LMH6560 Datasheet, PDF (15/23 Pages) National Semiconductor (TI) – Quad, High-Speed, Closed-Loop Buffer

Application Notes (Continued)
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FIGURE 4.
Z₀ can be calculated by knowing some of the physical di-
mensions of the pcb line, such as pcb thickness, width of the
trace and e_r, relative dielectric constant. The formula given in
transmission line theory for calculating Z₀ is as follows:
(1)
e_r relative dielectric constant
h pcb height
W trace width
th thickness of the copper
If we ignore the thickness of the copper in comparison to the
width of the trace then we have the following equation:
(2)
With this formula it is possible to calculate the line imped-
ance vs. the trace width. Figure 5 shows the impedance
associated with a given line width. Using the same formula it
is also possible to calculate what happens when e_r varies
over a certain range of values. Varying the e_r over a range of
1 to 10 gives a variation for the Characteristic Impedance of
about 40Ω from 80Ω to 38Ω. Most transmission lines are
designed to have 50Ω or 75Ω impedance. The reason for
that is that in many cases the pcb trace has to connect to a
cable whose impedance is either 50Ω or 75Ω. As shown e_r
and the line width influence this value.
20064243
FIGURE 5.
Next, there will be a discussion of some issues associated
with the interaction of the transmission line at the source and
at the load.
Connecting a Load Using a Transmission Line
In most cases, it is unrealistic to think that we can place a
driver or buffer so close to the load that we don’t need a
transmission line to transport the signal. The pcb trace
length between a driver and the load may affect operation
depending upon the operating frequency. Sometimes it is
possible to do measurements by connecting the DUT directly
to the analyzer. As frequencies become higher the short
lines from the DUT to the analyzer become long lines. When
this happens there is a need to use transmission lines. The
next point to examine is what happens when the load is
connected to the transmission line. When driving a load, it is
important to match the line and load impedance, otherwise
reflections will occur and this phenomena will distort the
signal. If a transient is applied at T = 0 (Figure 6, trace A) the
resultant waveform may be observed at the start point of the
transmission line. At this point (begin) on the transmission
line the voltage increases to (V) and the wave front travels
along the transmission line and arrives at the load at T = 10.
At any point across along the line I = V/Z₀, where Z₀ is the
impedance of the transmission line. For an applied transient
of 2V with Z₀ = 50Ω the current from the buffer output stage
is 40mA. Many vintage op amps cannot deliver this level of
current because of an output current limitation of about
20mA or even less. At T = 10 the wave front arrives at the
load. Since the load is perfectly matched to the transmission
line all of the current traveling across the line will be ab-
sorbed and there will be no reflections. In this case source
and load voltages are exactly the same. When the load and
the transmission line have unequal values of impedance a
different situation results. Remember there is another basic
which says that energy cannot be lost. The power in the
transmission line is P = V²/R. In our example the total power
is 2²/50 = 80mW. Assume a load of 75Ω. In that case a
power of 80mW arrives at the 75Ωload and causes a voltage
of the proper amplitude to maintain the incoming power.
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