If you routinely give attention to trace impedance but are not accustomed to thinking about via impedance, this article is for you. Or, if you are paying attention to via impedance yet are unsure what dimensions will yield the right impedance, this will help with that too. So, when should you use an 8 mil drill?

### Why Should You Care?

Serial links can fail because of impedance mismatches, or discontinuities. In practice, discontinuities are causing more problems than loss. While loss degrades a signal somewhat predictably and can be compensated by equalization, discontinuities cause reflections that are much harder to tame. So, you fix the discontinuities, and you fix the signal. Here’s an example of a 400% eye improvement achieved by correcting via impedance – a mere 1% of the interconnect, [1, page 4]. Also have a look at this method to improve via impedance and its resulting performance improvement measured in hardware, [2, page 21].

Although they are small, vias can significantly impact performance. This first became apparent when ¼ wavelength stubs crept into systems. A via stub left in a ¼ in. thick backplane can completely remove a 12 Gbps signal, per the approximation 3/12 (yes, just use 3/Gbps and get inches, see [3, slide 5]). While stubs can be disastrous, via impedance mismatch is also increasingly problematic as data rates increase. But how can we better understand the impedance of vias?

### Enter Via Modeling

A few decades ago, while my RF friends were busy with exotic 3D solutions of vias, we would place a 0.5 pF capacitor in our interconnect model at via locations and call it good. Over time, we learned that modeling vias as a transmission line is a better approach. Some tools implement fast via solvers ([4, page 4]) that expand on the transmission line concept to deliver correlated accuracy, as described in this paper [5]. Yet, even if you don’t have access to a fast via solver, it’s possible to gain an intuitive sense of via impedance, as described below. And if you want to try out a via solver, I’ll provide a link at the end of this article.

### Building Impedance Intuition

To build our intuition on what via dimensions will yield impedances we want, let’s begin with the more familiar differential trace shown in Figure 1. Indeed, vias behave a bit like traces – albeit in the Z dimension.

**Figure ****1. Differential Trace Impedances**

Figure 1 shows stripline trace impedance versus width, spacing, and distance to ground planes (X axis represents W=S=H1=H2 per the cross-section view). Interestingly, all dimensions yield impedances close to what we typically want, and minor adjustments are used to dial in the value more precisely. For example, increasing either or both H values moves the reference plane further away, making the trace more inductive, thus raising the impedance (Z=sqrt[L/C]). Widening the trace (W) makes the trace more capacitive, thus lowering its impedance. Visualize how these two changes impact impedance, because we’re about to apply them to via structures.

Figure 2 plots differential via impedance versus common drill sizes on the X axis. Pad sizes are drill+10 mils and circular antipad sizes are drill+20 mils. Spacing is 1 mm as would be found under a BGA or near a connector. The first thing we notice is the range of impedances has increased more than 4x when compared to the range of trace impedances in Figure 1. This wider range makes via impedance more challenging to control. Like traces, we can make changes to a via’s structure to adjust its impedance. For example, widening the antipads – or connecting them into an oval “racetrack” shape – moves the reference plane further away (like increasing trace H in Figure 1), making the via barrel more inductive thus raising its impedance. In contrast, increasing the drill size widens the barrel (like increasing trace W), making it more capacitive, hence lowering its impedance.

**Figure**** 2. Differential Via Impedances**

Again, the challenge with vias is the 4x+ impedance range compared to the narrower range associated with traces – seen clearly by comparing Figure 1 and Figure 2. As structural adjustments for traces and vias have similar dimensions, they also have similar effects on impedance – perhaps 5 or 10 Ohms in either direction. As such, it becomes difficult to get 16 or even 12 mil vias close to 100 Ohms because their “natural” (i.e., no structural modifications) impedances are ~70 Ohms. Thus, it should become apparent why 8 mil drills are gaining in popularity in a world somewhat reluctant to move towards 85 Ohm impedance – which is the “natural” impedance of the more common 10 mil via.

### Digging Deeper

You might be objecting to my generalizations because I did not state my dielectric constant (Dk). You’re right. It was 3.3. Indeed, Dk proportionally raises capacitance and hence inversely affects impedance. As such, the first time I solved 10 mil vias with a Dk=3.0 I found them closer to 100 Ohms than expected. With common Dk values varying 50% (3.0 to 4.5), Dk is indeed an important consideration. So when using the differential impedances shown in Figure 2, if your Dk is higher than 3.3, your impedance values will be lower. Likewise, if your Dk is lower than 3.3, your impedances will be higher. For example, as Dk ranges from 3.0 to 3.6, the Figure 2 impedances change +/- ~4 Ohms.

We should also discuss differential trace and via spacing. As traces or vias get closer together they become more capacitive and impedance decreases. While the trace impedances shown in Figure 1 can be increased ~10 Ohms by separating the traces, via impedances will decrease from those shown in Figure 2 as vias move closer together. However, due to their associated pads, via barrels cannot move closer together than ~20 mils, making it difficult to decrease impedance by more than ~ 5 Ohms.

Also be advised that as we pass 28 Gbps NRZ we need to stop thinking of vias as a single impedance, but instead as a structure whose impedance dips at the pads and rises in the barrel. At this data rate those elements are within the relevant feature size and, therefore, are modeled separately – see Figure 2 in [6].

As you start down the road of grappling with via impedances – and more tools and measurements become available for the same – the task will simplify, just as it did for traces. My goal has been to give you a reference point to make the task of implementing via impedances, and thus removing via impedance discontinuities, less daunting.

Want to try out automated solvers on your via dimensions? Here’s a free trial of Signal Integrity Toolbox, with which you can use the via solvers in MATLAB.

*This article is an excerpt from Donald Telian’s new book “**Signal Integrity, In Practice**.” A Practical Handbook for Hardware, SI, FPGA, and Layout Engineers.*

### References

[1] Telian D., Camerlo S., Matta K., et al. 2014. ‘*Moving Higher Data Rate Serial Links into Production – Issues & Solutions*,’ DesignCon Best Paper 2014.

[2] Telian D., Steinberger M., Katz B. 2016. ‘*New SI Techniques for Large System Performance Tuning*,’ DesignCon 2016.

[3] Telian D. (2007). *Adapting Signal Integrity Tools and Techniques for 6 Gbps and Beyond* [slides 1-33]. SiGuys, CDNLive! 2007.

[4] Telian D., Camerlo S., Steinberger M., et al. 2012. ‘*Simulating Large Systems with Thousands of Serial Links*.’ DesignCon 2012.

[5] Steinberger M., Telian D., Brock E. 2013. ‘*Fast, efficient and accurate: via models that correlate to 20 GHz*.’ DesignCon 2013.

[6] Telian D. (2022 April 1). ‘*Which Discontinuities are Small Enough to Ignore**?*’ Signal Integrity Journal RSS.

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