Broadband EMI Noise Measurement
in Time Domain
Florian Krug and Peter Russer
Lehrstuhl für Hochfrequenztechnik
Technische Universität München
Arcisstrasse 21, D-80333 Munich, Germany
phone: +49-89-289-23375, fax: +49-89-289-23375
email: [email protected]
Abstract—In this paper we analyse the statistical physical noise behavior
of the broad-band time-domain electromagnetic interference measurement
system. The digital signal processing of EMI measurements allows to emulate in real-time the various modes of conventional analogous equipment,
e.g. peak-, average-, RMS- and quasi-peak-detector mode. Because the signals encountered in typical EMI measurement scenarios are of stochastic
nature, a statistical physical noise analysis of the detector modes is necessary. The signal processing of white gaussian noise and the measurement
results obtained from the investigation of a DC/DC-converter obtained with
the time-domain electromagnetic interference (TDEMI) measurement system are discussed.
ing unit (RSU, Rohde&Schwarz), an ampli£er (ZFL-1000LN,
Mini-Circuits), a low-pass £lter (SLP-1000, Mini-Circuits), an
analog-to-digital converter (TDS7154, Tektronix, Oscilloscope)
and a personal computer (IBM compatible). A more detailed
I. I NTRODUCTION
Due to the rapid development of new electronic products and
due to emerging new technologies the ability to achieve and to
improve electromagnetic compatibility is a major challenge in
development of electronic products. EMC and EMI measurement equipment which allows to extract comprehensive and accurate information within short measurement times will allow to
reduce the costs and to improve the quality in circuit and system
development. In the past and currently, radio noise and electromagnetic interference (EMI) are measured and characterized
by superheterodyne radio receivers. The disadvantage of this
method is the quite long measurement time of typically 30 minutes for a frequency band from 30 MHz to 1 GHz [1]. Since
such a long measurement time results in high test costs, it is important to look up for possibilities to reduce the measurement
time without loss of quality.
The digital processing of EMI measurements using Fourier
Transform allows the decomposition of a signal measured in
time-domain into its spectral components. In general the digital
processing of EMI measurements allows to emulate in real-time
the various modes of conventional analogous equipment and it
is also possible to introduce new concepts of analysis [2], [3].
The paper covers new ways to use time-domain measurement
techniques to perform accurate and time ef£cient EMI measurements.
II. T HE T IME -D OMAIN E LECTROMAGNETIC
I NTERFERENCE (TDEMI) M EASUREMENT S YSTEM
The block diagram of the time-domain measurement setup
consisting of the TDEMI measurement system and a conventional EMI receiver is depicted in Fig. 1. The EMI receiver is
used for comparison. The TDEMI-System consists of a broadband antenna (HL562, Rohde&Schwarz), a line impedance stabilization network (ESH 2-Z5, Rohde&Schwarz), a switch-
Fig. 1. Time-domain EMI measurement setup
hardware description of the TDEMI measurement system has
already been presented in [4], [5] [6].
A. Classi£cation of Interferences
The electromagnetic interference (EMI) originating from the
equipment under test (EUT) depends on frequency, time and geometry of the test setup (position, distance and direction). The
interferences may be classi£ed on the basis of the receiver and
interference bandwidth as shown in Tab. I [7], [8].
TABLE I
C HARACTER OF THE DISTURBANCE
Class
A
B
C
Description
continuous narrowband
continuous broadband
pulse modulated
narrowband
Condition
∆fInterf < ∆fReceiver
∆fInterf > ∆fReceiver
pulse-duration
and -repetion
Furthermore EMI signals may be classi£ed on the basis of
their statistical behavior as random or deterministic signals. The
random signals can be further subdivided in stationary and nonstationary signals. The statistical properties of non-stationary
random signals may change considerably over the observation
time. The deterministic signals may be either periodic, quasiperiodic, non-periodic or a combination of these signal types.
Periodic and quasi-periodic signals exhibit line spectra. Transients and other non-periodic signals exhibit continuous spectra.
Finally, signals can be combinations of two or more of the above
classes.
III. T HEORY OF S IGNAL P ROCESSING
To analyse the statistical physical noise behavior of the timedomain EMI measurement system, the measurement of broadband white gaussian noise is necessary. The probability density
function for an amplitude s is given by [9]:
s−µ
1
p(s) = √
e− 2σ2
2πσ
(1)
Whereas µ the average and σ the standard deviation, respectively σ 2 the variance is. To get the noise amplitude of the
white gaussian noise the multiplication with the bandwidth B
of TDEMI-System is necessary. So the noise amplitude N (fk )
at a frequency fk is given by:
√
(2)
N (fk ) = σB
A. Signal Envelope Model for the conventional EMI receiver
A detailed description of the used model of the conventional
EMU receiver is shown in [6]. After the IF-£lter the broadband
white gaussian noise is a bandlimited noise. The envelope of the
band limited white gaussian noise s(t) is equal to the noise amplitude at the measured frequency fk . This envelope has a pure
stochastic nature. The probability density function p(s) of the
envelope s(t) for white gaussian noise is a rayleigh distribution
and is given by [9]:
p(s) =
s
2
NRec
e
−
s2
2N 2
Rec
(3)
Corresponding to (2), NRec is the noise amplitude after the IF£lter and is de£ned as the square root of the noise power. In
Fig. 2 the probability density function for amplitude values s >
0 is shown.
B. Model for the Average Detection
The average detector delivers the mean value of the envelope
s(t) over the observation time (= dwell time). The mean value
of the rayleigh distribution (3) yields to [10]:
mavg =
Z
∞
sp(s)ds =
−∞
With the integral [11]:
Z ∞
x2 e−a
2
1
2
NRec
x2
Z
dx =
0
∞
s2 e
−
s2
2N 2
Rec
ds
(4)
0
√
π
4a3
Follows for the mean value of the recti£ed signal s(t):
r
√
1
π
π
mavg = 2
=
NRec ≈ 1.253NRec
NRec 4 √ 1 3
2
(5)
(6)
( 2NRec )
The value mavg is not equal to the initial value of the average
detector, since the mean value needs a in£nite long observation
time of an exact estimation. It concerns thus only an estimation of the mean value of the rayleigh distribution, which is subjected again to a variance. The variance of the estimation is
smaller than the variance of the envelope signal s(t) and estimation variance decreases with longer observation.
C. Improving amplitude accuracy by Coherent Gain
The ADC samples and quantizes the continuous input signal
x(t) with a sampling frequency fs corresponding to a sampling
period of 1/fs = ∆t. Shannon’s Theorem requires fs to be
at least twice as high as the highest signal frequency. The upper
limit imposed on the signal frequency by the sampling process is
also called Nyquist frequency. After digitization, the data is being delivered to the evaluation routine in blocks of N samples,
where it is used as input to the spectral estimator. The mathematical basis for the spectral estimation methods used in the
context of the time-domain electromagnetic interference measurement system is the Discrete Fourier Transform (DFT). The
DFT being applied to each of the data blocks is de£ned as follows [10]:
X[r] = DFT{x[n]} =
N
−1
X
³
nr ´
x[n] exp −j 2π
N
n=0
(7)
The DFT transforms the discrete-time signal sequence x[n] into
the discrete-frequency spectral sequence X[r], with n and r denoting the discrete time resp. frequency variable:
x[n] := x(n ∆t);
X[r] := X(r ∆f )
(8)
with n and r running from zero to N − 1. Due to the basic
properties of the DFT, the quantities ∆f , N and ∆t form the
following simple relationship:
Fig. 2. Probability density function of the envelope s(t) with a noise amplitude
NRec = 1
∆f =
1
N ∆t
(9)
In the spectrum X, the value X[0] corresponds to the DC mean
value of the signal and the absolute values |X[r]|, 0 < r < N ,
Since the absolute value of the DFT of a real-valued signal is an
even function in r, all the spectral information is contained in
either half of X[r] below or above the Nyquist frequency. It is
therefore suf£cient to use only one half of X[r] for the further
evaluation steps. Because the signal energy is shared evenly between both halves of the spectrum, the values |X[r]| with r > 1
have to be multiplied by 2 for a correct single-sided representation of the spectrum. To obtain results analogous to the continuous Fourier Transform, the DFT spectral values further have to
be normalized to the number of time-domain samples N . Together with the scaling factors introduced above, this leads to
the following de£nition of the single-sided Amplitude Spectrum
S[r]:
½ 1
with r = 0
N · |X[0]|
√
(11)
S[r] =
2
·
|X[r]|
with
1≤r<R
N
The actual numerical implementation of the DFT is done by Fast
Fourier Transform (FFT). To prevent spectral leakage in case the
signal has periodic components which do not £t with an integer
number of periods into the observation interval ∆TN = N ∆t,
a window function w[n] may be applied [10]:
xW [n] = x[n] · w[n],
0≤n<N
(12)
A window function has a global maximum around the discrete
frequency value N/2 and smoothly rolls off to zero at the discrete frequency values 0 and N − 1, thus removing edge effects
when wrapping x[n] over. On the other hand, the windowed signal vector xW [n] has less energy content than the original signal,
since parts of the signal have been attenuated. To correct this in¤uence, the window sequence w[n] is scaled in such a way that
its integral over the observation interval ∆TN equals unity. The
scaling factor is called Coherent Gain GC of w[n] [12]:
N −1
1 X
GC =
w[n]
N n=0
(13)
Since GC is a scalar factor, it may be applied after the spectral
transform in the frequency domain together with the other scaling factors, due to the linearity of the DFT. Thus, we arrive at
the following de£nition for the modi£ed single-sided Amplitude
Spectrum SM [r]:
(
1
· |X[0]| with r = 0
G√
C N
SM [r] =
(14)
2
GC N · |X[r]| with 1 ≤ r < R
Various choices of window functions offer different compromises between leakage suppression and spectral resolution.
Commonly used window functions include the Hann-, the
Hamming-, and the Flat-Top-window.
D. Improving amplitude accuracy by Equivalent noise bandwidth (ENBW)
The equivalent noise bandwidth (ENBW) is the width of an
ideal rectangular £lter which would accumulate the same noise
power from white noise as the window function with the same
peak power gain. For a discrete amplitude spectrum H(fk ) the
equivalent noise bandwidth is given by
Bne = 2
kX
max
0
(15)
H(fk ) · ∆f
For comparison of the time-domain measurements with the EMI
receiver measurements the IF £lter characteristic of the EMI receiver has to be taken into account. So the equivalent noise
bandwidth for the IF £lter characteristics of the conventional
EMI receiver is considered in the spectrum calculation via the
Fast-Fourier Transform. In Fig. 3 the measured IF-£lter characteristics of the EMI receiver for the bandwidth 200 Hz, 9 kHz,
120 kHz and 1 MHz is shown.
0
−10
Attenuation / dB
to the amplitude of the complex phasor at the frequency index r.
To compute the RMS values,
each element of |X[r]| with r > 1
√
needs to be divided by 2, the crest factor for sinusoidal signals.
The frequency index R corresponding to the Nyquist frequency
is given by
½
N
2 with N even
(10)
R=
N +1
with N odd
2
−20
−30
−40
−50
−60
−70
−80 0
10
200 Hz
2
10
9 kHz 120 kHz 1 MHz
4
10
Frequency offset / Hz
6
10
Fig. 3. Measured IF-£lter characteristics
IV. M EASUREMENT OF COMPLEX EMI SOURCES
A. Measurement of White Gaussian Noise
To verify the statistical physical noise behavior of the
TDEMI-System a comparison of the measured amplitude spectra is required. Fig. 4 shows the result spectra obtained from the
TDEMI-System and the conventional EMI receiver, both using
the Average detector and an observation interval ∆TM = 50
ms. The step size was 50 kHz and the receiver used an IF £lter
bandwidth of 120 kHz. In Fig. 4 a match of the amplitude spectrum measured with the TDEMI-System and conventional EMI
receiver for broadband white gaussian noise of different noise
power levels is shown, the mean deviation is typically less than
0.5 dB.
B. Measurement of Emission from a DC/DC-Converter
A practical example for the scenario of broadband gaussian
noise involves measurements on an DC/DC-Converter. The radiated EMI was examined with a broadband antenna from a distance of about 1 m. Fig. 5 shows the result spectra obtained from
ysis of the detector modes is necessary. The signal processing of white gaussian noise and the measurement results from
a DC/DC-converter obtained with the time-domain electromagnetic interference (TDEMI) measurement system are discussed.
VI. ACKNOWLEDGMENTS
The authors wish to thank the Deutsche Forschungsgemeinschaft for the support for the acquisition of the EMC measurement chamber and measurement systems. Furthermore the authors wish to thank Rohde&Schwarz GmbH & Co. KG and the
Albatross Projects GmbH for £nancial support of the project.
R EFERENCES
[1]
Fig. 4. Comparison TDEMI-System / conv. EMI receiver: white gaussian noise
generator
the TDEMI-System and the conventional EMI receiver, both using the Average detector and an observation interval ∆TM = 50
ms. The step size was 50 kHz and the receiver used an IF
£lter bandwidth of 120 kHz. Comparing results, we see that
Fig. 5. Comparison TDEMI-System / conv. EMI receiver: DC/DC-Converter
the amplitude-spectrum measured with the TDEMI-System is
nearly identical to the amplitude-spectrum measured with the
conventional EMI receiver. Slight differences in the upper frequency range appear are detectable. These deviations are caused
by the differing noise behavior of the TDEMI-System and the
conventional EMI receiver.
V. C ONCLUSION
The presented broad-band time-domain electromagnetic interference measurement system allows to emulate in real-time
the various modes of conventional detector modes. Because the
signal encountered in typical EMI measurement scenarios are
stochastic in nature, a statistical physical noise behavior anal-
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