Need help calculating third order lowpass after valve stage

[lion]

I would really appreciate some help from the experts here.

How do I go about calculating/designing a passive low pass filter to go between the V2A valve and the P3 pot in the schem. I want it to have a steep roll of (18 dB/oct) starting at aprox 2.5 - 3 kHz.

I basicly understand 1st order RC filters - and that higher orders are obtained by cascading more RC's – but the theory gets complex and calculating the components values seems quite difficult, or above my head at least.

I have plenty of signal so a loss throught the passive filter won't be a problem.

Any help or advise would be much appreciated. TIA.

lion

[merlinb]

You can use the usual f =  1/(2 pi R C) for a single filter stage, then simply cascade three of them. The loss at the cut-off frequency increases by about -6.5dB with each stage you add (on top of the -3dB loss for the first filter). If you don't want that much loss at your desired frequency, use the same formula bu set the cut-off somewhere between two and five times higher than your desired frequency, e.g. 5kHz to 15kHz

[lion]

Thanks Merlin - very helpfull. I'll give it a try - and adjust as necessary.

lion

[PRR]

The 3-pole cascade filter gives a very round corner.

> calculating the components values seems quite difficult

A proper 3-pole filter is idiot math. I can NOT do it. I have an idiot does it for me.

A proper filter "can" be done this way:



However the required choke is NOT any stock part. The specs are very problematic: high inductance with low parasitic capacitance.

What I would try is a 120V winding on a 10VA-20VA power transformer. This also assumes a test-bench with signal generator and audio volt-meter, and a pad of plotting paper.

I believe you want a "bump" at the corner. If this is too shrill, increase the "10K" to maybe 50K.

This may be totally bogus in practice. 20H-30H coils have to be huge, lossy, or iron-core. Even as iron-core, they have lots of stray capacitance. An iron choke will pick-up all the electrostatic buzz and all the electromagnetic hum in the room. I actually have done a similar thing, but in an iron box mounted high in the rafters, and working at lower impedance.

[Digital Larry]

Is there any precedent of tube/valve circuits using an op-amp structure (or any other method) to get inductorless filters with complex poles?  For sure we see the phase splitter a lot in power amp stages and that's a lot of it right there.

[lion]

Thanks for the reply and suggestion Paul – interesting solution.
I could probably do with a sharper corner and the bump too, but I'm afraid the inductor issues are over my head - and this project (it's a vintage tape echo restoration – and the final fine tuning of the wet sound to replicate a certain echo character).  

The question is if the cascaded RC filters with it's imperfections can be made to do what I need – I'm expecting I may need to adjust and experiment with the Fc point to get the desired result.

lion

[Digital Larry]

It's hard to predict whether a given filter will achieve sound without having a LOT of experience (I'm guessing, but I don't have this experience).  3 cascaded 1-pole filter WILL eventually get to -18 dB/octave roll off.  What's different about it compared to something like Paul suggested is how many octaves it takes to get from the -3 dB point to say, -60 dB.  A chain of RC stages will get there gradually but smoothly without any peaks.  The sharpest filter you could get with cascaded Rs and Cs would be with the 3 "poles" in the same place - which doesn't mean that that R's and C's are all identical though.  It's starting to sound like factoring a third order polynomial or perhaps trying to find some tables in a filter design cookbook.  Sorry I don't have any more specific info.

[PRR]

> a vintage tape echo restoration

Ah. IMHO, rip out the bottles and chip-ify it. All but the best (and best-maintained) tube tape decks are endlessly problematic.

I doubt you will follow my advice.

> and the bump too

Ah. If it recirculates you do NOT want a bump. The loop goes into howl-around at the peak of the response curve. Best to have this low midrange than an ear-piercing 3KHz. You probably do want to maintain "flat" response as far up as you can for clarity, but not a top-bump. (Top-bump makes more sense for non-loop hiss reduction or for guitar speaker emulation.)

> get from the -3 dB point to say, -60 dB.

That's a useful metric in radio, where we have a weak distant station on 970KC and a strong (60dB more) local station on 990KC. Also in carrier telephony where a single line carries many conversations offset up on 4KC spacings and adjacent talkers should not hear each other above the -60dB level.

> 3 cascaded 1-pole filter WILL eventually get to -18 dB/octave

Far-far out. Like a decade?

But we don't really need 18. Slopes steeper than 9dB/oct sound "cut off", unless there is outstanding crap in the cut-band. (Sub-woofers with strong incidental midrange may need 18 to keep the singer out of the floor-box.)

Even so, the resonant C-L-C filter beats R-C-R-C-R-C (assuming you can manage the L!) by a pretty broad spread.

Here's a hasty-hack R-C-R-C-R-C. Green dot and curve. I do not pretend it is optimum; there isn't an optimum until you have clear specs for broadband loss and cutoff shape. I did trouble to stagger the impedances between the ~~70K at the plate and the 500K at the end.



There's 6dB broadband loss. You said this was unimportant but I don't think allowing more broadband loss would improve the shape. The 9dB/oct "audible cutoff" is 1.5 Octaves higher, with 4dB-8dB more hiss in the 5KHz-10KHz zone.

Even if you need tube flavor, I'd put sharp cut-offs in an opamp.

> tube/valve circuits using an op-amp ...inductorless filters with complex poles?

First you get your organization to blow a huge load of cash for an Analog Computer. Then you try to get it to work, and keep working. Korn & Korn wrote the book about programming these beasts. Any problem you could solve on a ball&disk machine you could solve with integrators, and tube-amps make dandy integrators. Two inties and a few resistors solves Pendulum problems. Which solves unstable-airplane and long power-line problems also. It was worth the cost and effort, for a few years in the 1950s.

Sallen-Key and the ilk seem attractive. However a single transistor follower has Zout like 30 Ohms, a tube follower like 1K Ohms. This foils the zero-impedance assumptions. A good tube "follower" for general active filter design gets into three triodes. And IMHO most tube tape systems already have too many tubes.....

Hmmmm.... for a high-cut, the plate impedance could be worked into the design. A 12dB/oct filter might do OK with one added triode. Too muggy here tonight to ponder on it.

[lion]

Thanks for the replies guys, much appreciated.

> IMHO, rip out the bottles and chip-ify it.........  - I doubt you will follow my advice.

I totally get your point, nevertheless – your are right, I won't 
I've spent a lot of time restoring the unit, actually it's been disassembled to the last bit, and everything cleaned up/restored. Complete circuit rewired with new components where nescessary – leaving out everything but the basic for a one channel guitar effects unit. For what it is I think it runs quite stable now.

> If it recirculates you do NOT want a bump. The loop goes into howl-around at the peak of the response curve. Best to have this low midrange than an ear-piercing 3KHz. You probably do want to maintain "flat" response as far up as you can for clarity, but not a top-bump.

A bump wouldn't be a problem in re to recirculation. The signal from the replay heads are split, with a dedicated valve stage/filtering for the feedback signal. The section I'm working on is the stage for the echoes to the output, setting the final echo sound. At this point everything runs/sound fine – I'm just trying/hoping to optimize the replay circuit for a certain echo character (what may or may not be possible with what I have).

> Here's a hasty-hack R-C-R-C-R-C. Green dot and curve. I do not pretend it is optimum; there isn't an optimum until you have clear specs for broadband loss and cutoff shape.

The signal direct from the replay heads have a limited response already  – for obvious reasons. Below a plot of the response from one head measure at the 500k resistor:


What I'm aiming for is a peak at around 1.5-2 kHz (bright) followed by a sharp roll off around 2-3k (woody).
(Note. This is by suggestion from people who have analyzed that particular echo type/character, but I realise that in the end it may not get me what I want – and further tweaks may be needed – but I won't know for sure until I've tried it  ).

By now I have tried a couple of RC-RC-RC filter combinations already (along the lines of Paul's last suggestion – but not those values), but I haven't been able to get much more roll off at the top end without affecting the peak I wan't to retain. Trying to solve this (and hear what it sound like) is my first priority.

Second priority. With the present response/circuit the peak freq is also a bit too low, but I'm thinking (with the right steep HF roll off in place) I might be able to shift the peak point up a bit by raising the high pass roll off point – or a "bump" might help.

Your help is much appreciated.
lion

[PRR]

> a plot of the response from one head

The wound-head is a differentiator. We "always" need a complementary -6dB/oct slope to un-do what it has done to the signal. See typical tape preamp curves.

With this in place you have ~~+/-3dB from <100Hz to past 1KHz.

But there are several high-frequency losses. Gap-width, oxide thickness, and more which I have forgotten. Response will go to zero when gap is half wavelength, and that notch causes losses several octaves down. The usual first-correction for this is to flatten the preamp 6dB/oct slope around 4KHz for 7.5+ips, 1KHz for 3.75ips. While the excess loss is near 6dB/oct this helps a lot. But it gets worse and worse. And by convention, playback EQ is standardized (several standards to choose from). Nearly all audio recorders will have some (or a lot) of high frequency boost in Record Amp in the top octave.

High impedance wound heads and their stray capacitance (winding, cable, tube grid) will also form a high-cut. In fact a fat cap across your head may be the quick/dirty way to force a 12dB/oct low-pass on tape hiss (does not do much for tube hiss).

> I'm working on is the stage for the echoes to the output, setting the final echo sound.

My ignorable advice is to box a chip-based Sallen-Key high-cut with a graphic EQ, and hide it behind the tubes.

[lion]

Thanks Paul 

Yes, the first time I looked into and measured vintage valve/tape echoes I was stunned by the simple circuit design and the poor response - compared to (even vintage/early) tape recorders.

> a fat cap across your head may be the quick/dirty way to force a 12dB/oct low-pass on tape hiss

Tape hiss is actually not really a problem in this unit, but your comment made me think.  Would a cap across the head also cause a peak before the roll off (the same as capacitance across a guitar pickup), and would it be calculateable from head induction/impedance specs?

> My ignorable advice is to box a chip-based Sallen-Key high-cut with a graphic EQ, and hide it behind the tubes.

I will pursue your suggestions, thanks.

lion