What is Trace Impedance and Why Do We Care?
Wednesday, October 26, 2011 | Douglas Brooks, PhD.


Background

All wires and traces have impedance and offer a moderate impedance to the current flowing 
from a driver. That seems like an astounding sentence given that (1) most wires and traces 
are made from copper, and (2) copper has the second-lowest resistivity of any known element 
(see Note 1.) Copper wires and traces seem almost like perfect conductors. After all, if you 
place an ohm meter across a trace, the DC resistance is extremely low. We almost always
ignore it in circuit calculations.

But impedance, of course, is an AC characteristic. That is, impedance is related to frequency. 
Resistance is not. So what we mean is that wires and traces present an AC impedance to the 
drivers driving them (see Note 2.) It is generally true (but not always) that from a practical 
sense the rise time of our signals must be relatively fast before this impedance becomes an issue. 
But the fact that trace impedance exists at all must be taken as a given.

So when we hear the term “controlled impedance” trace, our first confusion might come from 
the question: Why does a trace have any impedance at all? And if it does, what does it mean 
that we somehow control it?

Nature of Trace Impedance

So how is it that a trace has a potentially significant AC impedance? Well, we can develop the 
argument like this:

Every trace has series inductance. It is distributed along the trace and is inversely related to 
the cross-sectional area of the trace. It is admittedly small, but it is non-zero. Therefore, for 
fast enough rise times, the impedance it offers can be significant.

Every trace has capacitance between the trace and the return path of the signal on the trace, 
wherever that return path might be. It is distributed (see Note 3) and is related to the width 
(or diameter) of the trace and to the dielectric of the material(s) between the trace and the 
signal return path. It is inversely related to the distance to the return path. It is admittedly small, 
but it is non-zero. Therefore, for fast enough rise times, the impedance it offers can be significant. 
It is the current path through this capacitance that allows current to flow as the signal propagates 
along the trace (see Note 4.)

If we assume that any trace resistance is small in relation to this distributed inductance and 
capacitance (a reasonable assumption unless we want to talk about lossy transmission lines), 
then we see that every trace looks like a distributed LC circuit to the driver driving it. The (AC) 
impedance of the trace derives from this distributed LC circuit (Note 5.)

Unless we have carefully designed the trace and its environment, this AC impedance is “uncontrolled.” 
That is, the distributed inductance and capacitance can (and probably does) vary in value from point 
to point along the trace. Therefore, the AC impedance varies from point to point along the trace. 
In a great many cases this impedance is of no consequence and we ignore it.

There are a few cases where control over this impedance is important. For us board designers this is 
usually when we want to make the trace look like a transmission line (so we can terminate it in its 
characteristic impedance to avoid reflections.) When we do this we have designed a “controlled 
impedance” trace or a “controlled impedance” transmission line. This is in contrast to the 
“uncontrolled” situation referred to in point 4 above.

Controlled Impedance

“Controlled impedance” in this context means that the impedance is constant at every point along the trace.
The primary way we control the impedance of a wire or trace is to control its geometry and its environment. 
There are three primary (and one secondary) aspects to the overall geometry that must be controlled:

The width of the trace
The spacing between the signal trace and the signal return path (This is one reason why we use planes, 
it makes control over this spacing much easier.)
The relative dielectric coefficient of the material that surrounds the trace, and
(Secondarily) the thickness of the trace.
Coaxial cables are excellent examples of controlled impedance transmission lines where these variables 
are tightly controlled. The old “twin lead” cables are also examples of controlled impedance transmission lines.

“Controlled impedance” does not imply that these aspects cannot change along the trace. It means that the 
important relationship between them must not change. For example, if we change the width of a trace, then 
at least one other aspect must also change in order to maintain the correct overall relationship between the four aspects (and therefore maintain a constant impedance).

Scaling

It is not often clear to designers that the overall scaling of a trace can change without changing its 
impedance. For example, consider a microstrip trace with the following stackup:

W  = 10  mils
Th  = 1 oz.
H  = 12 mils above the plane
Er = 4.3 below the trace
Er = 1.0 (air) above the trace
Zo = 73.8 ohms

The characteristic impedance of this trace is 73.8 Ohms according to the Polar Instruments Quicksolver calculator (see Note 6).

The above trace will have the same impedance as one whose dimensions are exactly half:

W  = 5  mils
Th  = .5 oz.
H  = 6 mils above the plane
Er = 4.3 below the trace
Er = 1.0 (air) above the trace
Zo = 73.8 ohms

One way to envision why this is so is to look at the electromagnetic field surrounding each of these traces. 
Mentor Graphic’s HyperLynx simulation tool is one tool that will give an “image” of the field surrounding 
a trace. Such a field is shown in Figure 1.