Originally posted by Man Of Steel
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You are on the right track with your anaysis, but there are some more details that will help you form a good mental model and ultimately a good math model that will define and graph what is actually happening.
Remember that a transformer reflects the secondary load back to the primary by the square of the turns ratio (TR). So, in the CSE187L with a 1:500 TR you are reflecting a secondary load impedance back in parallel with the primary string loop impedance which is already pretty low in the sub milliohm range typically measured in hundreds of a microohm. This cannot be directly measured but what you can do is to measure the current transformer (CT) output AC resistance with the Extech LCR meter with the CT having (1) an open primary and (2) having a low imepdance string loop connected. Now, add a second CT on the other end of the same length string loop and note that the second CT will increase the output impedance of the output CT connected to the Extech LCR meter. Assume that the CT output is being sent into a mic input impedance of 2K ohms. Then, a reflected impedance of 2K divided by 250,000 (500 squared) or 0.008 ohms (8 milliohms or 8,000 microohms) will appear in parallel with the string loop impedance. Changing the gauge of the primary string loop will help tune the impedance range of the output CT. If you are going into an XLR input or a remotely mounted microphone matching transformer the microphone matching transformer input load can be optimized so that when the matching tranformer load impedance is reflecte back into the primary string loop, various harmonic ranges can be optimized to satisfy what the ear considers as being pleasing.
Lets take a more extreme case using a Prem Magnetics SPCT-251 CT with a TR of 1:2000 makes a 4,000,000 string reflected impedance. If you use two 5" lengths of .162 square copper wire, which easily fits into the SPCT-251 open primary space. Drill two .12" holes on each end of the 5" lengths to accomodate a solid piece of copper wire with a CT on each end forming a few hundred microohm primary loop. Look at the output AC resistance of once CT with the other CT open and you will see about a 20K ohm AC resistance both at 1000Hz and almost the same at 120Hz. Now, short out the second CT with a short jumper and see the reflected AC resistance will be about 10X lower or about 2K ohms on the Extech LCR meter. This is due to primary loop impedance being changed by the second CT reflecting a short back into the primary loop by an impedance ratio of 4,000,000, minus the leakage inductance but this shows how the gauge of the wire on the primary loop can change the tonal characteristics of the two-CT-string-loop under the guitar strings.
Velleman makes a 2-channel scope with a function generator PCSGU250 and software package PC-Lab 2000LT that can run Bode plots by feeding the signal generator into a 500 turn coil of AWG 32 wire on a HB pickup bobbin to stimulate the CT assembly. Try it with a CT open and then again with the CT shorted. Switch the outputs of the two CTs in series and parallel with a simple DPDT switch and listen to the tonal changes. Use an on-on-on swith to make a series/parallel/single coil selection. In the single CT mode, put a variety of pot loads across the second CT as wall as a variety of capacitors and listen to the tonal differences and then note where the most pleasing range of tone changes occurs and then run the bode plot to actually see what is happening. This will be most educational as well as open you mind to what is actually happening in an extremely low impedance string loops with a variety of CTs with different turns ratios. The SPCT-251 will provide you with about 100mv peak output from the 305 ohm secondary coil. Only the ear will tell you what sounds good, then you can graph and print out the Bode plots to capture a picture of the frequency response of what sounds pleasing and then see why it is pleasing.
Guitar strings tend to emphasize certain harmonics but since typical high impedance pickups with 6 to 10 thousand turns of very thin wire (AWG 42, 43) tend to be very low Q coils and have a low inductance. Enter the low impedance CT pickup domain and you can see new opportunities to voice the sound of the pickup by selecting the right gauge of the low impedance string loop as well as tuning that low impedance string loop with the second CT helping to tune the primary loop impedance. This analysis uses traditional transformer theory but because CTs have very high turns ratios, reflected loads can have a very noticable effect on the final pickup sound and the harmonics that are emphasized by the combination of CTs types, turns ratios, primary loop wire size, second CT loading and personal tonal preferences. Ultimately, you will notice that the extended frequency response can be well out beyond the 5KHz to 8KHz audio region where high impedance pickups do not produce very much upper harmonic content.
Lace, the makers of the Alumitone pickup, is missing an opportunity to put a second set of coils on the opposite side of the Alumitone frame where the second CT can be modeled to tune the pickups to sound new ways without needing active electronice. Lace can also put the two sets of secondary outputs in series, parallel or single (as explained above). I estimate that the tiny coils under the frame of the Alumitone frame have about 10,000 turns of wire smaller in diamter than typical AWG 42 or 43. Hint, if Don Lace is reading this post, this is a free design idea to expand the Alumitone pickup design to fully capture it's full design potential. This design concept is all based on using the second CT to tune the low impedance string loop formed by the Alumitone alumium frame.
This is just some more "food for thought" for those curious enough to play with CT pickup designs. Also, this design can make very good sounding magnetic acoustic guitar pickups without the classic resonant hump in the mid audio range that cuts off the upper harmonics that usually helps to define an acoustic guitar sound not adequtely sensed by high impedance magnetic passive pickups.
Joseph Rogowski
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