Guitar Amp Attenuators: How close to match amp impedance?

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Ive been designing and testing passive attenuators over the last year or so (thanks for some great insights about them on this forum). The results are working out well, and several others have built them too. Here's a page on the Marshall forum with the latest:

Simple Attenuators - Design And Testing | Page 11 | MarshallForum.com

The key to the designs is to control impedance, seen not only by the amp but by the speaker too. We get good consistent tones at all attenuation levels.

But here's my questions, looking for your opinions!

Lets say the attenuator is intended to use an 8 ohm amp tap. An 8 ohm speaker will be close to this at mid frequencies. But seen through a passive attenuator, the amp will see a somewhat different impedance, dependent on its design. How close does it need to be to work safely with any such amp? Variation arises through component values, and switching design. Closer matching adds complication or constrains versatility.

Ive been working on keeping nominally 8ohm settings to between 7 to 10 ohms seen by the amp at around 440hz. Does that seem reasonable? Many commercial designs go outside that range.(eg Weber, Airbrake)

At other frequencies, in my reactive version, I try to follow the typical rise in speaker impedance with frequency.
 
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Thanks for those views, which are helpful.

Here's where Ive got to in this thinking:

I think that one can consider the output characteristics of a tube amp driving a speaker in terms of first, small signal response, and then secondly,response to larger signals where the power amp is being pushed into non-linearity. An attenuator between amp and speaker can't sound right unless at least the small signal response is correct, and this is subjectively about 80% of the whole.

At small signals, the amp has a fairly consistent, essentially resistive output impedance that varies little with frequency. Its surprisingly high, dependent on design and how much NFB is in place. With my two Marshall amps, Ive measured output resistance of 20ohms or more with 8 ohm amp taps. (done by feeding in a small signal and measuring output with two different resistive loads, at a couple of frequencies, and back-calculating). The high output R lets the speaker reactance develop its rise in response with frequency and its low resonance.

So an attenuator needs to not only keep control of input R but also show the speaker a consistent high output R. I target around 20ohms.

The best simple building block for a resistive attenuator module, to control both input and output resistance, is a T pad, with three parts. But at around -7 or -8db, the leading resistor can go to zero and we have two resistors in a reverse Lpad arrangement, with 8ohm seen by the amp and around 20 seen by the speaker.

You can take those modules and stack several of them end to end for more attenuation, but still consistent tone.

Now, relative to my question above, if I want an attenuation module other than -7db (based on those parameters), something needs to give a bit. If I accept that the amp sees 10ohm, I can do a module with around -3.5db, which is a nice small step. Or, adding the third resistor to a T pad lets attenuation go to lower db. But if I accept a lower resistance seen by the amp, I can keep to two resistors. This lets me do a -14db module, if its stacked after a -7db module.

With all of these, I can do a chain of resistive attenuator modules that keep small-signal tone consistent, across a range of steps, down to any level needed, within a reasonable range of R as seen by the amp. The amp always sees close to 8ohm (+/- as noted), and the speaker always sees around 20(+/-).

The last 20% of the performance comes from adding reactance at the front end, so the amp responds to it. This becomes significant as the amp gets pushed harder. I try to capture the rise in impedance at high frequency that a speaker shows, but I'm not bothering with modeling the low resonance (the speaker can develop that itself, and it takes much larger L and C components to try to model it to show that response to the amp too). I use two inductor coils in the first stage, to show the amp a reactive load similar to a speaker, then also to compensate for it so that the resistive modules downstream keep their consistent tone
 
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… The high output R lets the speaker reactance develop its rise in response with frequency and its low resonance. ...

It is more precise to say that the high amplifier output resistance allows a relatively high voltage to develop across the speaker, when the speaker impedance rises.

Also keep in mind that the tone, when the amplifier output stage is distorting, depends on the reactance that the load (speaker, attenuator or their combination) presents to the amplifier output stage. This is because the load line of the output stage 'tries' to become elliptical when the load is reactive and follows a different path on the Vgk = 0 limit.
 
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