Impedance: actual, typical and measured from 20Hz to 20kHz

[trzesnk]

Hello,



Long time reader of the forum (and subforum), but never posted. A big respect for your willingness to share your knowledge!

I am guitar builder, building acoustic archtops. Single digit per year. As acoustic archtop players wants to play through the amp sometimes, I need a pickup capable to translate accurately the acoustic sound of my guitar to electric signals. I have decided to build a low impedance pickup with a step-up transformer at the amp end of the xlr cable using Hi-Z acoustic guitar amp input. Although I have build successful pickups before, I am not trained in electronics, so sometimes I hit the wall with questions, that is probably so basic, that I can not find an answer... 

Can you help me to understand impedance nomenclature? What is a typical impedance and what is an actual impedance given by manufacturers in specs? E.g. Shure A85F impedance matching transformer states on the unit itself 150-600 Ohm on XLR side and Hi-Z on TS side. On Shure web page I can find info that for A85F the primary actual impedance is 300 ohms and secondary is 40,000 ohms. At what frequency it is measured? When I measure impedance of my pickups it changes of course with frequency. E.g. my humbucker with 2x288 turns, 0.1mm wire, measure (not loaded) ~80 Ohm at low frequency, reaches 600 Ohm just above 8 kHz and 1.9 kOhm at 20 kHz (not reaching peak impedance at 20kHz yet). My second pickup is 2x432 turns of 0,14mm wire and its impedance starts at 230 Ohm at low frequencies. At which frequency should I measure pickup impedance and use this value to chose the right transformer to obtain good impedance bridging with step-up transformer (output impedance at least 10x smaller than input impedance, right?)? I experimented with 2 transformers until now: Neutrik NTE 10/3 in 1:10 wiring and Shure AF85F, but maybe Shure A95 would be better to one of my pickups? My pickups translates the acoustic sounds very nicely, have a very wide frequency range, well suppresses buzz and hi frequency noise, but when tweaking a design it would be good to know if one is not making a basic mistake with e.g. wrong impedance bridging.
So at which frequency manufacturers measure value of impedance given in specs?

Krzysztof.

[ms]

As a practical matter, if you have a transformer that is 300 ohms to 40 K and you connect the secondary to a 40K resistor you should measure about 300 ohms looking into the primary over the stated frequency operating range.  If you lower the frequency, you should see the impedance drop and become inductive as a result of the primary inductance.  Above the operating frequency range I would expect it to become capacitive as the importance of the leakage flux becomes more important.

You pickup is resistive at low frequencies.  I would make it 300 ohms or less to avoid losing bass as a result of the transformer inductance.  The load provided by the guitar amp is a lot higher than 40K, but this is not a problem.  It means that as the impedance of your pickup rises with frequency (a result of its inductance) you  should continue to get good performance.  However, at some frequency below the stated operating range you should start to lose high frequencies since the effects of the transformer leakage inductance might matter at a lower frequency than normal because of the pickup inductance.  But I think you do not really need to be good to 20 KHz, and it will be more than good enough.

My own preference would be to skip the transformer, and instead use maybe 1500 turns per coil rather than 5000, raising the resonance frequency (and losing some output level you do not really need in this application).  Then I would find the value of resistor across the pickup to adjust the high frequencies to get the most natural sound.

[aquin43]

The 300Ω impedance quoted for the A85f is just the nominal resistance it was designed to be driven from to produce a reasonable frequency response. Shure seem to provide no proper specification for this transformer. Assuming that it will be 3dB down at 30Hz when driven from 300Ω then the primary inductance will be around 1.6H. The impedance ratio is 40k/300 which would make the secondary inductance 213H. These transformers are not intended for use with inductive sources and whether they work satisfactorily is a matter of luck, particularly because some essential parameters are not specified.

Your first pickup behaves like 80Ω in series with 15mH. With this pickup connected and looking into the transformer secondary you will see the pickup multiplied up to 2H and 10k67 in series with the transformer resistance and the unknown leakage inductance and loaded by the transformer secondary capacitance. The effective turns per coil will have been raised by the square root of the impedance ratio to 3326.

If we guess at a secondary capacitance of 150pF and a transformer resonant frequency of 18kHz, that would give a secondary leakage inductance of 520mH. Add on the 2H from the pickup and a peak at 8kHz could be expected. This would be high enough to be OK for guitar and could be damped with a parallel resistor in the same way as a conventional pickup.

[trzesnk]

Thank you for your answer.

So it means, that if a guitar amp specs states a Hi-Z input of e.g. 2 MOhm, it is "seen" on the primary winds of 1:10 step up transformer as 20kOkm, yes? As this is more then 10 times bigger than output impedance of my pickup in any of acoustic frequencies, all is good, right? 

Both of my low impedance pickups designs under tests now have DCR below 300 Ohms as you have suggested (82 and 234 Ohms). The inductance at 100Hz is 0.07 and 0.19 H, but with transformer they both drives AER Alpha acoustic amp very nicely. I hear differences with different transformers and 2x288x0.14mm works better with Shure A85 and 2x432x0.1mm with Neutrik NTE 10/3, but it is subjective. Both transformers are stated to be 20 Hz - 20 kHz frequency range. Funny enough I made 2 coils on the same bobbins exactly as you have proposed with 1500 turns of 0.6mm wire, but they are not connected yet and they will be tested soon without transformer.

I still do not understand how manufacturers chose and state one value of impedance, e.g. for dynamic microphones, when their actual impedance change dramatically with frequency. And low impedance pickups' output is similar to dynamic microphones. This is where my question came from.

Krzysztof.

[trzesnk]

Jun 27, 2022 6:54:36 GMT -5 aquin43 said:

The 300Ω impedance quoted for the A85f is just the nominal resistance it was designed to be driven from to produce a reasonable frequency response. Shure seem to provide no proper specification for this transformer. Assuming that it will be 3dB down at 30Hz when driven from 300Ω then the primary inductance will be around 1.6H. The impedance ratio is 40k/300 which would make the secondary inductance 213H. These transformers are not intended for use with inductive sources and whether they work satisfactorily is a matter of luck, particularly because some essential parameters are not specified.

Your first pickup behaves like 80Ω in series with 15mH. With this pickup connected and looking into the transformer secondary you will see the pickup multiplied up to 2H and 10k67 in series with the transformer resistance and the unknown leakage inductance and loaded by the transformer secondary capacitance. The effective turns per coil will have been raised by the square root of the impedance ratio to 3326.

If we guess at a secondary capacitance of 150pF and a transformer resonant frequency of 18kHz, that would give a secondary leakage inductance of 520mH. Add on the 2H from the pickup and a peak at 8kHz could be expected. This would be high enough to be OK for guitar and could be damped with a parallel resistor in the same way as a conventional pickup.

Thank you for your answer and your rough guess calculations. It looks like it all could work...
Yes, not a lot of info about these transformers. A85F tested open: R primary is 27.3 Ohm, secondary 1738 Ohm, Inductance primary open (UNI-T UT602, 100Hz) 2.13H, secondary 148H. NTE 10/3 in 1:10 wiring respectively 43 Ohm, 1710 Ohm, 1.77H and 133H. Which transformers would be better if these are not intended to work with inductive sources? I want to make sure if I recommend a solution to a guitar player this will be working with all acoustic amp Hi-Z inputs, not counting on luck :/
I will be testing as well a 2x1500 of 0.6mm humbucker which will not need a transformer to work, so maybe it will be an easier path. Especially that volume control (I intend to skip tone control) in balanced setup is a new area to me, too.

Krzysztof.

[aquin43]

Jun 27, 2022 7:07:21 GMT -5 trzesnk said:

Thank you for your answer.

So it means, that if a guitar amp specs states a Hi-Z input of e.g. 2 MOhm, it is "seen" on the primary winds of 1:10 step up transformer as 20kOkm, yes? As this is more then 10 times bigger than output impedance of my pickup in any of acoustic frequencies, all is good, right? 

Both of my low impedance pickups designs under tests now have DCR below 300 Ohms as you have suggested (82 and 234 Ohms). The inductance at 100Hz is 0.07 and 0.19 H, but with transformer they both drives AER Alpha acoustic amp very nicely. I hear differences with different transformers and 2x288x0.14mm works better with Shure A85 and 2x432x0.1mm with Neutrik NTE 10/3, but it is subjective. Both transformers are stated to be 20 Hz - 20 kHz frequency range. Funny enough I made 2 coils on the same bobbins exactly as you have proposed with 1500 turns of 0.6mm wire, but they are not connected yet and they will be tested soon without transformer.

I still do not understand how manufacturers chose and state one value of impedance, e.g. for dynamic microphones, when their actual impedance change dramatically with frequency. And low impedance pickups' output is similar to dynamic microphones. This is where my question came from.

Krzysztof.

The transformer doesn't have a particular impedance. What is specified are the impedances of the source and load it works best with. An ideal transformer is completely transparent and without particular impedance in itself. It merely reflects other impedances presented to its primary as scaled impedances at the secondary and vice versa. A real transformer has inductances across primary and secondary, imperfect coupling and parasitic capacitances. It is these that limit its usefulness to a range of input and output impedances with peak performance from one particular source impedance. It is this that is quoted as the impedance.

Similarly for microphones. A 200Ω mic will have a resistance just under 200Ω together with some inductance. It will usually work best into a 2k load. The 200Ω and 2k are chosen and adjusted in terms of the frequency response and noise performance. There is no question of load matching as happens with radio frequency equipment.

When you start using a transformer outside its designed circuit impedance range such as with a pickup that has a varying inductive impedance over most of its useful frequency range you really need more information than is usually specified to know exactly how it will behave. Ultimately a transformer suffers from the same problems of inductance and parasitic capacitance as the pickup.

As an aside, your pickup should have enough output to directly feed a mixer mic input, most of which nowadays are transformerless. The 15mH one would have a bandwidth of 20kHz into a 2k load.

 

[aquin43]

Jun 27, 2022 8:07:09 GMT -5 trzesnk said:

Jun 27, 2022 6:54:36 GMT -5 aquin43 said:

The 300Ω impedance quoted for the A85f is just the nominal resistance it was designed to be driven from to produce a reasonable frequency response. Shure seem to provide no proper specification for this transformer. Assuming that it will be 3dB down at 30Hz when driven from 300Ω then the primary inductance will be around 1.6H. The impedance ratio is 40k/300 which would make the secondary inductance 213H. These transformers are not intended for use with inductive sources and whether they work satisfactorily is a matter of luck, particularly because some essential parameters are not specified.

Your first pickup behaves like 80Ω in series with 15mH. With this pickup connected and looking into the transformer secondary you will see the pickup multiplied up to 2H and 10k67 in series with the transformer resistance and the unknown leakage inductance and loaded by the transformer secondary capacitance. The effective turns per coil will have been raised by the square root of the impedance ratio to 3326.

If we guess at a secondary capacitance of 150pF and a transformer resonant frequency of 18kHz, that would give a secondary leakage inductance of 520mH. Add on the 2H from the pickup and a peak at 8kHz could be expected. This would be high enough to be OK for guitar and could be damped with a parallel resistor in the same way as a conventional pickup.

Thank you for your answer and your rough guess calculations. It looks like it all could work...
Yes, not a lot of info about these transformers. A85F tested open: R primary is 27.3 Ohm, secondary 1738 Ohm, Inductance primary open (UNI-T UT602, 100Hz) 2.13H, secondary 148H. NTE 10/3 in 1:10 wiring respectively 43 Ohm, 1710 Ohm, 1.77H and 133H. Which transformers would be better if these are not intended to work with inductive sources? I want to make sure if I recommend a solution to a guitar player this will be working with all acoustic amp Hi-Z inputs, not counting on luck :/
I will be testing as well a 2x1500 of 0.6mm humbucker which will not need a transformer to work, so maybe it will be an easier path. Especially that volume control (I intend to skip tone control) in balanced setup is a new area to me, too.

Krzysztof.

The ratio of inductances for the A85F 148/2.13 = 69.48 doesn't match the quoted impedance ratio of 40k/300 = 133.3. Neither does the ratio for NTE 10/3 match the 1:10 winding ratio. Obviously the inductances must be level dependent and can only really be deduced from the in-circuit behaviour.

The fundamental problem with transformer coupling pickups is that the transformer secondary can have quite a high capacitance since it defines the bandwidth by resonating with the leakage inductance which can be low in a well designed transformer. When you add the pickup inductance reflected up through the square of the transformer ratio, the bandwidth reduces and there will be peaking that will have to be controlled with a parallel resistor. The only real way to do this with the available information is to plot the frequency response and adjust accordingly.

[ms]

Jun 27, 2022 7:07:21 GMT -5 trzesnk said:

Thank you for your answer.

So it means, that if a guitar amp specs states a Hi-Z input of e.g. 2 MOhm, it is "seen" on the primary winds of 1:10 step up transformer as 20kOkm, yes? As this is more then 10 times bigger than output impedance of my pickup in any of acoustic frequencies, all is good, right? 

Both of my low impedance pickups designs under tests now have DCR below 300 Ohms as you have suggested (82 and 234 Ohms). The inductance at 100Hz is 0.07 and 0.19 H, but with transformer they both drives AER Alpha acoustic amp very nicely. I hear differences with different transformers and 2x288x0.14mm works better with Shure A85 and 2x432x0.1mm with Neutrik NTE 10/3, but it is subjective. Both transformers are stated to be 20 Hz - 20 kHz frequency range. Funny enough I made 2 coils on the same bobbins exactly as you have proposed with 1500 turns of 0.6mm wire, but they are not connected yet and they will be tested soon without transformer.

I still do not understand how manufacturers chose and state one value of impedance, e.g. for dynamic microphones, when their actual impedance change dramatically with frequency. And low impedance pickups' output is similar to dynamic microphones. This is where my question came from.

Krzysztof.

The amp you mention appears to have a low impedance mic input; it probably does not have a transformer, but rather a low noise differential input amplifier.  Have you tried your pickups into that with no transformer?  This would give you a reference.  If this is the amp the customer uses, you might consider not using a transformer.

[trzesnk]

Of course I have tried it   

This was one of the first things I did to have some reference as I thought this will be a reference sound to compare. And... I was disappointed. There is much more noise when I connect XLR without transformer directly to the XLR microphone input. Moreover the sound is dull without higher range of high frequencies. It was strange to me, because I expected a full range pickup through XLR input. The same pickups connected to Hi-Z input of the amp through impedance matching transformer sound more full, with nice highs comparable with good passive magnetic pickup for acoustic guitars (my reference is Fishmann Neo-D pickup). Of course it does not sound as good as a guitar through a good microphone. I can hear that not all aliquotes (harmonics) are present comparing to pure acoustic sound. But I understand this is a beauty of magnetic pickup, which is not translating the acoustic sound of string, and even less of the whole guitar, but interprets string velocity changes with its own idiosyncrasies. 

It is my amp, that I use to test guitars as I test any guitar with pickup through the full range guitar amp using its "full range" speaker and to hear the real thing through the headphones. As customers have different amps, not all of them have mic input, and I wanted quite a universal solution I decided to concentrate on Hi-Z input. 
I thought that maybe the mic input is defective in my amp. I bought the amp used several years ago and used it with SM58 only several times and it works pretty well. I checked it today - still works with mic well, although the noise level is higher through this input, but I treat that as normal, because of extra gain.

Nota bene, until now all the test are without any potentiometers or capacitors, pickup directly to cable with transformer on the other end then to amp. I still have to figure out how to do passive volume control.

Krzysztof 

[ms]

Jun 27, 2022 11:42:56 GMT -5 trzesnk said:

Of course I have tried it   

This was one of the first things I did to have some reference as I thought this will be a reference sound to compare. And... I was disappointed. There is much more noise when I connect XLR without transformer directly to the XLR microphone input. Moreover the sound is dull without higher range of high frequencies. It was strange to me, because I expected a full range pickup through XLR input. The same pickups connected to Hi-Z input of the amp through impedance matching transformer sound more full, with nice highs comparable with good passive magnetic pickup for acoustic guitars (my reference is Fishmann Neo-D pickup). Of course it does not sound as good as a guitar through a good microphone. I can hear that not all aliquotes (harmonics) are present comparing to pure acoustic sound. But I understand this is a beauty of magnetic pickup, which is not translating the acoustic sound of string, and even less of the whole guitar, but interprets string velocity changes with its own idiosyncrasies. 

It is my amp, that I use to test guitars as I test any guitar with pickup through the full range guitar amp using its "full range" speaker and to hear the real thing through the headphones. As customers have different amps, not all of them have mic input, and I wanted quite a universal solution I decided to concentrate on Hi-Z input. 
I thought that maybe the mic input is defective in my amp. I bought the amp used several years ago and used it with SM58 only several times and it works pretty well. I checked it today - still works with mic well, although the noise level is higher through this input, but I treat that as normal, because of extra gain.

Nota bene, until now all the test are without any potentiometers or capacitors, pickup directly to cable with transformer on the other end then to amp. I still have to figure out how to do passive volume control.

Krzyszt

Is this noise "hiss", as when you have to turn the gain up high for a weak source, or is it something else?

The dull sound might be the lack of equalization.  For example, the tone stack in in a guitar amp is not flat when the controls are set to the middle, but has a distinct emphasis in the upper midrange extending into the highs.  I do not know if the hi Z input you use for the acoustic guitar amp does as well, but if it is intended for a magnetic pickup it might.  Also, a magnetic pickup (normal hi Z) itself has a resonance that can give a significant boost to the upper mid range and low highs.  The resonant frequency of your low Z pickup  would be too high to have this effect.

[trzesnk]

It is a pure hiss, that my ear associates with extra gain. Maybe the mic preamp is not the best in this amp, or it is defective? 
The dullness may be, as you have wrote, because of different equalization curves for microphone and instrument input.
Now I need to figure out the wiring for volume control, but for that I will write separately in wiring sub forum.

Thank you all for your time and efforts! Appreciate it very much!

Krzysztof.

[aquin43]

The mic input stage will have a bipolar transistor front end that is optimised for low impedance sources. In order to keep the noise voltage low, the transistors are operated at a fairly high collector current. Because of the limitations of the transistor current gain this requires large base currents, part of which are noise. In normal operation this noise current at the input passes through the 200Ω mic and produces a noise which adds a little to the voltage noise. When you connect your pickup, particularly the second one, its impedance is higher and rising with frequency so the noise current produces a noticeable extra hiss.

[trzesnk]

Thank you for your input. 
I have checked the amp specs and it says 1.2 kOhm impedance for balanced microphone input, so it really gives less room for impedance bridging, especially for the 2x432 turns pickup, which reaches 300 Oms impedance already at 1 kHz and 1.2 kOhm just below 8 kHz (comparing to the 2x288 which reaches 120 Ohm at 1kHz, 300 Ohm at 3.5 KHz and 1.2 kOhm at 14 kHz).
The Hi-Z input impedance is comfortable 2.2 MOhm.
I checked as well a circuit diagram of the amp and it shows a "Voice filter" just after mic preamp, so yes, there are different equalizations for mic and instrument input.
Thank you both for directing me 

Krzysztof.

[ms]

I think that the 1.2K input impedance of the mic. preamp means that the effect of the current noise flowing from its input is limited, and so I doubt that the source of  the excess noise encountered with one of your pickups connected is its inductance.