This is why wires formed into a twisted pair work fairly well in AC
environments. Consider Figure 9-3. The twisted pair of wires carries a
signal and its return to and from an operational amplifier. Again,
position yourself off to the right of the page. At any given point along
the twisted pair, one wire will be closer to you than the other, so the
EMI radiation from it will be slightly larger than from the other. But
since the wires are twisted, on average they are the same distance from
you, so on average, the radiation from each one cancels the other.
Therefore, you receive very little net radiation.
Figure 9-3 A twisted pair has desirable features from an EMI standpoint.
course, the wires in a twisted pair can act as an antenna and receive
noise, also. Twisted pairs usually feed into differential circuits that
are (a) very sensitive to the difference in signal between the pair, but
(b) relatively insensitive to any (common mode) signal that exists on
both wires. The common mode rejection specification is one measure of a
circuit’s insensitivity to common mode signals.
Some Basic “Truths”
are a few truths you should always keep in mind. The first, and perhaps
most important, is that current always flows in a closed loop. Remember,
current is the flow of electrons, and if current does not flow in a
closed loop, where do the extra electrons come from or go? Because we
know we don’t have to deal with buildups of stray electrons on our
boards, it seems reasonably intuitive that currents really do flow in a
That means every signal has a return, somewhere.
And you (as the designer) need to know where that is. It sometimes
amazes us to discover that we designers spend an inordinate amount of
time worrying about, considering, and strategizing about 50% of the
signals, and then leave the other 50% (the return signals) somehow to
chance. So the first truth is that every signal has a return and you
need to worry about and control where it is.
A second rule is
that the return current will always follow the path of least impedance.
We all have heard the rule that signals follow the path of least
resistance, but that is a special case, not the general one. It only
applies to low-frequency signals. The general rule, for all signals, and
particularly the high-speed signals we worry about, is that return
currents follow the path of least impedance. This may not always be
where you think it is.
Figure 9-4. A changing current i1 is flowing down Trace 1. The changing
current creates a changing magnetic field around Trace 1. That changing
magnetic field couples into Trace 2 with a coupling coefficient whose
value is k. The coupling generates a current in Trace 2 whose value is k x i1
and whose direction (by Lenz’s Law, see Appendix B) is opposite to i1.
This is exactly how a transformer works, and is the fundamental basis
behind all transformer designs.
Figure 9-4 Traces can and do couple into each other.
coupling coefficient will have a value somewhere between 0 and 1.0.
Zero means no coupling whatsoever, which can occur if (a) the traces are
very far apart, or (b) the current is not changing (i.e., is DC). A
coupling coefficient of 1.0 means perfect coupling, which of course
cannot be achieved. The value of k, for our purposes, depends
primarily on (a) how fast the current is changing, or the rise time
(di/dt), and (b) how closely the traces are spaced (D in the figure).
Fast rise times and closely spaced traces lead to higher coupling
coefficients. Realistic values for k on circuit boards where the traces
are close together are in the range of .4 to .6.
Consider the special case where i1 is a signal and i2 is the signal return. Therefore, i2 = –i1. The coupled signal, k
x i1 actually helps boost the return signal. But the return signal, i2,
also couples into Trace 1, boosting the primary signal, i1. So, the
mutual coupling of the signal and its return work to reinforce, or
boost, each other. We can interpret the effect of this two ways: (a) It
takes less force (voltage) to push the same amount of current through
the circuit, since these currents reinforce each other; or (b) more
current can flow for the same voltage, since reinforcing currents are
generated on each trace. By Ohm’s Law, V = iZ. No matter which
interpretation you prefer, it means that the impedance goes down when
there is coupling of this type. Furthermore, the impedance gets
progressively lower as the coupling increases, or as k increases. And k increases as (a) the distance between the traces decreases, or as (b) the rise time decreases (gets faster).
consider Figure 9-5, which illustrates the simple case of a microstrip
trace placed over a plane. Assume there is a current flowing down the
trace and the return current is on the plane. A good question is: “Where
is the return current?” Assume the return current is at Point a.
Following the preceding discussion, there will be some mutual coupling
between the signal and its return current, resulting in some mutual
reinforcement. Now let’s assume the return current is, instead, at Point
b. Here, the coupling is stronger, because the signal and its return
are closer together. Since the coupling is stronger, the overall
impedance will be less. Therefore, Point b is a lower impedance path
than Point a. Point c represents a signal return path that is even
closer to the signal, so the coupling will be even stronger at Point c
and the impedance will be even less. Point c represents the closest
point between the signal and its return—it is directly under the signal
trace—and therefore the point of maximum coupling and lowest impedance.
This is why high-speed signals want to return directly underneath the signal trace: It is the path of lowest overall impedance. Be
careful to note, however, that this argument depends completely on the
coupling coefficient between the two signals. The coupling coefficient
depends, among other things, on di/dt, or rise time. If there is no rise
time (e.g., the signals are DC power signals) there is no coupling and
the return signal might be anywhere. In fact, the DC return will truly
follow the path of least resistance anywhere on the circuit board.
Figure 9-5 Cross-sectional view of a trace and underlying plane.
A return current will “want” to follow the path of least impedance, Path (c).
summarize, DC signals might return anywhere on the board. But AC
signals want to return directly underneath the trace carrying the
signals. This tendency increases as the rise time decreases (gets