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The following is an excerpt from The Printed Circuit Designer's Guide to... Signal Integrity by Example, written by Fadi Deek of Mentor, a Siemens Business. Deek explores how to reach effective design solutions and make strong engineering tradeoffs through analysis techniques, best design principles, and software tools to achieve accurate simulations and measurements.
Impedance: Characteristic Impedance vs. Instantaneous Impedance
A transmission line, or a trace on a printed circuit board with its associated return path, is electrically defined by two properties: its characteristic impedance, or Z0, and its time delay, TD.
As a signal propagates down the signal and return path, it will continuously encounter an instantaneous impedance. This means the signal will apply a voltage and drive a current through each infinitesimal section of the transmission line as shown in Figure 1-1. The impedance the signal sees is the instantaneous impedance. In a uniform transmission line, the instantaneous impedance is the same each step along the transmission line. That single impedance value is the characteristic impedance of the transmission line. This means that a non-uniform transmission line does not have just one impedance that characterizes it.
So, what elements of the transmission line can affect its impedance? To answer the question, a stripline configuration will be used. For the analysis covered in this section, an advanced high-speed analysis tool was used to model several types of transmission lines, wires, cables and connectors. One of the options available is a stripline modeler shown in Figure 1-2.
How does each term affect the Z0 and the TD?
The two dielectric height parameters will affect the capacitance per length of the trace by the following rough approximation, C = εw/H where ε is the material permittivity, w is the width of the conductor and H is the height or the separation between each conductor. By decreasing any of the heights H1 or H2, the capacitance will increase.
The connection between the characteristic impedance and the capacitance per length is Z0 = √(L/C). Any increase in the capacitance per length will decrease Z0.
Also, the width of the trace, if increased, will decrease Z0 since it will increase the capacitance per length.
Another factor that will affect the capacitance per length is the dielectric constant. From the capacitance approximation, any increase in ε will increase the capacitance per length.
The length of the conductor will not affect Z0 since, as mentioned before, the instantaneous impedance is constant in a uniform transmission line.
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