Reading time ( words)

**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 milsTh = 1 oz.H = 12 mils above the planeEr = 4.3 below the traceEr = 1.0 (air) above the traceZo = 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 milsTh = .5 oz.H = 6 mils above the planeEr = 4.3 below the traceEr = 1.0 (air) above the traceZo = 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.

Figure 1. Note the electromagnetic field lines around the traces. (Source: HyperLynx Simulation Tool)

Now, which trace is shown in Figure 1, the 10 mil wide one or the 5 mil wide one? The answer is that the figure applies to both situations equally. The only difference between the traces is the scale factor. Without any dimensional information on the figure, you can’t tell which one this was derived from. This illustrates a very important point --- one that occurs several times in electronics:

*It is not the trace dimensions that are critical in establishing the impedance of a trace, it is the distribution of the electromagnetic field that is important.*

Any changes in trace dimensions or environment that preserve the distribution of the electromagnetic field will leave the trace impedance unchanged!

**How Do We Determine Trace Impedance?**

If we know the geometry of a trace and the properties of the material(s) surrounding it, how do we then calculate the trace’s impedance? In decades past we used various formulas for this. These formulas could be found in various application notes and industry standards, and they were “close enough” then to be suitable. But as requirements have become more precise, these older formulas are no longer considered reliable for the precision we now require. Our requirements became more difficult as we began to want formulas for edge-coupled differential traces, and there never have been reliable formulas for broadside-coupled differential traces.

In the opinion of many designers, there are no impedance formulas that are now considered adequate. Instead, there are several techniques we must/can rely on for impedance calculations.

- If you are using one of the “high-end” PCB design systems, it will calculate trace impedance for you, and most will also provide you with differential impedances.
- Simulation tools (such as Mentor’s HyperLynx tool) will provide impedance information/calculations for you.
- There are some calculators available in the marketplace that will do these calculations. In my (personal) opinion, the best of these is the Polar Instruments Si8000 calculator (again see Note 6.) An alternative calculator is offered by UltraCAD (my company, see Figure 2.) We do not disclose the calculational technique we use with the calculator, but it is NOT formula-based (Note 7.)

Figure 2. UltraCAD’s Differential Impedance Calculator (Broadside coupled configuration).

**Summary**

- Every trace presents an AC impedance to the circuit driving it.
- This impedance is typically uncontrolled and unpredictable unless we have specifically designed the trace as a “controlled impedance trace,” as in cases where we are trying to make our traces look like well-designed transmission lines.
- We control the impedance of a trace by controlling its geometry and the Er of the surrounding materials.
- A controlled impedance trace does
*not*require a*constant*geometry. It does require, however, that if one aspect of the geometry is allowed to change, at least one other aspect of the trace must also change in order to maintain a constant (unchanging) impedance.

**Notes**

- Only silver has a lower resistivity, and it is lower by only about 5%.
**Click here**. - See my three-part series, “Resistance, Reactance and Impedance,” parts 1, 2, and 3, available
**here**. - When we say inductance or capacitance is
*distributed*, we mean that*every point*along the trace has series inductance and capacitance to the return path. Contrast this to a lumped inductance or capacitance that a component presents to a circuit. - In my article, “What is Current And Why Do We Care?” I point out that a fundamental law of electronics is that current must flow in a loop and current must be constant everywhere in that loop. In my article “Current Flow On Traces, Part 1, Transmission Lines” I show how this law squares with the idea that signals propagate down a trace with some finite propagation time. It is the distributed capacitance between the trace and the return path that allows this to happen. Both articles are available
**here**. - If a DC signal is applied to the trace, the inductance appears as a short circuit and the capacitance appears as an open circuit. So, under DC conditions, the only impedance the driver sees is the trace resistance. It is only under AC (or rapidly changing) conditions that the trace offers the impedance of an LC circuit.
- See
**www.polarinstruments.com/** - Available at
**www.ultracad.com/diff_calc.htm**. We believe the results from this calculator compare favorably with the Polar calculator.

*Douglas Brooks has an MS/EE from Stanford University and a Ph.D. from the University of Washington. He has spent most of his career in the electronics industry in positions of engineering, marketing, general management, and as CEO of several companies. He has owned UltraCAD Design Inc. since 1992. He is the author of numerous articles in several disciplines, and has written articles and given seminars all over the world on Signal Integrity issues since founding UltraCAD. His book, Printed Circuit Board Design and Signal Integrity Issues was published by Prentice Hall in 2003. Visit his Web site at *

**www.ultracad.com***.*