Transmission line losses—driven by skin effect and dielectric properties—play a critical role in degrading high-speed signal integrity and eye performance.
Transmission line loss directly affects eye diagram quality, with around −12 dB at Nyquist marking the limit before signal integrity rapidly degrades without equalization.
Sharp dips in S-parameter plots often indicate coupling to high-Q resonant structures, where specific frequencies are absorbed by PCB cavities or floating interconnects.
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:
Formula
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.
Eric Bogatin presented a webinar Reading S-Parameters Like a Book as Part 2 of a multi-part webinar series High-Speed Interconnect Characterization. That webinar covers more details on this topic. Click the button below to watch only Part 2 or to access the entire 6-part series, or download the transcript to preview the webinar content.
Eric is a professor in the EE department at Colorado University, Boulder and a Fellow at Teledyne LeCroy. He has a BS in Physics from MIT and a PhD in Physics from the University of Arizona, Tucson. He enjoys DesignCon and writing for SI Journal.
Mixed-mode S-parameters are derived from single-ended measurements through matrix transformations that reveal differential and common-mode signal behavior.
