A look at how data and power are transmitted in electronic circuits

1. 1
A More Complete Understanding of Power and Information Flow
in Circuits and the Origin of Electromagnetic Interference
R. Holoboff
MDC Vacuum Products, LLC
Introductory circuit theory courses rely exclusively on techniques that assume lumped parameter analysis which
are adequate for DC conditions and AC frequencies less than a few hundred megahertz (MHz). Under such
conditions, circuits can be analyzed through the use of voltage and current parameters rather than the more
generalized parameters of electric and magnetic fields from which they are derived. During the first year of circuit
theory, Kirchhoff’s laws are presented axiomatically from which the techniques of nodal and mesh analysis are
developed. It is not until the engineer encounters RF, microwave, or optical frequency applications that the
limitations of such techniques become apparent. For many engineers, the first-year, introductory path represents
the only insight into the “flow” of information, for example digital signals, in an electronic circuit. This necessary
pedagogical development often leaves the young engineer with a limited view of signal and power flow that is
likened to water flow in pipes. Using simulations that solve Maxwell’s equations via finite element analysis (FEA),
this paper presents a more nuanced view of signal flow in a circuit and the origins of electromagnetic interference.
The Imprint of Introductory
Circuit Courses: Electronic
design often begins with the
analysis of a circuit. Engineers
are taught to analyze
circuits like the example in
Figure 1 -first by hand and then
using more advanced simulation
tools called SPICE. The process is
similar to the way mechanical
engineers are taught
to draw –first by hand and then in
CAD. The goal of circuit analysis is to
identify all the nodal voltages
and the branch currents within
the circuit. Current is defined as
the number of charges that
are flowing past any point in a
branch and is measured in
coulombs per sec (C/s) or amps (A).
Figure 1: Example of a circuit. Software, known commonly as
SPICE, is used to solve for the nodal voltages and branch
currents within the circuit.
©2017
R. Holoboff, rholoboff@mdcvacuum.com

2. 2
Students are told that these charges
are in fact subatomic particles called
electrons. By convention it is assumed
the charge is negative with a measured
value of about -1.602 10^-19 C. So a
modest 10 mA current is equivalent to
about 10^16 (about 10 million billion)
electrons passing a given point in the
circuit each second. Another convention,
one dating back to Ben Franklin, ignores
the electron and assumes that current is
the net flow of positive charge carriers.
Electron flow is simply in the opposite
direction of the calculated and
assumed positively charged current.
Voltage (or potential difference) is
defined as the energy needed to
move a unit charge from one point in
the circuit to another.
Often, voltage is explained away as the
“pressure” that is required to move the
charge carrier from one point to another.
Thus, the connection between current flow
in metal wires or printed circuit board
conductors and the mechanical flow of
water in pipes is established. As is
customarily explained, voltage is the
motive force that pushes pointlike
charges, electrons specifically but
imaginary point positive charges by
convention, around the metal conductors
of the circuit. Often, “current” becomes
conflated with the mechanism by which
information and power is transmitted in
electrical or electronic circuits. For many
problems this convenient shorthand is
adequate. However, as we will soon see,
this is a limited view of what is actually
occurring.
©2017
Enter Kirchhoff: Circuit analysis relies
on rules (Kirchhoff’s laws) to derive
nodal voltages and branch currents.
Kirchhoff’s laws may be derived from the more
fundamental Maxwell’s equations. These laws
are useful re-statements of the law
of conservation of energy. Now, Kirchhoff’s
laws may be applied in circumstances where
the individual circuit elements can be
considered “lumped parameters.” Circuit
elements, for example resistors, inductors,
capacitors, may be considered a lumped or
discrete parameter when the voltage varies
smoothly across the element.
Figure 2: (A) Kirchhoff’s Current Law (KCL) and
(B) Kirchhoff’s Voltage Law (KVL)
KCL: The current going into a node is the same as the
current leaving the node.
KVL: The sum of the voltage changes around any closed
loop is zero.
Fig. 2 (A)
Fig. 2 (B)
node

3. 3
©2017
In other words, the voltage changes in
the circuit may be viewed as changing in
discrete steps. For this to be true, the
physical size of the resistor (or any
element) must be small relative to the
wavelength of the electrical energy exciting
the circuit. Figure 3 shows this condition
visually. Here we present a resistor whose
physical size is less than 1/10 of the
wavelength of the energy moving
through the circuit. The result is that the
voltage (vertical axis in Figure 3) changes
smoothly and therefore we can assign a
single value for the voltage change (drop)
across the resistor. If the situation were
reversed and the wavelength was 1000x
smaller than the resistor, the voltage would
be radically different at each point in the
resistor. At some points it would be a
maximum value and at other points it
would be zero. In this instance, what value
would we assign to the voltage change
across the resistor? Engineers capture this
Idea by saying the resistor is electrically small
(relative to the wavelength). When the
component or circuit is electrically small,
the voltage variation (vertical
displacement in Figure 3) is smooth and single-
valued. Changes in voltage across the circuit
may therefore be approximated as
occurring in discrete steps. This approximation
greatly simplifies the mathematical analysis and
makes traditional circuit analysis (using
Kirchhoff’s laws) possible.
The Hydraulic Analogy: One
consequence of this simplified approach
is that it leads to a misunderstanding about
how electromagnetic energy flows through
the circuit. The simplification gives rise to the
hydraulic analogy. The hydraulic analogy
states that current within the circuit
is due to microscopic particles (electrons) that
flow through wires the same way water flows
through pipes. The motive force propelling
these particles is voltage –the analogue of
pressure in the hydraulic case.
Component is Electrically Small:
L (length) << λ/10
Voltage (V)
Time (s)
λ
Figure 3: The physical length of the resistor is small relative to the wavelength (λ) of energy exciting
the circuit. This condition is referred to as being electrically small or electrically short. As a result,
the voltage variation (the vertical change) across the component is small and therefore may be
considered to occur in a discrete step.

4. 4
Figure 4: Electromagnetic energy flow in a PCB trace (horizontal and vertical views).
Models created in ANSYS’ HFSS 3D electromagnetic (FEA) field solver simulator.
This simplified model is accurate enough to
design and build many practical circuits, but it
is not generally correct. In Figure 4, we find a
more accurate visualization of
electromagnetic energy flow in a circuit. What
is actually moving along the circuit trace is an
electromagnetic field “disturbance.” What is
being shown is the electric field component.
(Now, a magnetic field is also present but, in
most problems, its amplitude is so small in
comparison to the electric field that its effects
may be ignored.) As the field disturbance
moves through the medium it pushes the
electrons along with it –much like an ocean
wave will push a cork as the wave passes. The
electrons, however, do not translate very far
before colliding with another electron. Hence,
the net velocity of the electrons (the drift
velocity) is very, very small when compared to
the velocity the wave disturbance is moving
along the circuit trace (i.e., at the speed of
light). It is here the hydraulic analogy begins
to fail. To be clear, it is the field disturbance
that is moving at the speed of light in that
medium along the wires or traces in any
circuit.
The Microstrip Model: Let’s unravel current
flow in a PCB circuit trace a little further. In
Figure 5 (A), we present a side view of the
trace shown in Figure 4. The construction of
the system is as follows. The top layer
consists of the “wires” known as traces or
microstrip lines. Traces are thin films of
copper that are installed onto onto the PCB’s
substrate or dielectric material.
©2017
Fig. 5 (A)
Fig. 5 (B)Figure 5: Electric field coupling
in a PCB microstrip
FR4
FR4 FR4

5. 5
The Origin of Electromagnetic Interference
(EMI): Traditional circuit analysis is valid
when:
• The circuit components are relatively small;
• The circuit is switching slowly; or
• The components are physically isolated from
one another.
If any of these assumptions fail or are invalid,
then the “electromagnetic” behavior of the
component or circuit must be taken into
account. Traditional circuit analysis,
involving currents and voltages, will not
provide adequate explanations of the circuit’s
behavior. An example of a component where
these assumptions are no longer valid is a
spiral inductor. Spiral inductors are used to
control current in oscillating circuits and may
be found in most RF or radio electronic
systems. For example, every cell phone has
several of these devices.
These components are large relative to the
MHz or GHz frequencies being used, are
experiencing high switching rates, and have
coils that are very close to another so that
electromagnetic coupling may be
occurring between the coils. In Figure 6, we
see an example of the energy flow along a
spiral. The FEA animation makes several “real
world” features apparent. First, note how the
color changes as the field travels along the
spiral path. This is capturing the effect of the
energy attenuation as the field progresses. No
real system is perfectly frictionless; there
always is an energy penalty. Second, note the
presence of a reflected wave at the input
port. Reflections often occur at boundaries
when material impedances are likely to change,
too.
A typical PBC dielectric material is FR4 –a glass
reinforced epoxy-based laminate. The bottom
layer is typically a copper ground plane.
All electric fields begin and end on charge
carriers. These carriers are electrons; however,
by convention we consider current as being
conducted by positive charge carriers. By
another convention, it is assumed that the
field is directed away from a positive charge
carrier and is directed towards a negative
charge carrier. The electric field lines shown in
Figure 5 (B) are therefore for positive charge
carriers. The field lines start from charge
carriers in the copper traces and couple to
separate charge carriers found in the copper
ground plane. The field lines pass through and
are concentrated in the dielectric substrate
(FR4). The substrate is critical. It contains the
bulk of the field disturbance and controls the
speed of the bits (digital data) along the trace.
What is shown in Fig. 4 is an animation
constructed by solving Maxwell’s equations
along the microstrip using finite element
methods. As shown in Figure 4, the electric
field disturbance moves along the trace. The
colors show the field intensity falling off as one
moves away from the trace.
The models in Figures 4 and 5 are constructed
with a dual microstrip trace. Two traces are
used in most of today’s high speed computer
and communication circuits. The digital signals
in the dual traces are compared and used to
ensure the correct data is sent between the
transmitting and receiving integrated circuits
(IC’s). If a bit error is detected (e.g., a zero is
detected that should have been a one) the data
is resent. That is, dual traces are used in a
technique known as Hamming bit error
detection and correction.

6. Business Confidential
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Figure 6: Electromagnetic energy flow along a spiral inductor.
The Virtues of Electromagnetic FEA
Simulation: In Figure 4, we show an
example of how energy flow through an
electrical wire or circuit trace is
always an electromagnetic event. In
Figure 6, we show an example of a
component whose behavior can only be
captured through electromagnetic FEA
simulation using electric field parameters
rather than currents and voltages. With this
component, the assumptions of circuit
analysis break down and no longer apply.
In the next example, we will motivate the
origins of electromagnetic interference on a
printed circuit board. In Figure 7, we have
recreated the same example as in Figure 3
with one exception. In this example, we have
removed a chunk of the ground plane and
have replaced the FR4 with another
dielectric -air. That is, we have two traces
which are sitting on top of a hole. The PCB
dielectric is hidden so that the model is
visually less confusing.
As before, we are injecting a signal into a dual
microstrip trace and are simulating the flow of
electromagnetic energy along the trace.
In this instance, we are showing the radiation
pattern on the ground plane –which now
consists of copper and air. Now, circuit
designers who are responsible for placing and
routing components on a PCB know not to
place a trace over a cut in the ground plane.
Why? Two problems are likely to occur. First,
because there is a boundary condition (i.e. an
impedance) change where the copper ground
plane meets the “air” of the cut, some of the
incoming energy will get reflected back to the
source. This results in less energy being
transmitted across the trace. This effect is
captured by the color change in the energy
disturbance as it progresses from top to
bottom. Second, the electric field itself has
inertia and cannot easily navigate around the
cut in the ground plane.
©2017

7. Business Confidential
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Figure 7: Transmission lines over a split plane illustrate the 3D nature of electromagnetic problems.
Attenuation
due to impedance mismatch
EMI radiation
This is the same effect one experiences
when traveling too fast around a
cloverleaf on a highway. In this instance,
the driver and passengers feel as if they
are going to be thrown from the vehicle.
In a similar fashion, the electric field
has a difficult time remaining coupled
between the copper signal trace and
the copper ground plane. As a result,
radiation begins to “peel away” from
the circuit. This is the genesis of a
troublesome phenomenon known as
electromagnetic interference or EMI.
Even simple traces are 3D structures.
Traditional 2D circuit methods based
on currents and voltages in nodes and
branches cannot capture these effects.
The only way to capture these effects is
through more sophisticated, distributed
element transmission line models or
3D FEA models that solve Maxwell’s
equations directly.
©2017
Conclusions: Signal (power and
information) flow in circuits, whether in
electric power transmission lines or printed
circuit board traces, is always and
everywhere an electromagnetic field
phenomenon. Such flow results from
electric (electromagnetic) field
disturbances moving through a dielectric
(air, FR4). Under certain circumstances
(electrically small circuits, low frequencies),
simpler circuit models using only currents
and voltages are adequate tools for
analyzing and explaining circuit behavior.
These simpler techniques tend to reinforce
the hydraulic analogy to explain circuit
behavior; while useful, the analogy is
limited in the breadth of applications it
can explain. For example, an analysis of
the root causes of electromagnetic
interference in a real circuit will often
force the engineer to seek tools with a
higher fidelity.