# Filter Theory Question

Discussion in 'Amp Tech Center' started by robrob, Feb 23, 2020.

1. ### robrobPoster ExtraordinaireAd Free Member

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I'm pretty sure I know the answer to this but I have read and heard conflicting info so I'd like confirmation.

A classic RC low pass filter (above) consists of a resistor then a capacitor to ground and the outbound signal is tapped at the resistor-cap junction. My question is does a resistor in series with the cap affect the filter corner frequency? (see tone control below) In the tone circuit below the RC resistance comes from the upstream circuit.

Filter theory suggests no, the tone pot resistance doesn't affect the corner filter but it lowers the effectiveness of the filter--the corner freq stays the same but less high frequency signal is shunted to ground. Can one of you EE types confirm this?

2. ### Jon SnellTele-Holic

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For a simple RC low pass filter, cut-off (3dB point) is defined as when the resistance is the same magnitude as the capacitive reactance: -
Transformation of formulae does the trick
I tried to write the formulae down but it won't post any intelligent detail.

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3. ### Digital LarryFriend of Leo's

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Put a resistor in series with the shunting cap and you get a shelving control. It will stop rolling off with increased frequency and just flatten out like you had a resistive voltage divider.

Typical oversimplified rules of thumb when looking at RC circuits:

a) At "low" frequencies, the caps are not there
b) At "high" frequencies, the caps become short circuits

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4. ### FenderLoverPoster Extraordinaire

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The R term is actually more complicated.

Take a high pass example: coupling cap and resistance to ground. The R value there adds the preceding output impedance to the shunted R value.

C and R of 10nF and 220K high pass:
1/(2*pi*R*C) = 1/(6.28*220K*10nF) = 72Hz

but, the Zout of the previous stage is in series with R:
(assuming 12AX7 gain stage with 1K5 cathode and 100K plate)
1/(2*pi*R*C) = 1/[6.28*(39K+220K)*10nF] = 61Hz

Regarding the Tone control, if you were to rock that control, you'd hear a wah sound because the corner is moving. The two C's are in series, but the coupling cap is typically much larger and has little effect on the calculation.

Short answer, look at the formula. If you change R or C the f will change.

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5. ### SplodgenessTele-Meister

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I had a feeling that it is not as simple as applying the 1/2piRC = f formula..... so I looked for the derivation and came upon this page

https://electronics.stackexchange.c...quency-and-phase-shift-for-rc-low-pass-filter

which gave it reasonably succintly...... but substituting (Xc + R2) for the original Xc propelled the maths beyond my ageing brain........... (it's been 40 years since I worked with complex numbers)

I look forward to seeing someone unravel it

Last edited: Feb 23, 2020
6. ### elpicoTele-Afflicted

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As far as that question goes Digital Larry has your answer above, you'd add a shelf to your low pass filter, but that question doesn't match the second drawing. The tone control shown isn't an RC filter, you've replaced the original R with a C so now it's actually a high pass filter. It's a CR high pass with a cap added in series with the R, which adds a limit (shelf) to the amount of low end cut. Considering only the three components shown in that drawing (and assuming both caps are 4.7n) changing the pot resistance does this:

The shelf imposed by the second cap is at -6db here. It would be a different value if the size of the two caps weren't equal.

Of course you'll need to insert this into a circuit, a circuit that has some unknown source impedance driving the input and something like a volume control or grid leak resistor hanging off the output. I assume from the simplicity of the thing that you're not looking to add a cathode follower to drive it, so add about 40K of source impedance to approximate driving it from the plate of a 12ax7 and you get this:

Last edited: Feb 23, 2020
7. ### robrobPoster ExtraordinaireAd Free Member

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Thanks guys for the help. This "simple" tone control is much more complex than I thought.

elpico, I know it's a big ask, but could you model the 5E3 using a 12AY7 upstream (shared 820 ohm cathode resistor, 25uF bypass, 100k plate), .1uF coupling cap and volume on 4 (500pF bright cap)? I'd like to include the graph in the "Voice an Amp" page if you would agree to that (with credit of course).

8. ### elpicoTele-Afflicted

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Sure, I do have a 5E3 model somewhere on here. I'll have a look tonight. Re-reading your post I see what you meant now about the low-pass thing. With the pot turned down lower than the driver's output impedance it does become a low pass. I guess it's both depending on pot setting.

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9. ### LudwigvonBirkTele-Holic

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Agreed, good thinking as usual Elpico.

(I started out as EE but pivoted to CS because the money looked better maybe. In retrospect that was a dumb pivot , except I guess for the money aspect.)

10. ### elpicoTele-Afflicted

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Okay have a look over this and see if the component values are what you need. Two pots might give two different values at "4" but you gotta pick something so I went with 100k/900k:

If that's the values you're looking for then this is what it gives when you sweep the tone control:

And this is a spice file for 5E3 if anyone wants a copy:

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11. ### robrobPoster ExtraordinaireAd Free Member

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The schematic looks perfect.

What are the pot values for the 4 colors?

It looks like the tone circuit is acting primarily as a CR low pass filter (trims high frequencies). I don't see any shelving going on. It seems the corner frequency (-3dB) moves lower in frequency as you turn down the tone pot. Do you guys agree?

12. ### elpicoTele-Afflicted

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pot splits (top half:ground half)

green = 1ohm:1meg
blue = 125k:875k
red = 500k:500k
turquoise = 1meg:1ohm

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13. ### elpicoTele-Afflicted

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I missed something packing up that LTspice file linked above so it doesn't work on other people's machines. Apologies for any frustration that caused if anyone tried it, it wasn't you it was me

I guess it's too late to change the file in that post (can you only edit a post for 24hrs?). So in case anyone stumbles across this thread down the road this is the fixed version:

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14. ### cobaltuTele-Meister

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Shouldn't "C5" on the tone stack be 5nF, not 500pF?

I just noticed that.

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15. ### robrobPoster ExtraordinaireAd Free Member

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Yes, you are correct cobaltu. The schematic shows two 500pF caps for the tone and bright caps.

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Oops

17. ### elpicoTele-Afflicted

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We might be blind when it comes to spotting capacitor values, but I can see the shelf effects a lot clearer now. I cleaned up the left db scale and tweaked the pot splits to suit this plot better.

green = 1ohm:1meg
blue = 330k:670k
red = 750k:250k
turquoise = 910k:90k
red = 1meg:1ohm

Last edited: Mar 6, 2020
18. ### robrobPoster ExtraordinaireAd Free Member

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Thanks for the redo elpico.

19. ### cobaltuTele-Meister

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That looks better! It also explains what I thought about the bass on a 5e3. I feel like the low "E" on the guitar seems to pop-out WAAAY more that other strings with the tone control below ~8. This is especially true on the normal channel.

This doesn't seem to corroborate why the tone seems to get duller above about 10 on the dial. Might be missing something...

Thanks though! An interesting thing to see.

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