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Transformer Match vs. Speaker Impedance

FractalAudio

Administrator
Fractal Audio Systems
Moderator
Why does 9.xx have these two separate controls?

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).
 
Last edited:

mesaboog

Inspired
Why does 9.xx have these two separate controls?

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 = 160 / 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).
Uummmm...run that by me again.
SmartSelect_20190928-101147_DuckDuckGo.jpg
 

Sharka

Experienced
Why does 9.xx have these two separate controls?

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 = 160 / 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).
 

JoKeR III

Experienced
Well, so much for thinking I was good at math....o_O. Seriously though, great information...I got lost in the formulas and had move to the explanations at the lower part of the post...but wow! Not only taking the time to explain the why but giving us practical ideas of how we mortals can implement and experiment with the new parameters. Thanks Cliff, you ROCK!!!!
 

chucma

Power User
Ah yes, this is in fact very similar to how they designed the Rockwell Retro Encabulator, although IMHO the dinglearm in the AxeFX probably needs it's thrusters adjusted a little.
https://youtu.be/RXJKdh1KZ0w

Thanks for attempting to help clueless wannabes like myself understand your awesome world Cliff, you are a legend in science and music!
 

Joe Bfstplk

Power User
Why does 9.xx have these two separate controls?

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 = 160 / 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).
Great, clear, concise (at least to another math geek and tube amp builder) explanation!
 

shatteredsquare

Power User
i will return to this sticky the next time i'm feeling smart

amps with no negative feedback (AC-30, Dual Rec) should respond drastically to speaker impedance adjustment yes? since the speaker impedance in those amps has such a strong EQ effect on the way the power amp distorts. can't wait to try this out
 

Joe Bfstplk

Power User
amps with no negative feedback (AC-30, Dual Rec) should respond drastically to speaker impedance adjustment yes? since the speaker impedance in those amps has such a strong EQ effect on the way the power amp distorts. can't wait to try this out
Yes.

Negative feedback effectively lowers the impedance of the output section, so it damps the speaker resonances and treble impedance rise a little bit.
 

REDD

Power User
The question is, how do you figure all that out and then model it with code? Top secret?
 

Adman103

Experienced
I really enjoyed reading all this! Thank you for such a detailed explanation. One of my favorite sounds back in the old real amp days was my old 6G6B Bassman with a 4 Ohm output into an 8 Ohm WGS Reaper.
 
Why does 9.xx have these two separate controls?

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 = 160 / 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).

Exactly what I was thinking...

The first sentence that is...totally missed the middle part...but loved the ending!
 

trancegodz

Power User
I noticed years ago that my real Marshall Plexis sounded best to me when the amp was set at 8 ohms and I was using two 16 ohm cabs (for an 8 ohm load). How do I set the new speaker impedance to equal this?

I sometimes used the Plexi set to 16 ohms with one 16 ohm cabinet. How do I set the new speaker impedance to equal this?

I sometimes even set the Marshall to 4 ohms and used four 16 ohm cabs. How do I set the new speaker impedance to equal this?

I never mismatched the head and cab impedance for fear of damaging the amp, though this wouldn't be an issue with the Axe FXIII.
 
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