Microstrip BALUN Design

microstrip balun

I'm designing a wide band microstrip tapered BALUN using Klopfenstein optimum taper.
The usage of BALUN will be feeding an archimedean two-arm spiral so I need to match 50 ohms unbalanced coax feed to ~150 ohms balance antenna.

My thought is to split the Balance to Unbalance and impedance matching parts.
first starting from a 50 ohms unbalance microstrip to a balanced parallel broad-side coupled striplines; by changing the width of the ground plane while keeping the upper strip intact.

In the second stage I change the width of two similar strips alike to reach the desired impedance.

FYI, the changes in width in both stages will be according the Z curve obtained from Klopfenstein formulas which I already prepared as a table.

So the problem is that for the first part I don't know how to calculate the impedance of a microstrip in which the upper strip doesn't change but the ground plane is narrowing!

The only literature I found directly pointed to the same work is a Czech paper which I have read by google translator. The following image is from there.
off course I've tried to contact the author but failed

Pls help.

balun design

If you have an EM simulator available, you can make a series of parametric runs of a quarter wavelength transmission line at your center frequency. By loading both ends of the line with 50 Ohm ports, you can read the transformed impedance (S11) on a Smith chart plot. Calculate the characteristic impedance of the line as the square root of the product of 50 Ohms and the transformed impedance.

microstrip balun design

Thank you for your hint but I didn't understand completely.
You mean I make a parametric taper? I'm using HFSS.
Would you pls make it more clear.

Thanks in advance

parallel plate balun

Hi...

Based on my understanding of your issue and the reply, the suggestion is to simulate impedances rather than calculating them. First, you should create a microstrip structure with a ground plane that has a parameterised width wgnd. The microstrip width ws can be anything, really, but it is easiest if it is fixed for 50 Ω in the effective medium (i.e., adjusted for the substrate used) - any microwave transmission line calculator can give you this. The length of the line (and ground plane) is a quarter-wave at your centre frequency (although you could repeat this process for lengths equal to λ/4 at the band edges too, to see how much of a difference there is).

Once the model is created, add a parametric sweep for various ground plane widths. Start from wgnd = 10*ws, and reduce to wgnd = ws. The step size is up to you; the smaller it is, the more simulations required and the longer it will take, but the more impedance you'll have. You can then determine the impedance from the S-parameters. This will allow you to approximate the taper by selecting points mapped to "known" impedances and putting small lines (curved or straight) between them. The more impedances you have, the smaller the sections can be and the better the approximation will be.

Could you provide a link or the name of the Czech paper you referred to? I'm interested to see what they did.

smith chart balun match

Thank you I'll try to do it but there is one thing about length: I'm splittingthe balun to two parts. the first is the tapered microstrip and the second is parallel stripline. Shall I take the total length λ/4 or each of them? i.e. λ/2 totally.
My own tough is testing both of them but it will be a bit time consuming to simulate both. Any suggestion ?

Regarding the Czech paper I've attached the pdf here.

micro-strip balun

Hi again

Thanks for the paper, I'll have a look at it on Google Translate.

In my opinion, the total transition (i.e., both tapered microstrip and parallel-plate line) should be λ/4. However, the Klopfenstein taper has a relationship between length and minimum reflection ripple in the pass-band, so you should determine the total length from your requirement for return loss over the band (or, if you only have a fixed amount of space to work with, you use that length and the Klopfenstein taper will give you the minimum reflection ripple possible for that length). Either way, you'll have a choice to make about how long the two parts are - are they equal in length (i.e., λ/8 each if the total length is λ/4) or unequal (e.g., 3λ/16 and λ/16)? There may be an optimum point, but I'm not aware of any research either way.

As far as the simulation time goes, that's not really avoidable. The only way to reduce it (assuming you have no supercomputer or cluster!) is to reduce the step size, which will affect the accuracy of the eventual taper and, therefore, the return loss. That can only be determined by you, according to your requirements.

Hope that helps.

tapered microstrip

Thank you.
I'm considering how it will be if I design two Klopfenstein tapers. The fist will do BALUN by fixing the strip width and changing the ground plane by the way you suggested (I still hope I find some calculator on the web!) and ending up with parallel equi-width stripes on about 64 Ohms and the second taper to start from parallel striplines just to match the impedance and both stripes will change together. So I guess each taper will be λ/4 and total structure will be λ/2 as the working frequency is the same for either parts.

I'm gonna start the simulation today and hope to reach the result by tomorrow. I expect the simulation runs fast as it is not the matter of radiation but the try and error sessions will be time consuming and boring :|