Microstrip Transmission Line

Hello,

Let me preface this with saying I have no formal training in microwave transmission lines. Everything I know, which is not much, is self taught. I was tasked with creating a microstripline for the purposes of carrying a field in the 500 - 2000MHz range. Our goal is to use the lateral H-field produced by the line to drive small micromagnetic structures deposited on top of the line.

To design the line I've mostly relied on "Handbook of Microwave Integrated Circuits" by Reinmut K. Hoffmann and the design equations available in that book since I do not have access to an adequate EM simulation program. For impedance matching at 50ohms I used the equations by Hammerstad and Jensen. The line is very thin, only 100 nm of gold, so thickness corrections were insignificant. I am also not planning on going above 2GHz so dispersion did not seem like an issue either. I had to add two 90 degree bends which I mitered according to the specifications in that book. For the substrate I am using 0.5mm crystal sapphire. I also had to add a taper to reduce the width of the line to about 10um to get a strong enough H-field above the line. For the taper I followed paper "A Transmission Line Taper of Improved Design" by R. W. Klopfenstein. I made the taper as long as I could (1.5cm) to try and reduce the reflection at that low frequency I want to operate in.

For the grounding plate we just used a large piece of aluminum on which the substrate and line sit. For the connections we used these sma to tab launchers found here
https://www.digikey.com/product-search/en?x=20&y=25&lang=en&site=us&KeyWords=A99392-ND

The connection is made via an insulating tab which applies pressure between the tab conductor and end of the line. I've attached a few images of the whole structure. I've also attached a sketch of the transmission line design and its dimensions.

To test the line I only have available an RF signal generator and a spectrum analyzer along with basic electronic components. I did a simple test to check the transmission by terminating one end directly into the signal generator and the other into the spectrum analyzer, both of which have 50 ohm terminations. Only about 25% of the signal amplitude was getting through the analyzer, so there are significant losses.

I have a few concerns. First due to the small dimensions of the center region with a cross section of 10um wide by 100nm thick the total dc resistance of the line is about 140 ohms. If I am not mistaken all of the design calculations assume that R << ωL. If the total inductance of the line is a couple of hundred nH then that is certainly not true in the 500-2000MHz range, so does that mean the impedance is off? I know at higher frequencies the current will tend to stick to the walls of the conductor due to the skin effect resulting in an increase of the resistance. From what I've been able to gather the total resistance goes something like \[ R_{dc} + R_{ac} \sqrt{ f}\] where Rac is inversely proportional to the skin depth. So I am assuming my biggest issue at the moment is severe conductor loss?

I am also concerned about the grounding plate and the connections. Is is that sma to tab launcher good for impedance matching? From what I read it is better to make contact via pressure rather than solder?

I apologize for the lack of specific details. I am looking for any general advice and issues that you folks might notice with my design/setup.

The length of your Klopfenstein taper sounds short for low frequencies. Connector choice and aluminum sounds good for these frequencies. Press down on the center of the board and see if your measurements change. That will tell if you have good ground contact between the bottom of your sapphire board and aluminum.
https://www.awrcorp.com/products/optional-products/tx-line-transmission-line-calculator Youtube has a video (advertisement for TXLINE)
Site www.microwaves101.com has an excel spreadsheet that will give you lengths and impedance for a Klopfenstein taper. Use TXLine to convert impedance to line width.

Thank you for the response. I knew the length of the taper would be an issue, unfortunately I don't think I could make it much longer. I have to fit the line between two poles of a large electromagnet and it is pretty close to touching the poles as is. Is there another way I might be able to taper the line and receive better performance at lower frequency? I was thinking of possibly reducing the thickness of the substrate further. This would allow me to reduce the width of the 50 ohm section and keep the tapered section at 10um but reduce the impedance.

How much bandwidth do you need? Klopfenstein is about the most space efficient algorithm for tapered lines. 1/4 wave transform is shorter but narrowband....
At 10um (0.394mils) you are going to have significant loss.

So initially I was told to design the line to work in the 3GHz range, which is what I did there with the taper. Now I've been asked to change it to work in the 100-1000MHz range, which is where my problem is. As you said, this taper is too short for this frequency range. To make it work it would need to be something like 100mm long, which is not possible for the experiment. Even a quarter wave transformer would have to be about 57mm long to work at 500MHz.

So I guess my issue is I can't really figure out a good way to reduce the width of the line at 500MHz without a very long taper or transformer.

I guess another question would be at what point do I even have to worry about impedance of the trace? Like I said I don't have much training in transmission lines so I am getting a bit too much of my information from the internet and one thing I keep coming across is this "1/8 wavelength" rule of thumb. Being if your trace is less than 1/8 the wavelength you don't really have to worry about the impedance of the trace. I don't really need the 10 um segment to be longer than 50 um. If I made the taper and 10 um segment much shorter than the wavelength would I be okay?

Attached is an image of a line used for a similar setup. The center segment is 18 um wide by 100 um long. The entire trace is about 1 mm long from end to end and the ends are match to 50 ohms. As far as I can tell they are just using a triangular taper and a fairly short one. So I'm not quite sure how they could make a taper so short work. Is it because the length of the trace is so small compared to the wavelength at that frequency?

Using an aperture ( so no GND plane ) just underneath of the thin line will increase the line width because of low dielectric ( Air ) coefficient but it will also be longer.
If I understood well your issue..

I think you have to lay out some more concrete specifications for what you're trying to do. How flat does your frequency response actually need to be? I doubt you'll be able to get 3dB of flatness over a decade of bandwidth with simple trial and error.

What sort of power/current are you trying to inject? Pulsed or CW? You don't want to spend a long time designing a nice TL if it turns out it's so thin that it burns during use.

Hello all I appreciate your assistance. In terms of the flatness, I have not given it much thought. I understand depending on the tapering mechanism the gain or loss will vary over the span I am interested in. In terms of what kind of signal we are looking to feed through. At the moment our rf signal generator with the rf amplifier we have won't give us much more than 300 mW. The line will be used for measurements, so it won't be running constantly, just short periods of time. Looking to use sinusoidal signal, no pulses for the moment, in the 100-1000MHz range.

I am looking to increase the thickness of the line since the H-field produced immediately above the line does not decrease significantly with increasing thickness. However, we are trying to maximize the amount of field we can get, thus the thinner segment which does greatly affect the field above the line. So that is sort of the reasoning behind such a thin trace at the center.

I guess my question is since I do not want to go above 1GHz at the moment anyways, can I just make the trace extremely small? I can match 50 ohms at the connections and taper the trace still, but make the total length much smaller than λ at 1GHz because that is not an issue for us.