A transformer as an effect

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I don't know if I need to generate saturation, in a tiny tranny or if a higher power rated one is best?

Try it. That's how you really learn stuff.

Generally, though it seems to be one of those terms that gets thrown in just about every situation, transformer saturation is a somewhat rare occurence in guitar amps and doesn't really sound all that great. It's analogous to chopping off random chunks from the waveform and will generate plenty of high order harmonic distortion.

e.g.
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Yes, sound much, much nastier than typical clipping.

You also need very high voltages and low frequencies to generate this. Basically, you need a bass amp, not a guitar amp. Saturating little transformers with guitar's "mid-range" frequencies and few volts of headroom...? No chance.

I make the assumption that a 600 OHM 1:1 device place in my send/return loop is the target.
I would really expect that FX loops are designed for other impedances than 600 ohms. Using a 600-ohm transformer will in such occasions be an impedance mismatch, which will cause drastic attenuation of low frequencies in a fairly steep curve. Usually what people hear as transformer sound is exactly that: An impedance mismatch kills all the bass.

If they would really hear saturation they would probably think something is horrible wrong.
 
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I've researched, designed and built about a half dozen very good sounding guitar amps. Various power ratings (5 - 60 watt). I've heard that transformers make a big difference, and I think that's an exaggeration. One of my best sounding amps has the very cheapest transformer they sell at Antique Electronics. It's about matching the impedance to the tube correctly, and knowing that if the tranny core is too small physically, it will have distorted and lower level bass. Much more often, the tranny is fine, and the EQ of the amp is the issue.

Electric guitars don't sound very good in a flat FR amp. The midrange is painfully honky, and the treble is very rolled off. They need considerable boost for the frequencies above about 1kHZ, and a 6 or so dB dip centered at around 900HZ is usually desirable. . The tone control circuit is where I'd try to improve the bass response. Use a different tone stack. Use the free Duncan program (which only works with Windows XP, not 7 or 8) to model the circuit and see the variations of frequency response. The "Big Muff" single tone control is actually quite good. Other options include using a different speaker driver. I've been very happy with the Celestion Greenbacks and the Jensen P10R and P10Q. Higher power speaker drivers have less extension of high frequencies, and can sound very painfully honky. I highly recommend using multiple lower power drivers such as the above mentioned.
 
I think the interaction of the output tubes, the transformer and the speaker is too complex to say a soft limiter is about the same thing. Any speaker is a significantly reactive device, with impedance that varies in real-time, and in a steady state measurement over frequency. This reactive element is reflected through the transformer to the tube, the gain of which varies depending on the loading effect it sees (in real time). Real-time means instantaneously, as in part of the waveshape will have a different loading effect on the tube than a different part of the same period of waveshape.

Negative feedback lowers the output Z of the amp, which reduces the speakers ability to resonate, but also raises the frequency of the resonance. The way a tube/tranny/speaker distortion mechanism varies with amplitude, frequency and with a combination of energies at many different frequencies (real world) is IMO what makes this distortion pleasurable. Any distortion that always sounds the same gets old after a while.
 
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