An Amplifier Change for my Wilson Sophia 2's?

Hi Mark,

Regarding the relationship between gain and wattage, as I mentioned there tends in general to be a loose correlation, but one that is so loose that it is typically of no usefulness.

As you’ve probably found, the gain of both integrated amplifiers and power amplifiers is very often not specified. If Stereophile has reviewed the product the measurements section of the review will usually indicate the measured gain. In other cases the gain can be calculated to a reasonable approximation from the specified maximum output power and the specified sensitivity (the input voltage that is required to drive the amp to the specified maximum output power), as follows:

Gain is the ratio of output voltage to input voltage, expressed in db.

The ratio of two voltages, V1 and V2, are converted to db based on the formula (20 x logarithm(V1/V2)).

The rated maximum output power into 8 ohms (or 4 ohms) can be converted into voltage based on the equation P = (Vsquared)/R, where P is power in watts, V is volts, and R is resistance in ohms.

So for example in the case of an amplifier rated at 200 watts into 8 ohms and having 2 volt sensitivity, if we represent the output voltage corresponding to the 200 watts into 8 ohms as "Vout" and the 2 volt sensitivity as "Vin," we have:

200 = ((Vout)squared)/8

From which it can be calculated that Vout = 40 volts

Therefore the gain in db is

20 x log(Vout/Vin) = 20 x log(40/2) = 26 db

That is an approximation, as I indicated, in part because it does not reflect margin that may be built into the maximum power specification. But it will generally be a reasonably good approximation for most purposes.

Also, note that for a tube amp having 4 and 8 ohm output taps the gain will be approximately 3 db less for the 4 ohm tap than for the 8 ohm tap.

If you have a scientific calculator these calculations are very easy to do. Alternatively, the calculator that is built into Windows can be set to scientific mode, although I find using it to be somewhat clumsy.

Best regards,
-- Al

Well, Al,
If you and few other poster were speaking about where 100W per channel can bring Wilson Sophia, it’s not truly the case and I’ll explain why.
That ARC VT100 would be able to supply to my guesstimate only a third or a quarter of specified power which is only 25...30W realistically at highest volume setting. Although tube amps soft-clip, there’s still not enough CURRENT to move drivers and therefore actual power halves or even quarters. ARC line preamps in general have 20dB of gain so combined 80dB of gain is substantially enough -- no need to move gain higher to 73dB.
Mentioned earlier Bryston 3B-st or 3b-sst/sst2 amps can do much better job but still not enough.
As I’ve mentioned before 250W Electrocompaniet amp wasn’t enough either. It was loud enough, but no 3d and imaging.
400+Wpc/8Ohm and 600+WPC/4Ohm is about right ’prescription’ otherwise money wasted.
There’s one Sunfire Sig 600 for sale here on audiogon and I wish to stretch my budget and get it. I was foolish not to get it at more than half of price years ago, but trust me It’s the best amp ever made for any budget.

Increasing from 100 watts to 400 watts would give another 6 db of volume. Doubling the watts equals a 3 db volume increase. A volume increase of 10 db would sound twice as loud twice as loud.

In other words the starting point isn't 100 watts. Try going from 30watts: 60, 120, 240, 480 ... 12dB -- Now these figures bring you much closer to reality.

Czarivey,

what at do you think about bryston 4bst or a pair of 7bst monos?  They are in the same price category of my vt100.  

That ARC VT100 would be able to supply to my guesstimate only a third or a quarter of specified power which is only 25...30W realistically at highest volume setting.

I would respectfully but completely disagree with this, Czarivey.

First, most tube amps providing 4 and 8 ohm output taps have the same or similar power ratings when a 4 ohm load is connected to the 4 ohm tap as when an 8 ohm load is connected to the 8 ohm tap. As you realize, a 4 ohm load requires more current but less voltage compared to delivery of the same amount of power into an 8 ohm load. And that difference is accommodated by the different output transformer winding ratios that are used for the two output taps.

In this case the amp is rated at 100 watts, and the measurements provided in Stereophile Volume 20 No. 3 for the original (non-MkII version) of the VT100 confirmed that that rating is essentially accurate for BOTH load impedances, when the corresponding output tap is used. (Aside, that is, for a very slight shortfall of well under 1 db that he measured in one channel, which was suspected to be due to a weak tube).

Furthermore, JA’s measurements of the impedance magnitude and phase angle of an earlier version of the Sophia speaker (linked to below) indicate impedance characteristics that are particularly benign relative to those of many and probably most other speakers that are rated as having nominal impedances of 4 ohms.

www.stereophile.com/content/wilson-audio-specialties-sophia-loudspeaker-measurements

Regards,
-- Al

I've known lots about price categories, but quit worrying about that long time ago.
Sunfire sig 600 was the amp able to make WS speakers literally disappear and bring REAL stage.
If you compare depreciation of 7bst vs. sig 600(both were actually manufactured at nearly same time), 7bst lost near 70% of value getting close to the end of bullet-proof Bryston warranty and sig 600 haven't lost a penny and sold often for higher dollar now than it was new.
That should tell quite something I dare to believe. 
There's no doubt to the quality of that amp despite being one of the first class D amps in high-end audio and if I had $30k+ speakers, I would be more than confident hooking them up to this unit.

Al,

The signal response measurements are done at 1kHz. Therefore for some particular reason called 'X', OP asks the question 'Y' for some same reason everything is perhaps 10...12db hungry of SPL and there's one analogy answer that speaks for itself:

If you have glass of water and you try to fill-up the jar, you will need much more than one glass of water.