Trace Width
Chapter 4: Clock Circuits, Trace Routing, and Terminations
4.7 CALCULATING TRACE LENGTHS (ELECTRICALLY LONG TRACES)
When creating transmission lines, designers need to be able to quickly determine whether a trace routed on a PCB can be considered electrically long during the component placement process. If a transmission line is electrically long, signal integrity and EMI concerns develop. An electrically long trace is defined as a transmission line that is sufficiently long
physically that a propagated electromagnetic wave that is sent from a source to load with its return back to the source occurs after the next edge transition. In other words, a second edge transition is injected into the transmission line prior to the return of the previous edge-triggered event.
A simple calculation is available that determines whether the approximate length of a routed trace is electrically long, under typical conditions. When determining whether a trace is electrically long, we must think in the time domain. The equations in this section are best used when doing
preliminary component placement. For extremely fast edge rates, detailed calculations are required based on the actual dielectric constant value of the core and prepreg material. The dielectric constant determines the velocity of propagation of a transmitted wave.
The typical velocity of propagation of a signal within a transmission line, using FR-4, is 60% the speed of light. The maximum permissible
unterminated line length per Eq. (4.20) must be calculated to determine if termination is required in the transmission line. This equation is valid when the two-way propagation delay (source-load-source) equals or exceeds the signal rise-time transition, or edge rate. Use the faster value of the two edge transitions, HI-LOW or LOW-HI.
Figure 4.9 illustrates Eq. (4.20) for quick reference with a dielectric constant of 4.6 used within the equation.
(4.20)
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where t
r = edge rate (ns)
t'pd = propagation delay (ns)
lmax = maximum routed trace length (cm)
Figure 4.9: Maximum unterminated line length vs. signal edge rate
(FR-4 material).
The equation is very liberal, since it considers only a single, two-way propagation time interval. A more conservative approach would be to consider more "round trips." In other words, the 2 in the denominator may be replaced by a 4, 6, or even 8.
To simplify Eq. (4.20), the real value of the propagation delay within the transmission must be determined using the actual dielectric constant value based at the frequency of interest. Both propagation delay and edge
transition rate must be taken into account. Equations (4.21) and (4.22) are presented for determining the maximum routed electrical line length before termination becomes mandatory. This length is for round-trip distance. The one-way length from source to load is one-half the value of l
max calculated.
The factor (k) used in the calculation is for a dielectric constant value of 4.6.
For example, if the minimum edge rate signal transition is 2 ns, the
maximum round-trip, unterminated trace length possible before termination is required, when routed microstrip is
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When routed stripline, the maximum unterminated trace length of this same 2 ns signal edge becomes
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These equations are useful when evaluating propagational time intervals between load intervals on a line with multiple devices. Figure 4.9 illustrates the relationship between rise-time transition and maximum line length distance before termination is required.
To calculate the constant "k," (9 or 7) found within Eqs. (4.21) and (4.22), use the following example:
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where k = constant factor for transmission line length determination (4.21)
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(4.22)
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Example: with ˝
r = 4.6, k = 8.87 for microstrip (in cm) or 3.49 (in inches) k = 6.99 for stripline (in cm) or 2.75 (in inches)
If a trace or routed interval is longer than l
max, termination should be implemented, for signal reflections (ringing) may occur within this
electrically long trace. Even with optimal termination, a finite amount of RF currents can still be in the trace. For example, use of a series termination resistor will achieve the following:
When locating components during layout that use clock or periodic
waveform signals, these components must be positioned to allow for the best straight-line path possible, with minimal trace length and number of vias in the route. Each via will add inductance to the trace, approximately 1–3 nH each. Inductance in a trace may also cause signal integrity
concerns, impedance mismatches, and potential RF emissions. Inductance in a trace allows this wire to act as an antenna. The faster the edge rate of the signal transition, the more important this design rule becomes. If a periodic signal or clock trace must traverse from one routing plane to another, this transition should occur at a component lead (pin escape or breakout) and not anywhere else. If possible, additional inductance presented to the trace can be reduced from using fewer vias.
Equation (4.23) is used to determine whether a trace, or loading interval, is electrically long and requires termination.
where l
max is the calculated maximum trace length and l
d is the length of the trace route as measured in the actual board layout. Keep in mind that l
d is the round-trip length of the transmission line.
Ideally, trace impedance should be kept at ± 10% from nominal. In some cases, ± 20–30% may be acceptable only after careful consideration has been given to signal integrity and performance. The width of the trace, its height above a reference plane, dielectric constant of the board material, plus other microstrip and stripline constants determine the impedance of the transmission line. It is always best to maintain constant impedance control at all times in any dynamic signal condition.
An example used to determine whether it is necessary to terminate a signal trace using characteristic impedance, propagation delay, and capacitive loading is now presented [9].
Microstrip Example
A 5 ns edge rate device is provided on a 5 in. surface microstrip trace. Six loads (components) are distributed throughout the route. Each device has an input capacitance of 6 pF. Is termination required for this route?
a = 30.5 for cm, 12 for inches
x = 0.5 (converts transmission line to one way path)
tpd = (for microstrip), (for stripline)
ƒ Minimize RF currents within the trace.
ƒ Absorb reflections (ringing).
ƒ Match trace impedance.
ƒ Minimize overshoot and undershoot.
ƒ Reduce RF energy generated by slowing the edge rate of the clock signal.
(4.23)
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Geometry
Trace width, W=0.010 in.
Height above a plane, H=0.012 in.
Trace thickness, T=0.002 in.
Dielectric constant, ˝
r = 4.6
A. Calculate characteristic impedance and propagation delay [Eqs. (4.1) and (4.3)].
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B. Analyze capacitive loading.
Calculate C
d, distributed capacitance (total normalized input capacitance divided by length).
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Calculate intrinsic capacitance of the trace—Eq. (4.19).
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Calculate one-way propagation delay time from the source driver—
Eq. (4.16).
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C. Perform transmission line analysis.
Ringing and reflections are masked during edge transitions if
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Given that the edge rate of the component is t r = t
f = 5 ns and propagation delay is 2.9 ns, termination is not required. Sometimes the guideline of (3 * t'pd * trace length) is used as a margin of safety. For this case, propagation delay would be 4.35 ns; hence, termination would still not be needed.
Assume now that the trace is routed stripline. Is termination required?
From above:
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Again, this trace would not require termination since 3.4 ns İ 5 ns. The propagation delay for stripline is 1.60 ns longer because t
pd (unloaded) is substantially greater than microstrip (0.65 ns margin). This factor helps prevent transmission line effects from being masked during edge rate changes.
Stripline Example
A 2-ns edge rate device on a 10 in. stripline trace is used. Five logic devices are distributed throughout the route. Each device has an input capacitance of 12 pF. Is termination required for this route?
Geometry
Trace width, W = 0.006 in.
Distance from a plane, H = 0.020 in.
Trace thickness, T = 0.0014 in.
Dielectric constant, ˝r = 4.6
A. Calculate characteristic impedance and propagation delay . [Eqs.
(4.7) and (4.9).]
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B. Analyze capacitive loading.
Calculate C
d, distributed capacitance (total input capacitance divided by length).
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Calculate the intrinsic capacitance of the trace.
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Calculate one-way propagation delay time from the source driver.
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C. Perform transmission line analysis.
The important condition of interest is (2 * t'
pd) * trace length İ t r or t
f.
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Since the edge rate of the component t r = t
f = 2 ns, and propagation delay (6.4 ı 2), termination is required to absorb transmission line effects.
Assume the trace is routed microstrip. Is termination required?
From above:
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Again, this trace would require termination since 5.20 ns ı 2 ns.
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Table of Contents 4.4: CAPACITIVE LOADING OF SIGNAL TRACES
Chapter 4 - Clock Circuits, Trace Routing, and Terminations
Printed Circuit Board Design Techniques for EMC Compliance: A Handbook for Designers, Second Edition by Mark I. Montrose
IEEE Press © 2000 Recommend this title?