Noise Analysis of State Variable Filter

Hi

I'm looking into noise performance of state variable filters in order to optimize opamp choice. As the analysis of an entire state-variable filter looks rather tedious I wanted to ask if someone knows of a reference which might have done the work already?

Thanks,
Samuel

I don't recall ever seeing a specific SVF noise analysis.

JR

Ihave tried to post my answer but it seems it hasn't got through. If it has, excuse me for the double post.
I have done a sim a few years ago; the basics are:
The noise contribution of both integrators combined is more or less equal to the noise voltage of one opamp (one is high-passed, the other is low-passed).
The noise contribtion of the control amp (the one that governs boost/cut) is roughly 6dB more than its noise voltage, as the noise gain analysis predicts.
The noise contribution of the mixer is selective and depends very much on the Q factor; the amplitude of the bell seems to be equal to Q (q=10 => noise gain at center = 20dB)

Pls find attached schematic, freq resp and LTspice file that I renamed to .txt. To open with LTspice, you nedd to rename to .asc.

Looks like some files didn't go through

Well, upload folder is full.. I'll try later to send schematic dgm

> upload folder is full..

So it seems. Reported to Ethan.

abbey road d enfer said:

Ihave tried to post my answer but it seems it hasn't got through. If it has, excuse me for the double post.
I have done a sim a few years ago; the basics are:
The noise contribution of both integrators combined is more or less equal to the noise voltage of one opamp (one is high-passed, the other is low-passed).
The noise contribtion of the control amp (the one that governs boost/cut) is roughly 6dB more than its noise voltage, as the noise gain analysis predicts.
The noise contribution of the mixer is selective and depends very much on the Q factor; the amplitude of the bell seems to be equal to Q (q=10 => noise gain at center = 20dB)

Pls find attached schematic, freq resp and LTspice file that I renamed to .txt. To open with LTspice, you nedd to rename to .asc.

Click to expand...

It seems a sim of the actual circuit should give a definitive answer. I have seen enough different implementations of SVF parametric that I doubt there is a single generic answer. I have seen dramatically different approaches for delivering a variable Q range that exhibit different noise gains which should have an impact.

It seems from inspection that the noise contribution of both integrators are locally low passed. However the sundry feedback paths complete the HP/BP/LP filter functions which also modifies and steers the noise. So it is consistent with your observation that that total output from the three outputs would typically approximate one full range opamp, plus a little something for the noise gain associated with varying Q.

FWIW I recall seeing some inexpensive SVF based crossovers that used slower cheaper opamps in the LF sections since they didn't need the speed. This always made me uncomfortable while on paper it seems logical. I have also seen, parametric EQ that varied the Q by changing the BP gain. Q can also be varied by shifting the integrator poles relative to each other which seems like it would have lower noise gain than the more common approach of hanging Rs to ground from + and - input of HP opamp (control amp).

Another important noise consideration is how do you turn the BP output into boost/cut? One common approach involve running the boost/cut summing stage at a noise gain equal to the max boost/cut, so even in full cut that stage noise will receive the full boost gain wide band.  A quieter approach is to subtract the BP output from the input for cut, or subtract from the feedback path for boost. This will provide large amounts of boost/cut with noise gain of perhaps only 6dB more than simple unity gain stage, and the BP noise gets approximately unity gain. 

I guess my point is there are several dramatically different SVF topologies for EQ, perhaps less variation for multi-pole SVF crossovers. I never did a by the numbers noise analysis, but did explore sundry topologies. Dead ends to avoid are running the SVF at more than unity gain, as this can cost you headroom. A less obvious gotcha is that you need to avoid any clipping, even in passband outputs that aren't being used since this will cause distortion in the unclipped outputs.

JR

Here's the sim file at last (I hope)
Rename to .asc and open with LTspice

JohnRoberts said:

Another important noise consideration is how do you turn the BP output into boost/cut? One common approach involve running the boost/cut summing stage at a noise gain equal to the max boost/cut, so even in full cut that stage noise will receive the full boost gain wide band.  A quieter approach is to subtract the BP output from the input for cut, or subtract from the feedback path for boost. This will provide large amounts of boost/cut with noise gain of perhaps only 6dB more than simple unity gain stage, and the BP noise gets approximately unity gain.
JR 

Click to expand...

I've chosen one of the commonest implementations, in which the noise gain of the control amp is typically 6dB. This may not be the most noise-efficient topology, but it can be optimized for excellent results. I had a product (marketed under the LA Audio brand, referenced PFL52) that combined 5 sections of bell with 20Hz-20kHz coverage in three ranges and a set of svf hi and lo pass filters with variable Q. The hipass was 4th order and the lopass 2nd order. In my opinion, the steepest the hipass the better, but very often second-order lopass filters are too steep for musical applications; with the Q control, one can use the lopass filter as a sound-shaping tool.
Noise optimization:
The integrators should be run with the lowest possible input resistors, just high enough not to exceed the current capacity of the preceding opamps. I used JRC4559 and later JRC2068's in that position
The mixer is definitely the one deserving the most attention. I used 5532's there. I experimented with 5534's and even LT1018's. Results were marginally better, deemed not justifiable of the extra cost.
And yes JR, one has to make sure that all opamps run with a similar output level, making sure one is not clipping.
The noise performance was -96dBu with all bands flat, lopass at 32kHz and hipass at 16 Hz with Butterworth response. Worst case noise was around -70dBu, though! (with silly curves, I must say)

I did a 4 band parametric in a console (LOFT) back in the late '70s.. I made the top and bottom bands switchable between peaking and shelving. I have no idea of noise floor, but i was probably using TL074s all around, and it was adequately below mic preamp.

JR

JohnRoberts said:

I did a 4 band parametric in a console (LOFT) back in the late '70s.. I made the top and bottom bands switchable between peaking and shelving. I have no idea of noise floor, but i was probably using TL074s all around, and it was adequately below mic preamp.

JR

Click to expand...

In a console, parametric EQ's generally don't offer very narrow filters, so the use of TL0's is acceptable, but in a more dedicated unit, offering 1/12 oct BW, the noise performance of the mixer amp becomes a major point of attention.

Thanks very much, I'll look at the sims ASAP. My application is an oscillator, so pretty high Q I'd say...

Samuel

Samuel Groner said:

Thanks very much, I'll look at the sims ASAP. My application is an oscillator, so pretty high Q I'd say...

Samuel

Click to expand...

If this is fixed and not variable you may want to experiment with varying the q by spacing of the SVF poles. I know this works for broad Q with no extra noise, but I don't know how narrow it can get.

JR

abbey road d enfer said:

In a console, parametric EQ's generally don't offer very narrow filters, so the use of TL0's is acceptable, but in a more dedicated unit, offering 1/12 oct BW, the noise performance of the mixer amp becomes a major point of attention.

Click to expand...

It's been a couple decades so I can't draw the schematic from memory, but one topology I used to reduce Q related noise gain was to connect the two end terminals of the Q adjustment pot, one to the + HPF opamp input and the other end to the - HPF opamp input. The wiper was grounded through an end limit resistor. This results in lower noise gain than the more typical approach of resistors to ground at both + and - inputs with one fixed and one adjustable. In that typical approach the adjustable leg must range smaller to also swamp out the fixed leg.  IIRC I ended up with an resistor in series with one of the pot legs since the desired Q range was not symmetrical.

This doesn't really matter for Sam's fixed application, only for adjustable parametric EQs.

JR

JohnRoberts said:

It's been a couple decades so I can't draw the schematic from memory, but one topology I used to reduce Q related noise gain was to connect the two end terminals of the Q adjustment pot, one to the + HPF opamp input and the other end to the - HPF opamp input. The wiper was grounded through an end limit resistor. This results in lower noise gain than the more typical approach of resistors to ground at both + and - inputs with one fixed and one adjustable. In that typical approach the adjustable leg must range smaller to also swamp out the fixed leg.  IIRC I ended up with an resistor in series with one of the pot legs since the desired Q range was not symmetrical

Click to expand...

Well, that's exactly what I did, for the same reasons. Les grands esprits se rencontrent, as we say here!

..ce ne sont pas les imbéciles qui diront le contraire.. 8)

JR

Samuel,

Yesterday I came across a book that was under a pile of IEEE transactions, called Modern Active Filter Design, IEEE Press, 1981. There are three papers presented all of which are mathematically well treated.

Noise Performance of RC-Active Quadratic Filter Sections
Noise Characteristic of Cascaded 2nd Order Sctive Filters
Optimization of the Dyanamic Range and the Noise Distance of RC Active Filters By Dynamic Programming

Obviously for copyright reasons I can not post them publically but I would happily send you photocopies if you wish to pm me your postal address.

Thanks, that's very helpful. I've got full IEEE access so no need for copies!

Samuel