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Old 8th Jul 2022, 11:51 pm   #81
regenfreak
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Default Re: 6-gang FM stereo tuner heads

Going back to the OIP3 measurement of an amplifier without costing an arm and a leg, here is a poor man's learning exercise to do it with cheap equipment in austere age of inflation, war and pandemic...

My RF power combiner has finally arrived. It is rated DC to 500Mhz. I think it is one of those hybrid resistive and transformer type. I have measured its port isolation with a NanoVNA, it is -46db at 13MHz and -37.4MHz at 100MHz respectively, which is respectable (attached).

One of the key requirement of third order intercept measurement is the adequate isolation of the two signal sources. Otherwise intermodulation products can be generated between the two sources. Ideally I should use two signal generators but it will get expensive to get two VHF generators. In my first attempt I have used the two channels of my new FY6900 which can goes up to 100MHz. I use two 20db attenuators as isolators as shown in the attachment. There is no guarantee that the IMD is not generated internally inside the signal gen between the two channels. There must be some sort of phase adjustment between two channels in most DSS signal generators that can create coupling in the circuitry. In future, I will try to use two of my signal generators Rigol DG1022Z and FY6900 together with matched source power doing OIP3 measurements below 20MHz.

According to IEEE standards published in 1975 (185-page 30) , the two tone fundamental frequencies are 98.8MHz and 99.6MHz for FM receiver IP3 measurements. My set-up is illustrated in the drawing attached. I have measured a homebrew MMIC MAR-1+ (on generic printed PCB) and Gali 51+ using the automated function of the TinySA for OIP3 measurement. If I used the standard frequencies of 98.8 and 99.6MHz, the power of the third order intermodulation products are too low near the noise floor of the TinySA for a given RWB. So I used two tones much closer to each at 98,9MHz and 99MHz.

I have got OPI3 about 14-17dbm for the MAR-1+. In the data sheet, it states at least 14dbm+.

I have repeated the test for Gali-51+, the TinySA seems to give incorrect readings of the OIP3. The TinySA has very very slow sweep rate at small RBW in OPI3 mode. I am not sure if it is firmware bug or whatever. The readings are fluctuating rapidly in each sweep cycles. However, I got the OIP3 about 30dbm manually which is close to the datasheet OIP3 of 35dbm.

Also I repeat the same test using my Rigol DG1022Z which can only go up to 20MHz, getting similar results.

I will try to use two separate signal generators (Rigol DG1022Z and FY6900) for OIP3 measurements limited to below 20MHz.
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Last edited by regenfreak; 8th Jul 2022 at 11:57 pm.
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Old 9th Jul 2022, 1:11 pm   #82
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Default Re: 6-gang FM stereo tuner heads

Quote:
My RF power combiner has finally arrived. It is rated DC to 500Mhz. I think it is one of those hybrid resistive and transformer type. I have measured its port isolation with a NanoVNA, it is -46db at 13MHz and -37.4MHz at 100MHz respectively, which is respectable (attached).
I made my own combiner for this frequency range many years ago and still use it. It was a copy of one from the ARRL handbook and was made in a hurry and looks ugly but works well. It has 6dB loss on each port and uses a resistive bridge and a balun transformer. Yours is probably very similar inside.

It's tempting to by one of those TinySA analysers to use as a portable interference sniffer for one thing. You are probably stretching its limits with the tests you are doing but it's interesting that it has an IP3 measurement feature. The little RSP1A SDR can also be used for stuff like this if used with the dedicated spectrum analyser program. It takes some experimentation to find the settings that give the best spurious free dynamic range with the RSP1A though. In this sense things aren't intuitive. I generally set it to a ref level of -20dBm and then add external attenuation as required.

I've got a GALI-51 eval module here from MiniCircuits so I'll post up a screenshot from the RSP1A SDR using my old combiner and a couple of sig gens. Your screenshot shows a fairly aggressive drive level for the IP3 test. I would normally do this at much lower distortion levels. Otherwise there is the risk of driving the device into a region where the IMD3 terms can rise more aggressively than expected or with some amplifier types they can actually start falling with increasing drive level. This effect is most noticeable with FET amplifiers where they can have a sweet spot drive level where the distortion levels dip to a low point.

I've also been tempted by the FY6900 but the prices seem to have gone up a lot recently.
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Old 9th Jul 2022, 8:22 pm   #83
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Default Re: 6-gang FM stereo tuner heads

Here's a screenshot from the RSP1A SDR when fed two clean tones from the combiner. The last time I looked these SDRs were still available to buy for 99.

The spectrum analyser program is quite neat as you can see below. However, it appears that development stopped on it which is a real shame. I'm not sure the windowing functions are working as they should and there isn't a flat top option. I think this program could have been developed into something really quite special.

The latest official release version is V1.1 but this is quite old now.
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Old 9th Jul 2022, 10:37 pm   #84
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Default Re: 6-gang FM stereo tuner heads

Quote:
I made my own combiner for this frequency range many years ago and still use it. It was a copy of one from the ARRL handbook and was made in a hurry and looks ugly but works well. It has 6dB loss on each port and uses a resistive bridge and a balun transformer. Yours is probably very similar inside.

It's tempting to by one of those TinySA analysers to use as a portable interference sniffer for one thing. You are probably stretching its limits with the tests you are doing but it's interesting that it has an IP3 measurement feature. The little RSP1A SDR can also be used for stuff like this if used with the dedicated spectrum analyser program. It takes some experimentation to find the settings that give the best spurious free dynamic range with the RSP1A though. In this sense things aren't intuitive. I generally set it to a ref level of -20dBm and then add external attenuation as required.

I've got a GALI-51 eval module here from MiniCircuits so I'll post up a screenshot from the RSP1A SDR using my old combiner and a couple of sig gens. Your screenshot shows a fairly aggressive drive level for the IP3 test. I would normally do this at much lower distortion levels. Otherwise there is the risk of driving the device into a region where the IMD3 terms can rise more aggressively than expected or with some amplifier types they can actually start falling with increasing drive level. This effect is most noticeable with FET amplifiers where they can have a sweet spot drive level where the distortion levels dip to a low point.

I've also been tempted by the FY6900 but the prices seem to have gone up a lot recently.
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Cool, man. I have repeated the OIP3 measurements with two separate fundamental frequency sources FY6900 and Rigol DG1022Z at 13MHz and 13.1MHz. The results are very similar to the measurements using two channels of one signal generator. I choose 13MHz because it hits the sweet spot of the combiner when it reaches maximum isolation of -46db. The combiner has flat insertion loss of 3db (S11, S21 attached) housed in high quality CNC machined casing. I didn't pay much for it.

With the two 20db isolators, the sources have effective attenuation of 40db looking at each other.
Yes, i am pushing the TinySa to the limit. For me it is an educational exercises to get an hands-on experience instead of all about the theory, fictitious point of OIP3 and maths functions... The TinySA uses time-averaging and automatic detection of the 3rd order intermodulation peaks. It has a RBW of 4kHz in this mode. I am not sure how much i can trust the results, The measured value for MAR-1+ is very close to the datasheet but I get OIP3 for Gali-51+ about 17-20dbm which way below the datasheet value of 35dm.

Yes I used -20dbm input too. I also increase and decrease the drive levels to see the changes in OIP3. It is sensitive to the drive level. The separation of the two tones is also important. If it is too close or two wide, the measurement wont work. I have repeated measurements for some commercial LNA, homebrew Wes Hayward I/O impedance invariant amp, but i never get high OIP3 like his in the video at 13:00:

https://youtu.be/HJKjrEZRAKg

I have the similar amplifier like his, I got OIP3 of about 19dbm and he obtained about 32dm. Also I think he might use an expensive signal generator....At 6;00 he seemed to use a simple sma T adaptor instead of a proper RF combiner

It suddenly dawns to me that I have a third signal generator. My NWT-200 can generate clean sine tone up to 200MHZ. So I can possible measure the OIP3 of an active mixer. The possible set-up using three signal generators is shown in the third attachment.

The RSP1A SDR looks interesting but I still use my NWT200 a lot. I just cannot normalise the trace and do calibration with internal or external attenuators due to software issue.

The FY6900 is ok. At 100MHz the sine wave looks clean and distortion free on my 200MHz scope. I have not managed to set it up as a wobbulator..I believe there is a way of doing it. I can set up the Rigol DG1022Z as a wobbulator easily.
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Last edited by regenfreak; 9th Jul 2022 at 11:07 pm.
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Old 10th Jul 2022, 10:30 am   #85
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Default Re: 6-gang FM stereo tuner heads

The way Wilkinson combiner works is very intriguing. It basically uses quarter wave transformer with a 100 ohm resistor across the port 1 and 2. It works in both even and odd modes (180 degrees out of phase) so that the two parallel transmission lines are balanced with zero potential across the two input ports and hence it achieves good isolation, it is a narrow band device with low loss:

https://rickettslab.org/bits2waves/d...ry-and-design/

I am looking into building the IF stages for the 6-gang tuner. Having seen Nelson Jones article in WW 1971, I am toying with the idea of having the design using three crystals and a 5-pole Cherbysher 10.7MHz LC filter (see attached block diagram).

The CA3035 is an early form of IC having the gain of about 20db. It can be used either in cascode or long tailed push-pull configurations as IF amp. The main advantage is that they have less feedback capacitance enabling it to be stable with good gain. In the IF amp with simple BJT and transformer, there is a tendency to oscillate and some form of neutralization is needed when it happens.

I prefer 280khz wide band crystal for the best MPX fidelity. Looking at the Murata datasheet, it has 330ohms I/O impedance. So I built a simple test jig using LC reactive matching pads using 3/6db attenuators on both ends. I did the sweep the Nanovna V4 plus 4. It hits the center of the Smith charter at the centre exactly at 10.7MHz. It shows that LC matching pad is a narrow band device only works at a specific frequency.

According to the manufacturer web site, we cannot use the NanonVNA V2 plus 4 to measure crystals. So i dont know how much it affects my measurement attached. When i connect the output of the V4 plus 2 to my scope, it shows pulsating waveforms which indicates rapid switching on and off to generate higher harmonics? My NaonVNA F V2 has started to malfunction unfortunately. It generates continuous waveforms that is more suitable for crystal measurements. I think the cheapest original version of the NanoVNA is more suitbale for crystal measurements as well.
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Old 10th Jul 2022, 12:14 pm   #86
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Default Re: 6-gang FM stereo tuner heads

Yes, I've got one of the early Hugen 2.8" nanovnas with the blue PCB. I made sure I got it from a proven vendor and it works surprisingly well. If it is of any interest I tested a suite of SMD resistors with it across the HF bands a couple of days ago. The resistance range was 0.167 Ω to 330 kΩ.

See below for the results. Obviously the nanovna struggled with the 330 kΩ resistor (the top trace) but it did remarkably well up to about 100 kΩ where the reflection coefficient is 0.999.

The 0.167 Ω resistor was made with three 0.499 Ω resistors in parallel so the resistance creeps up from 0.167 Ω to about 0.200 Ω by 30MHz. I think this is partly due to the metal losses involved in the stacking and soldering of three resistors in parallel.

The 0.499R resistor is a very good quality SMD resistor designed for current sensing and it has a 1% tolerance and the short and very fat package shape minimises metal loss. So it shows a flat response to 30MHz. Flatter than the regular 1 Ω 0805 SMD resistor above it.
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Old 10th Jul 2022, 1:20 pm   #87
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Default Re: 6-gang FM stereo tuner heads

I am very surprised it can measure from 0.167 to 100k ohms. I assume you use CW mode and read the real part of Z or dump the data to a SP1 file? Any 50 ohm measurement device does not give accurate readings of the DUT that has very low impedance due to uncertainty principle of impedance matching. Did you use 3db attenuators on both ends when you measure very low resistance?
I need to get the cheap orginal nanoVNA for crystal IF cascade filters measurement.
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Old 10th Jul 2022, 2:09 pm   #88
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Default Re: 6-gang FM stereo tuner heads

The resistor tests were all done as 1 port s11 measurements. Note that these are converted to parallel resistance measurements (Rp) rather than series resistance (Rs).

To get this level of performance from the nanovna I wrote my own software to assist with the calibration and also with the data dumping of s-parameter files. I'm not using the default settings and I've taken steps to minimise any compression errors in the receiver by using low power and a low value attenuator inline. I've also used a decent cal kit and test fixture to help set the reference plane right at the chip resistor.

It's also possible to display the parallel capacitance of the higher value resistors. My microwave test fixture has a fringing capacitance of about 0.06pF and I don't correct for this but you can see the result for the parallel capacitance is typically 0.11pF across 2-30MHz.

So the real result is close to the expected 0.05pF for an 0805 chip resistor. All these measurements across 0.167R to 330K (and for the capacitance measurement) were taken after a single calibration so I'm not fudging anything to get improved results for each test. I just did one calibration then measured all of the resistors one after the other. I'm used to using a regular lab VNA up at many GHz so I have quite a bit of experience when it comes to fixture design and calibration.
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Old 10th Jul 2022, 2:25 pm   #89
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Default Re: 6-gang FM stereo tuner heads

See below for the package inductance of the 0.499R resistor and a basic cheapo 1 ohm 0805 SMD resistor. This plot was taken from the original S1p measurement file. Again, this was all after the original single calibration of the nanovna.

This is series resistance Rs and series inductance. The 0.499R resistor is in a very wide and short package so it has lower inductance of about 0.5nH. It's designed for use in current sensing circuits. The cheapo 1 ohm 0805 resistor has a package inductance of just over 1nH according to the nanovna.

To get this level of performance from any VNA does require a lot of experience. It isn't possible to get results like this using the cheap and poorly corrected cal kits and the test setups shown in the numerous tutorial videos on youtube.

It is also possible to extract full 2 port s-parameter data for s11 s21 s12 s22 if a decent reversible test fixture is designed. This can be useful for filter design work because the s2p file becomes a model that you can play with on an RF simulator. A matching network can then be designed and optimised on a simulator to get the best match across the filter bandwidth.
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Old 10th Jul 2022, 5:16 pm   #90
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Default Re: 6-gang FM stereo tuner heads

Quote:
Originally Posted by G0HZU_JMR View Post
See below for the package inductance of the 0.499R resistor and a basic cheapo 1 ohm 0805 SMD resistor. This plot was taken from the original S1p measurement file. Again, this was all after the original single calibration of the nanovna.

This is series resistance Rs and series inductance. The 0.499R resistor is in a very wide and short package so it has lower inductance of about 0.5nH. It's designed for use in current sensing circuits. The cheapo 1 ohm 0805 resistor has a package inductance of just over 1nH according to the nanovna.

To get this level of performance from any VNA does require a lot of experience. It isn't possible to get results like this using the cheap and poorly corrected cal kits and the test setups shown in the numerous tutorial videos on youtube.

It is also possible to extract full 2 port s-parameter data for s11 s21 s12 s22 if a decent reversible test fixture is designed. This can be useful for filter design work because the s2p file becomes a model that you can play with on an RF simulator. A matching network can then be designed and optimised on a simulator to get the best match across the filter bandwidth.
Cheers. This is sophisticated. I have to play with the series to parallel impedance transformation online calculator to get " intuitive feel " of the transformation. It is not an easy concept to grasp:

https://daycounter.com/Calculators/P...lculator.phtml

I remember reading these articles a while back about the calculation of mismatch uncertainty between a source and a load:

https://www.microwavejournal.com/art...ch-uncertainty

and also this paper:

https://www.metrology-journal.org/ar...jmqe120005.pdf

max uncertainty limit (db) = 20log|1+TsTL|
min uncertainty limit (db) = 20log|1-TsTL|

Ts and TL are reflection coefficients of the source and load respectively. According to the paper, the mismatch uncertainty can be reduced by 50% if 10db attenuators are used the source and detector ports.

Also the mismatch uncertainty is high when the DUT has low impedance.
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Old 10th Jul 2022, 5:47 pm   #91
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Default Re: 6-gang FM stereo tuner heads

I forgot that I purchased a Wheatstone bridge type directional coupler a while ago which is based on this IEEE paper design:

https://ieeexplore.ieee.org/document/7345756

Attached files are the S23 isolation, S31 coupling and S21 insertion loss all the way up to 4GHz using the NanoVNA v2 plus 4.
The maximum isolation is -77db at 1.6GHz.
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Old 10th Jul 2022, 10:36 pm   #92
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Default Re: 6-gang FM stereo tuner heads

Yes, mismatch uncertainty can become very significant for some measurement tasks. The VNA calibration is very important in order to reduce systematic errors and I usually use a lab VNA and a decent mechanical cal kit or an Ecal module for stuff like this.

The little nanovna seems to work very well up to about 50MHz then the performance falls off after this. Even a modern lab VNA will struggle to measure some of those resistors up into VHF and UHF. Across the HF bands a decent VNA can deliver remarkable performance but above this it becomes increasingly difficult to correct the systematic errors mathematically.

The IEEE paper sounds interesting. I can access this tomorrow at work.
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Old 11th Jul 2022, 9:53 am   #93
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Default Re: 6-gang FM stereo tuner heads

Probably the worst thing for showing up VNA errors is in making an s11 measurement of quartz crystals.

HP had a phase where they saw it as a route to selling more VNAs and various people started generating apps notes and papers on doing it this way.

Our incoming inspection department took this to heart and carved up their beautiful Cathodeon three-key pi-network fixture to turn it into a 1-port crystal socket!

Along came a lot of trouble with parts now failing spec in incoming inspection. I got asked to look into it and found out about the s11 measurement push. The directional couplers in the analyser's s-parameter box could not compete with embedding the crystal (and switched load capacitor) directly into a two-port network.

We had to buy a new Cathodeon fixture. They'd binned the innards of the one they 'converted'. Fortunately, Cathodeon were still on the go at that time.

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Old 11th Jul 2022, 12:00 pm   #94
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Default Re: 6-gang FM stereo tuner heads

I think that the classic RLC model of a quartz crystal is slightly flawed because it doesn't include any shunt capacitance to free space.

I did some crystal testing a few years ago and noticed a subtle difference between s11 and s21 measurements. I think this is partly caused by distributed reactance in the crystal and this isn't included in the classic crystal model.

I found that the parallel resonance frequency is shifted slightly if measured with a VNA in s11. I'm not sure if this is an error because of the effect of any distributed capacitance within the structure of the crystal. If there is distributed capacitance then I'd expect to see a difference in the parallel resonance when comparing the null frequency in s21 against the parallel resonance frequency measured with s11.
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Old 11th Jul 2022, 12:11 pm   #95
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In other words, if you tried to reverse engineer the crystal's motional parameters C1, L1, R1 and C0 using an s11 measurement and then did it again using s21 measurements I think the result would be slightly different even if the VNA was perfect.
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Old 11th Jul 2022, 12:39 pm   #96
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Default Re: 6-gang FM stereo tuner heads

Quote:
es, mismatch uncertainty can become very significant for some measurement tasks. The VNA calibration is very important in order to reduce systematic errors and I usually use a lab VNA and a decent mechanical cal kit or an Ecal module for stuff like this.

The little nanovna seems to work very well up to about 50MHz then the performance falls off after this. Even a modern lab VNA will struggle to measure some of those resistors up into VHF and UHF. Across the HF bands a decent VNA can deliver remarkable performance but above this it becomes increasingly difficult to correct the systematic errors mathematically.

The IEEE paper sounds interesting. I can access this tomorrow at work.
It seems the calibration is only part of the critical considerations. The methodology is important whether it is: 1. shunt, 2. shunt through 3. series measurements:

https://www.signalintegrityjournal.c...dance-analysis

Quotes from the articles:

A one-port measurement of a shunt impedance DUT using a VNA is reasonably accurate between about 20 ohms and 200 ohms. The reason for this is covered in reference 1.

A two-port measurement is suitable for impedance measurements from 0.001 ohms to 20 ohms.


impedance accuracy for the three methods:


https://www.mwrf.com/technologies/te...ts-using-a-vna

The challenge of ultra low impedance measurement:

https://www.keysight.com/gb/en/asset.../5989-5935.pdf

When the impedance of the device is 1 Ohm, S11 is –0.96 or –0.35 dB. This is a reasonable value to be able to measure. When the impedance is 0.1 Ohm, S11 is –0.996 or –0.035 dB. This may seem like a very small amount of reflected signal, but in fact, 99.6% of the incident signal reflects. This is so close to 100% that it is difficult to measure the difference between 100% of the signal and 99.6% of the signal. This creates a large relative uncertainty.


Measurement of a very low resistance with VNA is beyond my scope and not something that I am too interested in as I have the DE-5000 that uses Kelvin four wire measurement. Unfortunately my first DE-5000 goes bananas after 3 years of abuse. Recently I had to buy a second unit from Japan. This hobby becomes a money drain.
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Old 11th Jul 2022, 1:14 pm   #97
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Quote:
Quotes from the articles:

A one-port measurement of a shunt impedance DUT using a VNA is reasonably accurate between about 20 ohms and 200 ohms. The reason for this is covered in reference 1.
That's applied over the full frequency range of a microwave VNA. i.e. up to 8GHz or so.

In the range 2-50MHz it's much easier to correct the systematic errors so much better results than that can be achieved in practice.
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Old 11th Jul 2022, 1:22 pm   #98
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Quote:
That's applied over the full frequency range of a microwave VNA. i.e. up to 8GHz or so.

In the range 2-50MHz it's much easier to correct the systematic errors so much better results than that can be achieved in practice.
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Old 18th Jul 2022, 10:26 am   #99
nemo_07
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Posts: 17
Default Re: 6-gang FM stereo tuner heads

Quote:
Originally Posted by regenfreak View Post
Going back to the OIP3 measurement of an amplifier ...

I have got OPI3 about 14-17dbm for the MAR-1+. In the data sheet, it states at least 14dbm+.

I have repeated the test for Gali-51+, the TinySA seems to give incorrect readings of the OIP3. ... I got the OIP3 about 30dbm manually which is close to the datasheet OIP3 of 35dbm.
So you think you have measured the OPI3 for the MAR-1+ with this little-tiny-weeny toy made in China. And all this in a single step?
You should perhaps look for informations supplied by reliable sites, not by wanna-be experts (remember the "negative group delay"?) like these:
https://tinysa.org/wiki/pmwiki.php?n=Main.OIP3
So they start with "After activating the OIP3 measuring mode ..."
They even didn't bother to realize the meaning of the term "intercept point" (which was explained in the math lessons in elementary school, but they obviously were absent).
So, what their gadget actually does when they talk of "OIP3 measuring mode" is visualizing 3-rd order intermodulation products (measuring their levels and calculating exact locations).

There is laking understanding of some fundamentals. And it is pandemic on the internet these days.
This exposes the simple truth, that the idea of "learning by doing" is fairly incompatible with the very basic principles of electronics (which is in essence the teritory of physics); and any careless and sloppy idea will be rigorously penalized.

To make the long story short: the OIP3 (Output related Intercept Point for 3-rd order distortion products) of any device is not its physical property, but merely a calculated value. It is an abstracted figure of performance in terms of linearity for given technology/device, not more, not less. It involves a number of power measurements (at least four).
Unlike the P1dB parameter, the OIP3 in most cases cannot be assesed through direct power level measurement. This is simply because the OIP3 power levels for most modern quality active devices lie way beyond the power handling capabilities of devices itself. This is clearly ilustrated in the Figure 6 here (you hate maths, so skip it):
https://www.maximintegrated.com/en/d...ls/5/5429.html
By now you should understand, that trying to get the real OIP3 power level of +35dBm (which is 3.16 Watt) from your https://www.minicircuits.com/pdfs/GALI-51+.pdf
operating even at its absolute thermal limits of around 0.5W supply power would be in violation of fundamental laws of physics.
Sort of "inventing free energy".

Anyway, I can't follow the sense of your investigations into the OIP3 of MMICs. Do you distrust the specs in the datasheets?

BTW: The simplest and cheapest way to make two-tone tests would offer two DDS chips from Analog Devices, with their outputs shorted together, and terminated into single 50 Ohm resistor. No combiner, and no attenuators required.
... And do not confuse "ceramic filters" https://www.vintage-radio.net/forum/...9&d=1657447624
with "crystals".

Quote:
Originally Posted by G0HZU_JMR View Post
I think that the classic RLC model of a quartz crystal is slightly flawed because it doesn't include any shunt capacitance to free space. ...
I found that the parallel resonance frequency is shifted slightly if measured with a VNA in s11. I'm not sure if this is an error because of the effect of any distributed capacitance within the structure of the crystal. If there is distributed capacitance then I'd expect to see a difference in the parallel resonance when comparing the null frequency in s21 against the parallel resonance frequency measured with s11.
Quote:
Originally Posted by G0HZU_JMR View Post
In other words, if you tried to reverse engineer the crystal's motional parameters C1, L1, R1 and C0 using an s11 measurement and then did it again using s21 measurements I think the result would be slightly different even if the VNA was perfect.
The model is perfectly sound. If you make some carefull considerations (or calculations) you will realize that the parallel resonance (called also antiresonance) frequency of a crystal depends on the total external shunt capacitance (manufacturers call it "load capacitance", and the number printed on the case of a crystal give this frequency), and so this frequency for any crystal can be "pulled" in a small range (perhaps up to around 1000 ppm at most) with the aid of a trimmer capacitor (alternatively an external variable series inductance can be used to pull the antiresonance of a crystal).
Contrary to this, the series resonance of a ready cut crystal is an invariable mechanical property of the crystal bulk itself, and as such it is independent of the external reactances, and so it can be regarded as a more precise parameter (at least within some reasonable range of mechanical stress caused by factors like vibrations, drive level, pressure, temperature, and, for space applications, also by the gradient of gravity and motional speed of spacecraft).
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Old 18th Jul 2022, 11:12 am   #100
G0HZU_JMR
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Default Re: 6-gang FM stereo tuner heads

I agree that the classic crystal model is extremely good but it doesn't take into account capacitance to free space. This capacitance might only be a tiny fraction of 1pF but it is there nonetheless.

It doesn't really matter though as long as everyone uses the same classic model and they fudge the C0 capacitance ever so slightly to take into account the tiny effect of the package capacitance to free space. A 2cm long piece of wire still has some capacitance to free space so a crystal will be no different.
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