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Digital Circuit Boards: Mach 1 GHz by Ralph Morrison

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2.4 Characteristic Impedance

Figure 2.3 shows how a wave propagates when a voltage with a finite rise time is switched on to a length of transmission line.

Figure 2.3 How a step voltage propagates on an ideal transmission line.

2.3

This line can be characterized as having an inductance and a capacitance per unit length. The step wave that propagates down the line will place charges on the distributed capacitance at a fixed rate. After the wave is established, a steady current is supplied by the voltage source. A steady voltage and a steady current imply that the transmission line looks like a resistance. This resistance value is called the characteristic impedance of the line. If the line is infinite in length, the current–voltage relationship will be given by Ohm's law as

2.1 2.1

where Z0 is the characteristic impedance.

In theory, the voltage V can have any wave form. In digital circuits, logic voltages are step functions with finite rise and fall times. In rf (analog) circuits, the signals are usually sine waves.

The characteristic impedance of a transmission line is given by

2.2 2.2

where L and C are the inductance and capacitance per unit length, respectively. In circuit board designs, ...

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