There are two concepts that physicists and acoustical engineers learn quite early on that are lost on PCB designers, until they start working on RF systems and signal integrity. These two concepts describe wave propagation, specifically how wave propagation varies with dielectric constant and frequency. These concepts are known as phase velocity and group velocity, or in terms of time, phase delay and group delay, respectively.
Phase delay and group delay describe how different frequencies can propagate at different speeds in a dielectric medium. The concept is brought up in digital signal integrity, but it also applies in RF devices that use modulated signals and a reference oscillator. Digital signal integrity engineers are the group that require the most knowledge on this topic because it relates to one important cause of intersymbol interference. Here is how these concepts arise and what they mean.
Propagation Delay Is a Function of Frequency
The dielectric constant of a material that is used to build a PCB, or any material for that matter, is not actually a constant. The dielectric constant of a material depends on the frequency of the electromagnetic wave that moves through it. This is why different electromagnetic wave frequencies will travel at different speeds. The same concept applies to any other wave, such as acoustic or mechanical waves.
Now consider this point: what if instead of a signal being composed of a single harmonic frequency, a signal contains many frequencies, like you would have in a square wave? Another simple example is an amplitude modulated wave, where the modulation seen in the amplitude envelope is very complex? In this case, we have to think about what happens when we take the Fourier transform of the wave and look at each frequency component.
Fourier components of a square wave with their velocities shown. If the dielectric constant is not the same at each frequency then the velocities at each frequency will not match.
Because the dielectric constant is not constant, the speed of each component that makes up that wave will be different. This is one of the reasons that a signal like a square wave changes its shape after it moves on a PCB trace over a significant distance. The phase for each frequency will be different, so the wave at the load end of the trace will not match the wave at the source end of the trace.
To quantify this effect from the dielectric constant, we have two different velocities:
Phase velocity or phase delay
Group velocity or group delay
What Is Phase Delay?
Phase velocity is sometimes misunderstood as a mathematical value for the phase of a wave. The phase velocity, or equivalently the phase delay, describes the velocity of an individual frequency component that makes up a signal. The phase velocity only depends on the value of the wave’s speed at the wave’s specific frequency. In other words, phase velocity only applies to one frequency component in a signal.
Ideally, we would like to have all of the frequency components in a signal all have the same velocity. The PCB materials industry has spent significant effort to reach this condition for their materials. While it is physically impossible for this to occur for all frequencies, you can usually get the condition to be reached over a large range of practical frequencies used in PCBs and in today's electronic components.
What Is Group Velocity?
Group velocity or group delay is a more complex concept and it relates to the entire signal, not just a single frequency. We can talk about the group velocity at a single frequency if we want, but that is not such a useful concept. The group velocity states what is the velocity for an entire waveform, not just a single component that makes up part of a complex waveform.
Because a complex waveform can be made up of many frequencies, and each of those frequencies could have a slightly different phase velocity, we prefer to look at the shape of a group velocity curve over some relevant frequency range. The group velocity curve tells you what is the expected phase difference between different frequency components. SI engineers will usually state this as a time value rather than a phase value, so measurements of group delay will usually be stated in time. An example curve is shown below.
Example group delay for two printed circuits.
The ideal group delay curve will be a flat horizontal line. For standard PCB materials, the curve will be upward or downward sloping in terms of phase, depending on the sign convention. This curve tells you the difference in propagation speeds for different frequencies and it can be used to predict signal distortion in a circuit.
Can Group Delay Be Measured?
Group delay can be measured in several ways. A few of these measurement methods include:
Measure the dielectric constant and calculate the wave speed at different frequencies
Convert S-parameter phase from a VNA measurement to a group delay curve
Take point measurements of dielectric constant and calculate group delay with a broadband model
These are more complex ideas that require a bit of math. The main reason we do this is to predict how a signal distorts in a PCB trace and what an eye diagram might look like at the load end of a trace. Once these things are known, a channel can be further optimized with a different material if group delay creates excess distortion.
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