SIMPLE ELECTROMAGNETICS
274
Lab 5. Coupling
Background:
between
LABS
signal lines
Circuits, Chapt~rs 6, 8, 15 and 16 in Introductory Electromagnetics
~.
~
A printed circuit board has a large number of signal lines that often run parallel to each other
and have a common ground plane at some other layer of the board. When there is a voltage
on one of the lines, there are charges on it, which induce charges on other lines (especially
neighboring ones). In other words, there are mutual capacitances between these lines and
the signal on one line will couple to the other lines through these capacitances. Similarly, if
currents are flowing in two adjacent lines, their mutual inductance makes a signal -in one of
them couple to the other. Unwanted coupling of signals is a common problem, and in this lab
we learn how to recognize it from measured waveforms.
Purpose:
to measure and quantify capacitive (electric) and inductive (magnetiC) coupling on
the example of a simple 3-trace model of a printed circuit board. We will do the experiments
so that we observe capacitive and inductive coupling separately, with a goal of being able to
recognize them in other more complex circuits.
Source
ie(t)
E
Coupled
-
line
+
vs(t)
Rc
line
vert)
1
(a)
(b)
Fig. L5.1. (a) Electric (capacitive) coupling between two lines on a printed circuit board, and (b)
equivalent circuit model.
Pre-lab
problems:
PL5.1. A simple model of two lines on a printed circuit board, with a common ground plane
underneath, is shown in Fig. L5.1a. A voltage generator of voltage vs(t) is connected to one
of the lines, called the source line. The source line produces an electric filed, which induces
charges and current in the other line. A voltage can therefore be measured across the resistor
connected to the other line, called the coupled line. A circuit model is shown in Fig. L5.1b.
Find an approximate expression for the coupled current ic(t) as a function ofthe source voltage
vs(t), assuming that the capacitance is small so that most of the voltage drop occurs across the
capacitor that models the coupling. For a 2.5-MHz triangular voltage vs(t) with 10V peakto-peak, a capacitance of 2 pF between the lines and the coupled-line load Rc = 50 f2, find the
coupled voltage vc(t). Sketch the voltage waveforms of vs(t) and vc(t). Is the assumption that
the voltage drop across the coupling capacitor is much larger than the voltage drop across Rc
a good one in this case?
I
275
LAB 5: COUPLING BETWEEN SIGNAL LINES
PL5.2. The signal line is next connected to the ground through a resistor, so a current can
flow through it, Fig. L5.2. In addition, we ground the end of the coupled line that was floating
in PL5.1. The current in the signal line causes a magnetic field and an induced electric field,
which will induce a voltage on the coupled line, dictated by Faraday's law. In an equivalent
circuit this type of coupling is -represented by a mutual inductance, M, between the lines.
The induced
voltage is given by Vm(t)
=
M dis(t)jdt,
where is(t) is the source line current.
Assume the same triangular wave for the generator voltage as in PL5.1, a mutual inductance
of M = 50 nH, source load Rs = 50 n, and find the inductively coupled voltage Vm(t).
....
Source
line
-
is(t)
I
H
+
+
Vg(t)
Coupled
line
Rs
:? vs(t)
vc{t)
Fig. L5.2. Magnetic (inductive) coupling between two lines on a printed circuit board.
Lab:
Equipment
and parts:
- a signal generator; a 2-channel scope (as in Labs 1 and 2);
- 3 metal traces on a board, or a standard breadboard and 3 wires that model the signal,
coupled and ground traces;
- 2 Tees with 50-n resistors that can change the input impedance of the scope, an additional
50-n resistor.
Part
1: Capacitive
coupling
Set up the experiment as in Fig. L5.3, with 50-n terminations on both scope channels. If
you do not have the capability to etch a board with traces with mounted connectors, use a
breadboard and parallel pieces of wire. In order to measure just capacitive coupling, leave the
coupled line open at one end, so that there can be no inductively induced current th'rough
resistor Re. Externally trigger the scope, and use a 10-V peak-to-peak 2.5-MHz triangular
generator waveform.
L5.1. Sketch the waveform of the capacitively coupled voltage, Ve(t), along with the waveform
of the source voltage, vs( t). Based on results from your prelab problem PL5.1, calculate the
value C of the coupling (mutual) capacitance between the lines. If your are using a breadboard,
measure also the internal capacitance between the breadboard lines.
Part
2: Inductive
coupling
Next observe inductive coupling alone by shorting the end of the coupled line. The current
now allowed to flow, so we see inductive (magnetic) coupling.
,
is
I
276
SIMPLE ELECTROMAGNETICS
LABS
L5.2. Are we still observing the capacitively coupled voltage across Rc? What happened to
the capacitively-coupled current?
L5.3. Sketch the magnetically coupled voltage, along with the signal voltage. Based on
the results from your prelab problem PL5.2, calculate the value M of the mutual inductance
between the lines.
Part
3: Capacitive
and inductive
coupling
when loading
is varied
Now observe the effect of different resistor loadings at the ends of the two lines. First, change
the coupled line resistance (channel 2 of the scope) to 1 Mn, and leave the source resistance
(channell) at 50 n.
L5.4. Is the capacitively coupled signal larger or smaller than in Part I? What about the
shape of the waveform? Explain. (Hint: is the assumption you made in PL5.1 valid in this
case?)
Coupled line
~
Source
line
Ground
line
Ch.2
(50 (1)
Ch.l
(1 M{1 or
50 (1 )
Oscilloscope
+
Signal
generator
Fig.
L5.3.
Setup for measuring
capacitive
and inductive
coupling.
L5.5. Now observe the inductive coupling (short the end of the coupled line). Sketch the
resulting coupled waveform. What do you think is going on? (Hint: there is also a selfinductance in the loop, which changes the equivalent circuit.)
In the last part, change the coupled line resistance
source resistance (channell)
(channel
2 of the scope) to 50 n, and the
~
to 1 Mft
L5.6. Sketch the capacitively coupled voltage. Explain.
L5.7. Sketch the inductively coupled voltage. This one will be confusing. To explain it, think
of what the current along the length of the source line looks like.
L5.8. Imagine now you had a digital signal on the signal line, consisting of a train of rectangular pulses. What would the capacitively and inductively coupled signals look like in this
case? Sketch the digital pulse and the two coupled signals.
,
Conclusions:
1. Voltages (charges) give rise to capacitive coupling, and currents give rise to inductive
coupling, for example, between signal lines on a pc board. This coupling can dramatically
change the signal waveforms.
2. A signal can appear
on a line even if the line is not connected
to a source or a load.
3. In general, capacitively and inductively coupled signals have the forms of derivatives
the original signal that they are taking energy out of.
of
.