# Passive Crossover for a Leslie Speaker

This article describes the process of designing and constructing a passive crossover for a Leslie speaker. Passive crossovers were installed in the classic Leslies: 147, 145, 122 etc. and in most other two-way and three-way loudspeakers. The alternative is an active crossover but this requires multiple power amplifiers. The drive units employed for this design are from a Leslie X77L and would seem to be similar to those used in the 710, 760 etc. which do use active crossovers. The impedance of the bass unit is a nominal 4 ohms and differs from the classic Leslies; those were 16 ohm but the horn drivers would appear identical. The differing bass driver means that the classic Leslie crossover cannot be used. Nevertheless this design is in most other respect similar to the original.

## Preliminary Stages

Crossover design would be simple if the impedance of a loudspeaker was constant throughout the frequency range. However, it is nothing like and a 4 ohm driver may well read between 3 and 30 ohm as frequency changes so before a design can commence, the drivers' impedance have to be derived for a range of frequencies.

## Measuring Driver Impedance

Given that there was little chance of finding the necessary data, I set about measuring it. The equipment needed is an audio oscillator, a small power amplifier, a resistor (say 47 ohm, 2W) and an ac voltmeter. I used my computer sound card as the oscillator and a digital multimeter. Here is the arrangement.

V is the RMS voltage generated by the oscillator (sound card and amplifier) at frequency f (Hz).

Vr is the voltage measured across the resistor and Vs, the voltage across the speaker.

The current I in the circuit is given by:

**I = Vr / R** where R is the resistance of the resistor.

Then the speaker impedance:

**Zs = Vs / I**

Measurements are taken at a number of frequencies and plotted. I did this for both the horn and bass speaker. Note that the horn measurements were taken with the rotating element attached whereas I considered it not necessary for the bass driver to be in its cabinet. My reasoning being: the horn driver impedance will be modified by the horn itself at the frequencies of interest; the bass driver impedance will be affected by the cabinet but only significantly around the bass resonance frequency which is well away from the crossover frequency. It would have been instructive to check this assumption but overly time consuming, I reasoned.

The plots show the wide variation of impedance with frequency. Now, if a flat frequency response is required, the impedance presented to the crossover by the speakers has to be constant well above and below the crossover frequency. For a Hifi crossover, the first stage would be to design RCL (Resistor Capacitor Inductor) networks to go between the crossover and the speakers. However, a Leslie speaker is not Hifi and the classic 122 design dispenses with this step. I have done the same, reasoning that the imperfect design may contribute to the character of the classic Leslies. Nevertheless, the design the based on the driver impedances at the crossover frequency. The values chosen were Horn: 15 ohms and Bass speaker 8.28 ohms. These values and the crossover frequency were entered into the on-line crossover calculator at DIY Audio and Video , a Linkwitz-Rliey second order crossover was designed. To be confident of the design thus produced, I tried other designers and generated and ran an LT-spice model.

## Making the Inductors

The next problem is how to make the inductors; this comes with a sub category of what to make them from. I am not a fan of air cored inductors, whilst they have the advantage of ease of design and freedom from saturation effects, they end up either having an unacceptable resistance or they are heavy and expensive in copper. I therefore adopted the Leslie standard of ferrite-cored inductors. I found what I thought was acceptable core material on ebay in the form of 1/2 inch diameter 98 mm long ferrite rod of a material described as F8. I did find some information about the material on the Web but insufficient to formulate the design, so I wound a trial inductor and measured its properties. I wound 360 turns of 1mm dia wire on a 45mm length of the rod and set about measuring its inductance.

### Measuring Inductance

Substituting the Inductor for the loudspeaker in the loudspeaker test circuit gives this circuit. Note that the inductor has an resistance which is effectively in series with a perfect inductor. Now because the voltages Vlr and VXl cannot be measured separately some Electrical Engineering and geometry has to be invoked. First the Phasor Diagram for the circuit is drawn:-

To calculate the inductance, it is necessary find the voltage across the perfect inductor at a particular current and frequency. The measurement taken are:-

V, the applied voltage shown as phasor O C

Vr, the voltage across the test resistor shown as phasor P Q

and

Vl, the voltage across the inductor, phasor O B

f is the frequency of the excitation voltage.

So we know the lengths of the three sides of the scalene triangle O, B, C. Therefore the angles *m* and* l *can be calculated:-

*m* = arccos (Vl^{2} + V^{2} - Vr^{2})/2 * Vl * V

*l *= arccos (Vr^{2} + V^{2} - Vl^{2})/2 * Vr * V

Then

angle *n *= *PI/2 - l - m*

So

Vlr = Vl * sin* l*

and

VXl = Vl cos *l*

The reactance XL of the inductive component of the inductor is:

XL = VXl* R / VR

and the inductance, L Henrys

L = XL / 2 * PI * f Henrys

These formulae were entered into a Spreadsheet such that the voltages and frequency cold be input and the inductance indicated.

The test inductor was measured using a test 6.35 ohm bifilar wound test resistor, my amplifier dummy load resistor. It measured 5.0 millihenrys. From this result, the number of turns needed to give the required inductances was calculated:

Let K be a constant where:

L _{test} = n^{2} k, k = L_{test} /n^{2}

then

n1 =sqrt ( L_{rqd} /k)

Again, using a spreadsheet for the calculations, the numbers of turns required was:

3.29 mH: 292 turns

5.97 mH: 394 turns

These values were used as a guide, recognising the fact that k would not be perfectly constant, especially as outer layers would have reduced magnetic coupling to the core.

### Construction

Wooden end cheeks were made to contain the windings and matching mandrels were made to chuck the bobbin. Here's one I made earlier (left) and below, the Heath-Robinson lathe conversion to a coil winding machine. Note the wire tensioning device: a piece of felt folded over the wire and clamped between two pieces of wood. It works well. What it lacks is a revolutions counter. I could not use the lathe drive directly, it is far too fast and powerful. The battery drill used is variable speed and very controllable and the torque limited.

I wound the two inductors thus with additional turns; you can always take turns off but adding them means a rewind and wasted wire. The turns count was an estimate based on layers and length. I measured the inductances as before unwinding and re-measuring until the desired values were achieved. Quite a satisfying and satisfactory job.

### Inductor Saturation

Ferrite like ferric materials are subject to saturation, they have non-linear magnetic properties. At low flux density the flux is largely proportional to the mmf (magneto motive force = current * turns /length) but as mmf increases, there comes a point where flux increases more slowly or not at all. The relationship is known as the B-H curve and in this application, it causes distortion, higher distortion at higher levels. In this crossover design, the two inductors are subjected to significantly different maximum currents. The spice simulation gave maximum peak currents as 400 mA for L1 and 6.3 A for L2 when driven from a 28 volts rms source; equivalent to 100w into 4 ohms.

Now, let's look briefly at the significance of saturation in the two inductors. For any inductor operating on ac, straying into saturation results in a lowering of inductance at the peaks of current, and producing even-harmonic distortion. For L1, the horn inductor, this would result in a change of the tonal quality and may increase dissipation in the driver. However, I expect it is more likely to reduce dissipation in that it will have a clipping effect but increasing hf may still have a deleterious effect on the driver. For L2, saturation will increase the high frequencies that get through to the driver as well as generating some additional harmonics of its own. Additional hf, beyond the response of the speaker will cause the cone to flex, known as cone breakup. I recall that Goodmans were quite keen that users of their bass guitar speakers should filter out the high frequencies, presumably through fear of their life being shortened. Bass guitar players, like Hammond players like to overdrive their amplifiers generating lots of high harmonics. For both inductors, it is advisable to steer clear of the saturation region. But how to test?

My test amplifier is an old Hifi amplifier rated at 20w /channel into 8 ohms so the current available is limited, as is the voltage. I paralleled up the outputs through two 2 ohm resistors and connected them to the higher inductance inductor. I managed to achieve 5 amps at 50 Hz in 5 second bursts. before clipping. Viewing the voltage waveform on an oscilloscope whilst adjusting the current showed that distortion was just visible at 2 amps rms (2.8 amps peak). Transposing this to the lower inductance, which has fewer turns and so will take proportionally greater current before saturation, gives a peak saturation current of 3.8 amps. So, referring to the currents that will flow in this design, L1 would be operating well within its capabilities but L2 would be inadequate. So back to the drawing board. I should point out that the currents I have designed to are above those that the X77L Leslie amplifiers could supply.

I made another inductor, this time with two ferrite rods as the core. I was unsure how many turns would needed so I put around 290 turns and measured its inductance. Proceeding as before, I achieved the 3.29 mH at about 280 turns, almost identical to the single ferrite core inductor but with double the csa of core material, the saturation current would be double that of its previous version. I did manage to get 5.5 amps peak through it without clipping and was unable to detect any distortion in the inductor voltage waveform. I conclude that it is good enough. Here are the three inductors.

I wonder at what current the inductors from my 710 saturate. They look puny things with thin wire? I may test one sometime.

### Capacitors

The capacitors are made up from parallel connected polypropylene types to achieve the required values.

### Mounting

A base-board was constructed from 3mm hardboard I laminated three layers of this wonderful material and drilled it for terminal posts, 4mm screws. The inductors were screwed from beneath and clips were made from brass sheet for the capacitors. The brass was hammered to work-harden it and impart some springiness. All connections were made via the terminal posts using solder tags. Here is the finished product.

### Testing

I connected load resistors in place of the speakers and drove the crossover from my test amplifier. Test tones and measurements were performed it a PC using the sound card for input and output. The software used to perform the tests wasHOLMImpulse. Whilst this free software was designed to measure the impulse response of acoustic spaces, it works well as a frequency response plotter. For the measurement, I connected the crossover horn outputs and bass outputs through an audio isolating transformer, one at a time, to one of the sound card inputs. Then the load resistors were removed and the actual speakers connected.

Here is the arrangement - not too pretty but effective. The bass speaker is sitting on the bass rotor made for the 710 project. The resultant graphs are shown below.

From the plots, the first thing to note is that the response measured into resistive loads of 15.2 ohm and 8.5 ohm (the nearest I could easily get to the design values) is that the bass and treble outputs are much as expected. This indicates that the crossover is much as designed. Now contrast these with the plots with the actual speakers connected. The 'real' plots are somewhat less ideal. The reason for the deviation is the variation of driver impedance with frequency. The impedance plots shown earlier in the article can be seen reflected in these amplitude responses. I would expect that the 147 Leslie tested thus would produce similar results.

The wiggly lines of the horn response may well be caused by reflections from the horn mouth; multiple resonances which affect the impedance and the frequency response. The horn mouth being rather small for a crossover frequency of 800Hz.

I did attempt to measure the acoustic response but the measurements were useless, changing dramatically with microphone positioning. Not unexpected.

## Comparison with a Leslie 710 Crossover

On the right is a passive crossover taken from a 710 Leslie. Admittedly, it differs from the classic Leslie crossover but it does look rather lightweight.