Using tube amp with electrostatic speakers.

I agree the fact that you or your customer(s) have tried it, and it sounds good, would trump my purely mathematical analysis.  And you are correct in noting that the formula I used does not take into account the third variable, which is the intrinsic change in speaker impedance vs frequency (although my off the cuff thought on that is that the actual -3db point with no resistor would be boosted above the calculated 4400Hz by a greater degree than is the calculated vs the actual -3db point with the 10 ohm resistor, because speaker Z is going down as frequency goes up, and the -3db point is inversely related to total Z).  

Something in my memory is telling me that both Will and I did try removing the resistor from the RC network in front of the old toroid, before proceeding on to Will's ultimate solution.  And the sound did improve when we did that, although not to the degree that we heard/hear with the replacement of the treble-only transformer with a full-range one and no R OR C in the circuit.  Anyway, I am happy that everyone else is happier, no matter how they got there.

@lewm 

Yes, the tricky bit is that the transformer impedance increases as frequency goes down. So with a given capacitance with increasing impedance, the crossover point moves lower- there is no set crossover point! This is why the resistor is there, so that the crossover point is not a moving target- the resistor dominates the formula of the -3db point. Removing it theoretically would open the transformer up to saturation caused by too much bass, but in practice I've not heard of that happening.

At any rate Dr. West seems to have it sorted with the newer Toroidal 2 version, and thanks goes to you for pointing out the problem with his simulation from years earlier.

atmasphere

Thank you for this explanation as it gets to the heart of the matter.  I just want to make sure I understand this correctly.  What occurs to the sound of the speaker when the transformer saturates or begins to saturate?  Is transformer saturation a voltage or current issue?

Are you saying:
1. That the resistor is not needed for either the Toroid l or Toroid ll?
2. That the concern of transformer saturation does not occur (at higher input signals) because:
     a) at higher frequencies the music power requirements are typically not high (so the Toroid will not/does not saturate); and    
     b) the Toroid impedance increases at lower frequencies to a level that the Toroid cannot saturate even with a higher voltage signal (in other words the Toroid by it's impedance nature is self-limiting to prevent saturation?).

Regards,
Gary

What occurs to the sound of the speaker when the transformer saturates or begins to saturate? Is transformer saturation a voltage or current issue?

Distortion- Its pretty obvious. Its a power issue- both current and voltage (of which neither can exist without the other).

Are you saying:
1. That the resistor is not needed for either the Toroid l or Toroid ll?

Not needed for the Toroid 1, needed for Toroid II

2. That the concern of transformer saturation does not occur (at higher input signals) because:
    a) at higher frequencies the music power requirements are typically not high (so the Toroid will not/does not saturate); and    
    b) the Toroid impedance increases at lower frequencies to a level that the Toroid cannot saturate even with a higher voltage signal (in other words the Toroid by it's impedance nature is self-limiting to prevent saturation?).

We're talking here mainly about the Toroid 1:

Bass energy can saturate the core of the part, because it was built with intention to optimize higher frequency performance. In practice it does not saturate with low frequency energy simply because its impedance is so high at lower frequencies (and there is a capacitor in series with its input) that most amps can't make any power at those impedances.

The Toroid II:

The crossover of the resistor and capacitor prevent lows from entering the input of the transformer; otherwise it too would saturate because its core is too small just like the Toroid 1.

Atmasphere,

Thank you very much for that explanation.

Best Regards,
Gary