slope of the filter at different frequencies do not seem to be the same
Good eye, although at first I couldn't tell which filter your were referring to, HPF or LPF, but after looking at it a little closer there are actually different reasons why both the HPF and LPF response for the widget I've made differ from the Broughton HPF+LPF. I know I make stupid long posts and this probably upsets the folks who just want the answer in 2 lines of text, but I'm putting all this information here so other people who want to make similar circuits can apply what I've learned in this process. What's that? Posts are still _way_ too long? Yea, I hear you.
Ok, so
let's look at each filter one at a time and understand the frequency response differences and relate this to the schematic, and more importantly the sound and function of the filter.
First the High Pass as it's the real business end of this device:
fDeck HP filter is actually a combo of two filters in concert
Correct. There is a fixed filter that cuts the subsonic and this is followed by a variable one. As one sweeps freq of the HPF from low to high the impact of the fixed filter on the variable filter is reduced and so the slope isn't the same across the frequency sweep. But there is one other thing fDeck did that impacts the 'shape' (Q) of the cut at the lowest cut (purple trace). The 133k resistor in the schematic tunes the resonance of the filter so that the corner is "sharper". The combination of the fixed filter with "tuned Q" plus the variable filter produces the response shown. If I wanted a different response I could change the frequency of the fixed filter, or even make it variable as well (4 gang 100k reverse log pots do exist...).
I could also alter the Q, and it's worth taking a quick look at how/why. Broughton does make some nice stuff - I've got thee of his pedals: always on HPF, parametric EQ and the RFE (resonant filter equalizer). The RFE is interesting because what he does is really tweak this Q resonance resistor concept really hard to produce this kind of response with the LPF - and there is a connection here between the fDeck low end response and Broughton's RFE with resonance control:
The dark blue-ish trace is the non-resonated standard filter response, but I think the purple trace is more like what we see in the low end response from fDeck's fixed filter - and this is due to the 133k resistor. Subtle, but quite intentional in fDeck's design - he's using just a tiny bit of resonance to tweak the response to flatten out the low end. In the case of the RFE this concept is is taken to a whole other level in order to produce the response above.
So which response is "better", stock like Broughton's or 'resonant flat' like fDecks? I'd say it depends on the filter's purpose. For the HPF-pre it's mostly about the upright bass and so I'd say fDeck nailed it with his implementation that provides the subsonic filter with a nice sharp corner that everyone needs even when the knob is turned to the 'no cut' setting. Then the single sweeping HPF with standard response takes over as frequency is raised. His cut-off at the high freq side was tuned for the upright, but I changed this to make the range slightly wider in my version (with my 7.5k stop instead of his 20k stops). In my case I want to use this to cut out low end at the front end of a tube amp to reduce blocking distortion. For that reason I will probably move this first fixed filter up to have a higher cut-off now that we know the hows and whys. This kind of change isn't so hard and I can tailor the circuit to be what I want.
Now let's take a look at the LPF response, which I had already noticed was close but not quite exactly what I expected. But it turns out that an oversight/mistake on my part actually got me closer to the 'sound' of the filter that I'm after! So, first, here is the basic topology of the filters in question taken from a Texas Instruments tech note:
If you compare the the schematic I ripped off from fDeck you can see that it's pretty much a straight forward implementation of these filters. With the HPF section it's two of them in series plus the extra 'resonating 133k resistor'. Now, when I added my own LPF filter I didn't consider a couple of things and this will impact the filter response. First TI suggests that the filter wants to see a high resistance for R3/4 before the filter and I don't know if I have that as I simply took the output of the buffer and went straight into the filter. When I put this filter into the on-board pre-amp design I'm working on I'll experiment with the pre-filter resistors more carefully as it may impact response and/or stability. Second (and more relevant here), I failed to notice that "C1=2C2" as it is "C1=C2" for the HPF and, well, I just did C1=C2 cause I'm a noob at this and wasn't paying attention.
Before we see the impact of this 'mistake' in my circuit, a quick side note on plots and comparing because I'm referencing the Broughton plot vs my plot a lot in this (long, I know) post.
the scale of his graph is skewed
This is true and if we don't have the same plot parameters then it's hard to compare. the db/octave cut of 12 db/octave is really only obtained in the linear portion that is deep into the cut. In the more practical region of 15 to 25db cut the slope isn't that steep and it actually changes slightly as the frequency is reduced. Looking at just the low pass filter, if I do a crude measurement of the slope from the plots at around -15 db cut I get the following table that indicates that both devices have similar performance (including the apparent increasing slope as freq shifts lower):
So what I'm seeing is that the overall response of the LPF filter is similar in terms of cut once the filter starts to dig in, but qualitatively I think the 'knee' or Q is different and this impacts the response at the corner frequency for both the HPF and LPF. It was your question about the difference in slope that actually got me to look at the filter response at the 'corner' more carefully for both HPF and LPF. We already saw why the HPF corner looks different, but with the LPF the slightly different response turns out to be a direct result of the values I chose for C1 and C2.
Take a look specifically at the purple traces in the Broughton plot vs my plot. In the Broughton the bandpass is very symmetrical while in my plot the purple trace in particular is noticeably
non-symmetric where the pots are set with no bass cut and full treble cut. The HPF has the corner resonance that is (purposely) different from the Broughton, but the LPF looks different too - the corner is 'softer' or more rounded compared to the Broughton. This is because I chose C1=C2 whereas Broughton probably used the proper C1=2C2 implementation. If you plug in values and calculate the response then it all starts to make sense (and shows us how the response can be tuned to our liking): Top is standard implementation C1=2C2, middle is mine at 1:1, bottom is even rounder at 1:3
The only difference in the three calculations is the ratio of the C1 and C2 capacitors. Top one is with the textbook C1=2C2 ratio and we see the sharper corner like in the Broughton response. This is what everyone expects to see. With my C1=C2, and maybe this is subtle, but I think you can see that the corner is softer or more rounded and matches the response from my plot. If you take this a step further and go 1:3 C1:C2 then the corner really starts rounding off.
Turns out that I'm much more interested in the response with a more rounded corner and so I'm more likely to either keep the current C1=C2 or maybe try to round it off just a bit more. The reason for this, and I've been trying to hide this because, well, this is talkbass... Full disclosure: the reason is because I'm going to use this on a guitar and not a bass. But we can't talk about this stuff on guitar forums as I'm sure you understand. So that's why I'm here. Now, I'm also one of these a on a stand-up bass too, but I've already got fDeck's device for that so my focus here is on how to modify it to suit my dual purposes: on an on-board preamp and as a integrated front end for a tube amp I've built.
The reason I put the LPF in this circuit is to act as an active "tone" control for the guitar. For whatever reason I really do prefer the sound of a LPF over a typical shelving HF filter. It's closer to the response from a standard passive tone control I think. Anyway, when I hooked up this latest prototype I noticed that I liked the response better than if I used, for example, the LPF filter on my Broughton Resonance Filter Equalizer (RFE) set at the "stock corner" shape (Q). I can hear the difference between a sharper corner and a rounder one. My rounder one is smoother and more pleasing to me and I noticed that with the RFE that the more I increased the resonance the less I liked it and the more round I made the resonance the more pleasing it was as a tone control. So what I've done (accidentally) in my circuit is to round it off even more than normal and it makes it sound more like what I want a guitar tone knob to sound like. Probably I'll round it off just a little more though - easy enough because it's just a matter of changing one cap. So my cap ratio mistake was one of those 'happy little accidents' and helped me understand more about how to modify the circuit to get the response I want to hear.
In the end I'm learning to make these circuits from scratch because I'm not able to buy exactly what I want with off the shelf products. I am a high pass/low pass guy. I am not a shelving filter guy. It's a personal preference I guess. But options are limited for HPF/LPF products. Now I'm getting closer to being able to make my own and tune them to get the response I want for the specific application at hand.
Note that the TLC2264 is spec'd for 16 Volts max. That should be fine with 9V battery or 9V regulated power supply, but the old line frequency (typically heavy) wall warts often run much higher than their rated voltage when operating at low current. If you're planning on using a power supply, I suggest measuring its output just to be safe. That's actually one of the reasons I went with the OPC1654.
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