Time-Domain Magnetic Field Waveform Measurement Near Printed Circuit

Boards

TAKASHI HARADA, HIDEKI SASAKI, and EIJI HANKUINEC Corporation, Japan

SUMMARY

This paper describes a time domain magnetic field

measurement process for measuring magnetic fields near

printed circuit boards (PCBs) with a loop probe. In carrying

out these measurements, the loop probe needs to be cali-

brated in the frequency domain. In this process, a microstrip

line with a teflon substrate serving as the standard magnetic

field source is employed as a means of calibrating the probe.

The standard magnetic field intensities of the line are cal-

culated by using an approximate equation obtained from

Ampère�s law to simplify the calibration. The sensor-factor

of the probe obtained from this method agrees with that

obtained through the use of a standard G-TEM cell in 2 dB

at frequencies below 1 GHz. The waveforms of magnetic

fields near a PCB having a four-layer construction are

measured using a 10 mm diameter loop probe as the cali-

brated magnetic field sensor. The generation of magnetic

field waveforms causing the radiated emission from the

PCB is found to depend on the circuit operating conditions.

Our results clarify the fact that the time domain magnetic

field measurement process is an effective tool for analyzing

the sources of emission radiated from PCBs and for inves-

tigating the radiation mechanism. © 1998 Scripta Technica,

Electr Eng Jpn, 125(4): 9�18, 1998

Key words: Printed circuit board; magnetic field

intensity; time-domain measurement; spurious electromag-

netic wave radiation; EMI; microstrip line.

1. Introduction

Spurious radiation may be emitted from electronic

equipment. In order to deal with such radiation, the most

effective way is to suppress the radiation from the source

electronic circuit, as the source, as well as from the printed

circuit board on which the circuit is installed. Magnetic

field distribution measurements near PC boards have been

studied in order to specify the radiation sources of spurious

electromagnetic waves on the printed circuit board [1, 2].

The measurement is usually executed as follows. The

frequency characteristics at a particular frequency are

measured at a particular point on the board, or a sensor is

swept along the printed board to measure the magnetic field

at a particular frequency, and the intensity distribution is

displayed. These measurement methods benefit from the

fact that the source of radiation can be specified at the

component level, for example, ICs and the signal lines.

When the entire printed board is the source of radiation [3],

however, it is difficult to specify the source.

In order to deal with this problem, a technique to

measure the magnetic field near the printed board as a

time-domain waveform has been proposed [4, 5]. By ob-

serving the time-domain waveform, the time-course of the

magnetic field due to radiation can be interpreted in relation

to circuit operation. Consequently, useful information can

be obtained by analyzing the mechanism of radiation or

considering the suppression of the radiation.

The time-domain waveform of the magnetic field can

be derived by deconvolution of the output voltage wave-

form from the magnetic field sensor and the sensor factor,

which is the ratio of the magnetic field received by the

sensor and the output voltage [6]. Consequently, in the

measurements it is necessary to know beforehand the fre-

quency characteristics of the sensor factor. Since digital

signals have a wideband frequency spectrum, the sensor

factor must cover that bandwidth.

As a method for calibrating the magnetic field sensor,

the authors proposed a method using an unbalanced micro-

strip line that can generate a wideband magnetic field as a

standard magnetic field generation source [7]. This method

has the following additional advantages.

(1) The microstrip line can be assumed to generate,

with little error, the TEM mode, if the cross-sectional size

is sufficiently small compared to the wavelength. Thus, it

is easy to estimate the standard magnetic field intensity.

CCC0424-7760/98/040009-10

© 1998 Scripta Technica

Electrical Engineering in Japan, Vol. 125, No. 4, 1998Translated from Denki Gakkai Ronbunshi, Vol. 117-A, No. 5, May 1997, pp. 523�530

9

(2) If the propagation constant is known, the phase

on the line can be estimated. In other words, the phase can

be calibrated.

(3) The electromagnetic field intensity decreases

rapidly with distance from the line. Consequently, there is

less disturbance to the electromagnetic field by placing the

sensor and the connection cable far away from the line.

In this paper, a loop probe was used as the magnetic

field sensor. Initially, we describe the calibration of the

probe, using a microstrip line as the standard magnetic field

generation source. In order to simplify the calibration pro-

cedure, the magnetic field intensity near the line is repre-

sented by an expression derived from Ampère�s law. The

conditions for that approximation to be valid are discussed.

By comparing the result to that obtained by the usual

method, using a G-TEM cell as the standard magnetic field

source, the range over which the proposed method can be

applied is analyzed.

Using the loop probe calibrated as above, the time-

domain waveform of the magnetic field near a four-layer

printed circuit board with installed digital circuits is meas-

ured. It is demonstrated that the proposed measurement

procedure is useful in analyzing the spurious electromag-

netic wave radiation mechanism.

2. Measurement of Time-Domain Magnetic Field

Waveforms

The time-domain magnetic field waveform is ob-

tained as follows [6]. The output voltage waveform v(t) of

the loop probe is measured by an oscilloscope. Then, the

following manipulation is applied:

where f is the Fourier transform, and f-1is its inverse.

If the waveform does not contain a dc component, the

manipulation simplifies to

where F.(w) [A/V/m] is called the sensor factor [8]. This is

defined as the ratio H.(w) /V

.(w) of the frequency charac-

teristic H.(w) [A/m] of the received magnetic field to the

frequency characteristic V.(w) [V] of the output voltage. For

calculation contained in Eqs. (1) and (2), both the amplitude

and phase of the sensor factor must be known.

In general, calibration methods for the magnetic field

sensor can be classified as follows. In one method, a mag-

netic field with known intensity is generated by a standard

electromagnetic field generation source, such as a TEM cell

and loop antenna, and the ratio of the output voltage to the

known field intensity is calculated [9]. The other method is

a three-antenna method that uses three magnetic field sen-

sors and measures the transmission coefficients between

pairs of sensors [10]. In either case the factors of individual

sensors are obtained. In this paper, a microstrip line is used

as the standard magnetic field generation source and the

magnetic field around the line is used for calibration.

In the case of a microstrip line composed of a strip

conductor and the ground plane, the electromagnetic field

distribution in the cross section of the line is the TEM, as

shown in Fig. 1, if the width of the strip conductor and the

distance between the ground plane and the strip conductor

are sufficiently small compared to the wavelength. For a

microstrip line with dielectric support, the electromagnetic

field is not strictly TEM, but the distribution can be consid-

ered to have an approximate TEM mode if the permittivity

is low and the dielectric is thin. In this study, a microstrip

line with a teflon board is used and calibration is attempted

in the range from 10 MHz to 2 GHz.

3. Calibration Using a Microstrip Line

Figure 2 shows the microstrip line used as the stand-

ard magnetic field generation source. The line length is 455

mm and the width of the ground plane is 305 mm. The

dielectric is constructed from teflon with a permittivity of

er = 2.1 and a thickness of 0.508 mm. The width of the strip

conductor is 1.65 mm and the characteristic impedance of

the line is 50.5 W. A high-frequency signal was fed to the

line through SMA plug receptacles attached to each end of

the line. The transmission characteristics of the line were

examined by a network analyzer. It was found that the

waveform reduction ratio of the line (l /l0) was 0.73 and

that there was no frequency dispersion below 5 GHz.

The magnetic field H near the microstrip line is

represented as follows, using the vector potential A pro-

duced by the current flowing along the line:

(1)

(2)

Fig. 1. Magnetic field pattern in a microstrip line.

(3)

10

where m0 is the permeability of a vacuum.

The calibration was conducted at the central point of

the line and the magnetic field at this point was estimated.

When the ground plane is sufficiently wide, the vector

potential A at the central point of the line can be determined

as the sum of the vector potentials produced by the current

Iz on the strip conductor and the return current -Iz flowing

at the mirror image position, as shown in Fig. 3. The current

flowing on the line is along the z direction. Consequently,

there is only a z component of the vector potential A®. This

is given by

where ks is the propagation constant of the line, k0 and r02

are the propagation constant and distance, respectively, of

the electromagnetic wave in air, kr and rr2 are the propaga-

tion constant and distance, respectively, of electromagnetic

wave in a dielectric, and L is the line length.

In the cross-section of the strip conductor, the current

concentrates at the sides [11]. However, when the distance

h exceeds five times the width w of the strip conductor, the

current can be considered as a line current (see Appendix

1).

At a height h above the strip conductor, the magnetic

field has only the Hx component parallel to the ground

plane. This is represented by

The second term on the right-hand side of Eq. (4)

gives the vector potential produced by the return current.

The phase term must be calculated by separating it into

terms for the dielectric and for air. In what follows, the

medium is assumed to be air in order to simplify the

calculation, and thus the following expression is used:

If the distance of the magnetic field sensor to be calibrated

exceeds five times the width of the strip conductor, i.e., it

is more than 8 mm for this microstrip line, the phase

difference of the second term obtained from Eqs. (4) and

(6) is smaller than a factor of 1.03. In other words, the effect

of amplitude and phase on the calculation is small.

The magnetic field near the microstrip line depends

on the length L of the line. Figure 4 shows the result of

calculation for the magnetic field intensities at heights 10

mm, 20 mm, and 30 mm at the central point of the strip line

when a current of 1 A flows along the line. The horizontal

line is the line length L. The frequency is set to 100 MHz,

300 MHz, 1 GHz, and 2 GHz for each height. It can be seen

that the magnetic field intensity is constant, independent of

the line length, when the line is long. The length for such a

situation is greater than 30 mm for a height h = 10 mm from

the strip conductor, and is greater than 50 mm for h = 20

mm. When the height h is 30 mm, the magnetic field

intensity is constant for lengths greater than 80 mm; it

remains constant for frequencies less than 1 GHz, but must

be greater than 350 mm for 2 GHz. The length of the

microstrip line used in the experiment is 455 mm. Conse-

quently, a constant magnetic field intensity is obtained for

Fig. 2. A microstrip line used as a standard magnetic

field generator.

Fig. 3. Current model for calculating the vector

potential.

(4)

(5)

(6)

11

the frequency range below 2 GHz by placing the sensor to

be calibrated at a height of 30 mm or less above the strip

conductor.

If the line length is held in the above range, the

magnetic field intensity is almost independent of the fre-

quency. In order to further simplify the calibration, the

expression relating the dc current on the straight microstrip

line of infinite length to the magnetic field

is used instead of Eq. (5) to calculate the magnetic field

intensity. Equation (7) is a consequence of Ampère�s law.

As can be seen from Fig. 4, when the sensor is far

from the strip conductor, the magnetic field intensity de-

pends increasingly on the frequency as the frequency is

increased. In order to examine the range within which Eq.

(7) can be used as an approximate expression, the difference

Hap - Hst between the magnetic field intensity Hst derived

from the vector potential based on Eq. (5) and the magnetic

field intensity Hap determined from Eq. (7) is calculated in

the height direction with frequency as the parameter. The

result is shown in Fig. 5. The frequency is set to 100 MHz,

1 GHz, 1.5 GHz, and 2 GHz. For either frequency, the

difference is small when the sensor is close to the strip

conductor and increases with the distance. When the height

from the strip conductor is limited to at most 30 mm, the

difference between the two is within 1 dB for the frequency

range below 2 GHz.

The sensor factor for the loop probe is defined by

assuming that the magnetic field passing through the loop

is uniform. In practice, however, the magnetic field inten-

sity near the microstrip line is not uniform, and a correction

for this effect must be applied. The output voltage of the

loop probe is proportional to the magnetic flux passing

through the loop. The magnetic flux density B in air is

proportional to the magnetic field intensity H (B = m0H).

Consequently, the average magnetic field Hav is obtained

by integrating the magnetic field intensity passing through

the loop over the entire loop and dividing the result by the

area S.

The difference DH [dB] between the magnetic field

intensity H at the center of the loop and the average mag-

netic field Hav is defined as the correction term. The behav-

ior of DH is calculated in the height direction for loops 10

mm and 5 mm in diameter. Equation (7) is used to calculate

the magnetic field distribution. Figure 6 shows the result. It

can be seen that the correction term is large when the sensor

is close to the strip conductor, since the magnetic field is

highly non-uniform, but decreases with distance from the

strip conductor. The correction term is small when the

diameter of the loop is small. The magnitude of the sensor

factor is corrected by DH, according to the placement height

of the loop probe.

The two short-circuit terminated shielded loop probe

sensors, with loop diameter of 10 mm and 6.5 mm and with

a gap at the tip, are designed as in Fig. 7, and the sensor

Fig. 4. Magnetic field strength above the strip

conductor.

(7)

Fig. 5. Difference between the magnetic field

intensities obtained from the approximation,

Eq. (7), and those from the vector potential.

(8)

12

factors F.(w) are determined. Figure 8 shows a block dia-

gram for the calibration. One end of the microstrip line is

match-terminated by a 50 W resistance, and the signal is fed

from port 1 of the network analyzer through the coaxial

cable. The loop probe to be calibrated is placed at the central

point of the microstrip conductor so that the loop is parallel

to the strip conductor. The output of the loop probe is

connected to port 2 of the network analyzer through the

amplifier. A 6 dB attenuator is connected to the output

terminal of the probe in order to eliminate reflections due

to impedance mismatch. As the network analyzer, an

HP3577 device is used for frequencies below 200 MHz, and

an HP8720 is used for frequencies above 200 MHz.

The calibration procedure is as follows.

À The cable, the amplifier, and the attenuator of the

calibration system are connected in cascade, and the refer-

ence for S.

21(w) of the network analyzer is calibrated.

Á The transmission characteristics of the microstrip

line are measured by the above system. The phase delay

q(w) of the line is determined for each frequency and the

phase q(w)/2 at the central point of the line is determined.

 Finally, S.

21(w) is measured by the calibration

system shown in Fig. 8. The magnitude |F.(w)| and the phase

ÐF.(w) of the sensor factor are calculated from the follow-

ing expressions (see Appendix 2):

Figure 9 shows the frequency characteristics of the

sensor factor F.(w) of each probe. The phase is shown only

for a loop probe with diameter 10 mm. The height from the

strip conductor to the center of the loop is set to three points,

i.e., 10 mm, 20 mm, and 30 mm for the loop probe 10 mm

in diameter, and two points, i.e., 11.5 mm and 21 mm, for

the loop probe 6.5 mm in diameter. The sensor factor is

almost constant when the frequency is low, but depends on

the height when the frequency approaches 1 GHz.

In the case of the loop probe with a diameter of 10

mm, the sensor factors are almost the same for heights of

10 mm and 20 mm in the frequency range from 700 MHz

to 1 GHz. There is a difference of about 2 dB between these

values and the sensor factor obtained at h = 30 mm. Above

1 GHz, a difference of 1 to 2 dB is produced between the

sensor factors at h = 10 mm and h = 20 mm. In the case of

the loop probe with diameter 6.5 mm, a difference that

depends on the height is found for frequencies above 1.5

GHz. The black dot in the figure is the sensor factor of the

loop probe with diameter 10 mm, obtained with the G-TEM

Fig. 6. Correction factor for the non-uniformity of the

magnetic field strength.

Fig. 7. Shielded loop probe.

(9)

(10)

Fig. 8. Calibration configuration.

13

cell as the standard magnetic field generation source. The

results agree to within 2 dB, except for a few frequencies.

From those results it can be seen that a calibration

equivalent to the conventional method is achieved by the

proposed method for frequencies less than 1 GHz by re-

stricting the height above the strip conductor to less than 20

mm. The reason for the dependency of the amplitude on

height at higher frequencies is presumably the deviation

from the TEM mode as one moves away from the line. The

details, however, are still being investigated.

4. Time-Domain Waveform Measurement of a

Magnetic Field Near a Printed Circuit Board

The amplitude and phase of the magnetic field sensor

are calibrated by using the above method and the time-

domain waveform of the magnetic field near the printed

circuit board bearing the digital circuit is measured. Figure

10 shows the board and the circuit used in the evaluation.

The board has a four-layer structure, with size 160 mm ´

24 mm and thickness 1.6 mm. The layer structure consists

of a signal layer, a ground layer, a source layer, and another

signal layer. The dielectric is glass-epoxy with permittivity

er = 4.8 to 5.1.

The installed circuit comprises a quartz oscillator, a

TTL inverter IC (74AS04), and four signal connection

patterns. Each signal line is terminated by a 75 W resistor.

The frequency of the oscillator is 20 MHz and the length of

the connection pattern is 105 mm. The ground layer and the

source layer form the ground plane and the source plane,

respectively, and cover the entire board. The signal pattern

is placed only on the first layer. The power is supplied from

an external stabilized source.

Figure 11 shows the spurious electromagnetic wave

radiation characteristics at a distance 10 m from the board,

when the circuits are operating. The measurement is exe-

cuted in accordance with CISPR Pub. 22. The board was

placed parallel to the ground plane.The measurement was

performed for both horizontal and vertical polarizations.

Since the frequency characteristics of the two cases are

similar, only the case of vertical polarization, where the

radiation level is higher, is shown. Clock type radiation with

the radiation spectrum at integer multiples of the oscillator

frequency dominates the radiation. Consequently, the levels

at those frequencies are connected by a solid line, in order

to show more clearly the behavior of the electric field

intensity. It is seen that the radiation level is significantly

higher at frequencies near 220 MHz and 640 MHz.

In the measurement of the magnetic field waveform

near the printed circuit board, the shielded probe with

diameter 10 mm described above was used as the magnetic

field sensor. Figure 12 shows the time-domain waveform

Fig. 9. Sensor factor.

Fig. 10. Printed circuit board.

14

of the magnetic field at a point 10 mm above the signal

connection pattern. The magnetic field above the connec-

tion pattern exhibits a waveform in which an oscillation

with a period of approximately 4.5 ns is superposed on a

rectangular wave with a period of 50 ns and a duty ratio of

approximately 50%. The frequency of the rectangular wave

is 20 MHz and that of the sinusoidal oscillation is 220 MHz.

The 20 MHz rectangular wave is equal to the frequency of

the quartz oscillator. Since the connection pattern is resis-

tor-terminated, it is presumed to be the magnetic field

produced by the current flowing on the connection pattern

accompanying the operation of the ICs.

220 MHz, on the other hand, agrees with the fre-

quency of the spurious radiation of the highest level. In

other words, this sinusoidal oscillation is considered to be

the source of the spurious radiation. It is also seen, by

observing the waveform, that the 220 MHz oscillation is

produced when IC is at the high level, i.e., when the current

is flowing in the circuit. These results suggest that the

spurious radiation of the electromagnetic field depends on

the operating condition of the circuit. It has been difficult

to identify this behavior from previous measurements of the

magnetic field in the frequency domain.

To determine the magnetic field at another position,

the time-domain waveform was measured at the edge point

of the board. This point of measurement corresponds to the

edge of the source and the ground layers, and the waveform

may easily be affected by the edges. The loop was placed 7

mm below the fourth layer at the central point of the printed

board edge. Figure 13 shows the measurement results. It

can be seen that at the board edge the waveform is domi-

nated by the 220 MHz oscillation, which depends on the

output level of the IC. The amplitude of this oscillation is

approximately 0.3 A/m peak-to-peak, exceeding the value

on the connection pattern by a factor of ten. The measure-

ment point is far from the connection point and the mag-

netic field due to the 20 MHz current on that pattern is of a

low level and is hardly observed.

Oscillation of the same 220 MHz frequency compo-

nent with a high radiation level is observed in the waveform

near the printed board as the component produced when the

Fig. 11. Radiated emission (vertical polarization).

Fig. 12. Magnetic field waveform near signal traces. Fig. 13. Magnetic field waveform near the PCB edge.

15

IC is at the high level and current is provided to the circuit.

In addition, the amplitude is high near the edge of the

printed board, where the effect of the source and the ground

layers are observed. From this perspective, it seems highly

probable that the radiation source of the spurious electro-

magnetic field in this printed board is in the source-ground

system.

5. Conclusions

This paper has discussed measurement of the time-

domain waveform of the magnetic field near a printed

circuit board, as well as the calibration of the loop probe to

be used for waveform measurement. A calibration method

is proposed in which the quasi-TEM mode produced by the

microstrip line is used as the standard magnetic field. Using

a microstrip line 455 mm long and with a ground plane

width of 305 mm on a teflon board of relative permittivity

2.1 and thickness 0.508 mm, the accuracy of the calibration

is examined. It was found that, even if the approximate

expression derived from Ampère�s law is used in the calcu-

lation of the standard magnetic field in order to simplify the

calibration procedure, a calibration factor almost equivalent

to the case in which a G-TEM cell is used as the standard

magnetic field generation source is obtained in the fre-

quency range below 1 GHz if the loop is placed within 20

mm of the strip conductor.

Using the loop probe calibrated by the proposed

method, the time-domain waveform of the magnetic field

is measured near the four-layer printed circuit board. It was

shown that a high-frequency magnetic field contributing to

the spurious electromagnetic wave radiation is produced,

depending on the operating state of the circuit. Thus, meas-

urement of the time-domain waveform is a useful means of

locating the source of spurious electromagnetic wave radia-

tion or of analyzing the mechanism of radiation.

APPENDIX 1

Effect of current distribution on strip

conductor cross section

Based on Fig. 14, the current distribution on the strip

conductor cross-section and the magnetic field intensity

immediately below the conductor are approximately repre-

sented by

Figure 15 shows the result of calculating the magnetic field

intensity as a function of the distance from the conductor

for the following current distributions: (A) shows the cur-

rent flow that concentrates on both sides of the strip con-

ductor. (B) shows the current that flows uniformly across

the cross-section of the strip conductor. (C) shows the

current flow that concentrates in the center of the strip

conductor.

The strip conductor cross-section in the microstrip

line is close to a combination of (A) and (B) [11]. In either

current distribution, the magnetic field is almost the same

as in (C), where the current flow is assumed to be concen-

trated at the center, if the distance from the strip conductor

exceeds five times the conductor width.

Fig. 14. Current distribution on the strip conductor and

magnetic field.

Fig. 15. Magnetic field intensity obtained from

different current distribution.

(A-1)

16

APPENDIX 2

Derivation of calibration factor by S21

measurement

The calibration factor F.(w) is defined as the ratio of

the received magnetic field intensity H.(w) to the sensor

output voltage V.(w).

Substituting Eq. (7) into H.(w) of Eq. (A-2),

Since the terminal of the microstrip line is matched,

the current I.(w) is represented by the output V

.1(w) of the

network analyzer and the characteristic impedance 50 W of

the line:

The output is zero at port 2 of the network analyzer, and

port 1 is reflectionless. Thus, the ratio of the input voltage

V.(w) to the output voltage V

.1(w) of the port 1 is equal to

S.

21(w). Consequently,

The amplitude of the calibration factor F.(w) is

The phase of the measured S.

21(w) contains the phase delay

to the center of the line, the point used in the calibration.

The phase delay q(w) of the entire line is determined

beforehand by measurement and the phase at the center of

the line is q(w) / 2. Consequently, by correcting this term,

the phase of the sensor factor ÐF.(w) is given by

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(A-2)

(A-3)

(A-4)

(A-5)

(A-6)

(A-7)

17

AUTHORS (from left to right)

Takashi Harada (member) completed M.S. program (Electrical Eng.) at Tokyo Metropol. Univ. in 1983. Joined NEC Corp.

Apr. 1983. Engaged in development of electromagnetic wave absorber and shield materials, as well as research on suppression

of radiation from printed circuit boards. Now, with NEC Resource Environmental Technology Lab., EMC Technical Center.

Member, IEICEJ, Circuit Implementation Soc., Society for Applied Magnetism, and IEEE.

Hideki Sasaki (member) graduated Mar. 1991 from Nihon Univ. Completed 1st half of doctoral program (Electronic Eng.)

Mar. 1993. Joined NEC Corp. Apr. 1993. Mostly engaged in research on electromagnetic field measurement techniques.

Presently, with NEC Resource Environm. Tech. Lab., EMC Tech. Center. Presentation Award 1995 IEEJ. Member, IEICEJ.

Eiji Hankui (nonmember) graduated Mar. 1988 from Tokai Univ. Completed 1st half of doctoral program (Electrical Eng.)

Mar. 1990. Joined NEC Corp Apr. 1990. Mostly engaged in research on electromagnetic field measurement techniques and

effect of electromagnetics wave on man. Now with NEC Resource Environm. Tech. Lab. EMC Tech. Center. Member, IEICEJ,

Japan Society for Hyperthermal Oncology, and IEEE.

18