Transmission Line Theory Applied to Digital Systems
Microstrip Transmission Line Techniques Evaluated Using TDR Measurements
11-22
TDR Example 1
Given the following:
Board material: Norplex Type G-10
Dielectric thickness: h = 0.062 inch;
Copper thickness: t = 0.0014 inch;
Dielectric constant: ε
r
= 5.3.
The formula for the characteristic impedance is:
(14)
For a line width, w = 0.1 inch, the characteristic impedance of the line is
calculated to be 51 Ω. A board was fabricated as shown in Figure 11-8 to the
dimensions specified above. Figure 11-8 and Figure 11-9 show the incident and
reflected waveforms observed with the TDR. The vertical scale is calibrated
both in terms of the voltage and the reflection coefficient, ρ. Equation 3 can be
rearranged to determine the characteristic impedance of the line:
(15)
where: Z
line
= characteristic impedance of the line under test
and Z
reference
= impedance of the known line.
The 50 Ω reference point is shown in Figure 11-9. The mean level of the
reflected waveform due to the line has a ρ = + 0.01. Substituting values into
equation 15 permits calculation of the line impedance:
which agrees closely with the calculated value.
Z
o
87
ε
r
1.41+
-------------------------
5.98h
0.8wt+
-------------------
ln=
Z
line
10.01+
10.01–
-------------------
Z
reference
•
=
Z
line
10.01+
10.01–
-------------------
50 ohms
•
51 ohms==
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