Low Impedance Pickup Research

[Helmholtz]

There is a lot to do, even in prototypes (reduce skin effect, maybe also proximity effect).

Skin and proximity effects have no influence on the bass response of your prototype: Skin and proximity effects essentially vanish at low frequencies.
The skin depth at 160 Hz is 5.24 mm. I.e. a wire of 10 mm diameter shows no resistance increase by the skin effect at 160Hz and lower.
The proximity effect requires the proximity of current carrying wires. A sole wire loop does not develop a proximity effect.

[Mike Sulzer]

The only way to replace the transformer with an active circuit would require very manyf devices (for example, junction transistors) in parallel. It would be huge and consume a too much power.

The way to replace the transformer is to use a coil with about 500 turns.

If I understand, the proximity effect is like the skin effect, but resulting from the magnetic field produced by current in other turns. I do not think that this is an issue in a 500 turn pickup coil since the normal resistance of the wire would dominate except at very high frequencies.

Josef,

as soon as You have active electronics in Your instrument anyway, the idea of the transimpedance amplifier will become interesting, especially if we find a cheap traditional (low noise, low power consumption) opamp that will do the job. Which actually means that i'd have a lot t learn until i could make some prototype. (i must have a few TL071 in my box... ) The active design will be more compact than the passive design and allow for traditional shapes or pickups that could be fit to an archtop

But anyway: at least for the new future i'll concentrate on the passive version. There is a lot to do, even in prototypes (reduce skin effect, maybe also proximity effect).

Do You think, something like nail polish or some other NC laquer would suffice as an insulation for a stranded wire? I would like to use the wire of electrical installation material, e.g. 1.5 mm^2, diameter 0.67 mm.

[bea]

Skin and proximity effects have no influence on the bass response

Indeed. But potentially a bit on the treble response: at 10 kHz the layer thickness is roughly 0.7 mm. Which translates into "at that depth the effective specific resistivity of the wire has almost tripled". Might already be noticeable regarding the wire thickness of 3.6 mm

Proximity effect - there is more than one. The 2nd type is caused by strong magnetic fields close to a wire. Although i tend to neglect that i would like to understand it better.

[bea]

The only way to replace the transformer with an active circuit would require very manyf devices (for example, junction transistors) in parallel. It would be huge and consume a too much power.

If a transimpedance amplifier is made using an opamp (there are even lists of suitable types on the net) its input impedance will be reduces by the negative feedback.

[Helmholtz]

..at 10 kHz the layer thickness is roughly 0.7 mm.

This means that there will be no noticeably effect for wire diameters <= 1.4mm. For bigger diameters the resistance will slowly increase proportional to (f)^0.5. But the final effect depends on the ratio of load impedance to the reflected DCR of the loop. A few hundred more Ohms of reflected resistance at the secondary will hardly be noticeable if the CT sees a load of 2.5k. Even if so, the easiest way to compensate is using the treble control of your amp.

The 2nd type is caused by strong magnetic fields close to a wire.

But not by DC/permanent fields.

[bea]

Maybe. IMO the skin effect might already have an effect on the current induced in the primary loop. Same argument why Josef always pointed out the importance of a large cross section, just for the higher end of the audio spectrum.
Anyway, it will be a simple experiment to use a few loops of 1.5 mm^2 wire, all through the CT and possibly interconnected (although i don't thing that will be needed because the CT will always see the sum of the currents in all wires through it).
If it works at least as good, it should have the additional advantage of being easier to solder, and it would also allow for flatter setups.

[Mike Sulzer]

If a transimpedance amplifier is made using an opamp (there are even lists of suitable types on the net) its input impedance will be reduces by the negative feedback.

There is no need to decrease the input impedance. The purpose of paralleling devices is to lower the total noise voltage, and this is not practical for such a low voltage. You must either use a transformer or put enough turns on the pickup coil.

[Helmholtz]

Maybe. IMO the skin effect might already have an effect on the current induced in the primary loop. Same argument why Josef always pointed out the importance of a large cross section, just for the higher end of the audio spectrum.
Anyway, it will be a simple experiment to use a few loops of 1.5 mm^2 wire, all through the CT and possibly interconnected (although i don't thing that will be needed because the CT will always see the sum of the currents in all wires through it).
If it works at least as good, it should have the additional advantage of being easier to solder, and it would also allow for flatter setups.

Don't get me wrong. Skin and proximity are high frequency effects. The large cross section of the primary loop, however, is necessary for good bass response. The lower corner frequency of a transformer is given by 2pi*f=Rp/L, where L is the inductance of the primary loop and Rp is given by the parallel resistance of the primary loop and the reflected secondary load resistance. As L is small, Rp has to be very small.

[bea]

Please don't misunderstand me - i do not intend to reduce Rp. Just use a few thinner wires in parallel.

[Mike Sulzer]

Please don't misunderstand me - i do not intend to reduce Rp. Just use a few thinner wires in parallel.

If a single turn pickup made with a single large conductor does not give enough high frequencies, then instead of putting many wires in parallel, put them in series, thus making a multi turn pickup and use a different or no transformer.

[bbsailor]

Helmholtz, Mike, Bea and other forum members,

To calculate the inductance of a single transformer turn (typically what I call the string loop) is done by doing this. This string loop and transformer loop is only a 3/4 loop around the transformer core.
1. Set the Extech 380193 LCR meter to 120 HZ measurement frequency.
2. With the primary open and the Extech LCR attached to the secondary of the CSE-187L current transformer, I get a 1H reading.
3. Divide the number in step 2 above by the turns ratio squared. In this case it is 500 squared or 250,000.
4. This answer or 1/250,000 is 0.000004 or 4 micro Henries per coil turn going through this particular transformer core.

The CSE-187L uses 1.8 inches of AWG 12 wire at 132.4 micro ohms per inch for a total of 238.32 micro ohms. Using transformer theory I then calculated what the ideal impedance of this single turn loop shorted loop should be. I took a needle nose pliers and bent the AWG 12 winding inward sort of like if you put one of your index fingers over the finger nail of your other index finger. Then I pulled them apart and bent the wires so they could be in line and touch each other sort of like if your two index fingers are now directly touching each other with a slight pressure still keeping these wires touching. Now, I use silver solder to join this joint with a blob of silver solder to make a shorted loop to measure. The measured output impedance of this shorted CSE-187L is 80 ohms after the joint has cooled. Transformer theory teaches us that it should have been close to 60 ohms. Why the difference?

Leakage inductance represents one of the major losses in current transformer based pickups and here is why. How much of the primary winding area is occupied by current carrying wire? Even if you connect the CSE-187L to very a thick AWG 4 string loop wire by drilling holes into the U- shaped ends to accommodate the AWG 12 primary turn wire diameter. Since these are in series, the most resistance losses are in the AWG 12 primary turn. The CT primary turn only makes a 3/4 turn with 1/4 of the turn open to add to leakage inductance.

Once you know the shorted primary impedance reading of your chosen CT, you can just add the resistance of the string loop to that impedance to get a very close estimate of the total output impedance of your CT pickup design using the wire size you choose to use.

I obtained a Triad CSE-186L current transformer and I removed the 3 primary turns of AWG 16 and it revealed a primary turn opening of about 4 mm square which could accept AWG 8 wire to form the string loop as well as the CT primary turn but with only one joint to form the continuous current transformer (CT) primary and string loop with the neo type magnet (.250 inch wide by 2 inch long, .125 thick) in the middle. I obtained an Extech LCR output impedance reading close to 100 ohms. After further investigation and calculations, I came to the conclusion that occupying more primary coil with the CSE-186L area (primary removed) made a significant contribution to these measurements and improved output level.

Now a balancing act occurs with skin depth and maximum current development with a simple solution. Round wire in a square transformer primary opening and round wire creates four small areas in each corner of the opening in which to run a thin wire to be placed on top of the wire now allow creative pickup designers to run 4 smaller wired on top of the thick string loop by using spiral wrap to secure the wire location. If the B string is too loud just dip the thin wires lower under the B string.

The evolution of this pickup technology has just begun!!!

Joseph J. Rogowski

[Mike Sulzer]

Concerning leakage flux:

Transformer cores contain nearly all of the flux produced by current through a winding. At the bottom of the frequency the effect of the little bit of leakage flux is irrelevant. The effect becomes important at high frequencies. Suppose the transformer must work from 20 HZ to 20 KHz. Then the effect of the leakage flux (a small inductance in series, say, with the secondary) is 1000 times greater at the top of the range than at the bottom. Leakage flux limits the bandwidth of the transformer.

So I do not see how leakage explains the measurement.

[Helmholtz]

Transformer cores contain nearly all of the flux produced by current through a winding.

True, especially for high µ toroidal cores. But good coupling requires the wire to be closely wound around the core. The string loop instead runs outside the core for most part and I think there must be some small uncoupled inductance, given approximately by the free air inductance of the loop. A single wire has a typical inductance of 10 to 20nH/cm depending on the shape of the loop (the inductance value tends to zero for zero loop area, of course).
If I assume the uncoupled part of the inductance to be around 100nH, this gets stepped up to a serial inductance of 25mH (or a serial reactance of 19 Ohms@120Hz) at the secondary. It should be possible to (approximately) measure this inductance at the secondary (string loop closed) with the Extech.

It would be interesting to repeat the measurements at a higher frequency (1kHz) to see if the secondary impedance rises accordingly.

Edit: Forgot to mention that also the DCR of the secondary coil appears in series with the stepped-up string loop resistance at the output.

[Mike Sulzer]

I think the inductance looking back into the secondary is about 1H on such a system. Also, I believe on the primary side it is possible to think of an inductance looking into the primary of the transformer, and another inductance looking back into the pickup even though it is only one turn. Also you want to make the inductance of the former larger than the latter to avoid attenuating the signal. That is, even though we might call these things current transformers because their normal application is to sense the current through a path without affecting the circuit much, in this application the pickup puts out a very small voltage, and the transformer steps it up to a much higher voltage.

True, especially for high µ toroidal cores. But good coupling requires the wire to be closely wound around the core. The string loop instead runs outside the core for most part and I think there must be some small uncoupled inductance, given approximately by the free air inductance of the loop. A single wire has a typical inductance of 10 to 20nH/cm depending on the shape of the loop (the inductance value tends to zero for zero loop area, of course).
If I assume the uncoupled part of the inductance to be around 100nH, this gets stepped up to a serial inductance of 25mH (or a serial reactance of 19 Ohms@120Hz) at the secondary. It should be possible to (approximately) measure this inductance at the secondary (string loop closed) with the Extech.

It would be interesting to repeat the measurements at a higher frequency (1kHz) to see if the secondary impedance rises accordingly.

Edit: Forgot to mention that also the DCR of the secondary coil appears in series with the stepped-up string loop resistance at the output.

[Helmholtz]

I think the inductance looking back into the secondary is about 1H on such a system.

As bbsailor wrote, 1H is the secondary inductance (measured with open primary loop). It is given by 500² times the AL value of the core. If the primary loop/circuit is closed, the impedance measured at the secondary is given by the secondary open loop inductance in parallel with the stepped-up/reflected primary loop/circuit impedance + the DCR of the secondary coil.

Measurements taken with my LCR meter on a different "CT" with and without a shorted primary loop in principle confirmed my theoretical considerations (based on transformer equivalent circuit, which is the same for "current" and "voltage" transformers). For instance, the inductance value at the secondary increases with the area of the shorted primary loop.