# Understanding Trace Impedance

Author: Donald Telian, SI Guys - Guest Blogger

**Capacitance and Impedance
Intuition**

Impedance intuition is readily acquired through two simple
equations. Trace impedance “Z” is
directly related to trace inductance (L) and capacitance (C), or *Z=sqrt(L/C)*. While I’ve met a few who prefer to look at
things inductively, the majority of us find capacitance simpler to grasp. In the realm of PCB traces, the terms in the common
approximation for Capacitance (*C=*ε*A/d*) are easily transferred to trace
construction and simple to visualize. In
the equation, “d” is a trace’s distance to ground, “A” is the area or size of
the trace (i.e., its width), and “ε” is the dielectric constant of the
surrounding material. Keeping this
equation in mind impedance intuition follows, allowing you to predict the
effects physical changes will have on impedance. Just keep in mind the inverse relationship
between capacitance and impedance. In
other words, as “C” goes up “Z” goes down, and vice versa.

So let’s try a few examples. Say I need to make traces thinner to route through a dense area, will the impedance go up or down? In this case “A” decreases causing “C” to decrease as well, resulting in an increase in “Z” or a higher impedance. Or what if production wants to swap in some modern materials that have a lower dielectric constant “ε”? Once again, capacitance goes down so impedance goes up. As both these common occurrences have raised impedance, is there something I can do in the stackup to lower impedance back to where I want it? You guessed it, manipulate “d” which is the trace’s distance to ground. Indeed, if I decrease “d” then “C” increases causing “Z” to go down. See how that works? If you keep the capacitance equation around, it will be simpler to keep an eye on maintaining trace impedance when you trade-off common PCB parameters.

**Typical Trace
Impedances**

Taking the capacitance equation (*C=*ε*A/d*) forward, we might
expect trace impedance to scale inversely with dielectric constant “ε” if we hold
the ratio of trace width and distance to ground constant (A/d). Figure 1 shows this is generally true. Spanning the range of common dielectric
constants (on the X axis), we note that trace impedance (on the Y axis)
decreases ~linearly. The upper cluster
of lines are microstrip (outer layer trace, ground on one side) impedances,
varied by constant H=W (Height=Width, or d=A) values in mils. The lower cluster shows stripline (inner
layer trace, grounds on both sides, hence two heights “H”) impedances, again
with a constant A/d ratio.

** Figure 1: How Trace Impedance Scales with Dielectric
Constant**

Today’s high-speed designs primarily use 50 Ohm stripline traces. Figure 1 shows this is easily achieved with modern dielectric constants of ~3.5 for nearly all heights and widths. Since all lines straddle 50 Ohms, minor parameter adjustments will easily bring almost any stripline PCB construction to your target impedance value. Try it yourself with this stripline impedance calculator.

Figure 1 also reveals that microstrip traces are not as amenable to 50 Ohms. That’s not too problematic because the use of microstrip is decreasing; it is primarily used for short connections from components to vias. Long microstrip routes are avoided for a variety of reasons, such as:

- Component density leaves little room for routing on outer layers
- Fabrication parameters such as pre-preg thickness and etch angle are harder to control
- Noise radiating from outer layer traces is not shielded by ground

**Differential Traces**

As serial links became the high-speed interconnect of
choice, PCB traces became predominately “differential”. In practice, signal connections now required
two routes instead of one; and that changes the impedance situation a bit. Furthermore, there are some differences in
how trace impedance interacts with differential and/or single-ended signaling
we need to be aware of.

Differential traces came into the mainstream for a number of good reasons. If you think about it, all signals are in a sense “differential”, because the logic level they transmit is always referenced to something – typically “ground”. As voltage swings decreased and “ground” became less consistent between components, PCBs, and systems, signals began to carry their own reference – or the other side of a differential “pair”. At the same time, single-ended signals became more fragile as the criticality and complexity of their design escalated and their margin to “reference” eroded.

Other reasons typically cited for differential signaling are decreases in crosstalk, power/ground rail noise, and EMI. Some of these attributes relate to the fact that a diff-pair often couples more to itself then its ground reference and/or neighboring signals – although some diff-pairs are implemented with wide gaps making them uncoupled or loosely coupled. And differential pairs are certainly better for long-distance connections.

The differential impedance of an uncoupled diff-pair is two
times the trace’s single-ended impedance, and is typically specified to be 100
Ohms or 85 Ohms. Impedance-wise, the
thing to remember is that as spacing between the pair decreases the
differential impedance also decreases.
One way to think about that is to picture coupling increasing, increasing
capacitance (“d” in *C=eA/d*
decreasing), and hence impedance “Z” decreasing. This decrease can be substantial. For example, the differential impedance of 4
mil stripline traces with distant grounds can decrease 30 Ohms as the traces move
closer together. However in practice, a
10 Ohm decrease is more common.

**Fabrication Factors**

PCB fabrication introduces a variety of factors that affect
trace impedance. Etch angle (the way fabricated
traces turn out to be trapezoids instead of rectangles) raises impedance
because “A” and hence “C” go down, causing “Z” to increase. Outer-layer plating (and hence etch angle)
and solder mask dielectric thicknesses vary as well – both issues causing more
change in impedances than you might think.
And the thickness of copper on your signal layers (½ ounce, 1 or 2
ounce) also affects impedance, albeit to a lesser degree.

Fiberglass weave effects, fabricator re-imaging, and pre-preg thickness variation also significantly affect impedance. These effects are discussed in more detail here.

**Impedance and Loss**

Serial links have forced us to pay attention to high-frequency
loss in traces, while trace impedance gets set to a constant. Differential impedances typically target 100
Ohms, I’ve been amazed by how stable links perform across a wide range of trace
impedance – as long as impedance discontinuities are managed. Figure 2 shows how chip-to-chip 15 Gbps
channel performance is influenced primarily by loss, or the choice of a dielectric
material’s Dissipation factor “Df” (red=0.2, blue=0.1, green=0.002 – sometimes
called “loss tangent”). Even though the
Tx and Rx impedances are 100 Ohms, eye heights (Y axis) are shown to almost
constant against a +/- 20% tolerance in trace impedance (X axis). More impactful are material choices, which cause
a 4x (blue) to 6x (green) increase in eye heights – even without any Tx or Rx equalization. Applying 30% Tx de-emphasis improves Df=0.2
performance 3x (light red, X markers) with no material change, demonstrating
again the
power of SerDes Equalization Settings, or SES.

** Figure 2: 15 Gbps Eye Heights, Varying Trace Impedance
and Dielectric Loss**

To emphasize the relevance of material loss the channel used in Figure 2 had constant impedance, as might occur in a simple chip-to-chip connection of about 7”. As such, the only discontinuities occurred at the chip boundaries. Note that channel impedance discontinuities must be carefully managed to realize Figure 2’s immunity to trace impedance. In practice this can be difficult, however – depending on data rate – some discontinuities can be ignored.

Though differential serial links show some immunity to trace impedance, the relevance of trace impedance to proper voltage swings in single-ended signaling schemes (such as DDRx) cannot be overstated. Indeed, this is the dynamic that forced us to get good at modeling, designing and fabricating PCB traces 30 years ago. So whether you are managing discontinuities in serial links, or buffer/trace impedance trade-offs in DDRx, a working knowledge of trace impedance is essential; which brings us back to the importance of understanding PCB trace impedance, in practice.

**Conclusion**

While the concept of trace impedance has been with us
throughout the digital signal integrity journey, its interaction with signaling
schemes has changed somewhat. What
hasn’t changed is the mechanics of trace inductance and capacitance, and hence
impedance. Equation-based schemes to
visualize how impedance changes against physical parameters are helpful.

SiSoft users working with DDRx buffer/termination/trace impedance choices can access a process and QSI-ready Kit that illustrates how to maneuver through the trade-offs, as well as more than a dozen implementation Kits targeting common memory interfaces. There are also numerous QCD-ready serial link Kits pre-configured to help you understand and apply relevant specifications to your particular implementation.

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