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Calculating Trace Lengths (Electrically Long Traces)
When defining a transmission line within a PCB, designers need a method that allows quick determination if a trace is too long for signal integrity purposes during the component placement cycle. A simple calculation is available that determines whether the approximate length of a routed trace is electrically long. When determining whether a trace is electrically long, think in the time domain. The equation below is best used when doing preliminary component placement on a PCB. For extremely fast edge rates, detailed calculations are required based on the actual dielectric constant value of the core and prepreg material present.
Assuming a typical velocity of propagation that is 60% the speed of light, calculate maximum permissible unterminated line length per the equation below. This equation is valid when the two-way propagation delay (source-load-source) equals the signal rise time.
where
tr is edge rate (ns)
t'pd is propagation delay (ns)
lmax maximum routed track length (cm)
To illustrate this equation, use the real value of propagation delay (actual dielectric constant based on frequency of interest). This length is for round-trip distance. The one-way length, from source to load is one-half the value of l max below. The following calculation is for a dielectric constant of 4.6.
xlmax = 9 * tr (for microstrip topology - in cm.)
lmax = 3.5 * tr (for microstrip topology - in in.)
lmax = 7 * t r (for stripline topology - in cm.)
lmax = 2.75 * t r (for microstrip topology - in in.)
For example, if a signal edge is 2-ns, the maximum round trip, unterminated trace length when routed on microstrip is
lmax = 9 * tr = 18 cm (7 inches) When this same clock trace is routed one stripline, the maximum unterminated trace length of this 2-ns signal edge becomes
lmax = 7 * tr = 14 cm (5.5 inches)
This equation is also useful when evaluating the propagation time intervals in a transmission line with multiple loads. To calculate the constant, k, either 7 or 9 for lmax, the following example is provided.
EXAMPLE
where
k = constant factor for transmission line length determination
a = 30.5 for cm, 12 for inches
x = 0.5 (converts transmission line to one way path)
tpd = value of the propagation delay of the microstrip or stripline transmission line
Example: with e r = 4.6,
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k = 8.87 for microstrip (in cm) or 3.49 (in inches) |
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k = 6.99 for stripline (in cm) or 2.75 (in inches) |
If a trace or interval is longer than lmax, then termination should be implemented, as signal integrity concerns may occur in this electrically long trace. Even with good termination, a finite amount of RF currents will still be present in the transmission line.
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