I am doing some scattering measurement (RCS) in X band using VNA and a pair of horns. Some references suggest that using time gating can reduce noise. It was also mentioned that this can be achieved by using software (Matlab) to process the measured data (S21). Since our VNA does not have the time domain option, I am looking into this software method.

After reading the application note (http://cp.literature.agilent.com/litweb/pdf/5989-5723EN.pdf) and a few previous posts, my initial attempt is to use IFFT of Matlab on a finite bandwidth, measured S21 (say 8-14 GHz), which is complex. My understanding is that this is corresponding to the bandpass mode of VNA. And I am only interested in the magnitude of the time domain data.

In previous posts "S21 time domain response ", "https://community.keysight.com/message/4826#comment-4826 ", there are some discussions on the bandpass mode.

_"In bandpass mode, the IFT is not analytically correct, for some non-obvious reasons. One key point is that the band pass transform does not assume a hermitian response, but rather, computes the response as though the data taken is single sided, with the "negative" frequency response being zero, rather than identical to the positive with opposite sign. The Low Pass mode makes the assumption that the negative frequency response is of the same magnitude and opposite phase, so in effect, creates data at negative frequencies. Doing this in low pass mode assures a pure real transform. In the band pass transform, the response is not pure real, but in fact must always be complex._

_The band pass response is computed by frequency shifting the data such that the center point is at DC, computing the IFT (complex form, as the data is not hermitian about the center point except in special cases), then applying the Fourier shift theory in the time domain to multiply the result by e^(jwt) where w is the center frequency of the "pre-shifted" data. Thus, you will see a cosine (on the real) and a sine (on the imaginary) data imposed on the low pass response (sometime this is called the modulation theorem as well)._

The modulation by e^(jwt) makes sense. Now since only the magnitude of S21 in time domain is concerned, does it mean that this factor can be dropped? In other word, simply applying the inverse Fourier transform will generate the time domain data for me?

One related question is that where is the t0 (starting time)? Does the transformed time domain start at t=0s? I guess in theory the time domain data is infinite and periodic. But is it possible to locate the t=0, or reference time? Apparently this can help to identify the scattering signal from the object since the distance between the transmitter is known.

Thanks!

https://www.sdr-kits.net/

You can download the software for that for free and load a .s2p file and show the time domain data. Of course option 010 is better, but it is not cheap.

If the VNA is old and obsolete, ask on the HP/Agilent Yahoo group and if you are lucky some kind sole might give you a code to enable option 010. In fact someone from Alltest wrote there they would add the option for $300-$400, but there are a couple willing to do it for nothing on very old instruments.

If you are working at X-band that means you are not using an 8753, for which codes to enable the option can be acquired. I know Techmaster Electronics do it on an 8720D, since my VNA says on the calibration certificate that option 010 was added. I think for a PNA you won't get a code, in which case the software I said above might be worth looking at.

BTW, I recently asked for an old Application Note on measuring RCS. Jvall kindly provided a copy. Hunt for the post by myself about 6 weeks ago about RCS?

Dave

Edited by: drkirkby on Mar 31, 2014 12:01 AM

I actually have tested my time domain Matlab code with a cable measurement by VNA. The obtained time domain signal after the transformation is attached. Most of it makes sense, but still some doubt. I hope the experts here can shine some light to it.

Our VNA is 8720D and I tested a 5 feet N-type cable. The frequency span is 8-12 GHz, with 201 points. So freq step is 20 MHz. S11 measurement calibrated at VNA port. The other side of the cable is shorted. I assume the cable's dielectric is PTFE with a velocity factor of 0.7

Looking at the time domain data, the first peak at 0.25ns seems to be the reflection at the beginning of the cable. The second peak at 14.75ns seems to be the reflected signal from the short, after going through a trip in the cable. The time - cable length does match pretty well.

Not exactly sure what is the third peak at 29ns, could it be the multiple-reflected signal?

I have not done anything special but the t=0 time seems to occur at the very beginning of the plot. Is it because calibration?

## Attachments

I have attached the measured S11 (freq, real, imaginary) in a text file. I am not familiar with the S1P or S2P format, though.

## Attachments

http://en.wikipedia.org/wiki/Touchstone_file

Here's the draft Touchstone (.sNp) spec

http://www.vhdl.org/pub/ibis/connector/touchstone_spec11.pdf

I don't guarantee it, but I think adding this line converts it to a Touchstone file.

*# S GHz RI R 50*

I have attached what I think is the touchstone file.

I've never done this before, but I opened the .s1p file I edited for you and loaded it into the software designed by DG8SAQ for the low-cost VNWA network analyzer. I'm sure there are a lot of things one can do with this in the software, (window function etc), but I was not sure how to do it. Anyway, this is what that shows. It will be interesting to see if what Joel gets on his PNA is similar.

To be fair to Tom, the author of the VNWA software, I don't know how to use it, so this should not be taken as the capabilities of the software. But you can at least see it is capable of plotting some sort of time domain plot.

*Correction. Now I see I was only looking at the default 1 ns span. See below for something quite similar to what Joel gets.*

Dave

Edited by: drkirkby on Mar 31, 2014 10:08 PM

Edited by: drkirkby on Apr 1, 2014 9:53 AM

## Attachments

Heres the TD response. It looks like it has some aliased responses (fourth peak). Take the data with greater density (1601 points) and post back.

Edited by: Dr_joel on Mar 31, 2014 4:48 PM

## Attachments

* Time domain response: Impulse DFT

* Mode: Bandpass

* Window type: Hamming

* Impulse resonse: Normalized to impulse height.

* Low frequency data: Extrapolated below 25 kHz.

* Start time: -5 ns

* Stop time: 45 ns

* Velocity facfor 1.0.

* /2 box: unticked (see note later)

What is odd is the markers are at virtually the same time and amplitude, but distances differ by a factor of 2. Taking the first marker

* Agilent PNA: 14.598 ns, -7.20 dB, 2.19 m

* DG8SAQ VNWA: 14.6 ns, -7.42 dB, 4.37 m

I guess one give the one-way path and the other a two-way path. *(UPDATE: It was pointed out to me by someone on the VNWA list, vnwa@yahoogroups.com that if I ticked the /2 box, the distances would be divided by 2. Sure enough, the distances for markers 1 and 2 change to 2.18 and 4.38 metres - for all practical purposes, the same as Joel got on the PNA)*

I think the original poster (meta5718) could do a lot worst than take a look at the software written by Tom (DG8SAQ, iphi@arcor.de), or better still, look on the HP/Yahoo mailing list, and see if some kind sole will give you option 010 on the 8720D. (Luckily mine has option 010, but there is no easy way I could take your data and load it into the 8720D to plot it in that).

BTW meta5718, did you use a waveguide cal kit, or a coaxial one? I'm wondering if there is any dispersion issues if you use coaxial calibration kit and a waveguide to coax transition. There were three HP P11644A (P-band, 12.4 to 18 GHz) waveguide cal kits sold on eBay UK recently. All three went for under £60 (GBP) / $100 USD. These kits are $7000 new! I somewhat doubt the people buying them knew what to do with them - the adapters in the kit would fetch more than the kit was bought for. I purchased the foam from Agilent to fit in the P11644A cal kits, and that was several times what the kits sold for. In fact, I could have bought all 3 kits for the cost of one bit of foam for the cases.

Dave

Edited by: drkirkby on Apr 1, 2014 10:08 AM

Edited by: drkirkby on Apr 1, 2014 10:12 AM

Edited by: drkirkby on Apr 1, 2014 11:50 AM

## Attachments

I am glad to see that my Matlab code is giving me mostly the correct answer: the returning signal peak in terms of time and amplitude. I can definitely see that applying some windowing functions will help to improve the SNR. This is probably useful when the measured data have multiple signals with similar magnitude (in time domain).

To dikirkby's question on the factor of 2: I think it simply depends on whether it is R or T measurement. In fact, your time scale (delta t) looks all good. To get the physical length or distance, you have to know the velocity factor (which you set to 1).

To me, this time domain transformation technique is mostly useful for analysis and diagnosis. in other words, how to interpret the time domain data and determine the physical meaning of each signal peak. I guess this is case by case. But even in this simple example, the possibility on alias and multiple reflections can make the analysis somehow tricky.

I noticed that both of your time domain data set the starting time as -5ns. Is this arbitrary or there is a reason behind it? This was actually my question on finding the t=0 time.

To dikirkby: I will look up the software you suggested. As for the calibration, we don't have a cable kit, and definitely not the WG kit. we just used a short and a not perfect 50 ohm load. In fact, you can see that the S11 data I posted is not good near 12 GHz. Thanks for the head up about the kit on eBay, i will ask my colleague to take a look.

If you don't even have a coaxial cal kit, I'm not sure how your results are going to be screwed up. At 12 GHz, a cheap load is likely to be pretty useless, and leaving the coax open is not going to create an "open" that is anything like any of the cal kits in the 8720D. You will get large residual errors, and so ripples on all S-parameters.

I chose -5ns as the start time just to get it as close as I could to Joel. So ask Joel why he chose -5 ns. I assume it is because it allows one to see the data from the simulated impulse at t=0.

The P-band waveguide cal kits that were on eBay cheap have all been sold. This looked to have been the best one, and sold for £56 ($93).

http://www.ebay.co.uk/itm/Hewlett-Packard-P11644A-Calibration-Kit-/141161298073

Someone got a bargain! It is just unbelievable that those kits sold for so little. I never got one myself at that ridiculously cheap price, although I do have a P11644A which I paid a lot more for, though still not the cost of a new Agilent one.

If you want an *excessively expensive* used X-band waveguide cal kit, there is one here

http://www.ebay.co.uk/itm/HP-Agilent-X11644A-Mechanical-Calibration-Kit-8-2-to-12-4-GHz-WR-90-/331102890349

If you want a *very reasonably priced* X-band waveguide cal kit, there is one here.

http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&item=171246739026

Joel is an expert on the time-domain method - his Ph.D. thesis is related to it, whereas mine is not related to VNAs at all.

Dave

Edited by: drkirkby on Apr 1, 2014 3:55 PM

Hi

I Have a Return loss (S11) versus frequency data from a Vector network analyzer. I should transform the data to time domain with ifft function.

The data includes from 1 GHz to 3GHz with 1MHz frequency step Return loss values

How could i use ifft function for this purpose?

Thanks in advance