- Signal Propagation Model
- Hierarchy of Regions
- Necessary Mathematics: Input Impedance and Transfer Function
- Lumped-Element Region
- RC Region
- LC Region (Constant-Loss Region)
- Skin-Effect Region
- Dielectric Loss Region
- Waveguide Dispersion Region
- Summary of Breakpoints Between Regions
- Equivalence Principle for Transmission Media
- Scaling Copper Transmission Media
- Scaling Multimode Fiber-Optic Cables
- Linear Equalization: Long Backplane Trace Example
- Adaptive Equalization: Accelerant Networks Transceiver
This chapter is from the book
This chapter is from the book
This chapter is from the book
3.9 Waveguide Dispersion Region
At frequencies so high that the wavelength of the signals conveyed shrinks to a size comparable with the cross-sectional dimensions of a transmission line, strange non-TEM modes of propagation appear. These modes do not by themselves portend a loss of signal power, but they can create objectionable phase distortion (i.e., dispersion of the rising and falling edges) that limits the maximum speed of operation (Section 3.2).
3.9.1 Boundary of Waveguide-Dispersion Region
If you attempt to operate a transmission line at such a high frequency that the wavelengths of the signals conveyed approach the dimensions of your conductors, strange modes of propagation begin to appear. These modes have to do with the possibility of signal power bouncing back and forth between two interfaces within the transmission structure. These bouncing modes are called non-TEM modes (see Section 5.1.5, “Non-TEM Modes”).
In a coaxial cable the critical dimension of interest is the diameter of the shield. In a stripline configuration it’s the spacing between the planes. In a microstrip it’s the thickness of the dielectric.
At frequencies high enough that the signal wavelength becomes comparable with the critical dimension, a full-wave analysis of the situation predicts received waveforms that have what looks like severe overshoot and ringing, even if the line is perfectly terminated.
The frequency at which fully developed non-TEM modes may exist within a transmission structure is
)
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where |
ωc appears in units of rad/s, |
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b is the interplane spacing of a stripline, m, |
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h is the dielectric thickness of a microstrip, |
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k is a constant in the range of 1/10 to 1/6, |
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d2 is the inner diameter of a coaxial shield, m, |
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c is the speed of light, 2.998·108 m/s, and |
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∊r is the relative dielectric constant of the insulating material, as measured in the vicinity of frequency ωc. |
Microstrips suffer more than other configurations from non-TEM modes because the bouncing modal power does not get a clean bounce off the dielectric-to-air interface. The properties of this interface introduce a significant phase shift into the modal equations with the result that non-TEM distortion appears in a noticeable way for microstrips at frequencies much lower than for other configurations. This peculiar form of non-TEM behavior is called microstrip dispersion.
For ordinary digital signaling on FR-4 printed circuit boards at 10 Gbps you may use microstrip trace heights up to 20 mils without encountering significant microstrip dispersion. At lower frequencies you can use correspondingly bigger traces. Above 10 Gbps, you must use correspondingly smaller ones.
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If the wavelengths of the signals conveyed approach the dimensions of your conductors, strange modes of propagation begin to appear.
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For ordinary digital signaling on FR-4 printed circuit boards at 10 Gbps you may use microstrip trace heights up to 20 mils without encountering significant microstrip dispersion.