Speaker sensitivity ratings and amplifier power

10 * log (power) = decibel

10 ^ (decibel / 10) = power

10db increase (10x the power) is perceived as twice as loud

Most desktop-size speakers are in the mid 80s db/W @ 1m sensitivity wise. We’ll call it 85db for the sake of calculating stuff. The sensitivity rating means that with one watt of power, you’ll get 85db of sound at one meter away. For reference, 80db is pretty loud. It’s about the level of a running garbage disposal or an alarm clock. You can listen at 85db for eight hours before you start risking hearing loss; this is also the sound level at which OSHA will fuck your shit up.

For nearfield listening, there may be less than a meter between you and the speakers. If you halve the distance, you can add 6db to the sensitivity rating. Now with the same speakers you’re getting 91db at half a meter with one watt of power. You should probably turn it down a touch to protect your hearing (2 hours at 91db is the maximum recommended duration). Every halving of the power deducts 3db, so one quarter of the power (0.25W) gets you back down 6db to a non-litigious 85db. If you want to listen at 80db (which is comfortably loud, believe me) you only need around 100mW.

Aren’t decibels fun?

This goes to say that you do not need a whole bunch of power for nearfield listening, even if the speakers have a low sensitivity rating. And if you have high sensitivity speakers in your “main rig”, a single-ended low wattage amplifier works there, too. Say you have speakers rated at 95 db/W @ 1m and like to listen around 80db. If you listen at one meter, you only need 32mW. If you listen at two meters, you need just 125mW of power.

The above discussion of power and decibels does not take into account dynamic headroom. It’s always good to have some power in reserve for music dynamics. Or for cranking it when OSHA isn’t paying attention. I try to have at least 10db to spare (10x the power) over what I expect my average listening levels to be. If you didn’t fall asleep while I fapped around with decibels and logarithmic math, you noticed that average, safe listening levels (80-85db) need only a fraction of a watt with average sensitivity speakers nearfield or high sensitivity speakers at a regular distance.  Ten times more power is just a couple watts and will often get you pretty comfortable listening levels with headroom to spare.

Just make them some high quality watts.

Back at it finally!  This is an excerpt from the first speaker amp write-up I’m doing for the site.  Happy Cinco de Mayo!

New Project: La Luciérnaga (PSU)

This write-up will have two parts.  The first (the PSU) is posted and hopefully I’ll have the amp write-up done shortly.  This project is the most ambitious one I’ve written up for the site so please excuse the omission of some of the finer calculations and details.

Although the power supply is rather complicated, the amplifier will be pretty straightforward (pinky swear). The supply can be used with other amps and the amp can be used with other supplies, which is one of the reasons I decided to split it into two pages.

Click here to descend into the madness!

WTF Daydreams: Going Commercial

I was thinking on this topic yesterday (while in an economics lecture). One of the issues standing in the way of making a living from building tube circuits (aside from capital) is that there are few concrete competitive advantages that can be maintained in the long run. Tube circuits are no longer patented for the most part and so any company that sees sudden success signals to other potential participants that there’s money to be made. More participants shifts supply up, which shifts equilibrium price down. So the market price hovers around a modest break-even (priced around marginal cost, like commodities).

Perhaps that is too textbook (and also sophomoric; I’m not pursuing a degree in economics), but I think there’s some truth to the idea that tube circuits are largely unprotected from copycats and so the tendency for successful ideas to become commodities is at play. So, what other potential competitive advantages are there?

  • Schitt seems to have found a place in the market as a low-cost manufacturer of some tube products (mostly headphone). In a way, they have a first-mover advantage here as they got into large scale production of tube headphone amps as the market began growing (still is, I think). The first mover approach is to grow as fast as possible to raise the barriers to entry for potential competitors. The caveat is that constant growth and diversification is necessary to stave off these nagging competitors (who are motivated by the amount of success they perceive you have).
  • Historic companies like McIntosh Labs have brand equity that simply cannot be replicated overnight. Although there are plenty of alternatives in terms of comparable products, McIntosh has done a really good job with their image and catalog (IMO). Failure for them would probably be more self-inflicted than competition-based if it ever comes (selling out, not keeping up with costs, poor management, etc). Their advantage is that they can charge a premium price that would be unrealistic for start-up competitors.
  • The most interesting example I can think of is those companies that thrive on outrageous claims and marketing (ie snake oil audio). Their competitive advantage is imaginary, but to a large amount of people that doesn’t matter. If a competitive product appears, these companies can simply wave it away because it doesn’t have their personal flavor of delusion baked into it. Not that I condone this approach, but there’s no denying it’s out there. Look at an audio commodity like cables and how they are marketed.

So I think getting into tubes as a business requires a very real evaluation of what competitive advantage a company could bring to the market and how it can be protected in the long run (there are more strategies than those above, to be sure). In the short run, coming up with a good sounding circuit or a cool look will always sell a few amps, but success will always invite copycats and push price down.

Updated El Estudiante BOM

After talking to a couple of builders that had parts questions, I’ve updated the BOM pdf on El Estudiante to provide a little more guidance. I avoided providing explicit part numbers initially because I didn’t want anyone to think that deviating from a BOM is wrong. So part numbers are now on the BOM, but please feel free to experiment!

On the bench: Zenith K731 (7M07)

This poor radio has seen better days and doesn’t quite live up to modern safety standards with regards to mains electricity.  But the look is great and there’s generous space inside for a small tube amp. Because the enclosure must be allowed to vent for the tube amp to dissipate heat, the speaker (which I also plan to modernize) will be a small challenge. This is a great candidate for a DIY tube radio restoration.

Probable features:

  • 3-5W single channel output
  • Bluetooth connectivity
  • Aux input (analog)
  • Volume control
  • EQ (either treble/bass knobs or loudness contour)
  • Safety!

 

DIY tube RIAA calculator sheet

All-In-One RIAA Calculator

Here’s a spreadsheet I built for calculating RIAA values in two stage tube phono preamps. When comparing results to other published designs using the same filter network, everything looks correct (within a few percent due to estimation of Rp). I used this sheet for El Matématico.

If you want to estimate values for something like a CCS loaded stage, you can set Rload on the appropriate stage to 1M or thereabouts. If you’re looking at using a cascode, mu follower, SRPP, etc 1st stage, you’ll need to make sure the Zout figure the sheet uses (cell I6)  reflects the Zout of the topology because it is used to calculate R1. Same thing goes for cell I3 (Miller capacitance of 2nd stage) if you use a gain stage after the filter that affects this (cascode, grounded grid, etc).

Go build a phono preamp!

New page: I/O Impedance

io z

I split the impedance and reactance pages into two because it was way too much math/theory lumped together. Impedance is now here. Impedance (as a concept) is really not too abstract. It’s once you start involving frequency dependent impedance that things get really messy.  Messiness and simplified explanations now have their own pages!

“All-tube” MC phono preamp (continued)

Not long ago I wrote a short post about MC carts and the noise contribution of tubes when amplifying such tiny signals. I focused on step-up transformers as the solution to noiseless amplification, but there is another approach.  If you don’t like solid state, stop reading. Ok, now that you stopped reading and checked out the going prices for step-up transformers, you’re back. Good. Don’t worry, this approach uses the tubeyist solid-state device: the JFET.

A cascode is a compound amplifier in a totem pole arrangement. Here’s a great explanation by Valve Wizard Merlin. This allows you to achieve huge amounts of voltage amplification with fairly economic current usage and without coupling capacitors or multiple phase inversions. The driving force in this arrangement is the transconductance of the lower tube. The lower tube and upper tube do not need to be the same, nor do they even need to be the same type of device.

JFETs (junction gate field effect transistors) are voltage controlled devices, just like tubes. In fact, they bias in a very similar way: Rsource in the above raises the n-type JFET’s source voltage above the gate, similar to the way a cathode resistor in a grounded cathode amplifier raises the cathode above the grid. On the other hand, even the lowliest JFETs have a higher transconductance (gm) than the mightiest small-signal tubes. Icing on the cake is that JFETs, properly chosen and cared for, are lower noise devices. As such, they make a great lower device in a hybrid cascode.

The overall gain of a cascode simplifies to approximately:

gm(lower) * Rload

This equation is a simplified expression of the total gain of both devices:

[gm * (Rp + Rload) / (Mu + 1)] * [(Mu +1) * Rload / (Rp + Rload)]

AKA [JFET gm * load divided down at tube’s cathode] * [grounded grid gain of tube]

Rp and Mu are characteristics of the tube upper device. The choice of upper device affects how much of the voltage gain is performed by the JFET by affecting the load it sees. A high Mu and low Rp upper tube (i.e. high transconductance) presents a lower load as divided down at its cathode, thus less voltage amplification by the JFET (and more voltage amplification made up by the tube due to the higher Mu). A low transconductance upper tube does the opposite. But regardless of the tube (assuming an appropriately sized Rload), the overall gain remains the same: ultimately the transconductance of the JFET multiplied by the load on the upper tube.

So where’s this headed? Obviously there’s a full design coming to try out this idea, but the takeaway is that a hybrid cascode is potentially a great way to step up the tiny signals from a moving coil cartridge with very low noise and hand the now-larger signal off to a tube amplification stage without multiple supply voltages, coupling caps, or an expensive step up transformer.

The catch? Cascodes have poor power supply noise rejection and a fairly high output impedance. But there are ways to minimize these factors, too.

Further recommended reading: 1, 2, 3, 4