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About Speaker LF Resonance

FractalAudio

Administrator
Fractal Audio Systems
Moderator
Most guitar speakers are roughly the same when it comes to the high-frequency reactive behavior. The impedance increases starting around 1 kHz and then increases at 3-4 dB/octave. This is due to the voice coil inductance. A pure inductance would increase at 6 dB/oct. but there are eddy current losses that make the voice coil look "semi-inductive". The Axe-Fx II models this with a high-order lossy inductor model.

The low-frequency response of guitar speakers, however, varies greatly between speakers of different makes and models. This low-frequency response is a sharp resonance typically in the range of 50-150 Hz. The magnitude of this resonance varies from several to 20 times the nominal impedance.

The impedance of a speaker influences the response of a tube amp since a tube power amp is essentially a transconductance amplifier. It creates a current for an applied voltage. This current in turn creates a voltage across the speaker terminals that is dependent upon the impedance of the speaker. Therefore the power amp will resonate at the resonant frequency of the speaker. This causes certain notes to become emphasized as they excite the resonant frequency. Negative feedback around the power amp will reduce the amount of resonance but not all amps use negative feedback (i.e. Vox).

The increased voltage amplitude at the resonant frequency also causes the power amp to clip sooner at the resonant frequency. Think of it this way: if the power tubes are swinging, say, 200 V at the midrange frequencies, they will swing X times more at the resonant frequency where X is the ratio of the resonant impedance to the nominal impedance. So if the resonant impedance is 10 times the nominal impedance the power tubes will want to swing 2000 volts. This is impossible so they will clip. For high-gain tones this can cause the tone to sound muddy or feel spongy. For lower gain tones this can thicken the tone and make it feel, well, more spongy.

Cabinet/speaker IR data does not contain the impedance information. The only way to obtain impedance data is to measure the current vs. voltage vs. frequency (despite what modeler advertising literature would like you to think).

The Axe-Fx uses default values of LF Resonant frequency and impedance for each amp model. For models based on combo amps these values are derived from measurements of the actual amp's speaker. For models based on amp heads the values are based on measurements of the cabinet most likely to be used with that head.

You can adjust the frequency and impedance to suit your taste. Reducing the impedance (Low Res) will reduce the bass response and can give tighter bass. Raising the impedance will increase the bass response and can give a fuller sound. Altering the frequency (Low Freq) will change the frequencies at which the power amp resonates and tuning this to the key you are playing in can be an effective strategy, e.g. set it to 82 Hz if playing in E.

Don't be afraid to try drastic settings. Try turning Low Res all the way to zero. Compensate by adding some bass with the Bass knob or the EQ section. As I mentioned earlier the LF Resonance will cause the power amp to clip earlier than it will when amplifying midrange frequencies. Turning down the Master Volume will increase the headroom in the power amp and reduce this clipping. Furthermore the Transformer Match also influences when the power amp clips. So there is a relationship between LF Res, MV and Transformer Match.

Many manufacturers publish impedance data for their speakers. Eminence and Jensen and probably others publish detailed impedance data. You can look at the impedance plots and set the resonance parameters to match (roughly). The Low Res parameter is indicated from 0 to 10 and sets the resonance in dB from 0 to 24 dB (dB is a ratio of powers so it's not really the proper units for this but that's semantics). For example, the Jensen P12N has resonant frequency of about 100 Hz so you would set Low Freq to 100 Hz. The impedance at this frequency is about 40 ohms. To get the Low Res amount use the formula (20 * log10(Zr/Rdc)) / 2.4 where Zr is the impedance at the resonant frequency and Rdc is the DC resistance. For this speaker Low Res is then (20 * log10(40/6.2)) / 2.4 = 6.7.

A power amp isn't perfect though. Winding resistance in the output transformer increases Rdc, typically by a couple ohms. Therefore our above example would become (20 * log10(40/8.2)) / 2.4 = 5.7. The exact value isn't overly critical though and all this is subtle nuances.

The resonance Q is a bit more difficult to calculate. It is derived from the bandwidth at the points where the impedance "gain" is the square root of the resonance impedance gain. IOW, if the impedance is, say, 10 times the nominal impedance then the bandwidth is given by the frequencies where the response is 3.16 times the nominal impedance. For our example the resonance gain is 5 (40 / 8 = 5). So the bandwidth is the frequencies at which the impedance equals sqrt(5) * 8 = 18. From the graph this is approximately 75 Hz and 130 Hz. Q is defined as f0 / bw so our resulting Q is 100/60 = 1.67. Most speakers have a Q of around 2.0 or so. Again the exact value isn't overly critical and don't be afraid to try extreme settings (you can't break anything).

Finally, just because real speakers behave like this doesn't mean we have to adhere to this behavior. Perhaps a better speaker has no resonance (Low and High Res are zero), or maybe the Q is a lot lower or higher. In our virtual world we can design a speaker that is impossible to construct in the physical universe.


tl;dr version: Mess with Low Freq and Res if you want, or not.
 

Rane

Inspired
Cool stuff. I remember reading one of your posts a year or so ago where you mentioned the importance of speaker resonance (especially when trying to match the Axe to a real cabinet). I've repeated it a couple times in threads, but have been surprised at how little it's usually mentioned.

Love the new sub-forum, BTW. Great idea.
 

Scott Peterson

Global Moderator
Moderator
I love this stuff.

I just 'tune' the low frequency resonance setting by ear. I play, raise it, play, lower it, and when it sounds/feels right - BOOM. What's great is that you essentially are tuning your chosen IR to your chosen amp model and deciding how/where/when it reacts by ear.

That's incredible stuff once you get over to trying it. I love this stuff!!!!!!
 

Dramelot

Power User
I was just playing with this last night, remembering one of Scott's videos. This is a powerful control. Make's some cabs sound awesome that I didnt normally like. While the HF didnt make as much difference, it was still sound shaping.
Now I just have to read Cliff's post a few times to understand what I was hearing

These recent posts by Cliff are super valuable to take advantage of the controls we have, fully understanding why is another matter...
 
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Stratoblaster

Fractal Fanatic
Turning down the Low Res can really bring woofy, bassy amps under control fast while retaining the fatness; I found that control worked especially well with the Badger 18 amp.
 

BigD1977

Power User
This is awesome! Both the fact that a lot of witchcraft is being cleared up and that everything has been moved to a separate part of the forum. My thanks go to whoever is responsible! :)
 

Rex

Legend!
Cliff, you're on a roll. I've scoured the Internet looking for information that you've broken down and clarified in a few paragraphs.

To anybody who thinks this stuff is over their heads: Read the posts again. There are things in here that are understandable by anyone, regardless of technical knowledge. If you want to understand more of what you're reading, google just one term or idea that you don't understand, and see what you can learn about it. If you don't want to understand more of it, just run with the parts you do understand. They're in there!
 

trb

Experienced
hi all

I really appreciate all these advanced technical information, helping us to understand the deep behavior of the modeling (i'm an engineer in modeling & simulation in mechanical domain...) in the AFX2.
It's great to have this "Cliff's section" to share and compare our own applications/experiences of these explanations to close the gap between the theory and our different practices with different gears around the AFX2.
looking forward to try that when back home...

Over the very good FAS forum, it's a great added value Cliff, and I don't know many editors with the same contact and feedback to their customers.
 

swervedriver

Inspired
Interesting stuff. I love reading about the what and how of the advanced parameters in the Axe I don't normally use, and especially how they were implemented from real-life amps. Gives me a bit of steady ground to walk on when I need to mess with these values. For example, with one of my guitars I'm having issues with the low end of a Friedman BE-based preset which I can't seem to fix using Bass and Depth (high end response is fine); having read this I have some new strategies to try and get that amp sounding the way I have it sounding in my head. :)

Also, since I use two guitars tuned to drop D and drop C I could experiment with setting the resonance frequency for those presets to 73 Hz and 65 Hz respectively. There goes my evening...
 

Lilarcor

Inspired
Very interesting read. Thank you Cliff!
But I've noticed this is a bit contrary to the "old method" of finding the low res freq by sweeping the freq and seeing/feeling when the cab resonates most. I get different results by that. I guess this is because the latter method depends on the cab a lot more than on the speaker built into. But what is the most correct way? I know that all that sounds right is right but sometimes I get the urge to get it as realistic as possible no matter if it sounds good.
I should add that I use a Matrix with a Celestion Century Vintage loaded 2x12 cab in stereo. Unfortunately Celestion doesn't give a lot of info on their speakers apart from the res freq (no impendance plot or similar).

Can someone elaborate?
 

Scott Peterson

Global Moderator
Moderator
Very interesting read. Thank you Cliff!
But I've noticed this is a bit contrary to the "old method" of finding the low res freq by sweeping the freq and seeing/feeling when the cab resonates most. I get different results by that. I guess this is because the latter method depends on the cab a lot more than on the speaker built into. But what is the most correct way? I know that all that sounds right is right but sometimes I get the urge to get it as realistic as possible no matter if it sounds good.
I should add that I use a Matrix with a Celestion Century Vintage loaded 2x12 cab in stereo. Unfortunately Celestion doesn't give a lot of info on their speakers apart from the res freq (no impendance plot or similar).

Can someone elaborate?
Not in my opinion. I still sweep the same way and listen.

Sent from my DROID RAZR using Tapatalk
 

yek

Moderator
Moderator
Many manufacturers publish impedance data for their speakers. Eminence and Jensen and probably others publish detailed impedance data. You can look at the impedance plots and set the resonance parameters to match (roughly). The Low Res parameter is indicated from 0 to 10 and sets the resonance in dB from 0 to 24 dB (dB is a ratio of powers so it's not really the proper units for this but that's semantics). For example, the Jensen P12N has resonant frequency of about 100 Hz so you would set Low Freq to 100 Hz.
Don't these specs apply to speakers in 'free field', as opposed to being mounted in a cabinet?

PS I use the sweep method and get great results (with "real" cab).
 
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dredlm

New Member
Very interesting read. Thank you Cliff!
But I've noticed this is a bit contrary to the "old method" of finding the low res freq by sweeping the freq and seeing/feeling when the cab resonates most. I get different results by that. I guess this is because the latter method depends on the cab a lot more than on the speaker built into. But what is the most correct way? I know that all that sounds right is right but sometimes I get the urge to get it as realistic as possible no matter if it sounds good.
I should add that I use a Matrix with a Celestion Century Vintage loaded 2x12 cab in stereo. Unfortunately Celestion doesn't give a lot of info on their speakers apart from the res freq (no impendance plot or similar).

Can someone elaborate?
+1 I would like to have it for the Matrix NL212 too. Maybe the peaple from Matrix can support...
 
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