An Amplifier Change for my Wilson Sophia 2's?

Hi Mark,

I can’t comment on how much amplifier power is likely to be optimal with your particular speakers, or on which amplifiers are likely to be particularly synergistic from a sonic standpoint.

But I agree with JPerry’s comments, to which I’ll add the following thoughts:

1)The two considerations referred to in my first paragraph figure to be inter-related, such that more or less power may be optimal depending on the design and sonic character of the particular amplifier.

2)The amplifier’s effects on volume control position depend on its gain, not on its power capability. There are many amplifiers that provide a combination of relatively high gain and relatively low power capability, and vice versa, although in general there tends to be a **loose** correlation between gain and power capability.

3)How much power is required is often determined by the dynamic range of the music that is listened to. In most circumstances not a great deal of power is required for most recordings, at least most of the time. But on recordings having a particularly great difference in volume between the loudest notes and the softest notes, such as some well engineered minimally compressed classical symphonic recordings, enormously greater power capability can be required to support their brief dynamic peaks than under most other circumstances, and at most other times during those same recordings.

Good luck. Regards,
-- Al

So if an amp i choose has more gain, that could be a benefit for the volume issues I have spoken about before.

It would lower the setting of the volume control that you would use to achieve a given volume level, everything else being equal.

And if the amp also has more wattage, it can control the speaker better ...?

Not necessarily.  That depends on several different characteristics of both the amp and the speaker, including amplifier damping factor and output impedance, how much damping is optimal for the particular speaker, how the speaker's impedance varies over the frequency range, the robustness of the amp's power supply, etc.  The bottom line is that it's hard to predict.

And if the amp also has more wattage, it can ... perhaps provide a better sound with high dynamic range music?

Stereophile measured the sensitivity of the Sophia 2 as being 88.3 db/2.83 volts/1 meter.  For its 4 ohm nominal impedance that corresponds to 85.3 db/1 watt/1 meter.  Neglecting room effects an amplifier capable of providing 100 watts into 4 ohms should be capable of driving a pair of speakers having that efficiency to a maximum SPL of about 99 db at a typical listening distance of around 10 feet.  That will be adequate for the great majority of recordings for the great majority of listeners. 

I for one happen to be among those for whom that kind of maximum volume capability would be inadequate, though.  I have a lot of classical symphonic recordings on audiophile-oriented labels such as Telarc, Reference Recordings, Sheffield Labs, etc., that have been subjected to minimal or no compression, and can reach 100 to 105 db at my listening position, on brief dynamic peaks, while being listened to at average levels of perhaps 75 db.

Would the increase of wattage of the amplifier allow me to hear the music better at lower volumes as well?

Again, it's hard to predict, and from a subjective standpoint it may depend on how the distortion characteristics of the particular amplifier vary as a function of the amount of power it is putting out.

All I can add at this point is that if you already haven't it may be worthwhile to research the Audiogon Virtual Systems to see what amps others have used with the Sophias.

One final point:  As with many ARC line stages and preamps, ARC recommends 20K as the **minimum** load impedance that should be presented to the LS25.  Keep that in mind in considering other amplifiers.

Best regards,
-- Al
 

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

The signal response measurements are done at 1kHz.

Most ARC amps have lower effective output impedances than the majority of tube amps, and the VT100 is no exception to that. Specifically, it has a specified damping factor of 11, which for the 4 ohm tap corresponds to an output impedance of approximately 4/11 = 0.36 ohms. Per JA’s measurements the minimum impedance at any frequency of the earlier version of the Sophia is 3.26 ohms, with a near-zero phase angle (i.e., an impedance that is almost purely resistive) at that frequency. And at nearly all other frequencies the impedance is significantly higher.

As you’ll probably realize, the result of the interaction of that kind of amplifier output impedance with those speaker impedance characteristics will be not much different than would occur with a solid-state amplifier, namely very little variation of output voltage as a function of frequency. And yes, in a narrow range of frequencies in the area of about 40 to 50 Hz, where the speaker’s impedance rises to around 14 ohms (assuming the speaker’s impedance characteristics are similar to those of the earlier version of the Sophia), and also in the upper treble region where the impedance also rises significantly, the amplifier’s power capability will therefore probably be significantly less than at 1 kHz. As a result of limitations that presumably would occur in output voltage, however, not as a result of limitations in output current as you had stated.

However in the rest of the deep bass region, as well as in the mid-bass and mid-range regions, which encompasses the regions where most music contains most of its energy, the 1 kHz power capability measurements can be expected to be essentially applicable.

Regards,
-- Al

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