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!

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!

Coming soon to a workbench near you…

In a world where near-field and headphone listening has become an unstoppable force. Where every DIY builder is bored to death of rational and safe two-stage, single-ended triode designs. Where power supplies have become an afterthought and parts values are just plugged and chugged. Prepare your butt for a new madness. Prepare it for La Luciérnaga…


Note db scale for the predicted frequency response graph: +/- 1 dB from 40-20khz. If that’s not good enough, I’ll show you how to make it even better. There’s mucho tube math coming your way, amigo.

Here’s the worksheet I used to create the above:


An open letter to transformer manufacturers…

Dear transformer manufacturers,
Here’s a quick list of existing products that I have found with comments on their suitability for the DIY market. This is followed by blue-sky ideal output transformer specs.
Edcor PCW10k-7k/300-32: this is a nice low cost but suffers the same issue as all of Edcor, namely lead time and lack of availability overseas.  The turns ratios and secondary taps are just about ideal for headphone applications (which I believe it was originally intended for).  The board mount style, on the other hand, is less than ideal for most hobbyists.  With a rating of 0.5W, 15Vrms on the primary, and no published inductance figures, it also hasn’t really seen much interest from a lot of the community. That said, it’s the only non-custom North American option I know of. This is non-gapped single-ended so it’s limited to parafeed applications. Honorable mention to Edcor’s WSM and XSM series, though.
Sowter options: by all accounts these are very nice non-custom options, but they are difficult to get in North America and the price is very high. The way the secondaries are wired also makes switching or wiring multiple jacks difficult. Because most headphone enthusiasts have multiple pairs at different impedance, using an output transformer with an easily switchable secondary tap is preferred to ensure consistent load reflected to the output tube. The Sowters don’t make this easy, unfortunately. Most of the Sowters are gapped for normal series-feed single-ended power. End-bells are nice.
Lundahl LL2765: this is a fancy c-core option with a secondary arrangement similar to the Sowters. The same caveats about easily switching the impedance configuration apply. The turns ratios and impedance options are close to ideal for the headphone market.  I haven’t been able to find a price (Lundahl is distributed by K&K Audio in the USA, though LL2765 isn’t on their price list). I expect it’s in the $200+ each range. No end bells, so no fun in showing off the iron. It’s available with a gap (series-feed) and without a gap (for parafeed or push pull operation).
As a DIY headphone amplifier designer and enthusiast, what I’d love to see is an output transformer that is readily available in North America and Europe at an affordable price.
Headphones broadly fall into impedance categories of 200-300 and 32-75 ohms (with most recent products trending towards the lower impedance). I think secondary taps of 200 and 50 ohms would make sense as these would be a ratio of 4:1 for full winding and center tap, easily selectable with a switch. The center tap secondary, rather than asymmetrical taps, might make this transformer useful for other balanced applications as well (and if so, might as well put a center tap on the primary, too).
A primary impedance of around 8k would work well for a good range of tubes. If rated for 8k:200, we’d have a turns ratio of about 6.3:1. With 300 ohm headphones it would provide a 12k impedance and with 150 ohm headphones it would provide a 6k impedance. If using the 8k:50 center tap, it would provide a turns ratio of 12.6:1.  That’s about 5k with 32 ohm headphones or 12k with 75 ohm headphones. All these numbers would work fairly well with small popular single-ended tubes (EL84, 6V6, 6S45Pi, etc).
The transformer would ideally be rated for 2-3W.  Headphone users are as silly about their power as speaker users are.  Never mind that they only need a few mW to reach 100db. Frequency should be rated 20-20k +/- a db or two or the transformers would be ignored by spec snobs. More similarities to the rest of the high end audio market there.
Gapped and rated up to 50mA would be excellent, but not if it compromises the frequency bandwidth through low inductance or the cost by making it huge. A non-gapped transformer for single-ended headphone amps works a little better than for speaker amps because we can use it as parafeed, keep the B+ voltage reasonable, and still make plenty of power. Non-gapped and an exotic metal core would be even better, but I don’t see it much in most transformer catalogs.
So, TL;DR, what I think would be ideal is:
– 8k:200ct impedance
– 2W+ rated output
– 20-20k rated bandwidth
– $100 per pair (less is better)
– option for end-bells
– gapped (~50mA if possible) or un-gapped
Turning that into a small product line, I could see it working out as something like:
– 2W gapped, no-end-bell
– 2W gapped, end-bell
– 4W un-gapped, no end-bell
– 4W un-gapped, end-bell
I’d imagine the cores for the above would be around similar sizes, so materials and winding are more or less consistent, but the more in depth transformer permeability math isn’t something I regularly do. The only differences would then be in adding a gap and/or adding end-bells, making a pretty efficient line in terms of manufacturing and materials.
As you probably know, the headphone market is growing pretty quickly.  Perhaps not growing as fast as the turntable market, but the overall size is pretty huge as of now and is still on the uptick. I think the high-end headphone products category will continue to grow. Most headphone companies are trending upwards in price points and releasing more designs that are meant for home-use (and maybe that’s partly driven by the growing turntable market, too). I don’t think I’m the only one waiting for a good practical headphone output transformer from an established and well-distributed manufacturer.
So who will step up to the plate?
WTF Amps

Why DIY?


If someone told me they hiked to the summit of Mt Everest, I’d think they’re pretty amazing. If they told me that their first thought when they got to the top was how much money they spent to get there, I’d probably think they’re not quite so amazing. If they told me they actually took a helicopter to the top instead because it was cheaper, I’d be sure that they’re an idiot.

DIY requires an investment in tools and parts, but more importantly, it requires an investment in time and patience. Your first project is not going to be the Mt Everest of projects, just like a hiker’s first backpacking trip shouldn’t be up the side of the Himalayas.  Like every hobby, excellence takes patience and practice.

It’s very tempting to compare the cost of building something yourself to the cost of buying something that’s commercially made. As you’re starting out in DIY, you won’t win this battle. The more you practice, the more you’ll refine your finish and design theory, and the more of a return you’ll see on the time you’ve invested. But price-points still do not capture what DIY is about.

Craftsmanship is what you pay for with high-end, high-dollar, boutique design. The craftsman that wields it didn’t buy his or her experience with money. He or she built experience and knowledge by making mistakes and a lot of crappy products first. When you buy commercial, you are paying for the mistakes it took for the craftsman to become exceptional.  DIY is about having the courage to overcome those mistakes yourself instead.

P.S. Yes, I know helicopters don’t fly to the top of Mt Everest.