

Not if you can get 0.1% caps... 

[Brymus]

Hurray for me I finally figured it out 
Who says persistance doesnt pay off.
The problem: substituting 454R for 680R = a doubling of the center frequency...roughly
Instead of 60/74HZ  my low band is centered at 110Hz
Someon can check (scaled values I used) 454R*454R*10uf*1uf = 110Hz
Now I can do this part of the work,Thank You Slotbot,RG,and PRR
Now I dont feel quite as dumb at least...

[Brymus]

I should mention for others...
That because the final say 13.51ms from Slotbot's example is milliseconds that means divide 1000 by 13.51 not 1 thats why my math was coming out wrong.
That and the fact I had forgoten how to figure square root until I looked it up today

[Brymus]

Ah hah with a grasp on the formula
My 15Khz band was actually 25Khz which is why I couldnt hear anything but hiss when the amp was cranked and the pot rotated full
My bands now are as follows,(note I changed some cap values)using 454R resistors
110Hz (10,1uf),235Hz(4.7, .47Uf), 504Hz(2.2 , .22uf), 1.1Khz(1, .1uf)(new) ,1.6Khz(.68, .068uf), 3.4khz(.33, .033uf), 5Khz.22, .022uf)(new)
So I will rework them to get better values

[R.G.]

Bryan, you've done something really, really valuable - you've learned about the importance of getting the multipliers and units right to get sane results on calculations. You will probably not forget that lesson, ever.

This is very different from where you'd be if you had found a plug-in-the-numbers calculator somewhere on line. That way, even if you got the "right" answers, you'd have no clue how you got there, and be ignorant of the complexity lurking underneath.

You should feel some pride in your achievement.

[PRR]

> there's a graphic EQ with constant Q

Yes, and for general musical "shaping" on fixed centers I think that's wrong.

> the importance of getting the multipliers and units right to get sane results

It's a hard lesson to keep. WtH is dirt sold by the cubic yard? I've avoided trying to work out how much gravel I need to skim my driveway.

[Brymus]

It's a hard lesson to keep. WtH is dirt sold by the cubic yard? I've avoided trying to work out how much gravel I need to skim my driveway.

Ha Ha now thats something I would actually be able to figure out

And Yes RG ,I do feel a bit better I finally got it,I made a chart with values of resistors I have and the common cap values.
Now I can look at what value gets what frequency.
Spent all my free time today trying to learn how to set the Q (quiesent) point of a transistor.
Actually how to choose the bias resistors to set it,is what I mean.
Stumbled across a much more complecated method of figuering the Beta of one ,makes me really appreciate your method.
Yet I still dont know where to begin,I at least have a good understanding of the cut off and saturation points and how a load line is derived from them,ect
All this was to use a 3 x 2n5088s instead of a second op amp,and to keep from copying a common emiter stage and emiter follower.
But hey I learnd alot of neat stuff about BJTs just not what I wanted...

[Brymus]

I think I meant to say common collector stage and emiter follower
So an emiter follower for the input ,which I am thinking a FET would be better,but already using so many NPNs (I thought I would keep it the same) and common collector for the gain stage ,then into the EQ/op amp ,and out to a pot as a voltage/potential divider into another emiter follower,then out
I think this is another way of doing what PRR suggested for removing as much noise as possible with out scaling again.
Still not sure ,still testing different set ups and frequency combos too.
And reading,and reading,and more reading...

[R.G.]

But hey I learnd alot of neat stuff about BJTs just not what I wanted...

That's why I'm an omnivorous reader. The thing is, one day you'll actually use those odd bits and bobs of learning. One day the question will come up and the answer will be there in your head. And the answer won't be "... uh, I think I found an internet calculator somewhere on line...". 

[PRR]

> thats something I would actually be able to figure out

Yes, I bet if you worked in any dirt-related trade, you'd look at my driveway and think "50cu.yd., $1,000 for nice screened driveway mix". Then for a formal estimate you'd work-out 55.555cu.yd. at $19 is $1,055.55, add your 20% mark-up, $1,267 half down half when done.

Somehow I kept getting answers like $5,000-$10,000. If true, nobody around here could afford to re-surface their drives.... yet some do.

Conversely, being paid to fix electric-toys, I can get a rough answer at a glance and let that guide me to a good-enough answer. And in many case that means skipping the small stuff: the curve in my drive needs a little more than a straight-line estimate, the finite gain of a transistor skimps the F and Q computations, but the customer won't notice 5% thin or 10% low.


> how to set the Q (quiesent) point of a transistor

I 'think' you know this, but just saying:

The "Q" of a resonant circuit (as in a tone-control or equalizer) is not the same as the "Q-point" of a transistor.


Biasing: Pick a general load-line suitable for slinging the load. Small signal, large signal, voltage/current ratio. Generally: make your DC load resistor 1/2 to 1/4 the actual load impedance, make the DC supply voltage 4 to 10 times higher than the peak signal voltage. Plan to bias the DC load resistor around half the supply voltage.

Assume the device (tube, BJT, FET) has infinite current gain and zero base-emitter voltage. Apply some "reasonable" voltage to the base. Pick an emitter resistor to give the desired current. Where you applied the reasonable base voltage, hack it to mix DC bias voltage plus signal voltage. This is usually a capacitor plus high-value resistors.

Done. (Except the tedious bits.)

What is a "reasonable" base voltage? Well the "zero base-emitter voltage" is really 0.5V-0.8V, changing with part and temperature. Since there is 0.3V uncertainty, you pick a bias voltage 10 times higher so that worst-case your prediction is within 10%. Aim for around 3V across the emitter resistor. (In 9V work we may have to cheat that down.)

If transistors had infinite current gain we could use infinite bias resistors and have zero loading of the source. There's no infinities in practice. MOSFETs can often use 10Meg bias resistors. Tubes and JFETs tend to 1Meg, though in a pinch you can go higher with small devices and may have to go lower with fat JFETs or 6550 bottles.

BJTs don't have infinite current gain; their inputs draw real current. Figure emitter current divided by Beta. Make your base bias voltage divider pass 10 times more current, the error will be 10% low. Beta has a wide spread, figure your lowest likely Beta and then your highest.

In many cases this leads to an annoyingly low input impedance just due to bias resistors. And we have not got to the voltage-gain versus input impedance tradeoff.

It's a jigsaw puzzle, where you can cut some of your own pieces, but they shrink/stretch uncontrollably. The key skill is not in finding "exact" answers, but in quickly finding an answer which "will work".

> I'm an omnivorous reader.

That's a common path to this key skill. I'll "read" ANY schematic. And wonder "why was it done this way?" And remember that if I am in a different situation which is really similar in some detail.

R.G. alluded to National Semi and Rane papers.... you want to read those, both EQ and NatSemi's basic opamp papers. While I argue that constant-Q EQ is not what music-shaping wants, understanding how and why gives insight into the gentler shaping techniques. Like knowing how the highway dept builds a turnpike gives insight into how a gravel driveway should be drained and leveled.

[Derringer]

Thanks John,I had thought that 15K was a little high for guitar use and suggested to Rick that we add 4Khz and 8Khz and change the 15Khz to 10Khz instead.Perhaps adding 4Khz and 8Khz and dropping the 15Khz would be better.
Here is the original scheamtic from www.4qd.co.uk if someone would PLEASE show me how to work the F and Q formulas ? I will then do them all myself.Are all the Rs supposed to be megaohms ? and what about the Cs what number would I use for say .047uf ?
If I understand right its R1 X R2 X C1 x C2 divided by 2 X Pi divided by 1 ,Is that correct ? SO would someone give an example
using the first band of the EQ as in the 60Hz band ? So I can see it longform and I should then be able to do it after that,thanks

so I understand the f and Q equations here ... or at least I know how to apply them
but I would like to know mathematically how series resistance affects Q

when looking at RG's Geofex article, specifically the "Notches, Peaks, and Q's - A Simple Parametric EQ"
http://www.geofex.com/article_folders/eqs/parmet.gif
http://www.geofex.com/article_folders/eqs/paramet.htm

The center frequency of an LC filter is F0=1/(2*pi*L*C), so the range of min to max frequencies is equal to the square root of the variability of the inductance, or about a 4.5:1 frequency range. The "Q" of the LC filter section is limited by the equivalent series resistance of the simulated inductor. The 470 ohm resistor always appears to be in series with the simulated inductance, so we can add external resistances to lower the Q. That is the function of the "resonance" control. This pot allows you to lower the Q substantially. In fact, you may never need that much resistance, so you may use a smaller pot as needed.

what's the equation to factor that series resistance in when calculating Q?


thanks

[PRR]

> mathematically how series resistance affects Q

Back to basics.

A capacitor has impedance which declines with frequency.

An inductor has impedance which rises with frequency.

Take any cap and coil. At some (calculable) frequency, they will have the same impedance.



The two impedances are of opposite signs, so they cancel-out.

If you "tap" this circuit, it will ring at this frequency.

Energy transfers back-and-forth between coil and cap at this frequency.

If there is NO resistance loading, it will ring forever, infinite Q.

Resistance can happen two ways: in series with the loop through L and C, or in shunt with both L and C.

If resistance is equal to reactance, Q is 1.

If resistance is 1/10 (series) or 10X (shunt) of reactance, Q is 10.