Audio qualia

experience the real sound of music !

designing a loudspeaker for use with a valve amplifier


I've decided to resurrect a valve based power amplifier to use with my Lenco transcription units (turntables!). And to hear the sound, I want to design and build a pair of loudspeakers. So why not just use the Epos M5's I have? Because valve amplifiers have some special requirements, so that not every pair of hifi 'speakers are suitable for use with a valve amplifier. The 'speakers must be sensitive and have a flattish impedance curve.

I must stress this is a design for an inexpensive loudspeaker, well at least the drive units are not expensive! The Lenco deck cost me £40, the valve amplifier (with a preamp) cost me £50, so spending much on loudspeakers seems to be way out of proportion.


The valve amplifier I have has an output of about  20-25 watts rms. For a reasonably loud sound, the loudspeakers would have to have an efficiency of at least 90dB/watt/m; my present 'speakers, Epos M5's are less than that, so they wouldn't go very loud. The M5 'speakers also seem to need a bit of power to show off their best, meaning they are more suitable for rock music or big symphonies, rather than small acoustic music. Another problem is impedance, valve amplifiers usually have an output transformer which has various taps to select different loudspeaker impedances, but they don't like impedances that vary too much across the audio spectrum, especially low down, or highly reactive crossovers or capacitive tweeter loads. So the design would have to accommodate these potential problems, and provide a benign impedance.

Drive units:

So there is a requirement for the drive units to have a sensitivity of at least 90dB/watt/m, and combined with a simple crossover which will not sap too much power. I have a few different drive units, and a few pine boxes which might be useful. A pair of Audax 8 inch (200mm) drive units I have have a sensitivity of 90dB/W/m, just what is needed. This leaves the upper mid range and treble. So couldn't the 200mm bass/mid range unit be used for mid range duty, its quite common. Well, there is a problem. Most large (ish) cone drive units have problems above 1kHz with cone breakup, where the stiffness of the cone loses the will to live. It can be seen in the frequency response as a region of huge peaks and troughs. Not ideal. And as the tweeters need to be crossed over at 3-5kHz or above, the response of the mid range like the profile of the Alps is not going to provide any sonic pleasantries!

Having said all that, finding a treble unit (in the UK) which is cheap enough, small enough and with enough efficiency is not easy. And to crossover to the 200mm bass/mid-range unit at 3-5kHz is going to expose the cone breakup area of the 200mm unit. One could use a separate mid-range unit, but then what would the crossover frequency be? If in the 300-500Hz region, the component values will be huge, and significant losses in the inductors will be incurred, and the capacitors will have to be electrolytic, or very expensive!!I have found a new type of tweeter, called a ring radiator drive unit, which is said to be 'flat' to above 20kHz, and have much lower distortion than dome tweeters. And the resonance frequency is below 1kHz, 837Hz is quoted, so a lowish crossover frequency is realistic.


So lets look at the bass/mid range unit, the Audax AP210M0:


The trace looks a bit odd. Up to 1kHz, everything looks fine, but above 1kHz and cone breakup is evident. That's no problem if we can crossover to the treble unit early enough to get the peaks at 2-3.5 kHz low enough. But the mid band around 200Hz to 1kHz looks lower than the quoted 90dB/W/m sensitivity. This is the problem, just looking at an average figure for sensitivity; the average may be 90dB, but the region we are interested in looks lower. The other odd thing is the resonance frequency, quoted as 46Hz by Audax, and although the resonance frequency will rise when put into a box, it still looks an odd value on the graph.

OK, I found this, and it looks a lot better. The impedance peak now looks correct, and we can see the true impedance across its frequency range. This will give the true impedance at the crossover frequency, which is often different from the average figure quoted. If we were to crossover at 3000Hz, for example, the impedance is not 8 ohms, but more like 14 ohms, and if we chose the crossover filter components with this understanding, it would not give the right result.  So, lesson learnt, go with your gut feeling!


Here are the results of applying a frequency sweep (from 400 Hz to 4 kHz) to the Audax AP210 bass/mid range unit. It shows the fundamental frequencies at the top of the graph, with the harmonic distortion below. These distortions are caused by vibrations, and it it hoped that the level of distortion will be reduced once the drive unit is mounted in the box enclosure.


Although the fundamental frequency response (top trace) looks rather undulating, it shows that a crossover frequency is possible, with a smoothish downward slope above the likely 1.8 kHz crossover frequency. The hump centred around 1.5 kHz can be ameliorated with a simple LRC filter, bringing the level inline with that at about 500 Hz. Cone breakup appears to be above the crossover region, so all seems to point to a sensible crossover at about 1.8 kHz.


Below is the treble unit I've chosen, it's a Vifa XT25SC90-40, it has a dual ring radiator diaphragm and a wave guide centre plug, well that's what Vifa's blurb says. It is noted for its clean, almost ribbon-like qualities, due to a much reduced harmonic distortion profile, so they say, so we will see. And its cheap, currently (2010) going for about GBP11. It is being used in the 'Acoustic Energy Aegis Neo 1 Mkii', a well reviewed GBP200 'speaker. It is also a 4 ohm unit, low for a valve amplifier (set at 8 ohms), but is sensitive, at nearly 92 dB/W/m (although it may be a 4ohm watt!), so it can have a series resistor to attenuate the tweeter's output to match that of the bass/mid units, which will be a little more attenuated by the crossover inductor dc resistances.




As can be seen above, this is the frequency response of the tweeter, and its impedance curve. Firstly, it seems to hold up well down to 1kHz, and secondly the impedance looks pretty benign. Smooth too, ±2dB up to 20kHz, and not much down at 40kHz! great for valve amplifiers.The unit will have to be flush mounted if it is to maintain this response flatness.



This is a device whereby the music/speech signal is split into frequency bands to allow the various drive units to receive the frequencies they have been designed to deal with. There is also attenuation applied to one or more drive units, to enable a smooth response to be derived. One major decision to be made is where to place the crossover frequencies. Often, this is dictated by the abilities (or inabilities) of the drive units. For example, the tweeter I want to use is only able to handle frequencies above 1kHz, whereas the bass unit lets go above 1kHz. And as crossover networks are composed of mainly capacitors and inductors (chokes), the size and values have to be considered (as well as the quality and price). The lower the crossover frequency from bass/mid range to the treble unit, the bigger the component values, the bigger the components, and (for a given quality) the higher the expense is likely to be. Of course, in such a design as this, the costs have to be weighed against each other and the value of the rest of the system. It looks as though a steep filter will be necessary to cut the bass/mid range unit above 1kHz, to reduce the affects of the cone breakup, and to lessen the impact of mid range getting to the tweeter. So I am thinking 24 dB/oct 4th order slopes. Although they contain more components than lower order filters, they are zero phase shift, (actually 360° phase shift, but that's about the same thing). However, a frequency sweep of the drive units may change my ideas.

The cabinets (or boxes).

I don't want to have to produce complicated boxes (again) for these speakers, so I have decided to use completed general purpose boxes, bought from a DIY store. They are made of thin real pine, with rounded edges. The problem I foresee is stopping the sound from getting through the panels! However, I have just carried out some work for a hifi company which has made me think about structures, and how I might incorporate different materials to reduce the panels from vibrating. And from an added damping point of view, a thin wall is better that a thicker one, it is easier to accomplish a dead panel if the panel is thin, so less added damping is necessary, as the BBC found.


To look at the responses of the drive units in their boxes will need a microphone and mic amplifier, and some software, so that examination of the loudspeaker output can be made. Most of the time, a loudspeaker response curve is produced by feeding a sine wave signal (via an amplifier) into the loudspeaker, and a microphone is used to capture the sound pressure. The signal from the microphone is amplifier and rectified, so that a voltage representing the average output is produced. One problem with this method is that the original waveform is not available, and that the sound pressure curve produced is from the drive units and cabinets combined, including any distortion, not just from the drive unit alone.

An advantage of just recording the output of a loudspeaker, preserving  the original waveform, is that it's possible to manipulate the data (the waveform) to derive certain information. It would be possible, for example, to record the output from separate drivers, then combine them in software to simulate the crossovers, and see which type of crossover suits best. And if the original waveform that is fed to the amplifier is recorded at the same time, a phase check can be done, leading to the correct time alignment being achieved between drive units, if that is important.

Whilst playing with my new microphone (made by Olympus, the camera/microscope people) I noticed that frequency sweeps are quite revealing. What is interesting is that when I detected a panel resonance of my lab speaker (by hand or accelerometer) I could see an increase in distortion, using the fast Fourier transform (FFT) function of the software I use. An FFT will transform a (periodic) waveform into its component parts, meaning individual frequencies, so that I could see a fundamental, its second harmonic, and more. What I saw most of the time was a fundamental and the second harmonic. I put the second harmonic down to the oscillator I was using, as it has a built in valve amplifier, known for their second harmonic distortion. But there were regions where I could only see the fundamental; so was the second harmonic being produced by the 'speaker? In other regions of obvious resonance, I saw third, fourth, even higher numbers of harmonics. This is on a 'speaker which started life as a mid range box for a KEF Concerto clone made by Wilmslow Audio that I bought in the 80's. I just tacked on some more mdf, so that the box is very rough and ready, but it sounds nearly as good as my Epos M5's, I'm not sure if that is good or bad!!

One thing to decide upon when designing a loudspeaker is the crossover frequency. In most two way 'speakers, where a bass/mid range unit crosses over to a domed tweeter, the crossover frequency is usually in the 2-4 kHz range. This puts a strain on the bass/mid range unit to control the cone breakup mode, usually above 1 kHz (see the graph above of the chosen bass unit). This usually results in a smallish cone diameter, certainly smaller than the 200mm unit chosen for this design. So one way of avoiding this breakup region is to lower the crossover frequency. But this can put a strain on the tweeter, especially if the resonance frequency is in the 1 to 2 kHz. I chose a tweeter where the resonance frequency is below 1kHz, hoping that the tweeter will not generate too much distortion below 1 kHz. I ran a frequency sweep by feeding a tweeter with about 2.83 volts of sine wave signal from a valve-based audio oscillator, and picking up the resulting sound pressure with a microphone, the electrical signal of which was fed into a computer running Audacity software. Analysing the waveforms using the FFT facility of the Audacity software gave data, which has been graphed:


In the graph, you are able to see the fundamental frequency response of the tweeter, in dark blue, and the harmonic distortions as indicated. The frequency scan has been attenuated by a 1 kHz 24dB/oct high pass filter in software. It is apparent that, although the distortions below 1 kHz are quite high, they are below 1%, and hopefully not intrusive. The tweeter was measured in free air, and so the actual response will be different when mounted above a large baffled enclosure, as intended, and some of the distortions may reduce.

The BBC investigated if these distortions could be heard, and came to the conclusion that, about about 500 Hz, and distortion above 30dB below the fundamental could be detected. Below 500 Hz, distortion could be heard more easily. However, it looks as though all the distortion from the drive units measured look as though the distortion should be undetected by the ear, or at least most of it, and that before the drive units are mounted on baffles.

It might be interesting to mention that harmonic distortion is not as bad as it is sometimes suggested. If we look at sound produced by musical instruments, ALL of them contain a fundamental and harmonics, the same harmonics that we see from hifi components.

Take a look at this FFT trace, a tone from my flute, an instrument with a very pure tone. 


The frequency is linear (along the bottom) so show the relationship between the fundamental and the harmonics. The fundamental, in this example, is the highest peak, at about 880 Hz (or A5 in musical parlance). The second harmonic has to be an octave above that, at double the frequency, here it is at 1660 Hz, or A6. The next harmonic, the third, is at 2540 Hz (or E7). Above this, can be seen higher harmonics at 3420 Hz (A7), 4300 Hz (Csharp8) and 5180 Hz (E8).

Now, for those who understand music, and chords in particular, they will realize that these notes are from the same chord, the chord of A major. These notes are A, C sharp and E, so they are related in a harmonious major chord. Also note that the fundamental, second and fourth harmonics are the same note (A), although one or two octaves apart.  All go to make a waveform that is interpreted by our brain as 'flute'.

It has often been said that even order harmonics are less objectionable, these are the ones generated by most valve amplifiers, solid state amplifiers tend to produce odd order harmonics, which are said to be more objectionable. And note that the fundamental, second and fourth harmonics are the same note, A, whereas the third and fifth are not the same, although harmonically related. It can be seen that the FFT of a flute note has the fundamental and harmonics in a reasonable monotonic way, that is, the amplitude of the harmonics are related in a reasonably linear way, and to be faithfully reproduced, must remain so. Unfortunately, the ravages of hifi components tend to conspire to disrupt this harmony!


Drive unit measurements and digital filters:

I've been having a look at the frequency response of the bass/midrange unit, just the bare driver, so anything under about 400 Hz can be disregarded. I generated a chirp (linear sweep of frequencies) sine wave from 400 Hz  to 4 kHz, and measured the output of the driver with a microphone fed into a computer running Audacity software.The scale down the side is in dB.

The first thing to note is the gently undulating frequency response, peaking around 1kHz, except for a peak near 2.8kHz, to the right hand side. Would it be possible to use this driver? Would it be possible to smooth those peaks using standard filters? Well, the Audacity software allows any filter profile to be designed (in the digital domain) and then applied to any data, to get an idea of the final response. What I am aiming for is a smooth transition to the tweeter, at, or above 1 kHz, the higher the better.

 With my first attempt, I obtained this:

...much smoother, and a crossover (passive) frequency around 1.8 kHz, so far, so good. The only problem, now, is the peak at about 2.8 kHz, which is evident in the manufacturer's data as well. Maye a notch filter can reduce the peak height. The filter's response looked like this:

The response drops off at 600 Hz at 6 dB/oct to a shelf at 1.2 kHz, then the passive crossover takes it at -24dB/oct at 1.8 kHz, crossing over to the tweeter. Exact matching, with regard to the tweeter amplitude and overlapping frequencies can be looked at later, but it's looking good, and 24dB/oct filters for the bass/mid range and tweeter is a good omen, and will hopefully accommodate the acoustic response of the tweeter below resonance, where only 12db/oct will be required. A time delay will also have to be incorporated if the tweeter is mounted with the front of its voice coil is different to that of the bass/mid range unit. Of course, in practice the filter responses will be a little rounded. So much to juggle with, its no wonder most expensive loudspeakers show different priorities as to what is most important, and to a budget!


Adding a couple of notch filters produced this:

Result! The band between 500Hz and 1800Hz (the latter being the crossover frequency) produced a level of ±0.5 dB, an almost unheard of figure!

 If the treble unit matches in well, the mid band and treble regions will be very tightly toleranced indeed. Will this mean they sound good? We will have to see.

 Drive unit placement:

One of the things that has to be decided is the positioning of the drive units, in relation to each other and the enclosure. Mounting the tweeter flush with the front panel is obligatory for a smooth frequency response, but where on the panel is the best place? Some say it should be vertically above the bass/mid range, (as suggested to me by no less a person that Spencer Hughes, who started Spendor, with his wife, Dorothy!), but other suggestions are that it should be mounted with respect to the Greek 'Golden Section', so that reflection/radiation from the edges of the panel do not add, and produce response abnormalities. I thought I would go for the latter.

The 'Golden Section' or 'Golden Ratio' is a number that prevents overlap of reflections/radiation of frquencies from the edge of the baffle so that they do not add or subtract. If a tweeter is mounted so that the distances to the edges of the front panel is the same, reflections from the edge will interfere with that directly radiated from the tweeter, and response deviations (of up to ±3dB) will occur. To overcome this, the tweeter is mounted so that the distances to the edges are in the 'Golden Ratio' with each other. The Golden ratio is 0.6:1.0:1.6 (to one decimal place). So a tweeter can be mounted so that the distance to the top edge is 0.6 that to one side (and 1.6 to the other) as shown below. Rounding the edges increases dispersion a little.










to be continued............