Unexpected Smith chart behavior

[AJ528]

Hi All,

I am trying to get a better understanding of Smith charts, so I set up a basic example today and got an unexpected result. I'm hoping someone can explain the behavior I saw.

I learned recently that making your transmission line longer will cause a phase delay, which causes the measurement on the Smith chart to rotate about the center. A phase delay of 1/2 wavelength causes one full revolution around the Smith chart.

I wanted to see this behavior in action, so I set up a simple example: I connected a 2 foot BNC cable to my nanoVNA, set it to display a Smith chart, and scan from 200 MHz to 300 MHz, then did OSL calibration. Next, I replaced the 2 foot BNC cable with a 3 foot BNC cable and measured the output shorted. I calculated that a signal somewhere around 250 MHz has a 4 foot wavelength, so by making my transmission line 1 foot longer, I expected to see the Smith chart measurement rotate 180 degrees and appear as an open. Instead, the measurement only moved 90 degrees. Anyone know why that is? Please see photos of my setup and weird result.

[A.Z.]

Let me try putting down some number, I'll use metric since that's what I'm familiar with and since wavelength is in meters

Let's start by calculating Lambda for 250 Mhz, we have 300/250=1.2 meters, that's our wavelength, now, since our transmission line isn't perfect we should take in account the coax velocity factor, let's assume it's 0.66, in such a case 1.2*0.66=0.792 or 79.2 centimeters, this is our "corrected Lambda", now, starting with such a value we can calculate 1/4 wave as 79.2/4=19.8 centimeters; now that we have 1/4 Lambda (with correction) we can calculate our coax length, willing to start with 1/2 wave we just do 19.8*2=39.6 centimeters and then, willing to add 1/4 wave we'll have 59.4 centimeters, at this point we convert 39.6 and 59.4 from centimeters to feet obtaining 1.299 ft and 1.948 ft which will be the lengths we'll use for our coax cables

HTH

[AJ528]

Hi A.Z.,

Thanks for the reply. The BNC cable I'm using is RG58 coax by Southwire, and their website says it has a velocity of propagation of 82% (https://www.southwire.com/wire-cable/low-voltage-cable/rg58-coax/p/ELC60). So calculating the corrected Lambda from that gives me a wavelength of 0.982 meters. 1/2 wavelength = 360 degrees, so making my cable 0.481 meters longer would cause a full rotation. I added 0.305 meters to the transmission line. 0.305/0.481 * 360 = 224 degrees (call it 225). So I would expect to see the measurement point rotated clockwise 225 degrees around the circle. But I'm seeing a 270 degree rotation. That seems like a big error to me. What could be causing that? Is my math wrong?

[Randy222]

I always start with the basics. Is that VNA a legit "nano"? Is the nano running latest firmware and you sure it's calibrated at 250MHz ?
After that, all the other basics for cable and what-not.

[AJ528]

I have no reason to believe it's a cheap clone. I bought it from Nooelec (https://www.nooelec.com/store/test-equipment/analyzers/nanovna-h4-bundle.html).

As for frequency calibration, how would I go about verifying that? I have a 300 MHz oscilloscope I trust, can that be used here?

Edit: I hooked up the VNA output to my oscilloscope and got 250 MHz on the nose. So that looks good to me.

[wasedadoc]

BTW it is Smith (capital S) after the name of its creator. Nor is it Smitch.

[AJ528]

BTW it is Smith (capital S) after the name of its creator. Nor is it Smitch.

Crap. I kept making that typo when I was writing the original post. I thought I caught them all, but apparently not. Is there any way to edit the post title?

[A.Z.]

I'd start by using the VNA to measure the effective velocity and move on from that

also, you may consider moving to 300Mhz that is a Lambda of 1 meter, not that important but may ease calcs a bit

[AJ528]

Good idea!

I used the transform function on the nanoVNA, calibrated it with the 2ft BNC cable, then replaced that with the 3ft BNC cable. When my velocity factor was 82% (per the datasheet), it said the end of the cable was 0.360 meters away. I was expecting it to be 0.305 meters. So I adjusted the velocity factor until the end of the cable was 0.305 meters away. That corresponded to a velocity factor of 68%. 68% VF turns my effective wavelength into 0.816 meters, so adding 0.305 meters to that would cause the Smith chart measurement to rotate 270 degrees! I think that is a mystery solved!

The only surprising thing here is the measured VF of 68% is much different than the advertised VF of 82%. Is that kind of VF deviation expected from affordable BNC cables?

[A.Z.]

no, not for good quality, reliable ones, but 66% is common for standard RG58

[Randy222]

As for frequency calibration, how would I go about verifying that? I have a 300 MHz oscilloscope I trust, can that be used here?

Edit: I hooked up the VNA output to my oscilloscope and got 250 MHz on the nose. So that looks good to me.

Go online and watch all the vids for calibrating S11 port using the open,short, and 50ohm caps. The VNA must be calibrated 1st. I do cal before each use when doing certain tests that require real good accuracy.
The cal will not change your funny looking Smith chart all that much, but in your test it's probably best to cal the device before doing your tests.

[TimFox]

RG-58/U is a military designation for a 50 ohm cable with single braided shield, solid center conductor, and solid polyethylene insulation.
That cable has a propagation constant of 0.66.
Your cable is not actually RG-58/U, but is a quasi-RG58 with the parameters listed on the datasheet.
There are other variations on RG-58/U, including 58A and 58C.

[Randy222]

Was looking at the pics again.
There's too many insertion points.
At S11 you have 3, two adapters + S11.
At the end you have 2, one adapter + sma cap.

Get a BNC terminator for the end, and use a single BNC-sma adapter on S11.

I bet ya with nano calibration and minimizing adapters, the expected number will get much closer to spec.

[EggertEnjoyer123]

The wavelength at 250MHz is c / 250 MHz * 0.66 (velocity factor) = 0.791m

1 ft = 0.3048m

1 ft is 0.385 wavelengths. Multiply that by 2 to get 0.77. You moved 0.77 of the way around the Smith chart, which puts you at about a 3/4 rotation, which is what you're getting.

In your calculation you forgot to consider the velocity factor of the cable you're using.

[AJ528]

RG-58/U is a military designation for a 50 ohm cable with single braided shield, solid center conductor, and solid polyethylene insulation.
That cable has a propagation constant of 0.66.
Your cable is not actually RG-58/U, but is a quasi-RG58 with the parameters listed on the datasheet.
There are other variations on RG-58/U, including 58A and 58C.

What makes you so certain the propagation constant is 0.66? The link I found (https://www.southwire.com/wire-cable/low-voltage-cable/rg58-coax/p/ELC60) said it was 0.82. My measurements clearly indicate 0.82 is incorrect, but what makes you say 0.66? Is there something else in the datasheet that tells you the actual propagation constant?

[AJ528]

The wavelength at 250MHz is c / 250 MHz * 0.66 (velocity factor) = 0.791m

1 ft = 0.3048m

1 ft is 0.385 wavelengths. Multiply that by 2 to get 0.77. You moved 0.77 of the way around the Smith chart, which puts you at about a 3/4 rotation, which is what you're getting.

In your calculation you forgot to consider the velocity factor of the cable you're using.

No, I included the velocity factor of the cable I was using, but the datasheet I found for my BNC cable (https://www.southwire.com/wire-cable/low-voltage-cable/rg58-coax/p/ELC60) it says the velocity factor is 0.82. Where are you getting 0.66 from?

Did I search the wrong information? Here's the 2 BNC cables I used

[AJ528]

Was looking at the pics again.
There's too many insertion points.
At S11 you have 3, two adapters + S11.
At the end you have 2, one adapter + sma cap.

Get a BNC terminator for the end, and use a single BNC-sma adapter on S11.

I bet ya with nano calibration and minimizing adapters, the expected number will get much closer to spec.

I'm gonna respectfully disagree. I OSL'd the VNA with the 2ft BNC cable and adapters hooked up. That should have cancelled out the parasitics from the adapters. I then switched to the 3ft BNC cable and kept using all the same adapters.

Why don't you think calibration would cancel out those effects?

[A.Z.]

The 0.66 is what's reported in the mil specs for the standard cable

[TimFox]

RG-58/U is a military designation for a 50 ohm cable with single braided shield, solid center conductor, and solid polyethylene insulation.
That cable has a propagation constant of 0.66.
Your cable is not actually RG-58/U, but is a quasi-RG58 with the parameters listed on the datasheet.
There are other variations on RG-58/U, including 58A and 58C.

What makes you so certain the propagation constant is 0.66? The link I found (https://www.southwire.com/wire-cable/low-voltage-cable/rg58-coax/p/ELC60) said it was 0.82. My measurements clearly indicate 0.82 is incorrect, but what makes you say 0.66? Is there something else in the datasheet that tells you the actual propagation constant?

Your cable’s data sheet shows 0.82.
That implies a foam dielectric, which has lower loss than solid polyethylene.
The military spec for RG-58/U cable shows 0.66, since the dielectric is solid polyethylene for the “real stuff”.
The actual term and spec are important.

[showman]

Here's a datasheet for Southwire 991043. Does not exactly match the jacket print, but I'd say close enough and the factor is 0.66. As suggested, just measure it, or alternatively contact the manufacturer for the correct factor for the specific cable.

[AJ528]

Here's a datasheet for Southwire 991043. Does not exactly match the jacket print, but I'd say close enough and the factor is 0.66. As suggested, just measure it, or alternatively contact the manufacturer for the correct factor for the specific cable.

Interesting....thank you for finding that datasheet! I wonder if I was looking at the wrong datasheet then. Maybe Southwire makes 2 different RG58 coax cables.

[A.Z.]

1. calibrate the VNA using the cal kit

2. connect the coax, terminate it and find the real VF

3. cut the cable at proper length

4. run the measurements

[RoGeorge]

0. edit the first post, and fix the typo in the title 

[AJ528]

0. edit the first post, and fix the typo in the title 

Thanks, fixed!

[AJ528]

1. calibrate the VNA using the cal kit

2. connect the coax, terminate it and find the real VF

3. cut the cable at proper length

4. run the measurements

Is there a recommended way to find the real VF of a cable? I hooked my cable up the nanoVNA, put it in time domain mode, then tweak the VF in the settings until the VNA measured length equaled the actual cable length. Not sure if there's a better method...