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Old 21st Jun 2021, 5:28 pm   #1
regenfreak
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Default Relaxation oscillation in LC resonance/ Toko testers

I have been using a cascade FETs (common source) LC coil tester for valve and transistor Toko IF transformers for some time (see attachment):

https://www.radio-collector.com/coil-resonance-tester/

or a variant of the Franklin oscillator:

https://www.on1bes.be/toko_tester_en.html

If you look at the output waveforms on the scope, it never gives a clean sine wave regardless of frequency but more resembles astable multivibrator waveform.
While it gives accurate resonance frequencies for 455kHz IF transformers (both valve and transistor type), I have the following observations (that has been bugging me for a long time):


1. it gives a completely wrong resonance frequency ( much lower) for valve FM IF transformers. The LC resonance impedance |Z| for valve radio 10.7MHz IF transformers is an order of magnitude at least 100k ohms. For 10.7MHz Toko IF for transistor radios, the resonance impedance |z| is about 10-20k, MAYBE it gives less error than valve type.

2. I compare the measurements with a commercial Toko coil/crystal tester which is also FET based oscillator, it suffers exactly the same problem as above.

It appears that the dual FET LC coil tester tends to suffer from the transition from sinusoidal harmonic oscillation to relaxation oscillation. The effect of the parasitic capacitance of the FETs increases with increasing resonance frequency:

https://www.radiomuseum.org/forum/re...cillators.html

It seems R1 and R2 in the link above have a big effect on the accuracy of measured resonance frequencies too:

https://www.radiomuseum.org/forum/dipper_ade.html


My questions are:

1. Referring to the circuit in the first link, would the LC resonance frequency error be minimised if I reduce the feedback capacitance (C2=33pF) to a very small value, 1~2pF for 10.7MHz IF transformer? The reactance of a 1pF capacitor is 14.87k ohms at 10.7Mhz; it drops to 450 ohms with a 33pF feedback resistor. What about replacing the feedback resistor R1 and R2 by a potentiometer?

2. the coil tester is useless for finding resonance frequency for the valve FM IFs because its LC resonance |Z| is large compared with the input impedance of cascade FETs oscillator AND frequency drift due to relaxation oscillation. Is this statement correct?


3. The effect of parasitic capacitance of the dual FETs increases with increasing frequencies. So we cannot trust the readings of the coil tester for FM transistor type Toko 10.7MHz transformer in spite of its lower resonance |Z|?
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Old 21st Jun 2021, 6:35 pm   #2
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Correction of error in my post above, looking at Toko FM datasheet, when manufacturer states 10K, it does not mean its LC impedance|Z| is 10k, but the primary-to-secondary impedance ratio is 10k to 300 ohms.

https://www.radioamatore.info/attach..._coil_data.pdf

For example, for 10.7MHz IF, C =80pF and it would need 2.77 micro H inductance to give correct resonance frequency. Its LC resonance impedance is |Z| = 116k so it is comparable with the impedance of valve FM IF.
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Old 21st Jun 2021, 7:32 pm   #3
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Oscillators are often the most misleading things to try and figure out, they live in some alternate universe at times.

I would fit a 0- 22pF variable trimmer cap in place of that C2 and have a play, it will be the only way to find out whether it will work.
I would imagine the value could be quite small at higher frequencies at least. You could always have a switch to put in 33pF or whatever to make sure it still oscillates at the lower frequencies.

I just use a series LC cct. (a series notch acceptor cct.) across the Speccy Analyser input and drive it from a 50 ohm Sig. Gen. I use a fixed L or C and figure out the unknown LC from calcs. It works up to many hundreds of MHz. As long as I see a dip, there is no prob.

Last edited by Cruisin Marine; 21st Jun 2021 at 7:50 pm.
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Old 21st Jun 2021, 8:26 pm   #4
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
Originally Posted by Cruisin Marine View Post
Oscillators are often the most misleading things to try and figure out, they live in some alternate universe at times.

I would fit a 0- 22pF variable trimmer cap in place of that C2 and have a play, it will be the only way to find out whether it will work.
I would imagine the value could be quite small at higher frequencies at least. You could always have a switch to put in 33pF or whatever to make sure it still oscillates at the lower frequencies.

I just use a series LC cct. (a series notch acceptor cct.) across the Speccy Analyser input and drive it from a 50 ohm Sig. Gen. I use a fixed L or C and figure out the unknown LC from calcs. It works up to many hundreds of MHz. As long as I see a dip, there is no prob.
I will try a silver piston trimmer. If the dual FET oscillator feedback is large ( with large feedback cap C1 or small feedback resistors R1 and R2) at high frequencies, the common source current would be large, clipping would occur so the resonance frequency is pulled down. This is my understanding of the explanation in the German forum.

It is easy to measure series LC resonance frequency because of its low resonance |Z|, for example 80pF cap in series with a 2.77microH inductor would give resonance impedance |z|=186 ohms, it is easy use impedance matching network or transformer to match spectrum analyzer 50 ohms input.
Most LC tanks are unfortunately parallel in radios. I have done some rough estimation, the parallel LC impedance |Z| of valve FM IF transformer is the order of magnitude 1 Mega ohms and not 100K. It is very difficult to measure the parallel resonance of 10.7MHz IF transformers using VNA or spectrum analyzer with sweep generator because of the high impedance.
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Old 21st Jun 2021, 8:36 pm   #5
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

It is easy to measure series LC resonance frequency because of its low resonance |Z|, for example 80pF cap in series with a 2.77microH inductor would give resonance impedance |z|=186 ohms, it is easy use impedance matching network or transformer to match spectrum analyzer 50 ohms input.
Most LC tanks are unfortunately parallel in radios. I have done some rough estimation, the parallel LC impedance |Z| of valve FM IF transformer is the order of magnitude 1 Mega ohms and not 100K. It is very difficult to measure the parallel resonance of 10.7MHz IF transformers using VNA or spectrum analyzer with sweep generator because of the high impedance.


Yeah, point taken. I suppose you could always pull the Cap off and measure it as a series LC? (Easier said than done I realise) The Formula is different, but would be easy to calc.

Still a bit of playing around with those component values in the oscillator must be well worth it, adding switches as need be of course.
Good luck mate

Last edited by Cruisin Marine; 21st Jun 2021 at 9:01 pm.
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Old 21st Jun 2021, 9:09 pm   #6
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
Yeah, point taken. I suppose you could always pull the Cap off and measure it as a series LC? The Formula is different, but would be easy to calc.

Still a bit of playing around with those component values in the oscillator must be well worth it, adding switches as need be of course.
Good luck mate
Sod's Law forbids the removal of cap or shielding can of a FM IF transformer in real world situations. At 10.7MHz, the metal shield can makes day and light difference of its resonance frequency. Try it if you dont believe me. The proximity of the metal shield raises its resonance frequency because the shield lowers the inductor coil's inductance. I have only noticed it recently when i tried to homebrew 40m SSB bandpass filter using Toko style tranformers.

Beside I am not interested in measuring the capacitance or inductance of the LC filter but its approximate resonance frequency. The error of the dual FETS common source oscillator is as large as 2MHz below the actual resonance frequency for valve type IF transformers at 10.7MHz. Well it gives rubbish readings.

Last edited by regenfreak; 21st Jun 2021 at 9:17 pm.
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Old 21st Jun 2021, 9:38 pm   #7
Cruisin Marine
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

A throw away idea- maybe you could work out the values of a series "coupling" C to put in series with the Parallel LC you are trying to measure as a "correction" value capacitor to increase the resonant freq. by a few MHz. ?
I dunno how well this would track in reality across freq's of course- but, worth an experiment of course.

Last edited by Cruisin Marine; 21st Jun 2021 at 9:53 pm.
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Old 21st Jun 2021, 10:02 pm   #8
regenfreak
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

In reality, I have some very old FM IF transformers stripped from valve radios. My universe is always complicated as the frequency goes up. Things behave differently as it goes up to 10.7MHz.

For the IF transformers (455kHz) in AM valve radios, you can happily use LC resonance equation to predict the approximate inductance if you know value of the capacitor inside. It is easy because you can just open it and look inside. The coil tester also works brilliantly too. This trick works most of the time.

For the IF transformers (10.7MHz) in FM radios, you cannot use LC resonance equation to predict the approximate inductance L for the coil if you know the capacitance of the parallel capacitor inside. If you try that, the resulting inductance will be way too big-completely wrong estimation. The dynamic resonance frequency of the FM transformer is highly sensitive to the inter-capacitance of the valve electrodes (Miller's effect). The actual inductance of the tuned LC installed in the receiver under operating conditions is significantly smaller than the value obtained from a simple calculation using LC resonance equation. I was hoping that the coil tester would give me a ball park resonance frequency for FM IF transformer taken out of the circuit but now it seems useless.
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Old 21st Jun 2021, 10:15 pm   #9
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

I suspect a changing of C2 that maybe suits lower and Higher frequencies, add to that a series C as a "correction" capacitor, and also a correction chart/graph may be the only way to get a close enough answer to the measurements you are after.
Even then, you may have to add the inter electrode valve capacitance as an extra factor to include of course.

This is not an easy problem to get a definite or easy answer to, you can't even couple in GDO style, perhaps a new approach may be worth thinking of, or perhaps someone else has already found an answer?
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Old 21st Jun 2021, 11:02 pm   #10
regenfreak
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
Originally Posted by Cruisin Marine View Post
I suspect a changing of C2 that maybe suits lower and Higher frequencies, add to that a series C as a "correction" capacitor, and also a correction chart/graph may be the only way to get a close enough answer to the measurements you are after.
Even then, you may have to add the inter electrode valve capacitance as an extra factor to include of course.

This is not an easy problem to get a definite or easy answer to, you can't even couple in GDO style, perhaps a new approach may be worth thinking of, or perhaps someone else has already found an answer?
I have re-read the threads in the German forum using google translation. It is a bit difficult to interpret the translation by robots. I will definitely try a silver-plated 0.5pF-8pF piston trimmer for C2 ...it is laying around somewhere in my junk box. Then i will replace R1 10k resistor by potentiometer of 100K.
Oh well, another project is on the pipeline.

I think the cause-and-effect is something like this:

As frequency goes up---> the effect of parasitic capacitance of the FETS prevails--->feedback increases----> quiescent common source current increases----> harmonic oscillation creeping towards relaxation oscillation----> lower oscillation frequency
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Old 21st Jun 2021, 11:14 pm   #11
Cruisin Marine
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Hmmmmm, maybe something based on a sort of Wien Bridge type AGC to control loop gain may be the answer then?

I would hope different C2's would be simpler to implement and get working though, at least initially.

Last edited by Cruisin Marine; 21st Jun 2021 at 11:19 pm.
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Old 22nd Jun 2021, 2:18 pm   #12
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

I found this paper last night before I went to bed:

https://www.researchgate.net/publica...pled_J-FET_VCO


It is a source coupled JET VCO and they claim it can go up to 3.2GHz. Magic? However you have to read small prints on the tin. I have not got the chance to read the paper. The LC tank is not isolated by capacitor but by impedance matching. I dont think it will work on high impedance LC circuit as fundamentally it has the same topology as above.

This is another one that uses RF choke to replace the resistor R1:
https://www.zl2pd.com/HFRFgen.html

Really there is no mention of relaxation oscillation issue. If something sounds too good to be true, it may be too good to be true?
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Old 24th Jun 2021, 5:55 pm   #13
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
It is very difficult to measure the parallel resonance of 10.7MHz IF transformers using VNA or spectrum analyzer with sweep generator because of the high impedance.
I'd recommend using a nanovna to make a 1 port measurement of your 10.7MHz resonator. This should do an excellent job of indicating the resonance frequency without introducing any detuning effects. You could also sweep through it with a two port S21 measurement if you configure the parallel resonator 'sideways' as a trap circuit. The resonant frequency will be where there is a deep notch. However, I think the 1 port measurement will be the easiest method.

Looking at your first oscillator circuit and test board I think you will be adding a lot of stray capacitance across the resonator. The J310 is a process 92 JFET and these tend to have higher internal capacitances and you have two of them in circuit. Also your test board looks to be introducing some extra stray capacitance in the layout. Even if you swapped the JFETs for process 50 parts and turned the 33pF cap value down you will still end up with several pF stray capacitance in the test board and the JFETs so I don't think this is a good test circuit to use at 10.7MHz if the aim is to measure the resonance frequency of your (Toko?) LC resonator.
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Old 25th Jun 2021, 9:59 am   #14
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
I'd recommend using a nanovna to make a 1 port measurement of your 10.7MHz resonator. This should do an excellent job of indicating the resonance frequency without introducing any detuning effects. You could also sweep through it with a two port S21 measurement if you configure the parallel resonator 'sideways' as a trap circuit. The resonant frequency will be where there is a deep notch. However, I think the 1 port measurement will be the easiest method.
I did that many times. I have both Nanovna v2 and Nanovna 4.3" F. Both S11 and S12 methods give totally wrong readings. The 50 ohms impedance of VNA is not good for measurements of very high impedance LC resonance circuits. There is massive impedance mismatch; the ratio of 50 ohms to 100k to many mega ohms.

Alternatively, it is possible to use a small inductive loop to the port 1. It can be weakly coupled to the coil LC of resonance tank circuit. There should be a dip in the reflection S11 working like a grid dip meter. As i mentioned above, it is pointless to measure the resonance frequency of an IF transformer with the aluminum shield or can removed. The inductor's magnetic field induces eddy current on the can and creates opposing flux that reduces the effective inductance. At 10.7MHz, the shield has a big effect on resonance frequency.
The inductive loop method is also not reliable because the S11 reading is very sensitive to the degree of coupling. Too much coupling it would give a bigger dip but also detune the circuit.

The dynamic range of Nanovna v2 is about 70db and the dip is very tiny introducing lots of error using 3db method. The new Nanonvna V2 plus 4 plus has the dynamic range of 90db which is a rather interesting device.

Quote:
Looking at your first oscillator circuit and test board I think you will be adding a lot of stray capacitance across the resonator. The J310 is a process 92 JFET and these tend to have higher internal capacitances and you have two of them in circuit. Also your test board looks to be introducing some extra stray capacitance in the layout. Even if you swapped the JFETs for process 50 parts and turned the 33pF cap value down you will still end up with several pF stray capacitance in the test board and the JFETs so I don't think this is a good test circuit to use at 10.7MHz if the aim is to measure the resonance frequency of your (Toko?) LC resonator.
Yes it is true. The effective capacitance of parallel LC is the sum of the C plus the input capacitance of the FET and part of the coupling capacitance. I have a commercial coil/crystal tester from ebay using SMD FETs and IC chips, it suffers the same issue at 10.7MHz even the seller claims it works at 10.7MHz.
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Old 25th Jun 2021, 2:23 pm   #15
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
The 50 ohms impedance of VNA is not good for measurements of very high impedance LC resonance circuits. There is massive impedance mismatch; the ratio of 50 ohms to 100k to many mega ohms.
In this case I'm not sure that matters much. The nanovna uses a resistive bridge and this exports a sinewave to the mixer/detector that corresponds to the reflection coefficient.

A typical resonator coil at 10.7MHz might be 47pF with an inductor of 4.7uH with a Q of 100. At resonance this will just look like a parallel resistor of about 31.6k ohm.

This would have a VSWR of 31600/50 = 632:1
The mag reflection coefficient would be (632-1)/(632+1) = 0.9968

The angle of the reflection coefficient will be 0 degrees at resonance. Of course, to measure resonance it only needs to measure this angle and this should be an easy task. I'd expect it to have a reasonable stab at measuring the 0.9968 magnitude of the reflection coefficient as well. It has to be calibrated correctly with a decent calibration kit that sets the reference plane right at the pin of the resonator. Otherwise the nanovna will not be able to indicate the correct reflection coefficient for the network.
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Old 25th Jun 2021, 6:03 pm   #16
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
In this case I'm not sure that matters much. The nanovna uses a resistive bridge and this exports a sinewave to the mixer/detector that corresponds to the reflection coefficient.

A typical resonator coil at 10.7MHz might be 47pF with an inductor of 4.7uH with a Q of 100. At resonance this will just look like a parallel resistor of about 31.6k ohm.

This would have a VSWR of 31600/50 = 632:1
The mag reflection coefficient would be (632-1)/(632+1) = 0.9968

The angle of the reflection coefficient will be 0 degrees at resonance. Of course, to measure resonance it only needs to measure this angle and this should be an easy task. I'd expect it to have a reasonable stab at measuring the 0.9968 magnitude of the reflection coefficient as well. It has to be calibrated correctly with a decent calibration kit that sets the reference plane right at the pin of the resonator. Otherwise the nanovna will not be able to indicate the correct reflection coefficient for the network.
I have great trouble understanding how a highly mismatched impedance DUT (device under test) can be characterized without proper impedance transformation (impedance matching network or RF transformer). From my experience, I got much lower or wrong resonance frequencies as the 50 ohms impedance of the VNA heavily load downs the high impedance LC tank.

How did you get 31.6k for parallel LC resonance impedance? I got |z|= 202k ohms for the unloaded LC resonance using this calculator:

https://www.translatorscafe.com/unit...-lc-impedance/

It is easy to correct the effects of the leads or test clips using careful calibration of the measurement plane using open, short and load standard. It is not the main issue here.

As far as I know, the only viable VNA measurement method available for parallel (not series) LC resonance is described under "Reflection measurement using a SWR Analyzer" in the figure 7 (ARRL):

http://ve2azx.net/technical/Q-Factor...C_Circuits.pdf

This works like a dip meter described previously which is limited by the degree of inductive coupling and dynamic range of the VNA.

The schematic of the nanovna v2 is here. The input and output ports simply consist of 50 ohm resistive network and DC blocker capacitors:

https://github.com/nanovna-v2/NanoVN...aster/v2_2.pdf
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Old 25th Jun 2021, 7:02 pm   #17
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
I have great trouble understanding how a highly mismatched impedance DUT (device under test) can be characterized without proper impedance transformation (impedance matching network or RF transformer). From my experience,

How did you get 31.6k for parallel LC resonance impedance? I got |z|= 202k ohms for the unloaded LC resonance using this calculator:
The reactance of 4.7uH at 10.7MHz is 316 ohms. The Q of the inductor is 100.

Rs = X/Q = 316/100 = 3.16 ohms

Rp = Rs*(Q^2 +1) = 3.16 * 10001 = 31603 ohms.


It's best to initially think of the reflection coefficient instead of impedance. When presented with a 31.6k resistor the 50 ohm VNA will send out a sinewave at 10.7MHz and nearly all of it will be reflected because the VSWR is 632:1.

The reflection coefficient will be 0.9968 so the reflected wave will be 99.68% the size of the incident wave.

This would need careful calibration to measure if you actually 'wanted' to measure the 0.9968 number. However, you are only interested in resonance and this means the VNA is comparing the phase angle of an open circuit (calibrated to a reflection coefficient of 1.000 / 0 degrees) to a 31600 ohm resistor that will have a reflection coefficient of 0.9968 / 0 degrees

All the VNA has to do is display which frequency displays an angle of 0 degrees for the reflection coefficient and your task is complete. The bigger challenge would be to measure the 0.9968 number because that could be used to calculate the Q of the resonator. But I'm not sure you are concerned about that?

It should therefore be a really easy measurement to find the resonant frequency.

Quote:
I got much lower or wrong resonance frequencies as the 50 ohms impedance of the VNA heavily load downs the high impedance LC tank.
It actually doesn't matter if the 50R VNA loads down the tank because it is measuring the unique reflection coefficient for a 50R VNA.

If the VNA was a 1k ohm VNA the reflection coefficient magnitude would be something like 0.939 because the reflection coefficient will be different for a 1k VNA.

If the VNA was a 5k ohm VNA the reflection coefficient magnitude would be something like 0.727.

If the VNA was a 30k ohm VNA the reflection coefficient magnitude would be something like 0.026 because there is almost a perfect impedance match to 31.6k ohm.

All of these reflection coefficients translate to a load resistance of 31.6k ohms if the phase angle of the reflection coefficient is 0 degrees.
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Old 25th Jun 2021, 7:38 pm   #18
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Here's an old library VNA measurement of a tiny 0603 packaged 0.1% 32400 ohm SMD resistor.

Because the VNA is a 50R VNA the VSWR will be 32400/50 = 648:1

The magnitude of the reflection coefficient will be (648-1)/(648+1) = 0.99692 and this is a very challenging measurement for a VNA!

I used a very expensive lab VNA and calibration system to make this measurement and you can see that the resistor isn't perfect as the angle of the reflection coefficient is not quite 0 degrees. This is because the resistor has maybe 0.06pF package capacitance and my measurement fixture has about 0.05pF stray capacitance.

This makes the resistor look like 32400 ohms in parallel with 0.1pF and the VNA has measured this out to 100MHz.

The reflection coefficient measured by the VNA is typically 0.9969 across the HF band and this agrees with the above equation based on VSWR. This requires a properly calibrated test fixture and a decent VNA but I'd expect a nanoVNA to give a similar result up to about 50MHz. The traces will be a bit noisier though as the nanoVNA tends to struggle when the reflection coefficient gets above about 0.995. I don't really trust the nanoVNA to make critical measurements like this above about 50MHz.
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Old 25th Jun 2021, 8:26 pm   #19
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
The reactance of 4.7uH at 10.7MHz is 316 ohms. The Q of the inductor is 100.

Rs = X/Q = 316/100 = 3.16 ohms

Rp = Rs*(Q^2 +1) = 3.16 * 10001 = 31603 ohms.
Thanks. So you assume the loaded QL= 100 and BW=0.107MHz, RP is the equivalent parallel resistance including the external load. The second equation is new to me. I will look it up on textbook. I only calculated the unloaded LC impedance.

Quote:
I used a very expensive lab VNA and calibration system to make this measurement and you can see that the resistor isn't perfect as the angle of the reflection coefficient is not quite 0 degrees. This is because the resistor has maybe 0.06pF package capacitance and my measurement fixture has about 0.05pF stray capacitance.
I use very cheap nano VNAs (V2 £65 and 4.3" F £78). There is no comparison. It is like day and light difference. I doubt the most expensive NanoVNA v2 plus 4 (£160) can resolve the reading difference of (1-0.9968) 0.0032 or 0.32% in the Smith chart even with the use of PC software. They dont have the dynamic range to resolve it. I mean if it is that easy, i would be a happy bunny by now. The metal cases for NanoVNF F and V2 plus 4 help to reduce the noises but they are toys compared with lab grade VNAs that cost thousands.
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Old 25th Jun 2021, 8:38 pm   #20
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Default Re: Relaxation oscillation in LC resonance/ Toko testers

Quote:
I use very cheap nano VNAs (V2 £65 and 4.3" F £78). There is no comparison. It is like day and light difference. I doubt the most expensive NanoVNA v2 plus 4 (£160) can resolve the reading difference of (1-0.9968) 0.0032 or 0.32% in the Smith chart even with the use of PC software.
My old/early £35 (Hugen) nanovnaH is a very good instrument when used up to 50MHz and I'm basing that statement on over 30 years' RF design experience using lab VNAs and I've even spent time using the classic old HP 8405A vector voltmeter at work and here at home.

In the right hands and with a decent cal kit and test fixture this nanovnaH really is capable of making measurements that are close to that of some lab VNAs when used up to 50MHz. Above 50MHz my nanovna can't be used for critical measurements. However, at 10.7MHz it can deliver excellent performance.

Give me a bit of time to set something up for a 10.7MHz resonator measurement with my nanovnaH here. I'll compare it to an Agilent VNA and an old HP8405A vector voltmeter (currently warming up...)
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