274 SIMPLE ELECTROMAGNETICS LABS

Lab 5. Coupling between signal lines

Background: 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 otherand have a common ground plane at some other layer of the board. When there is a voltageon one of the lines, there are charges on it, which induce charges on other lines (especiallyneighboring ones). In other words, there are mutual capacitances between these lines andthe signal on one line will couple to the other lines through these capacitances. Similarly, ifcurrents are flowing in two adjacent lines, their mutual inductance makes a signal -in one ofthem couple to the other. Unwanted coupling of signals is a common problem, and in this labwe learn how to recognize it from measured waveforms.

Purpose: to measure and quantify capacitive (electric) and inductive (magnetiC) coupling onthe example of a simple 3-trace model of a printed circuit board. We will do the experimentsso that we observe capacitive and inductive coupling separately, with a goal of being able torecognize them in other more complex circuits.

Coupled line

ie(t)-Source line

Rc

vert)

(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 planeunderneath, is shown in Fig. L5.1a. A voltage generator of voltage vs(t) is connected to oneof the lines, called the source line. The source line produces an electric filed, which inducescharges and current in the other line. A voltage can therefore be measured across the resistorconnected 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 voltagevs(t), assuming that the capacitance is small so that most of the voltage drop occurs across thecapacitor that models the coupling. For a 2.5-MHz triangular voltage vs(t) with 10V peak-to-peak, a capacitance of 2 pF between the lines and the coupled-line load Rc = 50 f2, find thecoupled voltage vc(t). Sketch the voltage waveforms of vs(t) and vc(t). Is the assumption thatthe voltage drop across the coupling capacitor is much larger than the voltage drop across Rca good one in this case?

I

+

E vs(t)

1

LAB 5: COUPLING BETWEEN SIGNAL LINES 275

PL5.2. The signal line is next connected to the ground through a resistor, so a current canflow through it, Fig. L5.2. In addition, we ground the end of the coupled line that was floatingin 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 equivalentcircuit 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 inductanceof M = 50 nH, source load Rs = 50 n, and find the inductively coupled voltage Vm(t). ....

Source line

+

Vg(t) Coupled line

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 additional50-n resistor.

Part 1: Capacitive coupling

Set up the experiment as in Fig. L5.3, with 50-n terminations on both scope channels. Ifyou do not have the capability to etch a board with traces with mounted connectors, use abreadboard and parallel pieces of wire. In order to measure just capacitive coupling, leave thecoupled line open at one end, so that there can be no inductively induced current th'roughresistor Re. Externally trigger the scope, and use a 10-V peak-to-peak 2.5-MHz triangulargenerator waveform.

L5.1. Sketch the waveform of the capacitively coupled voltage, Ve(t), along with the waveformof the source voltage, vs( t). Based on results from your prelab problem PL5.1, calculate thevalue 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 isnow allowed to flow, so we see inductive (magnetic) coupling.

,

is(t)-IH

+

Rs :? vs(t)

276 SIMPLE ELECTROMAGNETICS LABS

L5.2. Are we still observing the capacitively coupled voltage across Rc? What happened tothe capacitively-coupled current?

L5.3. Sketch the magnetically coupled voltage, along with the signal voltage. Based onthe results from your prelab problem PL5.2, calculate the value M of the mutual inductancebetween 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, changethe 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 theshape of the waveform? Explain. (Hint: is the assumption you made in PL5.1 valid in thiscase?)

Coupled line

~ Source lineCh.2 (50 (1)

Ch.l (1 M{1 or50 (1 )Ground line

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 theresulting coupled waveform. What do you think is going on? (Hint: there is also a self-inductance in the loop, which changes the equivalent circuit.)

In the last part, change the coupled line resistance (channel 2 of the scope) to 50 n, and thesource resistance (channell) to 1Mft

L5.6. Sketch the capacitively coupled voltage. Explain.

L5.7. Sketch the inductively coupled voltage. This one will be confusing. To explain it, thinkof 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 rect-angular pulses. What would the capacitively and inductively coupled signals look like in thiscase? Sketch the digital pulse and the two coupled signals.

~

Conclusions:

1. Voltages (charges) give rise to capacitive coupling, and currents give rise to inductivecoupling, for example, between signal lines on a pc board. This coupling can dramaticallychange 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 ofthe original signal that they are taking energy out of.

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I