This forum presents the contributions of Joseph J. Rogowski to the lost «Induction Pickup» forum, helping us to «understand the theoretical math of working with current based transformers, turns ratios, string loop resistance and how that translates into output impedance and ultimately how it all affects the sound you hear».
To allow for questions and discussions the original posts are presented separately in the original order.
The reason why stranded wire is the «secret formula» is due to the skin effect. See this web link: http://www.powerstream.com/Wire_Size.htm.
Solid AWG 6 wire only passes frequencies up to 1.23KHz to the center of the core before being limited by the skin depth of higher frequencies. This means that you can voice the sound of the pickups by using various bunches of wire sizes (in parallel). These wires could be in the form of stranded non insulated wires or be individually insulated magnet wires of about AWG 18 which is good up to about 20KHz. This is just electronics theory, but let your ear be the final judge just like the sound differences in traditional pickups with different magnet types, wire sizes and bobbin shapes.
Remember that with current based pickups, lower the string loop resistance means more current and potentially higher output voltage of the current transformer. Since higher frequencies do not penetrate to the center of the thicker wire, these higher frequencies will produce lower current and tend to affect the balance of low to high frequencies in the output. The key to analize this is to listen to determine what is the highest frequency you want to capture, not primary string frequency but harmonic frequency. Usually, higher harmonics have less energy so only design to what you can hear. Then, choose wire strands that will handle this frequency. AWG 12 handles up to about 5KHz, AWG 16 handles up to about 12 KHz, AWG 10 handles up to about 3 KHz.
Here is a little trick that I did with the CSE187L. I bent AWG 6 wire into a hairpin loop about 2.5 inches long (total length about 5.6 inches). I cut the ends even and filed the surface so I could put this U shaped wire into a vice on my drill press. I used a number 48 drill bit to drill a hole a little bit deeper than .125 on the two U shaped ends to press fit the transformer primary. Heat the wire to expand so it fits easier. Then I used a pointed knife blade to open the space between the secondary coil and the laminated frame. I cut an old credit card plastic to get rid of the glue careful to not damage the coil. Then I string 4 individual strands of AWG 20 wire on top of the AWG 6 string loop. Make the individual connection behind the transformer for each strand. Ground each strand to the transformer frame. Clean the glue off the metal frame with sandpaper to make a good solder joint. By putting these 4 strands on top of the thicker wire you will hear some more upper frequencies and can use this technique to voice up the pickup to your taste.
Fit as many strands as will fit in the toroid current transformer center opening and use thin wall copper tubing to join the individual wire ends together making many parallel loops. Adjust the loop length to make a visually nice coil. Solder a fine stranded wire to each solder joint to ground all strands of the string loop. If using a Neo magnet with a metal coating run this ground wire along the bottom with tape to minimize noise pickup.
See this web link for a good source for copper tubing: http://ksmetals.com/24.html.
Web search «Low Impedance Pickup Research» that I started in 2008 to see all the details about how these pickups work. Right now there are over 69,000 reads world wide. I have covered a lot of technical details on this music electronics forum post.
The reason why I chose 500 turns was because it has about one tenth of the turns of a traditional high Z pickup and when using a Shure 95U or similar matching transformer I get a 12X voltage boost. When the current transformer pickup output impedance is in the 150 to 250 ohm range the capacitance in the cable from the guitar to the amp does not affect the sound. If the transformer frame, string loop and Neo metal magnet are grounded, you minimize noise pickup and then can stand the extra gain from a mic mixer to have a very clean sound. Because the turns are low (500 up to 1000 being the absolute upper limit) there is a broadband frequency response without the resonant hump in sound between 3KHz and 5KHz where the human hearing is most sensitive (see Fletcher Munsen Curve).
If you use a transformer with 1000 turns, you need a string loop with four times the area (of a 500 turn transformer) to have the same output impedance. With a 1000 turn transformer you multiply the DCR of the string loop by 1,000,000 to estimate the output impedance and then add about 20% for leakage inductance.
The quality of the joint that forms the string loop should be a very low resistance as it will add resistance and ultimately raise the output impedance and restrict the current to a lower than potential full output from the transformer.
If anyone wants to see other things I have written do a web search on «making a fast pulse induction mono coil».
Another nice toroid current transformer that I have used is the Kernet CT-06-50, 500 turns or CT-06-100 for 1000 turns.
This series uses a high permeability tape wound core for detecting very low currents, like guitar strings. They have units that come in 1000 turns, lead wires or just solder lugs. Take a look!
It is good to see you guys using this technology. Let's not argue over who gets credit. I like sharing what I have learned from tinkering with guitars for over 55 years and doing my own experiments and research.
The reason why I chose the CSE187L current transformer is because it has a metal frame around the laminated core which is a convenient way to connect the ground of a two conductor shielded mic cable. Also connect the ground to one side of the thick wire string loop.
The string loop should be a very low resistance, usually measured in micro ohms to carry enough current to make a good output on the transformer output.
I chose the 500 turn current transformer because it produces an output closer to the range of a low impedance microphone, typically 150 ohms to about 300 ohms max. Most XLR mic inputs are about 2400 ohms actual input loading impedance to act as a bridging loan on the input source impedance of the mic or current transformer pickup.
When using the CSE187L if you bent the primary wires inward to short the primary and silver soldered this small loop together, you get a measured electrical output on the current transformer of 80 ohms. All you need to do now is to look up the total resistance of the string loop wire. AWG 11 is 105 micro ohms per inch so a 6 inch string loop adds 630 micro ohms. Multiply 630 micro ohms by the turns ratio squared and get 157.5 ohms. Add this to the impedance of the transformer loop portion of the string loop and you get 237.5 ohms which is right near the upper limit to feed an XLR input. If you were to use a 1000 turn transformer you would have an output close to 1000 ohms and would be severely loaded down by the XLR input impedance.
XLR mic inputs are typically 2400 ohms. That means that you want the current transformer to be around 240 ohms to not load down the pickup output and cut the high frequencies. A shorted CSE187L is 80 ohms measured output impedance. Then, just add the string loop resistance. AWG 11 is 105 micro ohms per inch so a 6 inch string loop is 630 micro ohms. Multiply this by turns ratio squared or 250'000 and get 157.5 ohms. Now add this to 80 and get a total output of 237.5 ohms. This is right near the upper limit to feed a mic mixer without affecting the sound too much. It would be very close to what you would measure with an Extech LCR meter at 120Hz.
Lace manufactures these pickups by stamping them out of 3/32 to 1/8 inch thick aluminum to match the footprint for either single coil pickups, humbucker or P90 pickups. Then, they are bent into the final shape to allow a space below for two transformer bobbins.
Look closely and see that they put interlocking U-shaped transformer laminations about 1.25 to 1.5 inches long around the pickup frame where the center aluminum strip joins the lower strip. This location is the place where the currents from each loop join together and where the current transformer passes the current through the transformer laminations, and two coils are placed on this U-shaped lamination, one on each side of the lamination bundle. The output resistance is listed to be about 2500 ohms, but these coils are connected in parallel so each coil is individually about 5000 ohms. The wire gauge is between AWG 44 to AWG 46 to put enough turns on the bobbins to provide an output in the range of a high impedance guitar pickup. Although I have not measured the number of turns, I can only estimate that each bobbin could have between 15,000 to 20,000 turns of very fine wire.
By balancing the thickness of the aluminum stock and the width of the side strips, Lace can control the string loop resistance and its relationship to the number of turns on the two coils on the transformer secondary under the pickup frame the same way you can use different wire gauges and current transformer turns ratios to adjust the sound or voice of your pickup. Once you find the pleasing sound with the right combinations, you can easily mass produce the frames and coils under the frames and have a very consistent product. Science does not tell you what will sound good but once your ears say, «this sounds good», science can help you analyze the characteristics and then help you replicate it.
Higher current transformer turns ratios produce more output but not near what a high impedance guitar pickup puts out. This is why I chose to target the commonly available range of low impedance microphone because commonly available commercial parts could be designed to work in this range. Unless you can find current transformers that have 5000 to 10,000 turns in a small size you are better off working in the 150 to 250 ohms output range. This way you can make a very low noise pickup with a very broad frequency range without the typical resonant hump that makes the typical electric guitar pickup sound.
Prem Magnetics makes the SPCT-251 2000 turn current transformer with a primary square opening of 0.160" which will allow a bundle of smaller wires to fit or a single piece of square AWG 6 copper wire to fill the space. The output impedance will be the calculated resistance of the string loop times the turns ratio squared or 4,000,000. If AWG 6 wire has 30 micro ohms per inch and the total string loop, including the approximate 2 inches that goes through the SPCT-251 primary for a total of 8 inches the output impedance is 8 x 30 x 240 micro ohms. Multiply .000240 times 4,000,000 and you get 960 ohms as the absolute minimum impedance not taking into account leakage inductance and mechanical resistance of joining the ends of the wire to form a low resistance string loop. What ever wire size you used on a 500 turn transformer you now need 16 times more wire area to have the same impedance as the 500 turn transformer. The 2000 turn transformer impedance is much to high to target a microphone XLR input but could drive a 10,000 to 20,000 ohm line input on a mic mixer but only have an output 4x that of the 500 turn current transformer at best. It could drive a guitar amp but the level would be low and you might be subject to more noise. To find a good online resistance calculator look up «Salvarsen resistance calculator». You can even change the metal type to see how using copper, aluminum, brass and other metals affects the resistance of the string loop that produces the current that ultimately drives the output voltage.
Once you understand the theoretical math of working with current based transformers, turns ratios, string loop resistance and how that translates into output impedance and ultimately how it all affects the sound you hear, you can begin to appreciate how you can see cheap electronic stuff on the web based electronic stores and get stuff to do your own experiments and have a high degree of success. Go to «The Electronics Goldmine», «All Electronics» and «Surplus Sales of Nebraska» and see their magnets, copper strips, copper wire, transformers, coils and inductors to get some inexpensive stuff to play with when they are on sale.
Bottom line, let your ears be the fine judge of what sounds good. As you change one variable like wire gauge and type (single strand versus stranded), current transformer turns ratios (1:500, 1:750, 1:1000, 1:2000, 1:2500, 1:5000, 1:????), magnet type and strength and the final interface (Shure A95U matching transformer or mic mixer) to your amplifier you can then tell that by doing this or that I get more bass or treble sounds, more or less noise, higher or lower output signal. The theory of what I am sharing just helps you better understand how all the pieces fit together. There is not too much published information about this stuff. You guys seem to like tinkering and I hope that the results of my tinkering can help.