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# Your Guide to Transmission Line Losses in Electrical Systems

Zachariah Peterson
|  Created: May 10, 2021

Anytime an experienced design engineer brings up transmission lines, questions about propagation behavior and losses start flying around the room. What causes transmission line losses? How can you design to minimize them? How are losses calculated? These are great questions for the new high speed designer, and once these points are understood, the deficiencies of typical transmission line calculators become obvious.

So, in order to give new high speed designers everything they need to understand transmission lines, I’ve taken the liberty of compiling everything you need to know about transmission line losses into this article. This is one area of electronics design where you need to look in multiple places to get some concrete answers, and everyone seems to have their own explanation of how to deal with transmission lines losses. I’ve tried to be brief by sticking to the important formulas and some brief analysis, and I hope you’ll find this mini-compilation useful as a cheat sheet.

## Brief Theory Overview

For the new or unfamiliar designer, just know that some theories are universal, and the ideas used to describe transmission lines in power distribution systems also apply in integrated circuits, circuit boards, and long cable assemblies. Here, we don’t need to solve the wave equation to spot losses in transmission lines. Although circuit models are difficult to reconcile in a layout, transmission lines are one system where losses easily relate back to specific aspects of a physical layout. We’ll start with the impedance from the RLCG model, and we’ll see how the structure of a transmission line and its material parameters determine transmission line losses.

### Defining Causes of Loss in the Impedance Function

The easiest way to describe transmission line losses is to look at the impedance of the line from the basic RLCG circuit model, as defined below:

Here, I’ve shown the equations as you’ll generally find them in an electromagnetics textbook, but you don’t really need to start plugging in numbers and running calculations just yet. What’s important is that only 3 of the parameters in the impedance equation contribute directly to losses: R, L, and G. The G term creates loss due to the loss tangent, and the R and L terms combine to create some loss due to the skin effect. Note that the skin resistance term can be written to include copper roughness. Finally, there is a less-known but still important loss mechanism: radiation loss, which depends on the loop area (L).

I think it’s important to note that the line capacitance C also plays a role, but only because G is proportional to C. In this way, the line’s geometry affects loss because it determines how the field is confined around the line. Now, we can start to think about the propagation constant and how it describes transmission line losses.

### Loss in the Propagation Constant

These quantities then appear in the propagation constant for signals traveling on a transmission line. With some manipulations involving complex algebra, you can see how the above parameters are related back to the losses on a transmission line. The propagation constant is:

From here,you want to take the square root of this complex number and take the real part: this is the loss experienced by signals traveling on the transmission lines. If you’ve never taken the square root of a complex number, don’t fret because there is a simple closed formula that gives you the answer. In the equation below, I’ve taken the real part of the propagation constant only as this tells you everything you need to know about transmission line losses:

The above equation is exact; there is no approximation. Unfortunately the above equation is totally unwieldy, so it makes sense to use a common approximation to describe losses. Every other guide on the topic of transmission line losses that I have seen gives an approximation to the above equation, so just remember this if you happen to be looking at a different guide. The loss can be nicely approximated as:

Now this is much nicer to work with. Although we’ve reduced this to an expression in terms of Z and R, the other terms still have their influence on losses. Notably, C will appear in the numerator, so a line with larger capacitance can have greater loss. This is one reason HDI traces can have lower overall losses; they can be much smaller so they can have lower capacitance.

### Linking Transmission Line Losses to Circuit Parameters

To summarize before moving on, we have four loss mechanisms that are related to 4 parameters in the transmission line. These are summarized in the table below.

 Parameters Loss Mechanism How Signals are Affected RS, L Skin effect, which has resistive and inductive contributions. Inductive and resistive contributions reduce amplitude and modify the phase, both as functions of frequency. RDC DC losses, although these are negligible at high frequency. Signal amplitude reduction, no effect on phase. L Radiative losses, as defined by the line’s loop area. Overall power loss during propagation, which becomes more noticeable at higher frequencies. G and C Dielectric losses as defined in the loss tangent and due to field confinement as driven by C. Signal amplitude reduction and phase shift.

In the above formalism, we can see exactly which loss mechanisms are linked to different parameters in the transmission line. If you find that one type of loss is too high, you now know which parameters in the line are responsible for this observation. You can now modify the line’s geometry appropriately by modifying the stackup, line width, PCB laminate material, etc.

### Reducing Losses in Interconnect Design

Knowing how different loss mechanisms are linked to the circuit parameters is important, but we ultimately need these to be linked back to the geometry of the line if you want to do anything actionable in your CAD software. By adjusting the geometry (height above ground plane, width, copper thickness), you’re adjusting these circuit parameters and affecting the transmission line losses.

Field solvers can help here as you can calculate the impedance for your PCB laminate material and stackup, and you can use the resistance to determine the propagation constant (real part) in the formulas above. As you iterate through different geometric values, you can map out exactly which conditions give you the desired impedance with low parasitics and low loss.

When you need to calculate impedance and other parameters to determine transmission line losses, you can use the integrated field solver in the Layer Stack Manager in Altium Designer®. For more advanced calculations involving S-parameter extraction, Altium Designer users can use the EDB Exporter extension to import their design into Ansys field solvers. This pair of field solver applications helps you verify your design before you begin a prototyping run.

When you’ve finished your design, and you want to release files to your manufacturer, the Altium 365™ platform makes it easy to collaborate and share your projects. We have only scratched the surface of what is possible to do with Altium Designer on Altium 365. You can check the product page for a more in-depth feature description or one of the On-Demand Webinars.