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27 May 2020

Reading S-parameters: Sharp Dips

Figure 1. A resonant cavity composed of two interior layers
on a four-layer printed circuit board.  The return current from
the signal path couples into the plane cavity and excites its
resonance modes.
The last pattern we'll cover in this series on reading S-parameters is sharp dips. These dips result from coupling to high-Q resonant structures and represent very narrowband absorption in S21 or S11.

Where do you see resonant coupling? Resonant structures can include coupling to an interconnect that is floating and not terminated. The structure does not have to be a uniform transmission line, it can also be a cavity made up of two or more adjacent plates as shown in Figure 1. Commonly, when a signal goes through a cavity and we hit the resonances of the cavity, it absorbs energy and results in narrow dips in the S-parameters.
In Figure 1, the signal goes through a via from top to bottom. The return current has to make the transition from the upper to the lower return plane. If the return path is not well controlled and is not in close proximity to the signal lines, the return current gets coupled into that cavity and we see that the energy of those resonant frequencies sucked out of the signal that gets transmitted.

Let’s look at a real-world example shown in Figure 2.

Figure 2. A printed circuit board with eight symmetrically
placed  SMA connectors serves as an example to show the
effects of  several high-Q resonance modes based on the
board's dimensions. 
This FR4 printed circuit has eight symmetrically spaced ports using SMA connectors. We’ll focus on the micro-strip transmission line connecting port 1 on the top layer to port 2 on the bottom layer. The signal line makes the transition through the vias in the center of the board, shown in the exploded view.  Note that there are no associated return vias. The return current has to make the transition from the upper internal layer to the lower internal layer, and in doing so it excites the resonance of the cavity formed by those layers. The frequencies of the resonances, based on the board dimension and the dielectric constant of the board material, can be predicted by the equation:

The principal modes are defined by the length and the width of the board. Another resonant mode is defined by the spacings of the SMA connectors, where the connector grounds short the internal planes. Using the given equation, we can calculate the resonant and list the expected frequencies.

Length (in)    Resonant Frequency (GHz)
3.25                0.92
1.187              2.5
0.8                  3.75

Now let’s look at the measurement of S21 for this board (in Figure 3).

Figure 3. The measured S21 of the PCB showing 3 principal modes.
As expected, we see that S21 at low frequency is 0 dB. There is the monotonic slope due to resistance and dielectric losses. And we see the three sharp dips related to the coupled resonances we calculated at 0.92, 2.5 and 3.75 GHz.

The Q of the resonance is the ratio of the resonant frequency to the width at half the maximum. The resonance at 2.5 GHz has a width of about 0.1 GHz, so the Q is 25.  Q’s of more than 10 are considered high.

The depth of the dips due to resonant coupling depends on the degree of coupling. The dip at 0.92 GHz has the smallest dip because the via in the port1 to port 2 path is symmetrically spaced at the center of the board length. Energy propagates equally to the left and to the right and the equal reflections cancel each other. If the via had been at either end of the board, the coupling would be greater. The via is closer to the upper edge of the board, and this asymmetry forces a higher degree of coupling for the resonant dip at 2.5 GHz. There are multiple resonances for the 0.8 inch spacing, and the via is not particularly symmetric with most of them, so the coupling is greater.

Eliminating these dips requires careful design. First, you should try to avoid transitioning the signal between different return planes. If you must, use return vias adjacent to each signal via to suppress resonance.

Watch the on-demand webinar Reading S-Parameters Like a Book by Dr. Eric Bogatin, Signal Integrity Evangelist, for a more in-depth treatment of this topic.


DE_T said...

Thank you for this article!! Can you please explain where the 12GHz in the formula comes from? Or is it explained in the webinar? Thank you again.

Teledyne LeCroy said...

Hello DE_T,

Sorry for this long delay in replying!

The formula above is for resonance frequency in GHz, taken from Dr. Eric Bogatin's book "Signal and Power Integrity Simplified" Third Edition, p. 653.

fres = 11.8/sqrt(Dk)*2*Len

--fres - resonance frequency in GHz

--Dk is the dielectric constant of the laminate inside the cavity nominal value of 4 for FR4

--Len is the length of a side of the cavity in inches

11.8 is the speed of light in a vacuum in inches per nanosecond. During his class, Dr. Bogatin rounded the number to 12 in order to simplify the calculation.

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