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).

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: