Bucking Coils

[Smudge]

The speed of H field in vacuum is not the same as the speed of the magnetization wave within a length of permeable core material.

Very true and we have means for reducing the speed within the material even more so as to make use of that speed at practical frequencies.  That time delay applied to the two bucking coils offers induced negative resistance, or when connected as non-bucking it becomes induced positive resistance.

[Itsu]

Smudge,

i happen to have a T107/65/18 grade 3F4 (measured / calculated µ_r=770) toroid from an earlier delay line experiment.

I put on 2x 6 turns Litz wire coils diametrically opposite to each other which measure each 52µH and when connected in series opposing/bucking, they measure 16.5µH.
With a 100pF capacitor in parallel, it resonates at 3.770MHz.

I tried to measure / calculate the Q-factor, but get different outcomes, but mostly around 14 which i find rather low.

What will be the best way to measure / calculate the Q-factor?



Itsu

[Verpies]

@Smudge

Itsu's equipment is capable of making these two and one-port measurements up to the GHz range with the following accuracy:



He can also pulse the DUT with a nanosecond pulse in the kilovolt range and observe the response on the oscilloscope, e.g.: see here.

[Smudge]

Smudge,

i happen to have a T107/65/18 grade 3F4 (measured / calculated µ_r=770) toroid from an earlier delay line experiment.

I put on 2x 6 turns Litz wire coils diametrically opposite to each other which measure each 52µH and when connected in series opposing/bucking, they measure 16.5µH.
With a 100pF capacitor in parallel, it resonates at 3.770MHz.

I tried to measure / calculate the Q-factor, but get different outcomes, but mostly around 14 which i find rather low.

What will be the best way to measure / calculate the Q-factor?



Itsu

I would be inclined to loosely couple the RF signal source to the LC circuit, perhaps by a single turn on a small ferrite rod placed within the electrical loop of L connected to C.  Sweep the input frequency through the resonant frequency to measure the response, then use the -3dB bandwith against the resonant frequency to get the Q.
Q = frequency/bandwidth.

[Itsu]

Thanks, that's one of the methods i used which resulted in a Q = 9.666.   (3770 / 390  where Fres. = 3770, F2=4000 and F1=3610).

My concern is the loading of the DUT by the scope probe as it was mentioned in the PDF to try avoiding this too much.
As my used probes are specified as 10Mohm impedance, thats only at DC, so at the 4MHz frequency of the DUT it is decreased to  about 4k, see:
Link removed as it was to private thread, copied the text and pictures below.

i was reading in an earlier post that the TPP0500B probe was used as a load (10Meg / 3.9pF), but after looking at this video: https://youtu.be/Pk7pMguQDy4?t=374 i understand that those values are only correct at DC or very low frequencies.

So i measured my two probes the same way as in the video using the RF spring for ground and measured the following using my nanoVNA:

The frequency range of the nanoVNA was from 10kHz to 60MHz and the marker was set to around 1MHz:

TPP0500B probe (spec: 10Meg / 3.9pF) measured at 1.059MHz 25.1K / 5.9pF
P6139B probe (spec: 10Meg / 8pF) measured at 1.059MHz 16.3K / 9.2pF

See below VNA output traces which show that the capacitance stays fairly stable (but somewhat higher as the specs) right after the start range, but the impedance quickly drops considerably between start and 5MHz range to only a fraction of the specified 10Meg.

Itsu

[gyula]

Hi Itsu,

The inductive reactance of the two bucking coils is XL = 391 Ohm (rounded) at 3.77 MHz when their L = 16.5 uH. The quality factor, Q is XL / r so even if the two coils
DC resistance is say r = 3 Ohm in their series connection (a rough estimate), Q should be around 130. (I did not consider core and skin losses.)

Perhaps use a single bipolar transistor like the schematic shows below. Measure the resonant voltage across the 100 pF capacitor by the 10x scope probe and divide it by
the input voltage of the signal generator driving the base. This method mimics a classical Q meter concept, the transistor replaces the wide band matching transformer.
You can check the input voltage across the emitter resistor too, it should be 0.9 - 0.95 times the input generator voltage and can use it for the calculation.

Gyula

[gyula]

Itsu,  use 200-220 Ohm emitter resistor instead of the 1 kOhm to have higher emitter current so the virtual emitter resistance (26 mV / IE ) should be lower. This way the coil Q will better approach the real value.
Insure the roughly 6 V DC voltage across the emitter resistance, this means 27 - 30 mA emitter current.
10 - 20 mV input voltage from the signal generator is enough to feed in and the voltage across the 100 pF capacitor may be around 1 V or higher if the loaded Q is around 100.  On loaded Q I mean the virtual emitter resistance
which appears in series with the coils+100 pF plus the coil losses of course.

  I wonder what is the DC resistance of the two coils in series?  Less than 1 - 2 Ohm?

Gyula

[Itsu]

Hi Gyula,

thanks for your info, i will take a look at your suggested circuit.

As far as i can measure with my Fluke DMM, the DC resistance of the 2 coils in series is 0.1 Ohm (0.2 Ohm of the DMM probes alone, 0.3 Ohm including the 2 series coils).

By the way, if i use this calculator: https://www.omnicalculator.com/physics/rlc-impedance with "RLC in parallel", R=0.1, L=16.5uH, C=100pF and f=3770 i get as result among other: Q=0.000246183.


Itsu

[Verpies]

My concern is the loading of the DUT by the scope probe

You have a FET probe that loads the DUT much less  ...also, there is always this with a larger resistor.

[Smudge]

As far as i can measure with my Fluke DMM, the DC resistance of the 2 coils in series is 0.1 Ohm (0.2 Ohm of the DMM probes alone, 0.3 Ohm including the 2 series coils).

By the way, if i use this calculator: https://www.omnicalculator.com/physics/rlc-impedance with "RLC in parallel", R=0.1, L=16.5uH, C=100pF and f=3770 i get as result among other: Q=0.000246183.

But the 0.1 Ohm is not in parallel, it is in series with the L and your frequency was 3.77MHz not 3.77KHz.  Try the calculator with RLC in series and you should get Q=4.  And that would apply to L (with its series R) in parallel with C and no shunt R present across C.  The online calculator doesn't allow you to input practical values for loss resistors within the L or C.

You previously reported a measured Q of about 10 which is quite low, but the experiment adding phase delay along the core should show increase of this Q indicating induced negative resistance.  Of interest is how far that Q can go, does it tend towards infinity (self oscillations) as you add more and more delay? That Q figure derived from frequency/bandwidth should be good enough for this exercise.

Smudge

[Itsu]

Smudge,

But the 0.1 Ohm is not in parallel, it is in series with the L and your frequency was 3.77MHz not 3.77KHz.  Try the calculator with RLC in series and you should get Q=4.  And that would apply to L (with its series R) in parallel with C and no shunt R present across C.  The online calculator doesn't allow you to input practical values for loss resistors within the L or C.

If i use "RLC in series" on that calculator i indeed get a Q=4 (by the way, i inputted 3770kHz for f, so it was 3.77MHz).

You previously reported a measured Q of about 10 which is quite low, but the experiment adding phase delay along the core should show increase of this Q indicating induced negative resistance.  Of interest is how far that Q can go, does it tend towards infinity (self oscillations) as you add more and more delay? That Q figure derived from frequency/bandwidth should be good enough for this exercise.

OK, i will use the Q derived from the frequency/bandwidth method (or ring down method which gives similar results) using the several probe solutions (Gyula's single bipolar transistor schematic and my FET probe) suggested.

Then start adding more delay and see what is going to happen.

Itsu

[Itsu]

I used 3 probes to measure / calculate the Q of my "parallel LCR" (16.5uH, 100pF and 0.1 Ohm) as shown earlier, by using the "frequency / bandwidth" method.


Scope TDS-3054B:

probe P6139B (passive) 10x (10MOhm / 8pF) Q=13
probe P6202   (active)  10x (10Mohm / 2pF) Q=11

Scope MDO-3054:

probe TPP0500B (passive) 10x (10MOhm / 3.9pF) Q=11

Surprising outcome as the probe with the highest load (P6139B) gives the highest Q (13)



Gyula his bipolar transistor probe schematic was also tested on the above device, but in "series LCR" configuration (had to run the scope channel in AC coupling)

Bipolar transistor 2n2222 (active) 11.2V input, 3.5V DC across emitter resistor (220 Ohm), 55mVpp input from FG, 565mVpp across 100pF cap.   Q=10.7


So i think this is enough to have a baseline Q (13) to see if when adding the delays it will increase.

Itsu

[Verpies]

How does the VNA sweep look like ?

[Itsu]

Well, i spend a few hours yesterday using the nanoVNA using several methods (shunt measurement S11 and shunt-thru measurement S21) but could not make any sensible (to me) readings out of it.

There are Q-factor graphs which i could show, but the figures presented did not make any sense to me (very low dip at resonance frequency in the 0.0024 range (same as the calculator results i linked earlier).
The resonance peak at 3.77Mhz was clearly visible, but i could not translate it into a valid Q-factor somehow (probably doing something wrong).
I tried both in parallel resonance as in series resonance setup.

Now i know it should be around Q=13 i could give it another try.


Below is a sweep from 10kHz to 10MHz using the "shunt-thru measurement" with the DUT in a series setup.
The Quality Factor S11 graph does not make sense to me (Q=0.017).



Itsu 

[gyula]

Hi Itsu,

Thanks for doing the test. The emitter current was 3.5V / 220 Ohm = 16 mA  this gives 26 mV / 16 mA = 1.6 Ohm virtual emitter resistance which appears in series with the coil, too high resistance.
IF you agree, would you reduce  the 220 Ohm emitter resistor to 120 Ohm, and reduce the top base bias resistor R1 to 2.2 to 4.7 kOhm?  This way the emitter voltage hence the emitter current should increase to 7 - 8 V at least
so the emitter current would be in the 60-70 mA range.   This way the virtual emitter resistance reduces to around 0.3 - 0.4 Ohm. So the original coil Q should increase to much closer to the real Q the coil may have.

Gyula

[Verpies]

Below is a sweep from 10kHz to 10MHz using the "shunt-thru measurement" with the DUT in a series setup.

So why does the VNA display S11 ?

Shunt-through and series VNA measurements are 2-port measurements so the VNA should display "S21" for them.

Let's keep this organized - there are four S21 measurement possible:
1) Shunt-through S21 measurement of a parallel LC DUT
2) Shunt-through S21 measurement of a series LC DUT
3) Series S21 measurement of a parallel LC DUT
4) Series S21 measurement of a series LC DUT


  S21 calibration fixture

[Itsu]

Well, the nanoVNA itself can display the S21 Q-factor graph, but the nanoVNA PC App only has the S11 Q-factor Graph to display.
As both graphs look similar i toke the nanoVNA PC app to copy it here.

I did use the 2) Shunt-through S21 measurement of a series LC DUT in the measurement shown.

Itsu

[Itsu]

Hi Itsu,

Thanks for doing the test. The emitter current was 3.5V / 220 Ohm = 16 mA  this gives 26 mV / 16 mA = 1.6 Ohm virtual emitter resistance which appears in series with the coil, too high resistance.
IF you agree, would you reduce  the 220 Ohm emitter resistor to 120 Ohm, and reduce the top base bias resistor R1 to 2.2 to 4.7 kOhm?  This way the emitter voltage hence the emitter current should increase to 7 - 8 V at least
so the emitter current would be in the 60-70 mA range.   This way the virtual emitter resistance reduces to around 0.3 - 0.4 Ohm. So the original coil Q should increase to much closer to the real Q the coil may have.

Gyula

Gyula,

i changed the resistors (120 Ohm and 3.3K now) which brought the emitter voltage to 8V

The Q now measured is 11.4


Itsu

[gyula]

I see, sorry and thanks.

[Itsu]

Gyula,

i used the "frequency / bandwidth" method to measure / calculate the Q using your schematic, but i understand i need to calculate the Q using  "the resonant voltage across the 100 pF capacitor by the 10x scope probe and divide it by
the input voltage of the signal generator driving the base".


If i do that i have 5467mV / 526mV = 10.4 as the Q, see screenshot:



Yellow = voltage across 100pF capacitor
Blue = input voltage FG (different voltage scale for clarity)

So the Q is very similar as the "frequency / bandwidth" method.

Itsu

[gyula]

Hi Itsu,

Thanks for these.  I assume the generator voltage across the 120 Ohm emitter resistor is pretty close to 526 mVpp. Generally, emitter followers has a 'gain' of 0.9- 0.95, but this 'improve' the calculated Q only a little.   
Unfortunately, a much higher emitter current would be needed to reduce the virtual emitter resistance.  If we choose say IE = 1 Amper emitter current, the  26 mV / IE gives 0.026 Ohm, this is much less than the coils DC resistance of 0.1 Ohm.
This would need say a RE = 10 Ohm and >10 W power rated resistor and a 2N3055 or similar transistor, R1 would be say 1 kOhm.  IF you agree and assign the time, maybe we can get a more correct Q value. 
(IF the power transistor has a low hFE value, use a small transistor in Darlington connection to the power transistor, R1 would be say 100 kOhm in this case to bias the base of the small transistor.)

Gyula

[Itsu]

Hi Itsu,

Thanks for these.  I assume the generator voltage across the 120 Ohm emitter resistor is pretty close to 526 mVpp. Generally, emitter followers has a 'gain' of 0.9- 0.95, but this 'improve' the calculated Q only a little.   
Unfortunately, a much higher emitter current would be needed to reduce the virtual emitter resistance.  If we choose say IE = 1 Amper emitter current, the  26 mV / IE gives 0.026 Ohm, this is much less than the coils DC resistance of 0.1 Ohm.
This would need say a RE = 10 Ohm and >10 W power rated resistor and a 2N3055 or similar transistor, R1 would be say 1 kOhm.  IF you agree and assign the time, maybe we can get a more correct Q value. 
(IF the power transistor has a low hFE value, use a small transistor in Darlington connection to the power transistor, R1 would be say 100 kOhm in this case to bias the base of the small transistor.)

Gyula

Gyula,

I assume the generator voltage across the 120 Ohm emitter resistor is pretty close to 526 mVpp. Generally, emitter followers has a 'gain' of 0.9- 0.95, but this 'improve' the calculated Q only a little. 

yes, the generator voltage across the 120 Ohm is 518mV (with DC offset, so need to set the channel to AC coupled).

Unfortunately, a much higher emitter current would be needed to reduce the virtual emitter resistance.  If we choose say IE = 1 Amper emitter current, the  26 mV / IE gives 0.026 Ohm, this is much less than the coils DC resistance of 0.1 Ohm.
This would need say a RE = 10 Ohm and >10 W power rated resistor and a 2N3055 or similar transistor, R1 would be say 1 kOhm.  IF you agree and assign the time, maybe we can get a more correct Q value. 

I do have the 2N3055, and a 10W 10 Ohm resistor, so i can set this up.

I also do want to make some nanoVNA measurements to see if i can make some sensible Q measurements with that.

Meanwhile, i have added the 2 extra delay line coils (21 turns each) around the toroid, and plan to solder some (21 each) 22pF smd capacitors to each winding when done with the base Q factor measurements:



Itsu

[gyula]

Thanks.  Probably you would need to use a Darlington configuration to surely drive the base of the 2N3055 with say the 2N2222 (join the two collectors on the +11V rail, connect the emitter of the 2N2222 to the base of the 2N3055. R1 is between the base of the 2N2222 and the +11V rail, input generator goes to the base of the 2N2222 via the coupling cap.  The DC voltage across the 10 Ohm should be around 10V. All this is in case the hFE of the 2N3055 proves to be too low at 1 A current. Try to use the 2N3055 alone first, with R1 in the range between 470 Ohm to 1 k.

Gyula

[Itsu]

I removed the last post as there is something wrong with the 2N3055 somehow.

Itsu

[gyula]

Hi Itsu,

Yes I agree.  Just was about to tell to check it.   

Thanks,

Gyula