How much do I need to spend to get a preamp that sounds better than no preamp?

Hi George

You are making an assumption in your last statement:  That an impedance value is all that matters.

Unfortunately, the universe is not quite that simple.  The type of output stage that provides the "100 Ohms" impedance (not resistance...) plays a huge role in the frequency domain performance, which is ultimately what we care about with music as the signal.  

At one single frequency, you may indeed measure 100 Ohms, like say at 1 KHz (a popular choice).  But this value is made up of resistance, transistor gain effects, and parasitic capacitance, of which the latter two are extremely sensitive to frequency, and temperature, and are intimately tied to the circuit design and its parts. 

One of the goals of an amplifier designer is to minimize these effects through a combination of clever design techniques that have proven their mettle.  However, not all output stages have the same frequency response (i.e., impedance at all frequencies).  In fact, there are hundreds, if not thousands, of topologies and permutations, and they all have varying limitations.  Some are good, some are ok, some are mediocre, and none of them are perfect.  Which you get depends partly on design budget, but mostly on the engineer's design experience.

But wait, there's more:  it is the same story for the input impedance of the amp or preamp!  Then, when you combine them together, they will interact in yet a third (new) way!   Especially with complex signals like music. 

So, at the end of the day, it's a crap shoot.  There really is nothing definitive in this crazy world we live in.  With a preamp might better, might not, have to insert a human in the feedback loop and check.  But then that simply becomes their opinion, and how definitive is that?

Most sources have output stages the equal of preamps today, except for wimpy capacitor coupled tube ones.

Cheers George

“No preamp” is a straight wire. It will add no noise, no distortion, and in 99.9% of cases no frequency response anomalies.

There is not a preamp made that has the same characterics. Thus, there is no amount of money that can be spent on a preamp that will sound better that a straight wire.

There are reasons someone might prefer a preamp to a plain interconnect. These include gain, impedance matching, and pleasurable distortion.

Personally, I have retired my preamps (I have three to choose from) and have my DAC connected directly to my amplifier. It is better. 

Hi OP

The gain control is varying the tube's circuit gain.  The volume control varies the level of the input signal.  They are completely different animals.

You can just put the gain control at some random point like 3:00, but is that the optimal point?  Not clear.  One would need to know a lot about the circuit design to make that call.  I'm not surprised AI isn't getting involved in the answer, as it can be quite complicated.  It's also why few amplifiers actually have gain controls (except for vintage ones, and that was because of the wide variety of speaker efficiencies back then).  

My suggestion is that you try a range of settings.  There is likely to be one spot you prefer for a 'given volume level.'  Most gain circuits have a sweet spot.  It will still work outside of that range (since they made it available to you to adjust) but it won't necessarily work as well (e.g., less linear).

What I do is listen one night with it turned all the way up.  Then the next listening session, turn it most of the way down.  Use the volume control to set the music at about the same level for both sessions.  Then try turning it to the midpoint, then vary from there, etc.  Trying the two extremes first will help you "frame" a reference point to fine tune the setting.  My MC240 clearly sounds its best between 1:30 and 2:00, but your results could be completely different.