Low pass filter properties?

[halfpower]

I've got a circuit depicted below. Another, more colorful diagram can be found at

http://www.seymourduncan.com/support/schematics/S_1singlecoil_1vol_1tone.html

. The circuit has a grounded guitar string that vibrates over an inductor in a magnetic field. The inductor is actually a composite inductor in the sense that it is six little inductors each wrapped around a magnet. When the string vibrates the inductor generates a voltage.

The resistor is a variable resistor, an I suspect that the resistance and capacitance values are arbitrary. How can I determine the frequency response of this filter? I have the equation

Vout = [Zc/(Zc + Zr)] Vin

where
Zc = 1/jwc
Zr = R

I'm not sure if that's right though.


[tt]

steel guitar string
|~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. ground
| ||
inductor pickup | ||||
.---------------L/L/L/L/L/L-----'-----||||||
| M/M/M/M/M/M ||||
| magnets to generate ||
| field
|
|
|--------------------------------------------
| Vout
|
|
| \
| / R = 250 K Ohms
| \
'---------------->/
\
/ ground
\ C = 0.022 mcF ||
| |/ ||||
'----------||-------||||||
|\ ||||
||
[/tt]

 

[zappedagain]

I'll start by saying Seymour Duncan was a hell of a designer! I had to look at this circuit several times to figure out what he did!

His circuit looks like a RLC filter, with a few caveats. For the math behind this circuit, check out:

http://en.wikipedia.org/wiki/RLC_circuit#Quality_or_Q_factor

That said, it probably has a resonant (peak response) frequency above the audio band, so it looks like a high pass filter in the audio band (caveat #1 - if you hook the variable resistor up backward so counterclockwise is more resistance you'll think it is a low pass filter). So that means as you tweak the resistance you change the slope of the response vs. frequency (less resistance gives you more higher end response).

Caveat #2 - I'm not in a band so this is assuming that the load at the mono audio jack is much larger than 250K; if that is true than the frequency response is independent of the volume control. Sweet!

Good luck trying to copy this circuit... I'm sure there are many more caveats to this design than what they posted on their web-page. Also see:

http://en.wikipedia.org/wiki/Seymour_Duncan

 

[VEBill]

Wiring a capacitor in series with a potentiometer across an audio line to provide a workable tone control is as old as the hills. I think that Herr Doktor Heinrich Hertz (*) may have been the first to use this design concept.

* Perhaps a slight exaggeration; it might have been Guglielmo Marconi instead. ;-)

 

[halfpower]

Since it is not evident in the linked diagram, and my ACSII diagram got botched up, I should probably point out that the guitar strings are grounded.

I think the only thing Seymour Duncan designs is electromagnetic pickups. I believe the basic circuit design was designed 40+ years ago by the Fender guitar corporation.

 

[benta]

Forget the inductance, it's a generator.
IIRC (having had electric guitars myself), the ohmic resistance of the pickup is in the range of a few kiloohms = negligible.

Model it as 250k in parallel with 250k (variable) in series with 22n to ground.

Input impedance of the amp is usually around 1Mohm = beligible.

Benta.

 

[e2zn]

For guitar pickups the L is large, making the RLC peak in the audio band. With the volume control at maximum you get this, right ?(I hope the ASCII works when it is small)

L------out
|
VR (0 - 250k)
|
C
|
ground

And if you turn the tone full CCW, then what you have is:


L------out
|
C
|
ground

The R part of the RLC is the series resistance of the pickup, which gives:

R-L------out
|
C
|
ground

For the R +L values, pull them off of Seymour's site. For example:

http://www.seymourduncan.com/products/antiquitydescr.shtml#texhotb

For this pikcup L = 4.08H (!) and the series resistance is 9.7k

For this pickup, with tone full CCW the peak is +3dB at about 480Hz, w/-3dB point at 750 Hz. With tone at 50% there is no peaking and -3dB is at 4.6kHz. (Thanks to Circuitmaker for the simulation.) This all omits the capacitive parasitics inside the pickup, which are significant, and will change the peaking depending on the value. Calculating backwards from the Q number of 2.52 on Seymour's website gives about 6800pF. I'm not sure how repeatable these specs are. You'd need to test a bunch of pickups.

Additionally, I'm simulating with lumped parts, and the parasitics are distributed throughout the windings, so that's another source of ugly reality creeping into nice simple simulations.

e2zn

 

[halfpower]

Is this

R-L------out
|
C
|
ground


the same as this

R--------out
|
C
|
ground


???

 

[Skogsgurra]

Yes - but only if L = 0 henry.

Gunnar Englund

http://www.gke.org