Symmetrically segmented wire-stator ESL's

Everything else is two dixie cups and a string 😎








































Above:  My personal ESL, which I call the 'Beam Splitter'.   
The transmission line woofer box/frame was built in 2008.  
The ESL panel was updated to segmented wire type in 2015.




Introduction

Greetings all from the Jazzman,

It still amazes me that an average Joe with practically no electronics experience can build a speaker at home that rivals the high-end commercial offerings and bests most of them.  And building the actual driver from scratch takes cool to a whole new level.    

Roger Sanders enabled my first ESL project in 2008, and my latest speakers would not have been possible without ESL gurus Rod White and Steve Bolser (a.k.a. Golfnut and Bolserst at diyAudio) sharing their knowledge on the diyAudio Forum.  Rod's white paper [1] and segmented speaker provided the inspiration and Steve's Segmented ESL Calculator and gift for explanation made it easy to derive the segmentation scheme and resistor values.  Roger, Rod, and Steve-- you guys are the best!  

I am pleased to share with you my DIY electrostatic loudspeaker projects.
Charlie Mimbs
Savannah, GA
jazzman1953@gmail.com

[1] Wide-Range Electrostatic Loudspeaker with a Zero-Free Polar Response, D. R. White, JAES Volume 57 Issue 10 pp. 822-831, Oct. 2009

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Mervyn's Eros Clone speaker build - June 2019:
The exquisitely crafted speakers shown below were built by my online collaborator Mervyn Tims.  Segmented wire panels mated to a 10" Aurum Cantus woofer in a compact transmission line and built with amazing skill-- has to be a killer combo.

I'm dying to hear them!  


  












































Audi Speaker Build - Sept. 2018:
I call this speaker the 'Audi' because it was built for my friend Martin, who needed the speaker pair to fit into his 2008 Audi for transporting, and they do (barely). 
















The 'Audi' H-baffle hybrid ESL


Video of the new speaker playing at Carverfest 











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The Basics
How do they work?


















If your hair has ever stood on end while unloading a clothes dryer, then you've felt the same force that drives an electrostatic loudspeaker (ESL).

An ESL is a push/pull motor consisting of a thin plastic diaphragm suspended in an electric field between two conductive screens called stators.  High voltages applied to the stators drive the diaphragm by electrostatic attraction and repulsion. 


A separate power supply puts a DC biasing voltage on the diaphragm and the output from an audio amplifier, routed thru a voltage step-up transformer, puts the driving AC voltages on the stators.  And the ultra-light diaphragm responds with instant precision to reproduce the music with exquisite fidelity.

Stators can be made from just about any conductive material, including perforated sheet metal, conductive-coated plastic, wires, metal rods or even bug screen.  

My first ESLs used flat perforated metal stators which gave great slam and imaging but beamed like crazy.  The next generation stators used segmented welding rod conductors and had switch-selectable wide and narrow dispersion modes. These had a nice, balanced sound but were just butt-ugly.  Finally; my newest panels are more finely segmented for optimal dispersion and they have beautiful oak lattice supported wire stators that both look and sound like fine musical instruments. 

Flat perf-metal panels are by far the easiest to build and they sound fantastic in the sweet spot.  They are also directional to the extreme, prone to arcing if the stators are not perfectly prepared and coated, and they require a very stable amplifier to drive their all-capacitive load.  

Welding rod panels can be electrically segmented for wider dispersion and balanced response, and when segmented with a resistor network, their part resistive/part capacitive load is easier on amps.  The downside is; they are time-consuming to build and should be coated for arc resistance.  
    
Insulated wire panels like the ones shown on this page are now my preferred choice.  They are very reliable and easily segmented for tailored dispersion, balanced response and easier load.  They are also time-consuming to build; requiring a support lattice and a stout jig to stretch the wires.  

More to come on electrical segmentation, but first:

My current home stereo speaker (top photo above):  
Dimensions:     66.5”H x 15”W x 19.75D
Bass cab:         4ft3, 9ft transmission line, V-section beam splitter    
Woofer:            10” Aurum Cantus AC-250MKII
Stators:             Segmented wire type, 10.5” x  46.5” active area 
Wires:               20 AWG solid copper, .010 XLPVC, .052 OD
Wire spacing:   11 wires/inch, 43% open area 
Diaphragm:       Mylar, 6-micron, 2.4 gm, Licron Crystal coating
Bias supply:      2.7kVDC, Cockroft-Walton cascade  
Transformers:   (2) 50VA 230V/2x6V toroidal, 76:1 ratio 
Crossover:        Behringer DCX2496, 48db/oct LR filter @ 228Hz 


Dispersion
Wavelengths shorter than a speaker’s radiating width tend to beam rather than spreading out (that's why tweeters are small).  And flat-panel ESL’s beam big-time because they are necessarily large to offset their limited excursion and dipole roll-off.  The resulting 'head-in-a-vise' sweet spot is great for solo listening at the focus but not so good for entertaining guests, where wider dispersion is needed.  

The typical way to widen an ESL’s dispersion is by curving its panel, and thereby it's projected wavefront.  A segmented ESL uses a flat panel and curves its wavefront electrically, using discrete stator conductors driving discrete zones on the diaphragm.

Below is a post by Steve Bolser on the DIY Audio Forum which compares the dispersion patterns of flat, curved and segmented panels: 


More About Electrical Segmentation
My segmented panel uses symmetrically arrayed vertical wire groups which are discretely powered by phase and frequency attenuated impulses to function as a line source projecting a cylindrical wavefront.                  

Each stator uses 90 insulated copper wire conductors arrayed in 15 groups of six wires.  These wire groups are apportioned into eight discretely powered electrical sections; consisting of a single center wire group comprising section one, and seven left/right paired wire groups, arrayed symmetrically on either side, comprising sections 2-8 (see Schematic).  

The center wire group connects directly to the amplifier interface and receives the full audio bandwidth above the crossover frequency.  The left/right paired wire groups are powered in series thru an RC (resistor/capacitor) transmission line consisting of resistors inserted between the wire groups.  The resistors couple with the wires' capacitances to form a series of low pass filters that progressively chop off the upper frequencies toward the panel edges.    

As driven by the segmented stators; the diaphragm radiates the top treble band from only a narrow vertical zone at its center, and the left/right paired zones on either side radiate progressively lower frequency bands, toward the panel edges.  In this way, the widths of the radiating zones do not exceed the radiated wavelengths, so all frequencies spread out uniformly, rather than beaming.  

Guidelines for Symmetrically Segmented Wire Panels (hybrid ESL):   

·                Diaphragm-to-stator gap (d/s):  0.063” (+.015/-.000)  
·                Span between diaphragm supports: 70-100 x d/s
·                Wires:  18-22 AWG single-strand copper, PVC or XLPVC insulation only
·                Max span between wire supports (wire gauge/inches): 22/2, 20/3, 18/4 
·                Wire O.D. (insulation included) should not exceed d/s
·                Gap between wires (insulation-to-insulation) should not exceed d/s
·                Ideal (max output) open area:  42%  (gap/OD)
·                [Down to 12mm] more/narrower wire groups = wider/smoother dispersion
·                Transformer(s) power/ratio (each speaker): 100-160VA / 50-100:1
·                Bias voltage: 1.8kV – 4kV
·                X- over frequency/filter slope:  >200Hz / 24db


Stretching the Stator Wires
Once the panel design is set, the next step is building a jig to stretch the stator wires. 

While not a strict necessity; stretching the copper wires to plastic deformation renders them perfectly straight and re-aligns their metallic structure such that they remain straight when subsequently relaxed.  Experiments showed that stretching to 1% elongation is sufficient, so my stators' wire loops were stretched from 47.5” to their 48” final length.   

Stretching ninety 20 gauge wires at once requires a strong jig and about 4,500 pounds of force.  My jig is a ¾ MDF platform mounted in a stout frame cut from yellow pine 4x4’s.  The wire loops wrap over .063 diameter x .250 length steel pins inserted half depth into drilled 3/16” aluminum plates.  The pins are angled 4 degrees from vertical to hook the wires.  One pin plate is stationary and the opposite moveable pin plate bolts to a 3/16 steel subplate that’s welded to two 3/4 x 12 all-thread jack rods.  Turning the coupling nuts on the jack rods pulls the movable pin plate to stretch the wires. 

Note:  For my stators' wire diameter, correct spacing required using 1mm pins.  However, 1mm pins proved too weak and bent over when stretching the wires so I had to increase the pin diameter to .0625", which messed up the wire spacing.  To compensate, I used 5/8-11 TPI all-thread rods as comb guides to hold correct wire spacing during glue-up.  


































Below: Stator wires on the stretching jig





















Stator Support Lattice
The wires are supported by an interlocking oak lattice which is assembled and glued down over the wires, in the stretching jig.  Before stringing the wires, the jig platform was covered with wax paper to prevent gluing the wires to the jig.  And before gluing, most wire tension was relaxed to prevent preloading and warping the stator.  Yellow wood glue was used for the wood-to-wood bonds and E6000 glue for the wood-to-wire bonds.

The vertical lattice rails were laid down into the jig first, and then the interlocking horizontal slats were glued down one-at-a-time, over the wires.  During this process, lengths of 5/8-11 TPI all-thread rods were placed over the wires as comb-guides to maintain correct wire spacing. 


CAD drawings for the cabinet, stator lattice, and stretching jig are available upon request.  Just email jazzman1953@gmail.com


Below:  All thread rod comb guides hold wire spacing during glue-up


Below:  Oak support lattice assembled over wires



























Below:  Completed stator 



















Diaphragm Spacers
The foam tape spacers bond the diaphragm to the lattice rails and set the diaphragm-to-stator gap (d/s) at .063”.  The vertical lattice rails are flush with the wires and their spacers are (1) layer of .063 3M double-sided urethane foam tape (3/4" width on side rails and 3/8" width on center rails).  The horizontal end rails run under the wires and anchor their end loops with glue bonds.  The end rail spacers consist of (1) .047 x .075 polycarbonate shim bonded onto the wires with E6000 glue, plus (1) layer of .015 x .075 wide 3M UHB double-sided foam tape over the shim (0.062 total).  The double-sided foam tape spacers bond the diaphragm to the stator instantly with minimal fuss. 


Diaphragm 
The 6-micron Mylar C diaphragm is vertically sectioned into equal thirds for stability and tensioned to 1.0% elongation using a pneumatic bike-tube jig.  The jig is an MDF platform sized two inches longer and wider than the stator and 2 inches high with all edges rounded over to .50” radius, sanded smooth and dusted with baby powder to prevent snagging the delicate diaphragm film.  A 700mm x 35mm Schrader valve type bike tube is stretched around its perimeter.  

The Mylar film is wrapped over the jig and secured on the backside with double-sided tape.  Inflating the bike tube with a hand pump tensions the diaphragm.  Tension is gaged by first marking reference points on the diaphragm exactly 12 inches apart using a fine tip felt pen.  As the tube is inflated, the target elongation is reached when the distance between the reference marks reaches 12.12 inches.  

For my panels' span between supports, 1% elongation provided enough tension to prevent driving the diaphragm into the stators at high volume, yet kept the drum head resonance low enough to set the crossover frequency below the ear-sensitive midrange region.  

Since the amount of elongation/tension required to stabilize the diaphragm is dependent on the span between supports, the elongation would vary for different spans-- 1% would not work for all panels.

The stator is then pressed into place over the diaphragm to affect the bond.   


Diaphragm Coating
The diaphragm must be made conductive enough to hold a biasing voltage yet resistive enough to slow the charge migration across its surface.  

So next, the periphery edges of the diaphragm were masked off with painters tape and the Licron Crystal ESD conductive coating was spray applied in one “just wet” coat and allowed to dry for eight hours before assembling the panels.  The coating dries to a pale blue-gray, almost clear coating about 2-microns thick with E7-E9 resistance.   



Below: Bonding stator to diaphragm on bike tube jig



Below:  Bonded diaphragm ready for conductive coating



Charge Ring  
The charge ring is ¼ inch wide copper foil tape applied to the periphery of the rear stator, centered on the foam tape spacers.  The wire lead from the DC biasing power supply is soldered to it and when the front and rear stators are mated together, the charge ring contacts and conducts the biasing voltage onto the diaphragm. 

Below:  Rear stator with spacers & charge ring
 
























Below:  Completed front & rear stators ready for assembly





















RC Segmentation Network
The RC (resistor/capacitor) filter network tailors the panel's dispersion pattern electrically by attenuating the frequencies and phasing of the music signals driving the separate wire groups.   
  
The wire segmentation scheme and network resistor values were derived using Steve Bolser's Segmented ESLCalculator spreadsheet.  From the spreadsheet options, I chose Symmetric Config 2, both stators segmented, in eight electrical sections, and a low-cutoff of 200Hz.  For my panel the spreadsheet calculated 120kΩ for R, with R/9 resistance on the section one wire groups, 0.75R on section two wire groups, and R on sections 3-8 wire groups. 

It’s common practice to move/reflect the section one resistances to the primary side of the transformer to protect against core saturation (see Schematic, damping resistor R1).  Reflecting section one's R/9 resistance across an ideal transformer would divide the sum by the turns ratio squared (4.6Ω in this case).  However, placing this much resistance on the primary side of a real transformer, interacting with its winding resistance, leakage inductance, and winding capacitance, would result in a significant roll off of high frequencies down into the audio band.

The transformer's winding capacitance adds to the load capacitance and its leakage inductance combines with the load capacitance to generate an ultrasonic resonance peak in the frequency response and rapid roll off above it.  Coincident with this response peak is an impedance minimum which can be a difficult load for the amplifier.  When series resistance is added on the primary side it dampens this resonance peak.  However, as previously noted, too much resistance over-damps the resonance, rolling off the audible highs. 

The spreadsheet assumes an ideal transformer is used, so it doesn’t calculate the effect of resistance on the primary side of a real transformer.  
The general guidance is to omit the section one resistors on the secondary side, add a 1Ω series resistor on the primary side and give it a whirl.  My panels sounded really good with this initial setup. 

From there the only tuning, if any, is adjusting the series resistance on the primary and/or the first two stator sections to dial in the treble response.  Less resistance increases treble and visa versa.  My old ears don’t hear the highs so well but I didn’t want less than 1Ω on the primary side and the section one resistors were already omitted, so I reduced the section two resistors from 0.75R (90kΩ) to 60kΩ to brighten up the treble, and that works for me.  


The schematic and parts list show the spreadsheet values except with section one resistors omitted and reflected as 1Ω on the primary.  I think this would be optimal for most listeners. 

All remaining resistors on the secondary side are 2W, 500V in series.  Wattage/voltage are highest across the first resistors and decrease down the line.  Multiple resistors are ganged to spread the load, as follows: 

Section 1:          none  (reflected as 1Ω on TFMR primary)
Section 2:          (3)  30kΩ
Sections 3, 4:    (3)  40kΩ
Sections 5-7:     (1)  100kΩ + (1) 20kΩ
Section 8:          (1)  120kΩ


Below:  RC network resistors (Audi speaker)



















Schematic
















Setup:

















Parts list for two speakers:
























Amp/ESL Interface
Each stat panel has an interface to its amplifier; consisting of a high voltage DC power supply to bias the diaphragm and one or more step up transformers to convert the amplifier’s output into the higher voltage AC required to charge the stators.  Unlike most commercial hybrid ESLs which include a passive crossover network in the interface, my speakers use an active digital crossover upstream of the amps, and the interface can be much simpler.  

Each interface uses (2) 50VA 230V/2x6V toroidal transformers wired in tandem with the 6V windings in parallel as the primary and 230V windings in series as the secondary; giving a 76:1 winding ratio. The DC biasing supply uses a floating ground that’s center tapped between the transformers 230V windings.

The DC biasing supply is a simple half-wave rectifier and voltage multiplier outputting 2.7kV.  It’s powered by 115VAC mains current into a 115V/230V transformer and diode/capacitor ladder with a 20MΩ charging resistor at the output.  The charging resistor helps stabilize the charge on the diaphragm and limits the potential current that might otherwise sustain any arcing to the stators.     


Below: Amp/panel interface (Audi speaker)




















Bass Section  (Beam Splitter Speaker) 
The woofer box is a single-fold, tapered transmission line stuffed with 0.5lbs/Ft3 of polyfil.  The line’s sectional area is 125% of the woofer’s cone area at the front, tapering to 100% of the same at the terminus.  The cabinet is ¾” MDF sheathed in 5mm red oak plywood and the panel frame is solid red oak.  

To minimize the woofer box’s profile and footprint, its volume extends upward, behind the stat panel, and its frontal surfaces are angled to form a V-shaped “beam splitter” which deflects the panel’s rearward sound out the open sides of the speaker rather than back to the diaphragm.   

When designing the bass section I followed Roger Sanders’ lead and opted for a transmission line enclosure and a woofer with low moving mass, low QTS, and low inductance coupled with a very strong motor magnet.  The ideal matching woofer doesn’t exist of course but low inductance takes priority and the Aurum Cantus AC250 MKII I chose works pretty well.  


Power & Control  
The speaker pair is vertically bi-amplified using a Behringer DCX2496 digital crossover feeding a pair of vintage Carver TFM-25, 225 watts/channel stereo amplifiers.


The general guidance is to set the crossover frequency is least two octaves above the diaphragm’s drum head resonance with a 24 db/octave filter slope or at least one octave above resonance with a 48db/octave filter slope.  My diaphragms resonate at about 90 Hz and the crossover is set at 228 Hz using the Behringer’s 48db/ocatve Linkwitz-Riley filter.  


Below: Beam splitter transmission line bass section





















 











































Below:  Bob Carver loves my speakers!
               Cellphone Video from Carverfest 2016





















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