About Fractal Audio's amp modeling

This is an overview of Fractal Audio's progressing amp modeling, starting with the Axe-Fx II, based on the firmware release notes and quotes.

Also read White-box modeling for additional information.

Cygnus X-3

Firmware Cygnus 25.xx

Upcoming ...

Public Beta #2:

New “Cygnus X-3” amp modeling:

Improved preamp algorithms.
Improved power amp algorithms.
Improved output transformer loss modeling.
Improved preamp supply voltage modeling.
Nearly all amp models have been “remastered” as a result of new measurement techniques and analytical methods.

As a consequence of the new modeling many default parameter values have been changed. Existing presets are automatically updated to the new parameter values upon recall. The updated parameters are:

Preamp Low Cut Freq
Preamp Hi Cut Freq
Triode1/2 Plate Frequency
All Cathode Follower parameters
Preamp Bias
Preamp Bias Excursion
PI Bias Excursion
Power Tube Bias Excursion
Transformer LF/HF
Transformer Drive
Power Tube Grid Bias
Cathode Resistance

Cathode Time Constant

Negative Feedback
Supply Sag

FRACTAL AUDIO QUOTES

[1] Every amp was measured for quiescent B+ vs. full-power B+. Supply Sag was then calibrated to give the equivalent sag.

[2] This firmware has more rumble and sizzle and if you drive the power amp hard you'll get less clarity.
Using new measurement techniques we found that the real amps were creating more of a certain type of intermodulation distortion than our models. Our new algorithms recreate this more accurately.
If you want a clearer sound you can achieve that by turning down Master Bias Excursion. This will reduce the rumble and sizzle and snarl and all the other nasty stuff. But be aware it's all this nasty stuff that makes amps sound "organic". The goal is always accuracy. If you prefer less accurate but more "clinical" tones we give you the ability to achieve that with the advanced parameters.

Cygnus X-2

Firmware Cygnus 24.xx

Improved speaker compression and amp interaction modeling.

Firmware Cygnus 23.xx

Due to the improved triode algorithm introduced in 23.00 many amps have had their preamp bias points updated. Existing presets are automatically updated upon recall.

Improved Amp block triode algorithm.

Firmware Cygnus 22.xx

The Amp block now features “Auto DynaCab Impedance”. When set to ON the speaker impedance curve of the Amp block will follow the Cabinet Type in the first mixer slot of the associated Cabinet block. I.e., if the Cab Type in the first mixer slot of Cabinet 1 is, say, 4x12 5153 and the Mode is DynaCab then Amp 1’s speaker impedance will automatically be set to 4x12 5153.

Improved Amp block channel switching speed.

Firmware Cygnus 21.xx

Improved dynamic speaker modeling in Amp block.

Improved Speaker Thump algorithm in Amp block.

New “Cygnus X-2” amp modeling:

Improved Amp block output transformer algorithm. New algorithm more accurately models B-H curve resulting in a clearer low end. New algorithm now also accounts for effect of speaker impedance on transformer response.

Improved power tube modeling. This yields better dynamics, improved low frequency accuracy and more accurate interaction with output transformer.

Improved cathode follower algorithm. Provides more accurate “cleanup” when volume is rolled off.

Improved triode algorithm more accurately models plate bypass capacitors.

Improved dynamic frequency response accuracy. This yields more “crunch” and less “fizz” with high gain tones, especially for detuned styles.

Various other improvements.

All amp models have been updated as a result of the aforementioned improvements.

The default values of various parameters have been updated. Existing presets are automatically updated to the new values upon load.

Added “Overdrive Volume” parameter to Dumble-type amp models (ODS-100, Two Stone, etc.). This is sometimes labeled “Ratio” or “Lead Master”. As the Master Volume on these amps often has a bright capacitor the Overdrive Volume control allows setting the Master Volume higher to counteract the bright cap and then lowering the power amp drive with the Volume.

Added “Plate Suppressor Diodes” parameter. This value is set automatically when the amp model is chosen but the user can override the default setting. Most amps do not have suppressor diodes but some do (e.g., Trainwreck Express). These diodes (also called “snubber” or “flyback” diodes) prevent undershoot on the power tube plates due to inductive kick and reduce upper harmonics thereby reducing “fizz”.

The Ideal amp controls have been updated.

Various other fixes and improvements.

FRACTAL AUDIO QUOTES

[3] The B-H curve is essentially the inductance of a transformer vs. applied magnetic force. A transformer is a very nonlinear device. At very low and very high flux intensity the inductance is less than at nominal. Furthermore the curve has hysteresis so the inductance decreases when the flux changes direction.

[4] Every amp model was updated. The amps on the list underwent revisions due to the new algorithms.

[5] Things should be tighter now without any loss of fullness. No need for low cuts or anything IMO.

Cygnus

Firmware Cygnus 20.xx

Improved speaker impedance curve fitting algorithm. This results in more accurate and more “colorful” modeling as the previous algorithm tended to damp box resonances somewhat. All the speaker impedance curves have been updated using the new routine.

Added Speaker Thump control to Amp block. Speaker Thump models the dynamic, nonlinear behavior of a guitar speaker. A value of 5.0 roughly corresponds to an amplifier running into a speaker rated at the same power as the amplifier, i.e., a 100W amplifier running into a 100W speaker. The reset value is a conservative 2.5 which represents, i.e., a 50W amp running into a 100W speaker. Note that the majority of the response is in the subsonic region and the effect is primarily tactile. Existing presets are not affected and the value will be zero.

Improved Amp block output transformer modeling. This requires updated Transformer LF/HF values for the amp models. Existing presets are automatically updated to the new values upon recall.

New Speaker Drive algorithm in Amp block. This new algorithm more accurately models the frequency dependent distortion of guitar loudspeakers. The default value (upon resetting the block) is 2.0 which gives roughly 1 dB of compression. Setting the value to 0.0 defeats the speaker drive modeling. Higher values give a smoother and more focused sound, rounding off the “sharp edges” and yielding greater compression.

Firmware Cygnus 19.xx

Improved CNFB algorithms in Amp block resulting in smoother distortion and improved clarity.

Version 19.00 firmware represents the first use of the Chase Nonlinear Feedback (CNFB) technique for the solution of nonlinear ODEs. The power amp algorithm has been completely rewritten using the CNFB method. This provides improved accuracy, especially in the clipping and power supply sag behavior vs. frequency.

Added 11 power tube types from various manufacturers.

Improved Phase Inverter Bias Excursion accuracy for some amp models (mostly non-MV types). Note: The improved PI Bias Excursion accuracy results in an increase in bias excursion in most cases. Bias excursion primarily manifests as intermodulation distortion, particularly subharmonic distortion. This produces a chunkier tone with more growl and also yields a thicker tone when rolling off the volume or playing lightly. The amount of bias excursion can be adjusted using the PI Bias Excursion control in the Advanced menu.

FRACTAL AUDIO QUOTES

[6] I would say that the biggest change in 19.x vs. 18.x is the clipping behavior of the power amp. The preamp is not changed at all so anything you are hearing is due to the new CNFB power amp stuff.
The power amp clips softer now. This is more accurate, however. If you want a harder power amp clipping, which people that are into aggressive styles may desire, increase the Power Tube Hardness parameter. Or turn the MV down a little.
19.x also introduces an improved feedback algorithm in the power amp. It uses what I call "hybrid feedback" and is a way of replicating analog feedback in a nonlinear discrete-time system. This yields better frequency response accuracy above 10kHz compared to 18.x. 18.x tended to be a little brighter as a result. To get this brighter sound in 19.x increase the Transformer HF value.
For FAS Modern III nothing else has changed from 18.x to 19.x

Improved CNFB algorithms in Amp block resulting in smoother distortion and improved clarity.

Renamed Speaker Impedance to Voice Coil Resistance to more accurately describe the function of the control. Note that this includes all other “parasitic” resistances, i.e., speaker cable resistance, output transformer winding resistance, etc.

Improved Amp block transformer/speaker interaction modeling. The “Voice Coil Resistance” parameter has been repurposed/renamed “Speaker Impedance”. The various parameters work as follows:

- Transformer Matching: Sets the impedance ratio (square of the turns ratio) of the output transformer.
- Speaker Impedance: Sets the relative nominal impedance of the speaker. To simulate connecting, e.g., a 4-ohm speaker to an 8-ohm output you would set Speaker Impedance to 0.5. Conversely to simulate connecting a 16-ohm speaker you would set it to 2.0.

FRACTAL AUDIO QUOTES

[7] It should sound and feel anywhere from marginally to substantially better depending upon the amp and/or speaker impedance curve.

Update PI Bias Excursion parameters for many Amp models based on new measurement technique.

Added “Oversampling Mode” to Global menu. This parameter allows selecting between BEST PERFORMANCE and MIN. LATENCY.

Firmware Cygnus 18.xx

Improved Amp block cathode follower algorithm. Algorithm now uses higher order solution of nonlinear ODE for more accurate low frequency response.

Improved Amp block power amp algorithm. New algorithm more accurately models dynamic changes in speaker impedance resulting in more “complexity”.

FRACTAL AUDIO QUOTES

[8] It will sound different but not greatly. To me it sounds more "analog", due to the new cathode follower and dynamic speaker impedance stuff.

Firmware Cygnus 17.xx

Improved accuracy of Master Volume in Amp block for low settings.

Firmware Cygnus 16.xx

Improved power amp cathode current calculation accuracy for cathode biased models.

New “Cygnus” amp modeling algorithms.

Cygnus uses Fractal’s proprietary SpectrumTrackTM technology, which improves the response of amp models across the entire range of input levels, especially for amps with cascaded gain stages. The result is truer and more dynamic “voicing,” remarkable touch sensitivity, and exceptionally satisfying “chugs.”

FRACTAL AUDIO QUOTES

[9] SpectrumTrack(TM) ensures that the frequency response of the model matches the real amp at all levels of input excitation.
If you've played other products you may notice that the response deviates if you roll down the volume on your guitar. For example, the ****** gets noticeably more midrangey when you roll off your guitar volume. The ***** gets thinner. Etc, etc. This error in response also manifests when varying your picking intensity, especially for low- to mid-gain tones.
SpectrumTrack(TM) compares the model to the reference amp at a wide range of excitation levels and ensures that the model's response matches that of the reference amps.

Public Beta: [10]

The power amp bias algorithm is changed and the bias control works differently now. As with a real amp as you turn the bias down the gain also goes down. Typical values for bias are between 0.45 and 0.5 for fixed bias amps and 1.0 for cathode biased.
Dynamic Presence and Dynamic Depth have been removed as they are incompatible with the new algorithms.
On the Dynamics tab there is now a "Master Bias Ex." parameter. This scales ALL the bias excursion parameters. The default value for the various bias excursions is usually 100% now but there are some amps where a bias excursion may be 0%. Depends on the topology.
In general high gain amps should feel tighter and sound more "vocal". All amps should feel quite a bit more dynamic. You may need a compressor to tame things if you're recording (as you would a real amp).
There is a lot more variation in feel between models now.
The Hicut and Presence are now separate parameters. In most cases this is invisible to the user. However for the Komet models you get both, just like the amp.

Public Beta: [11]

This firmware will update various parameters to default values when loading presets. This includes Power Tube Bias, Bias Excursion, Negative Feedback, etc., etc.
I have adjusted the Power Tube Bias vs. the previous beta. In the previous beta the Fender (et. al.) default bias values were based on the original factory values. After much consideration I have decided to use "best practice" bias points.
The reason for this is that Fender amps were biased very cold from the factory to ensure the tubes lasted beyond the warranty period and cut down on warranty claims on tubes. However when replacing the tubes in ANY amp the best practice is to bias the tubes at 60-70% of max plate dissipation (for Class-AB amps).
I have some old Fender amps here with the original tubes in them and they are biased around 50% which is extremely cold. If I were to replace the tubes I would adjust the bias to around 66% (my personal preference).
So the bias point for all models is now commensurate with the typical bias point a technician would set the amp at rather than the factory value as the factory value almost always errs on the cold side for tube reliability reasons.
Therefore you will now see bias points of around 0.5 to 0.6 for 6L6 amps and 0.45 to 0.5 for EL34 amps and so forth. Feel free to experiment with colder or hotter bias points. Setting the bias colder (lower) results in a more dynamic response but harsher breakup and more crossover distortion. Setting the bias higher results in a warmer but less dynamic tone. For a Fender model the factory bias equivalent may be as low as 0.45.
For "Class-A" amps the bias point is adjusted using the Cathode Bias Resistance parameter. For those amps that parameter now appears on the Power Amp tab of the amp block. Increasing the value results in a COLDER bias point and vice-versa (opposite of the bias parameter behavior).
This firmware is more aggressive in the very high frequencies than the previous beta. There was a mistake in the power amp algorithm that reduced the drive into the virtual power tube grids by about 30% typically. So the grids weren't clipping as soon as they should resulting in reduced high frequency overtones. This typically will only be noticeable on non-MV amps. On non-MV amps you should hear a bit extra "sizzle" in the top end.

New Speaker Dynamics modeling. The Speaker Dynamics control adjusts the amount of virtual voice coil heating. Higher values result in more heating and commensurately higher voice coil resistance. The Speaker Time Constant will be reset to 2 seconds for existing presets. A typical guitar speaker has a voice coil thermal time constant in the range of several seconds."

FRACTAL AUDIO QUOTES

[12] It can be a bit shocking at first. Those "vintagey" amps are quite a bit different in some cases. Spitty, gnarly, nasty, angry sounding. The "polished" sound is gone. The low end is tighter. High gain amps growl and chug with a vocal quality. Medium gain amps purr like a big cat. Low gain amps sound big and chimey.
The whole impetus for this was I was doing some critical listening and I noticed that certain amp models didn't have the same distortion "texture" as the real amp. The amps sounded like rubbing two rocks together while the models sounded more like sandpaper. There was also a vocal quality. The amps went "chug, chug, yowwwwww" while the models went "chit, chit, yeeeeee". That led to a complete rewrite of the preamp algorithms. What I learned from that I applied to improvements in the power amp algorithms.

Cygnus, in general, may feel like it has less gain because it is more "open", especially for amps that get their distortion from the power amp.

The taper on many of the Fenders has been changed to be more similar to the original amps. The original amps (not the reissues) used a "2-35" taper which was a custom taper that Fender ordered from CTS. The reissues use a Log30. The 2-35 is closer to Log20 so those amps use a Log20 now.

[13] […] So what I do is try to replicate a real tube amp as accurately as possible as that is the gold standard. Cygnus is demonstrably more accurate. I have the math and measurements that prove it.
IMO it makes playing the amps more enjoyable. It may make recording require some more work, just like you would with a real tube amp. I don't know as I haven't tried that.
For now if you don't like the changes go back to 15.01 or try some of the advanced tweaks. One of the things that Cygnus models more accurately is bias excursion and, in general, there is more bias excursion than before. You may not like the sound of bias excursion but it is part of what makes a real tube amp sound and feel the way it does. So one tweak to try is to reduce Master Bias Excursion or any of the individual bias excursion parameters.
The other thing with Cyngus is the power tube bias. The previous firmware biased the virtual power tubes a bit hot in comparison to real amps. This was necessary because of the algorithm to prevent unwanted crossover distortion. The new algorithms are more accurate and, as a result, the power tube bias matches the real amps. If you want that old sound increase the Power Tube Grid Bias. Try around 0.6 to start.

[14] The early Cygnus betas were colder than the later betas. Originally I had set the bias equal to the reference amps but many of the reference amps are biased cold because most manufacturers bias amps cold from the factory for warranty reasons. In the later betas I put the bias points at where a technician would typically bias an amp after replacing the tubes, i.e. 60-70% of max. plate dissipation.

[15] The updated modeling primarily affects amps with cathode followers (i.e. Marshalls, etc.), amps with many gain stages (i.e. Boogies, etc) and amps with significant negative feedback. Vox and Matchless amps don't have cathode followers, don't have many gain stages and don't have negative feedback.

Improved output transformer / speaker impedance interaction modeling. This yields more accurate low frequency response. Note that the Transformer LF parameter effectively adjusts the transformer’s inductance. Increase this value to simulate a smaller transformer, decrease to simulate a larger transformer.

Improved power amp cathode current calculation accuracy for cathode biased models.

Updated default Power Tube Grid Bias and Negative Feedback on many models based on new measurement technique. NOTE: As a result of this existing presets will update the aforementioned parameters to the new default values upon recall.

Improved Amp block power tube grid bias excursion algorithm. The default Excursion Time and Release Time values have been updated as a result. Existing presets are automatically updated to the new default values upon recall.

FRACTAL AUDIO QUOTES

[16] The "Class A" type amps are probably the most noticeable, i.e. AC-30, DC-30, etc. but the Plexis and Fenders also benefit.

[17] It's an improvement to all amps.

Added Power Amp Modeling ON|OFF control to Amp block and removed that functionality from the Supply Sag control. Existing presets are automatically updated upon recall.

Updated Amp block default Excursion Time and Release Time values as some were entered incorrectly. Existing presets are automatically updated to the new default values upon recall.

Improved Amp block power amp transient response accuracy.

Ares

Firmware Ares 15.xx

Improved Amp block power amp modeling. Improved algorithm yields accurate dynamic frequency response which results in clearer bass and extended highs. More “chug”, “thump” and “chime”. NOTE: Existing presets should be auditioned. While the overall tone isn’t significantly changed, the transient frequency response is enhanced which may alter the tonal perception.

Many of the Fender® amps have been “modified” with authentic presence and depth networks even if the real amp doesn’t have them (this was required for the new power amp algorithm). When the Tone Control Display is set to IDEAL the Presence and Depth controls can be used to shape the power amp response just as if the real amp had been modified. Setting the Presence and Depth controls to zero effectively removes the modifications. WARNING!!! If your presets use non-zero values of Presence and/or Depth for amp models whose real counterparts do not have presence and/or depth circuits your presets may sound different and should be adjusted accordingly. I.e., if you have turned Presence up for the Deluxe Verb model your preset’s tone will have changed as a real Deluxe Reverb does not have a presence network (and Presence defaults to zero for that model).

Improved output transformer modeling in Amp block. For typical values of Transformer Drive the difference is subtle but mathematically more accurate adding a pleasing low-end growl and improving “tightness” in high-gain sounds. For high values of Transformer Drive the difference is more pronounced. If you have increased Transformer Drive on your presets above the default value then you should audition your presets.

Firmware Ares 14.xx

Improved Amp block cathode follower accuracy. The Hardness parameter has been removed and the default values have been changed. Existing presets are automatically updated. If you have edited the cathode follower parameters you should audition your presets as these parameters will automatically be reset to default values when the preset is loaded.

The Tube Pre model has been changed so that the power amp is off by default.

Improved Amp block power tube grid clipping algorithm.

Firmware Ares 13.x

Added “Headroom” monitoring meter to Amp block. The most common reason for “muddy” tones with high-gain amps is incorrect setting of the Master Volume control. The Headroom meter displays the voltage at the virtual power tubes in dB. If the Master Volume is too high the meter will be near 0 dB most of the time. Note that this only applies to amps where the power amp is intended to run “clean” like the 6160, Recto, etc. Non-Master Volume amps get their distortion from the power amp distorting so this recommendation does not apply.

Firmware Ares 12.x

Improved Amp modeling.

None of the amp models are "legacy". All models were updated for the III. [18]

Improved power tube modeling yields smoother overdrive especially for semi-clean and edge-of-distortion tones.

Increased Amp block B+ monitor range as Variac settings can cause B+ voltage to fluctuate beyond visible limits.

Added 6CA7 power tube type. While the 6CA7 is generally regarded as a substitute for the EL34 it is actually a different tube with the 6CA7 being a beam tetrode. This particular tube type is modeled after the original Sylvania “Fat Bottle” 6CA7.

Changed Amp block Input Trim to read in dB.

Improved Amp block Speaker Compression modeling. New algorithm is more accurate and sounds smoother with more “growl”.

Firmware Ares 11.x

Amp block now uses new high-order speaker impedance modeling. 52 speaker impedance models (and two LB-2 models) are included and can be selected using the Speaker Impedance Curve parameter (on the Advanced page). Selecting an amp model will load an appropriate default Speaker Impedance Curve for that amp model. The Cabinet Resonance parameter can be used to adjust the amount of cabinet resonance in the impedance curve. NOTE: The 2x12 Bassguy, 2x12 Jazz 120, 4x10 Brit JM45 and 4x12 Hipower data is incomplete and will be updated in a future release.

Setting Global “Update Pre-11.x Presets Spkr Imp Upon Load" parameter to YES will automatically update the Speaker Impedance Curve for the Amp blocks upon preset recall to use an appropriate Speaker Impedance Curve for that amp model. Setting the parameter to NO will leave existing presets unaffected. NOTE: Setting this to YES will also cause the EDITED LED to light indicating the preset has been modified.

FRACTAL AUDIO QUOTES

[19] There is no difference in frequency response. The modeling changes only improve the dynamic range. I'd estimate we picked up 3-4 bits of additional resolution on average.

Firmware Ares 10.x

New power amp modeling algorithm. This algorithm improves the plate impedance accuracy substantially. This yields tighter bass, crunchier midrange and “chimier” highs.

Due to the changes in the power amp modeling algorithm the Power Tube Hardness parameter now behaves differently. Selecting a Power Tube Type loads the “knee voltage” for the power tubes and this voltage can be adjusted up or down using Power Tube Hardness. Higher values yield a lower knee voltage and more abrupt clipping and vice-versa. Existing presets will have Power Tube Hardness reset to 5.0 upon recall.

The range of the Transformer Match control has been reduced to 0.5 to 2.0. Existing presets will have this value reset to 1.0.

The Ideal Tetrode and Ideal Pentode power tube models are no longer applicable and have been replaced with 5881 and 6L6GB models, respectively.

The PI Bias Excursion values have been updated for some amp models. Existing presets will automatically be updated to the new default values. If you typically alter this parameter you should audition your presets.

The Amp block Dynamic Impedance parameter is no longer applicable and has been removed.

Added KT77 power tube type.

FRACTAL AUDIO QUOTES

[20] […] Firmware 10 uses new "FASPICE XD" modeling in the amp and drive block. It requires a bit more CPU but the accuracy is far better. I figured out a way to ensure that transcendental equations are always stiffly stable and converge in a fixed amount of time. Significantly faster and at least as accurate as trapezoidal, modified trap, gear, etc. algorithms. It dampens numerical ringing without the side-effect of damping actual circuit ringing. Once you see how it works it seems hard to believe that no one has thought of it before but I can't find a single paper or article that uses the technique. The only drawback is that frequency response is limited to about 1/2 Nyquist but since we oversample that's irrelevant.
So that's why you get the "amp feels like it's going to explode" but without the noise and artifacts.

Firmware Ares 9.x

New power amp modeling algorithm. This new algorithm now also separates the transformer matching from the speaker impedance. A new parameter, Speaker Impedance, allows adjusting the relative impedance of the virtual speaker. For example, to simulate connecting a 16-ohm speaker to an 8-ohm output set Speaker Impedance to 2.0. Transformer Matching, on the other hand, changes the impedance ratio of the virtual output transformer.

To support the new power amp algorithm the internal transformer matching values and negative feedback values have been updated. The new negative feedback values will load when selecting an existing preset. If you typically adjust Negative Feedback when creating a preset be sure to audition your presets as the parameter value will be reset to the default value upon preset load.

Added “Gain Enhancer” mode to Amp block Output Compressor. This mode can be used to simulate the acoustic reinforcement of a loud amp coupling into the guitar and enhancing the output signal.

FRACTAL AUDIO QUOTES

From Cliff's Match vs. Speaker Impedance Tech Note:

Prior to 9.xx the "matching" was controlled by a single Transformer Match parameter. 9.xx introduces a new Speaker Impedance parameter. The distortion of a tube power amp is dependent upon the load presented to the power tubes. The overall sound, however, is also often dependent upon the voltage at the speaker since that voltage is fed back to the input.
The following examples illustrate the difference.
First we define several variables: Zs is the load (speaker impedance) on the secondary of the output transformer. N is the transformer turns ratio. N^2 is the transformer impedance ratio. Ip is the current into the transformer primary. Zp is the impedance "seen" by the transformer primary.
A power tube is effectively a dependent current source so Ip is the current from the power tubes.
Zp is the load impedance "reflected" to the primary and is given by Zp = Zs * N^2.
The voltage at the primary is Vp = Ip * Zp.
The voltage at the secondary is the primary voltage divided by the turns ratio Vs = Vp / N.
Ex. 1: Let N = 10, Zs = 16 ohms, Ip = 0.1A.
Then
N^2 = N*N = 10*10 = 100
Zp = Zs * N^2 = 16 * 100 = 1600 ohms
Vp = Ip * Zp = 0.1 * 1600 = 160V
Vs = Vp / N = 160 / 10 = 16V

Ex. 2:
Let's reduce the impedance ratio by 50%.
N^2 = 50
N = sqrt(50) = 7.07
Zp = Zs * N^2 = 16 * 50 = 800 ohms
Vp = Ip * Zp = 0.1 * 800 = 80V
Vs = Vp / N = 80 / 7.07 = 11.3V

Ex. 3:
Now let's reduce the speaker impedance by 50% instead.
N = 10. N^2 = 100. Zs = 8.
Zp = Zs * N^2 = 8 * 100 = 800 ohms
Vp = Ip * Zp = 0.1 * 800 = 80V
Vs = Vp / N = 80 / 10 = 8V

In Ex. 2 and Ex. 3 the voltage at the power tubes (Vp) is the same (80V) so the power tubes will distort the same amount. However the voltage at the speaker is different. In Ex. 3 there is less voltage at the speaker so, if the power amp has negative feedback, there will be less signal fed back.
What to use Transformer Match for:
The turns ratio of transformers varies by manufacturer, era, etc. For example the original Drake transformers used in old 50W Marshalls had a primary impedance of 3.5K. Some newer transformers have an impedance of 3.2K, about 10% less. To replicate this set Transformer Match to 0.9. This will give a more "open" sound but also a harsher distortion. Increase matching to simulate a higher primary impedance. This will give a more compressed and smoother distortion. Some amps intentionally overmatch their transformers (Trainwrecks) which gives them their characteristic sound.
What to use Speaker Impedance for:
The actual impedance of a speaker can vary quite a bit. For example a Celestion Greenback is available in 8 and 16 ohm versions. The 8-ohm version has a DC resistance (DCR) of 6.57 ohms. The 16-ohm version has a DCR of 12.13 ohms. The Plexi models in the Axe-Fx assume 16-ohm speakers were used as the Marshall cabs used 16-ohm speakers.
The DCR normalized to the speaker impedance is therefore different for the two versions. For the 8-ohm version the DCR normalized to the impedance is 6.57/8 = 0.82. The 16-ohm version is 12.13/16 = 0.76. The relative impedance is therefore 0.82/0.76 = 1.08. Therefore the 8-ohm version of the speaker will increase the voltage at the primary by 8% which means the power amp breaks up a bit earlier (more gain). To simulate this increase Speaker Impedance to 1.08.
All the models use a DCR commensurate with the original speakers when available. For amp heads with no matching cabinet the DCR is assumed to be 6.7 ohms. I contemplated naming the control "Speaker DCR" but figured that was too vague but it's actually a better description of what the control does (and the internal parameter name is speaker_dcr).
Another use for Speaker Impedance is to simulate intentional mismatching. SRV, Joe Walsh, etc. would intentionally mismatch their amps by connecting the speaker to the "wrong" output jack. For example, to simulate connecting a 16-ohm speaker to the 8-ohm output jack set Speaker Impedance to 2.0 (or 1.9 in the case of a Greenback).

Firmware Ares 8.x

Improved amp modeling.

Firmware Ares 7.x

Improved power amp modeling. New algorithm accounts for variation in load voltage as a function of transformer turns ratio. I.e. reducing the Transformer Matching will reduce the output level and vice- versa

Firmware Ares 6.x

Improved Amp block power amp modeling.

Firmware Ares 5.x

Completely new Amp block cathode follower algorithm yielding more accurate results. The “Ideal” cathode follower type is no longer supported as it is incompatible and has been removed from the GUI. The Cathode Follower Time and Ratio parameters have also been removed as they are no longer applicable. A “Grid Clipping” parameter has been added which allows the user to adjust the grid clipping in the cathode follower. Lower values reflect the softer response of classic British and American tubes like Mullard, Sylvania and RCA. Higher values simulate the response of modern Chinese and Russian tubes with more abrupt clipping.

Updated various Amp block parameters related to new cathode follower algorithm. Existing presets are automatically updated to the new values.

NOTE: Due to the new algorithms several amp block parameters are reset to default values when loading old presets. Included in these parameters is Preamp Bias Excursion. If you had altered this parameter in a preset note that it will be reset and you may want to readjust it.

FRACTAL AUDIO QUOTES

[21] All models have been improved as there was a change to the triode algorithms as well.

[22] That crispy/crunchy is what real amps don't do. It bugged me for years. Real amps go "bong" not "bzzzzz". If you look at the waveform out of a cathode follower it's almost a triangle wave whereas the previous firmware was halfway between a triangle and square. I finally figured out what makes that triangle wave.

[23] The other thing you should hear is that low power chords growl.

Firmware Ares 4.x

Improved Amp block preamp tube modeling.

Improved Amp block cathode follower grid modeling.

Improved power amp modeling for “Class-A” type amp models.

Firmware Ares 3.x

Improved amp modeling.

Improved speaker compliance algorithm.

Added Global "Tone Control Display" parameter. When set to Authentic (default) only those controls present on the actual amp are displayed. When set to Ideal all tone controls are displayed. Also, when set to Authentic the Bass, Mid and Treble controls are reset to default values when changing models to ensure accuracy for models that may not have these controls.

Firmware Ares 2.x

Improved Amp block speaker dynamic parameter modeling. The new Speaker Compliance parameter controls the nonlinear behavior of the virtual speaker. Existing presets will load with this parameter at 0.0 and will be unchanged tonally from the previous firmware (IOW your presets will not be altered). Selecting a new amp model or resetting the block will set the value to 5.0 which is a typical value for guitar speakers.

Improved Amp block cathode follower modeling.

Improved Amp block phase inverter modeling.

Firmware Ares 1.x

Initial release for the Axe-Fx III.

Improved Amp block output transformer modeling.

Added Tilt EQ to Amp block Input EQ types.

Added Boost Type and Boost Level to Amp block. There are seven boost types: Neutral, T808, T808 Mod, Super OD, Full OD, AC Boost and Shimmer. All boosts act as “clean boosts” replicating the oft-used “Drive on 0, adjust Level as desired” boost technique. The boost allows boosting the amp block without requiring a separate Drive block. The Boost Level parameter controls the amount of boost.

Firmware Ares 1.03

Ported most of the “Ares” modeling from the Axe-Fx III. NOTE: To make space for the required additional code, support for presets created prior to Quantum 7.00 has been removed. While these presets will load certain parameters may not initialize correctly. Be sure to audition any presets created before Quantum 7.00.

Quantum

Firmware Quantum 9.x

Removed the “Motor Drive” and “Transformer Grind” algorithms and associated parameters from the Amp block. These have been replaced by the new “Speaker Compression” algorithm. This algorithm models the interaction of the power amp with the power compression of the virtual speaker. The “Spkr Comp” parameter controls the amount of virtual speaker compression. This value defaults to 3.0 when the Amp block is reset. It does not get reset when changing the model. If using the Axe-Fx II with a tube power amp and conventional guitar cab you may want to reduce this value to 0.0. The gain reduction meter shows the amount of virtual power compression (select the Spkr Comp knob to monitor the gain reduction). Typical guitar speakers compress between 3 and 6 dB depending upon construction, age, volume, etc. The default value is conservative and yields about 3 dB of compression. Note that the Master Volume control will interact considerably with the Speaker Compression algorithm as will the Presence and Depth controls. Higher values of Master Volume will cause more virtual speaker compression.

Minor change to the phase inverter algorithm. [24]

Improved Speaker Compression algorithm so that the change in the speaker impedance is accounted for.

Improved power amp modeling.

Disabled Amp block active Presence control if power amp modeling is bypassed because too many customers not realizing the feature exists.

Improved speaker compression modeling and interaction with power amp. This results in a more dynamic response.

Changed default cathode follower hardness (CF Hardness) to 0.75 to align better with measured values.

Firmware Quantum 8.x

Improved amp modeling. Improves clarity and sounds more “open” especially for non-MV amp models or when the MV is turned up.

The bias excursion values for most amp models have been updated based on new measurement techniques. Existing presets will automatically be updated to the new values.

Fixed minor bug in Amp block output transformer modeling which caused slight attenuation of upper treble frequencies. This results in clearer, more chimey tones.

Firmware Quantum 7.x

Improved phase inverter modeling in Amp block. This provides thicker power amp distortion. New algorithm also includes bias shifting which results in more harmonic spectrum variation with input amplitude. This improves feel, “knock” and creates sweeter single note soloing. The new “PI Bias Shift” parameter controls the amount of phase inverter bias shift. Note that some real amps are “spitty” in nature due to PI bias shifting, i.e. Trainwrecks, and the new algorithm is designed to replicate that behavior accurately. If you find the behavior undesirable reduce the PI Bias Shift value as desired although this will reduce authenticity.

Improved output transformer modeling. This results in tighter, less boomy and smoother bass when the virtual power amp is driven hard. Note that this change may be significant and initially alarming with certain amp models. While the new algorithms are much more accurate they may be disconcerting to those who are accustomed to the old algorithms. In these cases the user may want to decrease the Transformer Drive and/or Low Res parameters in the amp block at the expense of accuracy. It is recommended instead, however, to readjust other parameters in the preset (i.e. Drive, BMT, etc.) which will achieve more authentic results.

Improved Amp block cathode follower modeling (again). This results in tighter bass and “chunkier” tones. As a result nearly all amp models that use cathode followers have been reworked with updated parameters. It is recommended that the model be reloaded by deselecting and reselecting the desired model which will load the pertinent default values.

Changed default value of Speaker Drive to 0.5. When selecting an amp model the Speaker Drive parameter will now default to a value of 0.5 which is commensurate with a small amount of speaker breakup. Adjust this value to taste, if desired. If using the Axe-Fx II with a power amp and conventional guitar speakers you may want to reduce this value as the guitar speakers will impart their own distortion.

Firmware Quantum 6.x

Improved Amp block output transformer to power tube interaction modeling. This results in less “smear” in the overtones when the virtual power tubes are driven into clipping.

Improved Amp block plate clipping modeling. New algorithms more accurately replicate the gradual onset of clipping and never fully hard clip resulting in a more dynamic and “open” tone. Note that the increased dynamics may result in some amp models having higher peak volumes which can result in clipping with existing presets. To remedy this simply turn down the Level control in the Amp block.

Recalculated Amp block preamp tube parameters. The “12AX7A SYL” (Sylvania 12AX7A) is now the default type as we think it sounds the best.

Improved background calculation accuracy for cathode follower parameters.

Improved speaker overdrive modeling in Amp block. New algorithm captures the “throaty” sound of an overdriven speaker along with the gentle compression. The “Spkr Drv” (Speaker Drive) parameter has been moved to the Spkr tab on the Amp menu. NOTE: If you are using Speaker Drive in existing presets you should audition these presets and adjust the parameter as necessary as the sound and behavior of the algorithm is considerably different than before. NOTE: Setting this parameter to higher values will simulate a blown speaker.

FRACTAL AUDIO QUOTES

[25] […] the preamp modeling in 6.00 is the same as 5.xx except the parameters for the default tube type (12AX7A SYL) are different. The Sylvania 12AX7A is more nonlinear than other 12AX7As which results in more dynamics but will also result in more "background" distortion because the waveform is being distorted even when it isn't being clipped. The JJ version is more linear which will result in a tighter tone and less background distortion but less dynamics.
For 6.01 I've also added back the old 12AX7B type which is the most linear of the types and clips hard. People who play with lots of gain tend to like this as it results in tighter tone and more aggressive harmonic content.
There are two primary parameters associated with our preamp tube models. "Preamp Hardness" determines how abrupt the tube clips when it enters the saturation region. There is another parameter that determines how nonlinear the tube is between cutoff and saturation. This is currently not exposed to the user but I've been contemplating adding it.
I've also changed the default type for British amps to the ECC83 model as these amps typically were equipped with ECC83s (duh). The ECC83 was the European equivalent of the 12AX7A and tended to be a bit more linear and clip a little harder.

Firmware Quantum 5.x

Improved preamp tube modeling for tubes driving cathode followers. In models that use cathode followers this results in warmer distortion with smoother decay. The shape of the cathode follower distortion can be adjusted with the new “CF Hardness” parameter found on the Advanced tab in the Amp block.

Increased maximum amount of virtual power amp sag in Amp block. The maximum amount of sag is now twice what was previously available. Existing presets will automatically be adjusted to compensate for the increased range of the Supply Sag control, i.e. if the Supply Sag was set to 8.00 it will be adjusted down to 4.00 so as to yield the same amount of sag. High values of Supply Sag can be used to make the feel “easier” and/or replicate the behavior of other products that intentionally exaggerate compression.

Firmware Quantum 4.x

Improved power tube plate current vs. grid voltage accuracy. New models more accurately reflect how the response is higher order at lower grid voltages and “relaxes” into a lower order response at higher grid voltages. This improves feel when the virtual power amp is overdriven and improves harmonic content accuracy.

Firmware Quantum 3.0

Improved Amp block output transformer modeling. New model more accurately simulates dynamic core losses and leakage inductance. The “Xfrmr Grind” knob controls the intensity of the effect. Higher values result in more high frequency response and a more “open” sound. Very high values can yield a raspy, spitty tone common in vintage and/or low wattage amps. Modern “big iron” amps tend to have low values. Note that the audibility is dependent upon how hard the virtual power amp is driven and is more noticeable as the MV is increased. Also note that the effect in real amps is highly dependent on the speaker. Some speaker/transformer combinations exhibit significant high frequency dynamic boost while other combinations yield almost none. As always use your ears as the final determinant.*

Improved triode plate modeling for cases when plate load is complex.

Firmware Quantum 2.x

Improved tube modeling. New algorithms uses more accurate plate current formulas based on actual measurements rather than theoretical values. This results in smoother, thicker distortion and better dynamic response.

Improved power supply modeling. New algorithms improve sag and feel. For convenience the virtual power supply voltage (B+) can now be monitored on the PWR DYN tab of the amp block. When the Supply Sag control is selected the gain reduction meter will display the supply voltage in dB relative to the idle voltage.

Improved cathode bias algorithm for “Class-A” amp models (i.e. Class-A 30W, AC- 20 Dlx, etc). In conjunction with this the Cathode Squish parameter has been repurposed as “Cathode Bias” and controls the value of a virtual cathode resistor. A value of 50% is “optimum” and biases the power tubes at true Class A operation (neglecting any bias shifting due to supply sag, screen droop, etc.). Values greater than 50% increase the resistance and therefore bias the power tubes “colder”. Values less than 50% bias the tubes beyond Class A. In a real amp this would probably destroy the tubes but that limitation does not exist in our virtual amp. Most real amps of this type actually operate far below Class A and the default values for the models will reflect this. Note that the Power Tube Bias value should be set to 1.00 for these amp types (since that parameter controls the grid voltage and the grid voltage is at a maximum in these types of amps).

Further improvement of preamp tube models based on measurements. The existing theoretical models, i.e. “Modern”, “Vintage”, etc., have been removed. There are now six extremely accurate preamp tube types: 12AX7A, ECC83, 7025, 12AX7B, ECC803 and EF86. Note that the EF86 type has been normalized to have roughly the same gain as the triode types.

Improved power tube saturation modeling. This yields warmer, “tubier” distortion. The PA Hardness parameter is automatically set for each power tube type but may be overridden if desired.

Improved tube interaction modeling. A new parameter, “Harmonics”, controls the amount of interaction. Higher values yield softer distortion. The default value is set for each amp model but may be overridden.

Improved virtual output transformer saturation modeling.

FRACTAL AUDIO QUOTES

[26] The previous firmwares were based on theoretical tube models. One thing I began to notice is that the theoretical models simply weren't agreeing with measurements. So after much research we realized that the theoretical models are just that, theoretical and that real tubes do not behave exactly as theory predicts. I can't reveal the details of what aspects don't agree and why those aspects are important.
Q2 is based on the actual tube curves which gives a different character to the distortion and a more bouncy and responsive feel.

[27] Many of the amp models had their speaker parameters updated based on new measurements.

Firmware Quantum 1.x

This is the initial release of our “Quantum” firmware. Quantum represents a milestone in amplifier modeling technology. Our new Real-Time Spice (RTS) algorithms offer a degree of accuracy not found in any other product.

New RTS triode models. There are three new triode models based on our new algorithms: 12AX7A (default), ECC83 and 7025. The previous models are still available and may be selected with the Pre Tube Type parameter. Note that the models have all shifted and if you were using a model other than default previously you will need to adjust your preset to the desired model.

The “CF Comp” parameter has been renamed “Preamp Comp” to better explain its function.

Added new Preamp Compressor Type “Comp Type” parameter to amp block. There is a new menu page that contains Preamp Comp, Comp Type, Dynamics, Preamp Bias and Output Level (the last repeated from other menus for convenience). Preamp Comp Type selects between “Authentic”, which accurately models the compression in a tube amp, and “Ideal” which is an idealized distorting compressor. The idealized type is more focused and has tighter bass whereas the authentic type is bolder and looser. High gain players may prefer the ideal type due to its tight character.

Added a new mode to the “Character” controls in the Amp block. A Char Type of “Dynamic” engages an exciting new mode of tone control. This can be used to fatten or scoop the tone as a function of picking strength. For example, set the Type to Dynamic, Char Freq to 450.0, Char Q to 0.7 and Char Amt to 4.0. This will cause the tone to get fatter and thicker as you play hard but without getting honky when playing soft.

FRACTAL AUDIO QUOTES

[28] Personally I consider Quantum the biggest improvement from previous firmware than any other release. The day I first got it working I was so shocked at how good it sounded I jumped out my chair. I then crafted an email to Matt with the title "I did it!!!". I'm sure he'll be happy to verify.

[29] Q1.01 models the power tube plate current slightly more accurately than Q1.00. It's a subtle difference but some may prefer the more idealized sound of Q1.00 so I made it a menu option.

Improved triode grid conduction model. This improves edge-of-breakup tones as it keeps the distortion on the edge of breakup more and improves high-gain tones as it tightens up the bass. Also improves feel and dynamic response.

Improved cathode follower model. This improves harmonic accuracy yielding less “glare”, more detailed treble (more “chime”) and more bite. The previous cathode follower model can be selected from the Global menu by choosing a Modeling Version other than 1.03.

Improved triode saturation modeling based on new measurements. The new modeling results in more accurate saturation behavior which, in turn, results in smoother overall distortion characteristics and more accurate harmonic content. Due to the new algorithm the default Preamp Hardness value is now 6.0.

FRACTAL AUDIO QUOTES

[30] Tube amps are amazing in some ways. The just naturally do the right things. One of these things is that the grids sort of "self-align" so that the distortion stays on the edge. You can tell when a modeler isn't modeling this right as you will get fizzy decay (some people erroneously call this "crossover distortion") and flubby bass. If you can't boost treble without it getting harsh then it's not modeling the grids properly. If you need to put a shelving EQ to roll off some bass before the model then it's not modeling properly. With this latest version of Quantum you can put an EQ after the amp or cab and crank the highs as much as you want without it getting harsh and causing ear fatigue.

Pre Quantum

Firmware 19

Improved Amp block power tube plate current calculation. This results in increased clarity, improved feel/attack and better edge of breakup distortion texture. The default Power Tube Bias values have been updated to reflect this change and existing presets will be updated automatically to the new values.

Firmware 18 (G3)

This firmware incorporates all-new amp modeling algorithms. With this update the Axe-Fx II now incorporates our “Generation 3 (G3) Amp Modeling Technology”. G3 modeling improves upon our previous modeling with better touch sensitivity, better dynamics, better distortion texture (or “grain”) with less fizz, more crunch and improved frequency response accuracy.

Added “Preamp Tube Type” parameter to Amp block. “Modern” (default) selects a triode characteristic representative of modern production tubes. “Vintage” selects a characteristic typical of tubes produced in the 50’s and 60’s. “Long Plate” replicates the softer saturation characteristic of so-called “Long Plate” triodes.

There are now only two Preamp Tube Type options in the Amp block: Short Plate and Long Plate. The Vintage type has been removed. Short Plate is similar to the previous Modern model but has the improved saturation characteristics that were developed for the Long Plate model.

Improved power tube grid conduction modeling. This yields better dynamics and edge-of-breakup tones, particularly when the virtual power amp is being overdriven.

Improved Amp block phase inverter model by incorporating effects of power supply sag.

Improved Amp block output transformer model by incorporating secondary losses.

Improved Amp block power tube transfer functions.

FRACTAL AUDIO QUOTES

[31] G3 modeling is a proprietary technique that learns the characteristics of a nonlinear circuit.

[32] I have three units here in my lab. One has 17.04 and the other two have 18.00. A/B'ing them it's immediately apparent and as Manny noted the most apparent thing is the punch in the chest aspect. That's exactly what I mentioned about a week or two that I noticed being the biggest difference. You can feel the speakers "jump" for lack of a better term.
One caveat, though, is that punch is dependent upon MV. The higher the MV the more punch but too high and things can get stuffy and/or raspy. You have to find the sweet spot and that depends on the other controls as well as your guitar and playing style. The higher the MV, the more the power supply sags and bounces. That power supply sag and bounce is partially what contributes to the punch.

[33] You should notice better midrange and treble clarity on certain high gain amp models compared to the beta. I did a lot of critical listening and comparing of the new algorithms over the last few weeks and noticed a tiny bit of "signature" to the sound. I traced that to the triode cutoff formula being too "soft". The new formula removes that signature which also yields increased clarity and string separation for models that rely on preamp distortion.

[34] In general the improvements are subtle but there should be improvements in the "bounce" and slightly smoother power amp distortion. I realized I wasn't accounting for the fact that bias excursion is a function of the B+ voltage. I also derived more accurate formulas for the behavior of the various power tubes when they enter saturation. The improved OT modeling results in fewer ultrasonic overtones which, while inaudible on their own do result in more intermodulation "garbage" when playing multiple notes so you should hear better string separation and chord clarity.

Firmware 17

Added “DYN EQ” GUI page to Amp block. This page now holds the Dynamic Depth, Dynamic Presence, Character Amount (Char Amt, previously named “Character”) and Character Freq parameters as well as two new parameters: Character Type and Character Q. Character Type selects between a shelving behavior or a peaking behavior. The previous behavior was always shelving. Character Q controls the bandwidth of the response when the peaking behavior is chosen. The Character parameters now control a powerful dynamic equalizer that can be used to achieve tones and feel impossible with a real amplifier. Negative values of the Character Amount along with a peaking behavior result in midrange scoop where the scoop increases as you play harder. Positive values result in a midrange boost as you play harder. Experiment with the frequency, Q and amount to achieve interesting dynamic response.

Improved Amp block power supply modeling by accounting for DC sag due to quiescent bias currents.

A “Presence Shift” switch has been added to certain “USA” amp models (those based on amps with a “Pull Shift” on the Presence knob). This switch is found under the Presence control and replicates the behavior when the Presence knob is pulled out on these amps. Note that the behavior of this switch is authentic and may result in volume reduction when active since the negative feedback is increased which lowers the loop gain.

Improved power amp screen grid and anode voltage dependence calculations. This results in more “open” tone and improved dynamic response especially when the virtual power amp is overdriven. This has necessitated changes to the default Cathode Squish value for the some models. Existing presets will have the Cathode Squish value updated automatically upon recall.

Improved power amp cathode squish accuracy by accounting for dependency on bias point.

Improved power amp modeling. This results in better touch sensitivity, more explosive dynamics and improved low note clarity when the virtual power amp is driven hard.

Firmware 16

Improved Amp block cathode follower model. New model includes effects of grid resistance which results in more accurate clipping characteristics.

Improved Amp block virtual power tube model. Improved algorithm more accurately models plate current vs. grid voltage yielding a more accurate transfer function which results in more pleasing power amp distortion and improved feel.

Improved Amp block virtual power tube interaction with virtual output transformer. This yields improved low-frequency accuracy and feel. Furthermore this improves the output waveform accuracy resulting in much improved interaction with the cabinet block. IRs should now sound fuller and more resonant with more “thunk” and “knock”. The Low Res parameter in the Spkr tab can be used to increase or decrease the amount of knock.

Added Power Amp Hardness parameter to Amp block. This parameter controls the hardness of the virtual power tube grid clipping. Models default to “Medium” and any presets created with earlier firmware versions will be set to Medium upon recall.

Improved Amp block output transformer modeling. New algorithm more accurately simulates effects of inter-winding capacitance and the resulting load on the virtual power tubes. This results in improved high frequency response. Tones have more “chime” without being harsh. This is especially noticeable for amps with low negative feedback or when the Presence is turned up high.

Added Slope parameter to SPKR page in Amp block. This parameter allows fine adjustment of the high-frequency impedance of the virtual voice coil (which affects the slope of the impedance curve). A speaker voice coil is “semi-inductive” due to eddy current losses in the motor. This presents an impedance to the power amp that isn’t fully inductive nor fully resistive. The amount of resistive loss varies by brand and type. Reducing the Slope simulates a speaker that is less inductive, increasing Slope simulates a speaker that is more inductive. Typical speakers range from 3.0 to 4.5 with the median being about 3.7. Lower values yield greater midrange while higher values are more scooped and sizzly.

Added “Dynamics” control to amp block. This parameter controls a dynamics processor that can be used to alter the dynamic response of the amp algorithms. When set below zero the amp compresses resulting in a smoother, less dynamic sound. When set greater than zero the amp expands resulting in a punchier, crunchier and more dynamic sound. Note that extreme values can have undesirable side-effects such as pumping and clipping.

Added AC voltage control to Amp block. This parameter, called “AC Voltage (Variac)” in the Advanced menu sets the relative AC line voltage into the amp simulation implementing a virtual “Variac”. Note that normally the volume would vary with the Variac setting in a real amp but the simulation compensates for the volume change by applying the inverse. This mitigates having to manually compensate using the Output Level.

Firmware 15

The amp modeling improvements have resulted in a significantly increased “sweet spot” for the Master Volume control. Previous advice to keep the Master Volume low for high-gain amp types no longer applies and, in fact, increasing the Master Volume can result in better tone (more bloom and swirl) and much better feel (due to power supply sag). Therefore most non-MV amps now default to a higher value than previously. This may result in louder preset volume which will necessitate reducing the Output Level to compensate.

Improved Amp block virtual power amp algorithm. The new algorithm improves realism and offers much more “punch” and a “crunchier” tone when overdriven.

Improved cathode bias modeling. This improves so-called “Class A” amps (e.g. Mr Z Maz 38, AC-20 Dlx, etc.).

Improved Amp block output transformer modeling by improving the accuracy of the flux density vs intensity curve (B-H curve) and resulting primary inductance. Because of this, the default Transformer Drive value for many amp models has been changed. Existing presets will be automatically updated to the new default value upon recall.

Improved Amp block feedback network accuracy especially for those amps that have depth networks. This causes the Presence and Depth controls to interact (as they would on a real amp) but yields greater realism.

Improved Amp block power supply accuracy. This provides more open, less compressed response. Because of this, the default Supply Sag for many amp models has changed. Existing presets will be automatically updated to the new default value upon recall.

Improved Amp block triode modeling. Models now incorporate reactive plate loading effects.

Improved Amp block Hi Cut control accuracy.

Changed Amp block so that Presence control is set to a default value when an amp model is selected. This is done because many amps, i.e. Double Verb, Deluxe Verb, et. al., have no presence control and the value should be set to zero for best accuracy. On the other hand some amps, i.e. Jr. Blues, 65 Bassman, et. al, have fixed presence networks. The Presence control will default to the appropriate value for these amps. For amps that do have a presence control the Presence parameter will default to a value that is deemed typical for the model.

Added Power Amp Bias parameter to Amp block. This parameter can be used to adjust the offset voltage of the virtual power amp (this should not be confused with the Power Tube Bias parameter which sets the quiescent operating current of the virtual power tubes). Power Amp Bias allows the user to vary the symmetry of the clipping of the virtual power amp. A value of zero produces nearly symmetrical clipping which will produce very little even harmonics. Higher values will produce increasingly asymmetrical clipping which increases the amount of even harmonics. Small amounts of even harmonics can make the power amp distortion sound “warmer” and more bell-like while higher amounts will give a “fuzzier” tone. Most amps have some amount of offset and the amp models will default to a typical value. Note that this parameter is only applicable for push-pull power amp types. For single-ended power amps the Power Tube Bias parameter sets the symmetry (as always).

Added exact tone stack solutions for all amp models with treble roll-off networks, e.g. PVH 6160, Triptik, Tucana, 5153, etc.

Changed Amp block Sat Switch operation. Sat Switch now operates like actual amp. Note that this will cause a reduction in level when the switch is engaged (as in the real amp).

Added “Out Comp” (Output Compression) control to Amp block. This parameter controls a compressor specifically tailored to reducing the output dynamic range of the Amp block. Note that this compressor runs in the master DSP and if set to a non-zero value will increase CPU usage. The Out Comp parameter controls the amount of compression (compression ratio). In the Advanced menu the user can also adjust the compression threshold via the “Comp Thrshld” parameter, if desired. The bar graph at the bottom of the menu displays the amount of gain reduction.

Removed Amp block Thunk parameter. This processing operation is no longer deemed necessary due to the improved Amp block algorithms.

The Amp block Modeling Mode choices have been reduced to “Authentic”, “Smooth”, “Ideal” and “Ideal/Smooth”. In “Smooth” mode Triode Hardness is set to minimum. In Ideal mode grid conduction is defeated. In Ideal/Smooth mode grid conduction is defeated and Triode Hardness is set to minimum.

Renamed “Damping” control in Amp block to “Neg Fdbk” (Negative Feedback) as this is a more accurate term.

Amp block Sat Switch now has three settings: Off, On (Auth) and On (Ideal). On (Auth) replicates authentic saturation circuit behavior and will lower the volume out of the virtual preamp. On (Ideal) replicates the idealized behavior present in Version 14.xx and earlier firmware.

Improved Negative Feedback calculation accuracy by including virtual feedback of phase inverter.

Improved Amp block Dynamic Depth algorithm. The new algorithm uses the low- frequency speaker information from the speaker page to set the inverse-homomorphic filters resulting in a more musical control.

Improved Amp block cathode follower. New algorithm includes loading on previous triode plate and resulting effect on distortion characteristics.

Firmware 14

Improved Amp block triode model. New model more accurately replicates behavior when triode enters saturation. This results in a warmer and punchier tone with smoother distortion characteristics.

Improved tone stack accuracy at extreme knob settings (i.e. when Treble is near maximum) by accounting for impedance loading. In most cases this is barely audible but for certain tone stacks that are heavily loaded there may be a small change in tone, especially as the tone controls are set near their minimum or maximum values.

Improved power tube grid conduction modeling. This more accurate modeling improves dynamic response resulting in a more powerful tone and feel. This also improves post-PI Master Volume behavior.

Removed “Dynamics” control from Amp block. This control is no longer deemed necessary due to the improvements in the underlying modeling.

Renamed Amp block “Comp” knob “CF Comp” since this knob controls the amount of compression in the Cathode Follower (CF) modeling.

Improved Amp block power amp dynamic impedance modeling.

Improved Amp block X/Y switching time for presets with high CPU usage.

Improved Amp block power amp dynamic impedance modeling.

Firmware 13

Improved power amp modeling via improved modeling of the plate impedance of the power tubes. This gives tighter bass (less flub) and warmer highs when the virtual power amp is heavily driven (higher Master Volume settings). This also improves the feel and dramatically increases the “3-dimensionality” of the tone. The plate characteristics are adjustable via the new Dynamic Damping parameter. This parameter defaults to the appropriate value when an amp model or power tube type is selected.

Added selectable power tube types for Amp block. Available types are: EL34, EL84, 6L6, 6V6, KT66, KT88, 6550, 6973, 6AQ5 and 300B (triode). Also available are an ideal tetrode and ideal pentode. The power tube type defaults to the appropriate type when the amp type is selected but may be overridden by the user. The power tube type presets the Dynamic Damping parameter as well as several internal parameters.

Added Preamp Sag parameter to Advanced menu in Amp block. This parameter allows turning the preamp sag modeling on or off. Turning it off replicates the behavior of separate preamp and power amp. Turning it on replicates the behavior of an integrated tube head or combo amp.

Firmware 12

Improved Amp block power supply current draw modeling which improves “feel”.

Improved Amp block phase-inverter-to-power-tube-grid interaction modeling which improves transient response resulting in faster attack. This also improves the clarity of notes especially when using heavily overdriven power amp settings.

The Amp block “Grid Modeling” parameter has been renamed and repurposed. The new name is “Modeling Mode” and offers the following choices:

Authentic – Replicates a tube amplifier with the utmost accuracy.
Grid Cond Off – Turns off grid conduction modeling in the power amp modeling. This reduces blocking distortion.
Smooth – Sets Triode Hardness to the minimum value essentially creating an ideal preamp and turns off grid conduction modeling in the power amp. This removes most of the “nasty” distortion that tube amps create.
Ideal – Removes most of the “warts” from the modeling which includes grid conduction, output transformer distortion, bias shifting and AC power supply modeling. Supply sag, screen voltage effects and crossover distortion are still modeled.
Ideal/Smooth – Same as #3 but also sets Triode Hardness to its lowest value. This is in essence an ideal preamp plus an ideal power amp.

The audibility of these settings is dependent upon the particular amp model and various parameters. The use of these modes in conjunction with other parameters can yield idealized tones not achievable with real tube amps. The first two choices duplicate the previous behavior of the deprecated “Grid Modeling” parameter so no changes are required to existing presets. Note that when “Ideal” is chosen the global Modeling Version parameter is irrelevant.

Greatly improved “cathode squish modeling” for cathode biased power amp models. This improves the feel for affected amp types, i.e. Class-A, Mr Z, etc. Two new parameters have been added which allow the user to alter the pertinent variables: Cathode Squish and Squish Time. Cathode Squish sets the amount of bias shift due to cathode voltage rise and Squish Time sets the time constant of the cathode network. These parameters are set to default values upon selection of an amp type. Setting Cathode Squish to zero defeats the cathode squish modeling.

Preamp modeling now uses screen voltage from power amp in calculations rather than operating independently. This improves feel as preamp voltage will drop with power amp sag. The effect is more noticeable as Supply Sag is increased. Note that preamp sag has a long time constant and, as such, the initial pick attack is relatively unaffected while sustained sounds undergo compression. This results in a “chewier” sensation.

Improved single-ended power amp modeling.

FRACTAL AUDIO QUOTES

[35] […] The harder the virtual power amp is driven the more noticeable the improved preamp modeling will be.
Before I was treating the models as separate preamps and power amps as though you were using a rack system with a preamp unit and a power amp. I did some tests and noticed that there is quite a bit of interaction between the power amp and preamp in an integrated amp (combo or head). So now the modeling feeds the power supply voltage from the power amp algorithm back into the preamp algorithm. As the B+ sags (and the screens droop and bounce) the preamp is affected as it will in a real amp.
What happens is that as you hold a note or chord the B+ sags. The preamp voltage sags as well but at a slower rate due to all the extra capacitance and resistance between the screen voltage and the preamp tubes. Eventually the preamp voltages sag enough to compress 10-20% depending on the amp. This is a couple dB or so of compression. It's a slow compression though so your pick attack is unaffected.
I don't think I hear much, if any, difference but the feel is definitely different. It feels a lot easier to play like I don't need to press on the strings as hard.
I imagine the low end will be affected as the compression will cause less drive into the power amp and therefore less saturation at the resonance of the speaker.

Firmware 11

Improved pre-amp algorithms.

Improved cathode follower algorithm. There are three parameters exposed for the cathode follower algorithm: Cathode Comp (which is also the COMP knob), Cathode Time and Cathode Ratio. Cathode Comp sets the amount of compression. Cathode Time sets the attack time of the compressor. Cathode Ratio sets the maximum amount of compression with lower values giving more compression.

Improved power amp algorithms. New algorithms yields smoother highs and more open sound.

Exposed “MV Cap” parameter in Amp block. This parameter sets the value of the bright cap across the Master Volume pot and is located in the Advanced menu.

Firmware 10

Implemented “Multi-point Iterative Matching and Impedance Correction” technology (MIMICTM P.A.F.) to amp models. MIMIC applies analytic signals to an amplifier and captures the fine nuances of each amp at various points in the circuit and corrects each model vs. its theoretical implementation. In some cases the difference can be substantial, in other cases the difference is minimal. This depends on the layout of the amp and the various parasitics involved. MIMIC has the advantage of applying these corrections at the appropriate location in the amp model rather than as just an output EQ so that the various controls of the model behave virtually identically to the actual. For example, the Modern modes of a Dual Rectifier are highly sensitive to Master Volume with the tone becoming thicker as the MV is increased. MIMIC preserves this behavior rather than just getting louder as the Master Volume is increased. The equalization correction portion of MIMIC processing can be turned off in the Advanced menu tab of the Amp block, if desired. Note that the nonlinear correction and other aspects of MIMIC are integral to a model and cannot be turned off. In many cases the equalization correction can be subtle and many not be immediately audible when switched on or off.

Updated numerous amp model details in light of MIMIC's identification of deviations between the models and actual amps.

Tweaked power amp modeling slightly to increase even-order harmonics. This makes most models “sweeter”.

Improved triode modeling removes “glare” from distortion yielding greater clarity and string separation.

Improved power tube modeling gives more punch and pop, especially to tones that rely on power amp distortion. Additionally this provides a more dynamic response, better touch sensitivity and improved pick attack.

FRACTAL AUDIO QUOTES

The models are statistically matched to the amps in both frequency response and distortion profile. In some cases this gives a certain sizzle. Some may not like this but it is accurate.

[36] The amp modeling in V10 is very similar to V9. There are only a few changes to the algorithms. The big difference between V9 and V10 is the inclusion of the MIMIC data and many of the cabs were remixed. Of those two the remixed cabs will be far more audible. So to get that V9 sound the most important thing is to go to the cab block and select the equivalent V9 cab(s). These are indicated by "(V9)" in the name. For example, if you preset is using "1x12 Brit G12H30" it has a remixed cab. Therefore change the cab to "1x12 Brit G12H30 (V9).

Firmware 9

New power amp modeling with improved dynamic response. This new modeling features improved transformer/plate interaction modeling resulting in better feel and a punchier response. The Supply Sag parameter is more responsive as a result. Additionally, crossover and transformer hysteresis distortion modeling is improved resulting in more overtones when playing softly. This improves controlled feedback performance and yields a more aggressive tone at lower Power Tube Bias settings. Note that Version 9.xx is slightly quieter so don’t be swayed by Fletcher-Munson effects when evaluating differences.

Greatly improved cathode follower modeling. The cathode follower modeling now varies the amount of distortion in addition to compression. This results in a more dynamic attack, improved feel and more “punch” and “thunk” (since this also creates low frequency energy into the power amp). The amount of cathode follower affect is controlled, as always, by the COMP parameter in the Amp block. Note that the higher the COMP value, the more effective distortion on sustained notes. Therefore as you increase COMP, you may want to decrease Drive. Also note that excessive values can result in pumping or blocking distortion. Note that the “cathode follower effect” occurs even in common cathode stages as well so even amps that don’t have cathode followers may exhibit some cathode follower-like effect.

Firmware 8

Improved phase inverter modeling provides “juicier” tone when PI is driven hard (MSTR set high).

Doubled resolution of internal amp matching data.

Added input matching data to many amp models. While this may not be audible in many cases, especially for higher gain amps, it does affect the feel.

Firmware 7

The dynamics processing of the amp block was totally rewritten for this release. A complex set of formulas was developed that completely describe the various voltages in a tube amp. Unlike other modelers that simply model an amps dynamics as a first-order compressor, the Axe-Fx II now accurately models the complex interaction of the power tubes with the surrounding circuitry including the power supply and screen voltage network. You may notice a difference in the feel of the various amp models. Please refer to the descriptions below to understand the operation of the various controls. Doing so will enable you to adjust the dynamics to your personal preferences.

Improved preamp modeling. Harmonics now move more with input level which results in a more open and less congested tone.

Firmware 6

Reworked power amp modeling based on new research. The power amp modeling has been totally rewritten based on “amp matching” studies. This includes improved output transformer saturation modeling.

Most amp models have been matched to their respective physical amps. Exceptions are those models which don’t have a physical counterpart, i.e. FAS MODERN, etc. The matching data is integral to the amp block and is transparent to the user. This has increased the size of the firmware slightly and also uses the master DSP for part of the calculations which increases the CPU load associated with the amp block slightly.

FRACTAL AUDIO QUOTES

[37] Almost everything has been reworked. Almost all the "real" amps are "matched" to the actual amp. This involved much more than just Tone Matching. It also included gain matching, harmonic content matching, tone-stack matching, etc.

Firmware 5

"The new firmware (V5) is all about dynamics. The power amp modeling was totally rewritten. If you listen to those early VH albums you can hear the amps knock and ring when he hits them hard. Lots of work went into discovering why that happens and replicating it. It's due to several factors: the power supply sagging, the bias point shifting as the supply sags, the screens ringing and power compression in the speakers." [38]

"Much improved grid modeling in Amp block preamp and power amp stages. New modeling very accurately replicates grid conduction and resulting bias excursion. This results in a more dynamic, thicker and bouncier tone. The power tube grid conduction parameters are exposed to the user in the GUI. The Bias Excursion parameter controls how much the grid voltage droops when the grids conduct. The Excursion Time and Recovery Time parameters control the time constants associated with the excursion."

"Added dynamics processing to Amp block. A new tab, “DYN”, in the amp block, allows adjusting various parameters of the dynamics processor along with several other parameters related to amp dynamics. The Dynamics parameter controls the amount of dynamics processing and models the interaction between the power amp, power supply and loudspeaker under high power-level conditions. The Dynamics Time parameter (ADV tab) controls the time constant of the associated processing."

Firmware 4 and earlier

Amp modeling in the Axe-Fx II was originally called G2 and Virtual Vaccuum Modeling modeling (see Fractal Audio website). Part of it was ported back to Standard/Ultra firmware 11.

FRACTAL AUDIO QUOTES

[39] […] As you listen to clips from modelers what you start to recognize is a certain "stationary" aspect to the tone compared to the every-changing tonality of a tube amp.
Another thing is finger response. With a good tube amp you can vary the tone quite a bit just by how you fret the note and attack it. Modelers tend to make every note sound the same.
So I tested some hypotheses and came to the conclusion that it's because a real vacuum tube has a transfer function that is not static. The transfer function is dependent on time, frequency and amplitude. Where you really hear it is in the in-between regions where the tube is just starting to distort.
At first I tried some dynamic transfer functions but that was a lesson in futility. So then I created the VVT stuff. In VVT there is an actual vacuum-tube replica in software. You enter the values of the resistors and capacitors on the grid, cathode, etc. and it behaves just like a tube complete with Miller effect, cathode memory, etc. The problem is that it requires an obscene amount of horsepower so the only solution was a dedicated DSP.
The other big part of the G2 sound is the output transformer modeling. The OT distorts and as it distorts its inductance decreases which changes the bandwidth and loop characteristics."

MIMIC

Multi-Point Iterative Matching and Impedance Correction (MIMIC) is a technology that identifies deviations in the response of the simulated amplifier to the actual amplifier and generates corrective data bringing a level of accuracy that has been heretofore unachievable. MIMIC was introduced in firmware 10.

MIMIC whitepaper (PDF)

FRACTAL AUDIO QUOTES

[40] If Power Amp Modeling is off, the pertinent aspects of MIMIC are defeated.

Attributed to Cliff:
[41] The whole impetus for V10 was actually due to the Rectos. I hooked up my Dual Recto one day and was A/B'ing to the Axe-Fx. The real amp had this fizz and sizzle on the notes whereas the Axe-Fx did not. If you play a single note you can hear a crackling noise on the decay, almost like frying bacon or something. The Axe-Fx was more of a smooth fuzz on the decay. Outside of a mix context that sizzle can be a bit annoying but in a mix it cuts like mad. Anyways I sat there wondering why the Axe-Fx lacked this sizzle. No amount of tone matching would recreate it. So I wrote a statistical analysis module (it's hidden in the TM block btw) that allowed me to compare the distortion profile of the real amp to the model (there's a hidden switch that gathers statistics along with tone match data). I was a bit shocked at the results. The real amp had a much harder clipping profile than the model. So I tested a bunch more amps and found the same thing. Then I decided that the best thing would be to simply compare the statistics and then have a feedback loop that adjusts the parameters until the statistics match. This, along with the other stuff in the whitepaper, was the foundation of MIMIC.

[42] MIMIC is distortion profile and frequency response matching. Hidden in the debug version of the firmware are special test tones and analysis modules that allow me to compare the real amp to the model.

Axe-Fx Standard and Ultra

Not included on this page.

Amp modeling

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