The transmission loss associated with any conductive transmission media increases monotonically with frequency. Sweeping from low frequencies to high, the slope of the loss curve changes in a predictable way as you pass the onset of various regions of operation. The progression of regions, and the transmission performance within each region, is the subject of this chapter.
Alternate forms of transmission structures exist, such as fiber optic waveguides and various forms of RF waveguides, that cannot convey DC signals. In these alternate structures the loss function must be necessarily be nonmonotonic, leading to a different hierarchy of performance regions. The discussion of regions presented here applies only to conductive transmission structures as normally used in digital applications.
Figure 3.2 illustrates the general arrangement of performance regions pertaining to copper media. The particular data shown in this diagram represents a 150 m m (6mil), 50 W FR4 pcb stripline . The waveguide dispersion region for this trace begins at frequencies higher than shown on the chart.
Figure 3.2. Performance regions for a 150 m m (6mil), 50 W , FR4 stripline.
The distinguishing features of each region may be determined by analysis of the transmissionline propagation coefficient [3.13], propagation function [3.14], and characteristic impedance [3.15].
Equation 3.13
Equation 3.14
Equation 3.15
where 
R ( w ), L , and C ( w ) represent the permeter parameters of resistance, inductance, and capacitance respectively, 
the line conductance G is assumed zero, and 

the propagation function H at frequency w (rad/s) varies exponentially with the product of the length l and the propagation coefficient g . 
Near DC the magnitude of the inductive reactance, w L dwindles to insignificance in comparison to the DC resistance. All that matters below this point is the relation between the DC resistance of the line and its capacitance. Lines at such low frequencies are said to operate in the RC region.
At higher frequencies the inductive reactance grows, eventually exceeding the magnitude of the DC resistance, forcing the line into the LC region.
Beyond the LC transition the internal inductance of the conductors (a mere fraction of the total inductance) becomes significant compared to the DC resistance. This development forces a redistribution of current within the bodies of the conductors. The redistribution of current heralds the arrival of the skineffect region.
Dielectric losses are present at all frequencies, growing progressively more severe at higher frequencies. These losses become noticeable only when they rise to a level comparable with the resistive losses, a point after which the line is said to operate in the dielectriclosslimited region.
At frequencies so high that the wavelength of the signals conveyed shrinks to a size comparable with the crosssectional dimensions of the transmission line, other nonTEM 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. The region in which nonTEM modes must be taken into consideration is called the waveguide region.
At any frequency, regardless of the mode of operation, a transmission line can always be shortened to a length l LE ( w ) below which the line operates not in a distributed fashion, but in a mode reminiscent of a simple lumpedelement circuit. The lumpedelement region appears as a broad band underlying all the other regions in Figure 3.2, bounded by two dotted line segments describing the function l LE ( w ).
As the length of a transmission line continues to shrink, at a point several orders of magnitude below l LE ( w ) it acts as a perfect wire.
POINTS TO REMEMBER
3.2.1 A Transmission Line Is Always a Transmission Line
POINTS TO REMEMBER
Fundamentals
Transmission Line Parameters
Performance Regions
FrequencyDomain Modeling
Pcb (printedcircuit board) Traces
Differential Signaling
Generic BuildingCabling Standards
100Ohm Balanced TwistedPair Cabling
150Ohm STPA Cabling
Coaxial Cabling
FiberOptic Cabling
Clock Distribution
TimeDomain Simulation Tools and Methods
Points to Remember
Appendix A. Building a Signal Integrity Department
Appendix B. Calculation of Loss Slope
Appendix C. TwoPort Analysis
Appendix D. Accuracy of Pi Model
Appendix E. erf( )
Notes