Right angle RF tracks - case study


Let’s try this again. I find that calling other people names doesn’t actually improve me as an engineer and doesn’t help me to learn something new. So, I will make an attempt to consider actual data. If you choose to add to the discussion, do so with data, not just by speaking in generalities and regurgitating stuff from other forums and websites.

I personally don’t like to generalize. In many cases (see how I didn’t say always :slight_smile: )there will be an exception to most of the rules. Or the rule might not be applicable. I think the case about right angle RF tracks follows the suite. There is a camp that will argue that having a right angle track turn makes absolutely no difference. I’m sure there are many cases when that is true. Is it a universal rule? Are there cases when having a right angle track would completely change your circuit tuning? Let’s see if we can come up with one.

Ok, suppose you have an RF device with an output impedance of 50-j415 Ohms and we need to match it to a 50 Ohm load. Let’s say it is a RF amplifier connected to an antenna. And let’s say we are operating at 10Ghz.

To match that you would simply need to connect a 6.6nH inductor in series to have a pretty decent match.

Now, suppose we make a single right angle turn in the trace after the matching inductor. According to the formula discussed in the article, parasitic shunt capacitance would be 0.012fF that’s 12 *10^-18! That’s a really small number! Let’s see how it affects our impedance with the same matching.

That doesn’t look like a perfect match to me. Not even close! Our final impedance is 28.9 + j98 Ohms. What does it mean? It means that your VSWR in that circuit will be around 8.8:1 and you return loss around 1.98dB. That means that 63% of the RF power is going to be reflected from the antenna instead of being radiated! That seems like a big problem to me.

Now I can just as easily come up with a case when by varying initial conditions a single right angle turn will have absolutely negligible effect.

What does it all mean? It means that more often than not the right answer to a complex problem would be “It depends” . Things pertaining to science are not established by a majority vote or by the size of the camp that supports your point of view.


I do agree with your general point of view, but example you provide is constructed wrong. And you seem to have made a error in capacitance.

You say 0.012 fF, but in smith chart use 12fF. Also, you added the “corner” capacitance right at the device port not after matching network.

Here I did quick calculations:
Add series inductor for matching XL = j415
Z = 50
Now you done matching and of we go with transmission line.
But here comes corner with XC=-j1.326 MOhms
We get Z = 50 - j 0.002

I would say not so bad.


See, that’s why it is good to use numbers instead of general statements! You are absolutely right! I did make a typo. The corner capacitance is supposed to be 0.012pF which is 12fF, which is 12*10^-15F. Other than that everything seems to be right. So you used the wrong value in your calculations.

You right about the position of the corner as well. It should’ve said “…suppose we make a single right angle turn in the trace before the matching inductor.”

Other than that, the results stand.


OK, but why would anyone create a transmission line before matching port to the line itself furthermore at 10 GHz? I would say your hypothetical model is not about the problem we are discussing.

If I do same calculations but with real corner capacitance I get Z = 49.9 - j1.88.


“Why” is irrelevant. There may be a lot of reasons. Most often it can be dictated by the constrains of the board layout. Just recently I did a board where an amplifier and an antenna had to be positioned in precise locations and couldn’t be moved. How about a reason like this: “I just read on the forum that right angles don’t matter so I just added one” Could be a perfectly valid conclusion after reading some of the posts on the previous thread.

Show your work, I’ll let you know where you made a mistake


Then start a topic about matching networks and I will agree with you completely.


Z(port) = 50 - j 415
ZL = j415 (matching inductor)
Z1 = Z(port) + ZL = 50 - j 415 + j415 = 50 Ohms
XC = 1 / 2pifC = 1 / (2 * pi * 1010^9 * 0.012 * 10^-12) = 1326 Ohms
ZC = -jXC = -j1326 Ohms

Now switch to admittance
Y1 = 1 / Z1 = 1 / 50 = 0.02 S
YC = 1 / ZC = 1 / -j1326 = j7.54*10^-4 S

Y = Y1 + YC = 0.02 + j7.54*10^-4 S

Now back for final value
Z = 1 / Y = 1 / (0.02 + j7.54*10^-4) = 49.93 - j1.88 Ohm


What exactly are you disagreeing with? I’d like to have a discussion, I just don’t understand what you are trying to prove? The original premise of the topic was to demonstrate that right agnle trace turns can make a drastic difference in your circuit performance. I think I demonstrated that.

You did your calculations for series L shunt C. Look at the circuit in the picture. I already explained it. It is shunt c and series L looking from the source. So you will have source impedance and capacitor impedance in parallel and inductor impedance in series.


Yes, I agree.

My understanding was that we are discussing transmission lines of 50 Ohm as commonly used. I assumed RF tracks to mean transmission lines. So my calculation is for introducing corner capacitance in 50 Ohm line.


Incorrect. You calculation was for a different circuit. (Z1-L||C as opposed to Z1||C-L)

We ARE using 50 Ohm transmission line in this example. We just ignore trace lengths, since it would introduce additional terms to the equation and, as you might argue, would fall out of the scope of this discussion. We just assume that we keep each segment of the trace half wavelength.


Yes, that is what I meant. I was talking about line that starts after matching and ends at load, also implied.


http://www.ultracad.com/articles/90deg.pdf from 1998

90 Degree Corners: The Final Turn

Only a few topics generate the kind of enthusiastic
discussion that a right angle corner on a trace does. Just
the mention of 90° corners — regardless of whether you
say that they shouldn’t be used of if you say that they are
harmless and can be used without concern— guarantees
a response from people with the opposite view

The TDR data do not show any measurable reflections from
either 45° or 90° corners in microstrip traces. In
theory, there is a change in Zo caused by a corner, but the
effect is not sufficient to be resolvable with a 17 ps
rise-time pulse.
The radiated emission measurements (up to 1.3 GHz.)
do not show an increase for 90° corners, compared to 45°
corners, that is larger than measurement uncertainty.
All of the trace geometries measured produced radiated
emissions that were 35-50 dB below the emissions of a
3-cm long monopole antenna and only slightly above
those from a straight trace with no corners.
For most circuit boards it is expected that discontinuities
encountered at IC packages, connectors, and vias
will produce much larger reflection or radiation effects
than either 45° or 90° corners


Your post doesn’t add any value to the current discussion. I already asked to not mindlessly regurgitate information from other sites. We all here know how to use Google. My goal was not to resurrect the former thread. If you got anything to add to the case being discussed, which clearly demonstrates a significant effect of a 90 deg trace turn, then by all means, have at it. Just one more thing, in case you haven’t noticed, we are not really talking here about emissions of any kind.


I don’t really get what you are comparing in your calculation.

Do you compare a straight trace to one with a single “bend” (whatever form) in it?
Or are you comparing a sharp 90° turn to a slow bend? (<- this would be the same topic as we already closed.)


How rude you are!

Your contrived, theoretical simulation actually adds nothing to the discussion. OTOH, considered articles written by industry experts carry a lot of weight.


The first case would, in first approximation, depict a trace with a 45 deg turn or rounded trace (or a straight trace for that matter). The second case is the same trace with a 90 deg corner. There is no minimum radius. You can even have two traces meet at 90 degrees and have a rounded outside corner (which would be harder to accomplish in a board editor). As long as you are removing any extra copper that creates additional capacitance it will all work.


Just to demonstrate, that you can run into trouble with much lower frequencies, let’s consider the same case for 915Mhz bandwidth.

Here is the matching for 915Mhz

Now for a 50 Ohm microstrip at 915Mhz for regular FR4 you corner impedance will be around 0.043pF.

So our final matching becomes:

It is not as bad as 10Ghz frequency, but still nothing to write home about! VSWR is roughly about 2.3:1 and return loss about 8dB. Roughly 15% of power lost to reflection. That’s just for a single corner. Definitely not a negligible influence.


I get what you’re saying, but why not just correct that with your matching network. You could use less inductance and add shunt capacitance.

Edit: Also, you will end up in exact same spot on smith chart only if you have half wavelength lines before and after corner. So this is pretty unrealistic anyway.


Here is another article from a respected member of the electronics community:

Who’s Afraid of the Big Bad Bend?

Right-angle bends in PC-board traces perform perfectly well in digital designs in speeds as fast as 2 Gbps. In most digital designs, the right-angle bend is electrically smaller than a rising edge

Today, only microwave designers need to worry about right-angle bends. At microwave speeds, roughly 10 times the rate of most digital designs, parasitic capacitance presents 10 times more of a problem. Also, microwave designers often use big, fat, 100-mil traces to reduce skin-effect losses, so their corners appear electrically 10 times bigger. They also tend to linearly cascade multiple stages. Cascading sums the imperfections in each stage, making microwave designs about 10 times more sensitive to tiny imperfections. Overall, contemporary microwave designs can be 1000 times more sensitive to right-angle bends than are digital designs.

As digital designs push toward higher speeds, you may eventually reach a point where the right-angle bends begin to matter. For example, corners are just beginning to affect the design of 10-Gbps serial connections, and they also contribute perceptibly to skew in certain poorly routed differential pairs. If you accumulate a lot of corners, as in a serpentine delay structure, you may begin to see a little extra delay. Other than these extreme applications, right-angle bends remain electrically transparent.

If I could find articles presenting a contrary case, I would post them.

BTW, this thread is now on Google, should we dismiss it’s conclusions ? :slight_smile:


More actual measurements showing that nothing could be seen in practice at 1 GHz:


At the conclusions, it is clear that all considerations about 90 degrees corners are useless up to 1GHz frequency, but after that frequency the ‘music’ is different…