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United States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1381

Rapid Evaluation of

Mode-Stirred Chambers

Using Impulsive Waveforms

John M. Ladbury

Robert T. Johnk

Arthur R. Ondrejka

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996

NIST Technical Note 1381

Rapid Evaluation of Mode-Stirred Chambers

Using Impulsive Waveforms

John M. Ladbury

Robert T. Johnk

Arthur R. Ondrejka

Electromagnetic Fields Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

June 1996

U.S. DEPARTMENT OF COMMERCE, Michael Kantor, Secretary

TECHNOLOGY ADMINISTRATION, Mary L. Good, Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Arati Prabhakar, Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1381, 40 pages (June 1996)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1996

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
RAPID EVALUATION OF MODE-STIRRED CHAMBERS

USING IMPULSIVE WAVEFORMS

John M. Ladbury, Robert T. Johnk, and Arthur R. Ondrejka

Electromagnetic Fields Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303

In this paper, we present an experimental technique for the rapid evaluation of

mode-stirred (or reverberation) chambers. The measurement provides an estimate

of the average chamber quality factor (Q) by measuring the chamber impulse

response and observing the decay of the spectral components of the response. The

results show good agreement with those obtained using conventional CW

techniques. The measurement is well suited for low-frequency analysis of a chamber, where costly and time consuming mode-tuned approaches are generally

employed. Since this technique does not use paddle stirring, the time required to

evaluate a chamber can be significantly reduced.

Key words: Decay time; impulse response; integrated impulse response; modestirred chambers; Q; quality factor; reverberation chambers; short time Fourier

transform; time-domain; time-frequency analysis; windowed Fourier transform

1. Introduction

We propose a method for estimating the quality factor (0 of a mode-stirred chamber by

exciting the chamber with an impulse and measuring the decay time of the electric field in the

chamber for frequencies in a narrow band. This is accomplished by passing the resulting impulse

response through a short-time Fourier transform (STFT), and observing the decay rate of the

various spectral components. First, however, we will give a brief description of mode-stirred (or

reverberation) chambers in general, as well as the traditional methods which have been employed

for their evaluation.

Electromagnetic reverberation chambers provide an excellent environment for immunity

testing [1-3] and have recently been employed for emissions testing as well [3,4]. Before any

chamber can be used, it must be carefully evaluated so that the field intensity inside the chamber

1
as a function of input power can be estimated. It is therefore necessary to obtain an estimate of

the chamber quality factor Q. The quality factor is important because it measures the ability of a chamber to store modal energy in the form of high field strengths. Q is defined as

^ Stored energy

Dissipated power

where o>o is the excitation (angular) fi-equency [1,2].

The traditional method for measuring chamber Q is shown in figure 1 . The net input

power P, and the received power P^ are measured, and a calculated value Q ' is given as [1]

<, V P

where Fis the chamber volume in cubic meters, and A is the wavelength in meters. Since Q

depends on the specific cavity mode excited in the chamber, the modes must be "mixed" or

"stirred" to excite other modes. This may be done either by changing the chamber boundary

conditions [1-5] or by changing the drive fi^equency [6,7]. Whatever technique is used, the resuhs

must be weighted and combined in some fashion to generate a representative value. This method

is usefijl when the chamber has a simple geometric shape and Fis easy to calculate. Complex

shapes, however, make this approach impractical.

Another method, which does not require an estimate of the chamber volume, is used in

acoustical reverberation chambers [8-11] but has not been widely used in electromagnetic

reverberation chambers. This method involves observation of the transient response of the

chamber and evaluation of parameters based on those observations. For example, the decay rate

of the transient response is directly related to the quality factor of the chamber, as shown below.

Jackson [12] shows that if a single mode in a cavity is excited, once the exciting fianction

is turned off, the electric field E(t) will decay exponentially as

E{t) = £

/2e^-/K*A-)r ^

-2.^-/K^A.)r^ (3)
where Eg is the initial electric field magnitude, t is the exponential decay time, and (wq + A w)

represents the fact that the oscillation is not a pure fi^equency, but a superposition of frequencies

about Oq. Thus, we could measure E{t) and calculate the decay time t fi-om the measured data.

From T and eq (3), we can calculate Q as

OqT (4)

Unfortunately, it may not be possible to excite just a single mode in a complex

environment such as a reverberation chamber, especially at higher fi^equencies. This is because

the spacing between modes decreases as fi^equency increases [1]. If multiple modes are excited,

the electric field can be represented by the superposition of several exponentially decaying

sinusoidal functions of the same form as eq (3):

"*' t

E{t) =

Y. ^*^ "^^ -^('^**^^'^^>' =Y, E^e '^'e

-^^'^**^^"^>', (5)

where Mis the number of modes excited, the subscript k refers to the Ath mode excited in the

cavity, and the notation (A {Si\ indicates that each mode can have a unique bandwidth. Liu et al.

[13] show theoretically that, for a narrow band of fi"equencies, if 6^ is the skin depth of the

chamber walls, the values of \l{Qk^^ are tightly grouped about a central value. From this, we can

deduce that the values of the decay rates I/Tjj. will also be tightly grouped. If they are assumed to

be constant, the electric field can be approximated as

Thus, the electric field is a decaying exponential times an unknown modulating function, which is

caused by the beating of the various modes against each other, as well as other interference

effects. This modulation is well known in the acoustical literature [10, 1 1], where similar results

have been obtained in acoustical reverberation chambers and the measured parameter is sound

pressure rather than electric field.
Another approach showing the exponential decay of a transient signal is given in [14].

Here, the authors assume a uniform energy distribution throughout the chamber and also assume

that the loss of energy due to imperfect conductors in the chamber walls is proportional to the

instantaneous value of the total energy in the cavity. The resulting differential equation also

results in an exponential decay of the chamber energy.

Our method is described in the remainder of this paper. Section 2 gives a detailed

description of the equipment setup. Section 3 describes the data processing involved, and Section

4 shows our experimental results. In Section 5 we review the advantages and limitations of our

proposed method, discuss new questions which have been raised by our resuUs, and recommend

improvements and future endeavors which should improve our understanding of mode-stirred

chambers.

2. Equipment Setup

The system's transient response was measured using the setup shown in figure 2. The test chamber was the NIST mode-stirred chamber, with the paddle removed. This chamber is made of

steel and has dimensions of 3.05 m by 4.57 m by 2.74 m. An impulse generator with a bandwidth

of approximately 1 GHz drives a transverse electromagnetic (TEM) horn antenna, which is placed

inside the National Institute of Standards and Technology (NIST) reverberation chamber. A

second TEM horn inside the chamber measures the continuous time impulse response x(t), and a

high-speed digitizing oscilloscope records the results. A measurement delay /q of 150 ns was

present in the oscilloscope, and will show up in all plots of data versus time. The oscilloscope

sampled the response with a period 7" of 40 ps per point, which gave an effective measurement

bandwidth of 12.5 GHz, so aliasing was not a problem. The duration of the impulse response was

between 4.5 ^is and 6 ^s. Technically, the duration of the impulse response is infinite, but for

practical reasons we are interested only in the portion of the response where the signal is greater

than the noise floor. In an effort to be conservative, data were captured over a full 6 ^s range,

but only the first 4.5 ^s of data were used for the subsequent processing and parameter

estimation. To capture the entire record, 1 50 000 data points were measured by the oscilloscope.

This was accomplished by measuring 60 records, each 5000 points or 200 ns long, and shifting the

4
origin of each record by 100 ns. The number of averages per record and the oscilloscope

sensitivity were kept constant for each record in an effort to avoid changes in measurement

characteristics from record to record. We then combined the records by averaging the

overlapping time segments in each record to produce a final record of length 152 500 points. The

first 2500 points and the last 2500 points of this final record are not averaged, since there was no

overlap. The final record is shown in figure 3. If we assume that the receiving antenna's response

is roughly proportional to the electric field amplitude in the vicinity of the antenna, then the decay

rate ofthe voltage in any given frequency band should be identical to the decay rate of the field

inside the chamber. For this reason, all subsequent processing will be performed on the output

voltage waveform, and the results will be assumed to be applicable to the fields inside the

chamber.

The number of captured records could be reduced by a factor of 2 if no overlap is allowed.

In this measurement, the overlapped regions were used to verify the oscilloscope timing and noise

amplitude by comparing the data in each region. Poor agreement would show that the signal has

decayed below the noise floor of the measurement system or that the time stability of the system

was not sufficient for this measurement. Analysis of the data showed that this was not a problem

for our system. There was an expected decrease in sensitivity in the later records due to the

decaying nature of the signal, but agreement remained excellent throughout the entire

measurement time. Based on these observations, we think that fiiture measurements can be made

without the redundancy in the data. Even without the redundancy, the amount of data required

for the measurement remains formidable.

3. Data Processing

The sampled data were processed using a sliding-window fast Fourier transform (FFT),

also known as a short time Fourier transform or spectrogram [15-17]. The FFT is simply a method of calculating the discrete Fourier transform (DFT) at several frequencies simuhaneously,

and the sliding window provides an estimate of the spectral content of a signal as a function of

time, similar to passing the signal through a bank of band-pass filters. The equation for the

windowed DFT of a discrete signal x is given by
In this equation, A^is the window width, or number of points from the original signal used in

calculating X„, n selects the central frequency / = n/NT , with T defined previously, and w^ is the

window weight, described below. The frequency resolution and bandwidth of the transform are

determined by the value ofA^. For the DFT, the frequency resolution R is equal to the bandwidth

BWand is given by

BW = R = —. (8) NT ^

'

In order to generate values oiX„ as a function of time, we must introduce an offset into

the equation:

/-O

Here, k selects the time associated with a particular transform, t = kT+ to. The squared magnitude [X^J^ of the output gives an estimate of the spectral power

contained in the signal. For our purposes, the parameters we are interested in are based on the

shape of the waveform, not the amplitude. For this reason, the plots for all decay records given in

this report are measured in relative power, and no axis labels are given. This convention allows us

to plot multiple decay records in a single figure and separate them vertically.

The time response of the output signal is greatly influenced by the window shape w, and

the window size, N. The window shape associated with spectrographic analysis has been

thoroughly analyzed and documented [16-18]. The consensus is that windows should gradually

taper to zero or nearly zero at the endpoints. This results in smooth data, but compromises the

ability to respond to abrupt changes in the signal. The window we chose, the Manning window,

was selected on the basis of simplicity and ease of implementation, and is given below:
w = — cos( ) for i = 0, 1, ..., N-l. (lO)

* 2 2 N-l ^

Figure 4 shows the effect of using a tapered window and a simple rectangular window (w^ = 1) for

a frequency of 500 MHz and A'^= 5000. The relative smoothness of the data processed with a

Harming window demonstrates the improvements gained by windowing. The long-term

characteristics of the two signals are very similar, however. Thus, it appears that window shape

will not significantly influence the measurement of the decay time. Many of the figures shown in

this paper are calculated for a central frequency of 500 MHz. These figures are representative of

our data in general, except where noted.

The window size plays a greater role in the processing of the decay records. Large values

ofA^ accentuate long-term phenomena and give better frequency resolution than small values,

which are better at tracking rapid changes in signal characteristics. Ideally, since we are interested

in modal decays, a large value ofA'^ should be used to examine the long-term narrow-band

characteristics, as mentioned by Carin and Felsen [15]. Unfortunately, it is possible to make A'^

too large. Figure 5 shows two plots of [X^^J^ versus time for a central frequency of 500 MHz and

windowed using a Hanning window. The smooth plot was generated with A^= 10 000, and the

coarse plot was generated from the same source data, but with A^= 500. While the curve with

A'^ = 10 000 is smoother, the exponential decay characteristic of the other curve is more apparent.

This can be explained by the fact that a longer window slows the maximum rate of modulation of

the signal and increases the correlation between nearby points, and as a result, there is less

information about the signal characteristics as a fiinction of time. In contrast, a narrow window

allows rapid modulation and shorter correlation times, which improves our ability to extract the

decay time from the data. For this reason, we chose the narrowest window possible while

maintaining our minimum desired frequency resolution for most of our processing, except where

noted. Since we wished to generate data every 50 MHz, a spacing ofN= 500 was selected.

The correlation caused by the sliding window can be used to our advantage. Since

adjacent points ofX„ ^. cannot change abruptly, it is not necessary to calculate values ofX^,^ for all
values of ^. We determined experimentally that, given a window width A'^ we can increase the

sample time ofA'^;^ from Tto NTIIO without compromising apparent signal resolution.

Once a window size and shape have been selected, the data must be processed to produce

an estimate of the decay time. Although there is an apparent linear (exponential) trend to the

data, it is difficuh to select a line of best fit. (From this point on, when we refer to a linear trend,

we will be referring to the linear decay of the data when plotted on a semi-logarithmic graph, as

shown.) A least-squares regression analysis on this raw data is possible, but several problems

present themselves. First, deep nulls at either end of the series can drastically affect the final

parameter estimates. Second, if the data depart from the ideal decay model, it will be difiBcult to

detect. Finally, linear regression may produce good results for a wide variety of applications, but

data must have a roughly gaussian spread about the central line if we wish to generate a maximum

likelihood estimate of the decay parameters [18]. This obviously is not the case for the data

presented here. For these reasons, the data should be smoothed before any regression analysis is

performed. Several types of smoothing, such as time averaging, frequency averaging, and spatial

averaging are possible. In addition to these methods, an integrated impulse response method

(IIRM) [19,20] can be applied after or instead of the other methods. These methods, as well as

the advantages and disadvantages of each, are described below. Any of these methods can be

combined to produce additional smoothing.

3.1 Time Averaging

Time averaging involves passing a time sequence through a low-pass filter. The most

simple and often used example is the moving average filter, where a data point is replaced with

the average of itself and a fixed number of its neighbors:

. k*L X ^ = -^— Y X ^, (11) '^ 21+1 Ul "-^

where X is the resultant time averaged data and L is the number of neighbors on each side of the

data point included in the average. Since the sample periods for X^^. may vary for different

8
window widths, it is more convenient to refer to an averaging time A . If we represent the sample

period ofX^^ as 7^, then the averaging time is A = 2LTj^

Figure 6 shows a plot of time-averaged spectral power versus time for a central frequency

of 500 MHz. Also plotted is the moving average of the data for various values of A, along with

the line which best fits the moving average data. An exponential curve fit to the original data

results in a similar decay rate. Therefore, the moving average makes the data appear more

attractive, but does not significantly change the results. The primary advantage to this method is

the ease of implementation. The disadvantage is that the amount of smoothing is directly related

to the value of A . Large values of A result in smooth data, but tend to disguise important

characteristics of the signal, such as changes in decay time.

The noise floor of the measurement system is revealed by a flattening of the decay curve. No obvious flattening was observed for fi^equencies below 1 GHz, and we therefore assume that

the dynamic range of the system was adequate for this fi"equency range. Above 1 GHz, however,

the system becomes less efiBcient for both transmission and reception, and the noise floor becomes

apparent. Figure 7 shows the limitations of the measurement due to noise for a decay record with

a central fi^equency of 3 GHz. The flattened response in the last half of the decay record is

characteristic of the records we processed above 2 GHz. The relative noise amplitude could be

improved by using a pulse generator and antennas designed for higher fi-equency applications.

3.2 Frequency Averaging

Frequency averaging is closely related to time averaging. Instead of averaging adjacent

time samples, adjacent fi^equency samples are averaged:

where X is the fi^equency averaged data. From eq (8), a single point has a bandwidth equal to the

frequency resolution 7? of the DFT, so the approximate averaging bandwidth of X is R{2D + 1).
Figure 8 shows frequency averaged data for a central frequency of 500 MHz, N= 500, and

averaging bandwidths of 50 MHz (no averaging), 150 MHz, 250 MHz, and 550 MHz.

The frequency averaging method is based on the assumption that each of the decay

records X^,^ have similar characteristics, that is, similar values for initial power, decay time, and

decay characteristics. It may be possible to correct for variations due to measurement system

effects by compensating for the nonideal characteristics of the transmitted signal, but these will

only compensate for variations in incident power; reflected power from a time-domain signal is

difficult to measure and correct. The assumptions of similarity between records are realistic as

long as the frequencies are close, but close is defined somewhat arbitrarily. For these reasons,

frequency averaging must be used with great caution. These same assumptions must also be valid

for any other technique as well. Since the DFT has a nonzero bandwidth, the signal

characteristics must be assumed constant across the passband. The frequency band in question is

generally narrower than that associated with frequency averaging, so the assumptions are easier to

justify.

Despite these drawbacks, frequency averaging has strong advantages. Hill [6] shows that

frequency averaging improves the spatial uniformity of the field, and also reduces the interaction

between the transmitting antenna and the chamber walls in a two dimensional chamber. (This is

yet to be experimentally verified in a three-dimensional chamber.) Also, it is not necessary to

acquire as much data for frequency averaging as for the other techniques, as described below.

It is possible to overcome some of the problems associated with long time windows: long

windows resuh in greater frequency resolution and therefore allow more decay records to be

averaged over a given bandwidth. An example of the effects of frequency averaging on data

processed with a long window (A'^= 5000) is shown in figure 9 with averaging bandwidths which

are substantially smaller than those used in figure 8. These figures show that frequency averaging

works best for data processed with long windows. This is caused by the improved frequency

resolution associated with long windows. For example, as shown before, a 500-point window has

an effective bandwidth of 50 MHz, so averaging over a 50 MHz bandwidth results in only a single

point, and no averaging. A 5000-point window has an effective bandwidth of 5 MHz, so

averaging over a 50 MHz bandwidth allows 10 points to be averaged together. Thus, if we

10
restrict ourselves to a specific bandwidth and either time averaging or fi^equency averaging, then

fi-equency averaging with long windows appears to give better results.

Figure 9 shows another advantage of fi"equency averaging. If the fluctuations about the

central trend line are small enough, then it is not necessary to acquire as much data. If we were to

estimate the decay time fi^om only two samples on this curve, shown as X on figure 9, the estimate

of T is 538 ns rather than 547 ns, or a difference of less than 2 percent. Thus it is possible to

estimate the decay time by capturing only 2 records, instead of the 60 records required for the

other methods mentioned here. This is an extreme example and very sensitive to small errors in

the measurement of the two points. The fact that these two methods agree so well should not be

viewed as an indication of how well similar results would agree, but it demonstrates the potential

strength of the technique. Obviously, we lose the fine detail and any opportunity to observe

multiple decay characteristics. We therefore recommend additional measurements to verify the

results, but for well-behaved environments, this is a practical alternative. This technique was

introduced by Johnk and Ondrejka [21] for use in aircraft and anechoic chambers, and is the

precursor to the work presented in this paper.

3.3 Spatial Averaging

Spatial averaging requires multiple records, one for each of several antenna

configurations, to be captured and processed as described above. Alternatively, records can be

captured for each of several different paddle positions, which yields similar results. Once the

records have been processed, the various X^^ must be averaged together, resulting in a smoother

curve. Since this method can make use of narrow bandwidths, it is not as sensitive to some of the

assumptions associated with the other techniques, and it is therefore possible to avoid some of the

pitfalls associated with frequency averaging. The chamber characteristics should be the same for

each measurement, so the risks of one measurement masking the characteristics of another should

not be present. The smoothing effects should be comparable to those presented for frequency

averaging, but it is possible to obtain these results over a narrow frequency range.

The primary disadvantage of spatial averaging is the increase in complexity and data. The

antennas must be moved by the person making the measurement or by a mechanical positioning

11
system. Spatial averaging significantly increases the storage requirements of the processing

computer, as well as processing time, because the data must be processed for each configuration.

This limitation may be reduced somewhat by taking fewer records and relying on the smoothing

effect of spatial averaging, as in frequency averaging. It would still require a substantial effort to

collect and process the data. For these reasons, this method was not tested and is mentioned here

only for completeness. We hope to present results in a fiiture paper.

Spatial averaging is roughly equivalent to frequency averaging. Pierce [8] analyses the

statistics associated with both spatial and frequency averaging, and gives estimates of the possible

reductions in measurement variance associated with each method. These estimates could be used

to show the relationship between averaging bandwidth and number of independent measurements,

and how to combine these techniques, if desired. Johnk and Ondrejka [21] have shown that

frequency averaging and paddle stirring give similar improvements to the measured data, and the

combination of both methods yields additional improvements.

3.4 Integrated Impulse Response Method

Another method of time smoothing, known as the Integrated Impulse Response Method,

was presented by Schroeder [19]. Schroeder suggests integrating a modulated decaying

exponential signal u(t) as follows:

P[uit)] = I

uix)dx. (13)

Griven the sampled nature of our data, we can approximate the integral as a sum:

CO (^[«l)*=E"/» (14)

i-k

where u is the sampled version of w(/), «, is the ith sample of «, and iP[u])^ is the Ath sample of

P[u]. If II is the squared magnitude of the DFT of our chamber response, then all values of m will

12
be nonzero, and P[u] will be monotonically decreasing. This feature alone should improve the

smoothness of the curve.

Another approximation must be made because we do not know values of w(/) for all future

times. If we truncate the integral (sum) at some finite value t^ (K), we have

jtr-i (PM), = E «/ (15)

This will introduce an error because the value of the sum must approach zero as k approaches K.

We can analyze the effect of this error on the estimation of the decay time by assuming the u(t) is

an ideal decaying exponential e'"'^. Truncation of the integral results in a multiplicative error a

given by

a = 1 -."-'>". (16)

This error term is strictly decreasing for / < /j, and any decay time based on the truncated integral

will be biased below the actual value of x . The bias will be greatest near t = t^, and for large

values of t . We can minimize the bias by analyzing only the data for t«ty Unfortunately, this

has the disadvantage of reducing the amount of data available for estimating x. As a compromise,

we would like to find a processing range for / that allows enough data for estimating x but is

sufficiently separated from t^. We can solve eq (16) for (^^i):

(Wj) = iln(l-a). (17)

Equation (17) gives an estimate of the time constraints we must place on the least-squares

regression estimate of x; that is, we must only evaluate the data for / < /i+xhi(l-a). This requires

an initial estimate of x, which can be calculated using one of the other techniques, estimated fi-om

early data, or evaluated iteratively. We must also select an allowable value for a. The parameters

we used were determined by trial and error. For our measurements, we used a value of

t^ = 4.5 |is and estimated x based on the data for /< 3.5 ^s. The longest observed decay time was

748 ns, which corresponds to a ~ 0.74. For an ideal exponential, these parameters resulted in a

bias of less than 5 percent, which was considered acceptable.

13
Once an estimate of t has been obtained, it is possible to estimate the bias introduced by

the truncation and correct for it, if necessary, by adding our estimate ofP[m]j^ to P[u]. This

results in forcing the endpoint ofP[u] to match the endpoint of our exponential curve fit. This

may seem like cheating, but the result is more accurate than assuming that P[u] is actually equal

to for yt s: K.

Figure 10 shows the effect of using the integrated impulse response method on the raw

data calculated at 500 MHz. No additional smoothing is required other than the IIRM. The

IIRM appears to work best on data processed with a short window. Figure 1 1 shows data for a

central fi^equency of 500 MHZ, A^= 10 000, processed with the IIRM. The fluctuations about the

central line are greater, but the results are still useful.

4. Experimental Results

Decay time was calculated for several frequencies using the IIRM with TV = 500,

ti = 4.5 |is, and / < 3.5 ^s. A graph of decay time versus frequency is given in figure 12. These

results were used to calculate Q based on eq (4) given in Section 1 . We compared our results

with those calculated using traditional measurement techniques [1], and both sets of data are

presented in figure 13. The traditional technique provides estimates for the maximum, minimum,

and average values ofQ. The maximum estimate corresponds to the maximal coupling between

the transmit and receive antennas over several paddle positions. The minimum corresponds to the

minimal coupling, which could be zero or nearly zero in some configurations, and are therefore

not presented. These conditions usually occur only at specific paddle positions and therefore do

not represent the general chamber characteristics. We therefore assumed that our data would

correspond best v^th the average estimate of ^, and the graph seems to validate this assumption.

Our estimates of Q are substantially higher in the low frequency range, below about

300 MHz. We hope to address this difference in the future. The modal density is low below

300 MHz, and it is possible that the antennas cannot couple to all of the modes which are present,

and the results using the traditional techniques would probably be biased on the low side. Also,

the error bounds associated with measurements in the NIST mode-stirred chamber are greater

than 8 dB below 300 MHz, and according to personal communications with G.H. Koepke at

14
NIST in Boulder, recent measurements demonstrate a change in chamber statistics below

300 MHz due to the limited number of modes below this frequency. Another possibility is that

some unknown property of the chamber is influencing the results. Figure 14 shows the decay

record at 200 MHz. Two distinct decay rates are apparent, with substantially different decay

times and associated quality factors. A similar but smaller effect occurs at 250 MHz. One

possible explanation of this result is based on the work of Hill et al. [14] which shows that two

primary loss mechanisms will determine the quality factor of an empty chamber: antenna losses

(power dissipated by antenna loads) and wall losses (power dissipated by resistive losses in the

walls). Antenna losses dominate at lower frequencies and wall losses dominate at higher

frequencies. Once a large number of modes have been set up inside a chamber, those modes that

couple strongly to the antennas will decay at a different rate than those modes that are weakly

coupled to the antennas. Thus, at frequencies where antenna losses dominate, there should be an

initial rapid decay as the power in the strongly coupled modes is dissipated, followed by a slower

decay caused by a combination of week coupling to the antennas and wall losses. The decay time

values in figure 12 and the Q values in figure 13 were calculated with a linear regression based on

the first 3.5 us of the decay record. If there are two distinct decay rates, evaluating the entire

record will result in an estimate of x between the estimates based on the rapid decay or slow

decay portions only. The entire record resulted in an estimates of t = 537 ns and Q = 675. If we

base our estimates on the slow decay portions only, we obtain estimates of t = 586 ns and

Q = 736. If the faster decay is used, then our estimates will be t = 373 ns and Q = 469. Based

on these observations, estimates based on the initial rapid decay result in Q values that are closer

to those measured using traditional techniques. Unfortunately, this means that there is less

information available for making our estimate. If this analysis is correct, heavy loading by the

antennas may result in such a rapid decay that we cannot make accurate estimates of chamber Q,

and that this technique is valid only for those frequencies where wall losses dominate the total loss

inside the chamber.

In the mid-band range from 400 MHz to 800 MHz, our estimates are somewhat low. This

could be due to the difference in antennas used in each type of measurement. The traditional

technique used log-periodic antennas. Ours were resistively loaded TEM horns, which are larger

15
and could easily load the chamber and lower the chamber Q. Even with these differences, the

agreement is good, especially considering the tremendous differences in measurement techniques.

An estimate of the errors related to our measurement is based on the work of Davy [20].

In his paper, Davy gives an expression for the spatial variance of the decay rate (l/x) . This

equation gives an estimate of the differences in decay rate which could be expected for various

source and receive positions throughout an acoustical chamber, but the results are also applicable

for electromagnetic measurements. These differences appear to be the dominant contributor to

the uncertainty of our measurement. We will therefore concentrate on the spatial variance in this

paper. The variance estimate is

o/ = var (-) = (- y—— (—y F( D\ (ig)

X InlO BW A \0 ^ ^

where BWis the bandwidth, A is the total time interval over which the exponential curve fit is

calculated, D is the factor by which the power decays in A seconds, expressed in dB, and F is

given by

F(x) = l-l(l+^-)-i^e-+i^(l-e-) . (19) ^ X X

If we assume that the values of (1/T)are accurate within ±a„ then, as a gross approximation, we

can assume that the values of x are accurate within ±l/o^, and Q is accurate within ±uija^. As

an example, for the data at 500 MHz, processed with a window of 500 points, the bandwidth BW

is 50 MHz, the observation time is approximately 3.5 ^s, and over this time, the power decays by

approximately Z) = 30 dB. Entering these values into the equation yields a value of a^ of

1.03 • 10". Given an estimate for 1/t of 1.82 • 10^, this implies an accuracy of 18 percent; we

estimate the uncertainty of our estimate of x, and therefore Q, as also 18 percent. The estimated

uncertainty of our data is shown in figure 15.

16
5. Conclusion and Recommendations

We have presented a method of evaluating the quality factor ^ of an electromagnetic

reverberation chamber. This method does not require tuner averaging, and gives results that

appear quite similar to those obtained using traditional techniques. Several methods of processing

the data were also presented, and each gave consistent results. Data processed with short time

windows should be processed with one of two methods: time smoothing or the integrated

impulse response method. Ofthese, the IIRM results in the greatest smoothing, but time

smoothing is better suited for short time records where it is not possible to eliminate a portion of

the data from the estimation process, as required with the HRM. Frequency and spatial averaging were also addressed, and references were given which show that these two methods are roughly

equivalent. Frequency averaging decreases the number of measurements required for accurate

evaluations and uses a given bandwidth more effectively than time smoothing or the HRM.

The combination of frequency averaging and the HRM could perhaps be combined to

provide better estimates of the decay time. The smoothing of frequency-averaged results could be

further enhanced by the IIRM without loss of frequency resolution. We are examining the

optimal values for the combination of window width A^ and averaging bandwidth, and will present

results in a future report.

The test method can be extended to higher frequencies by using components which

operate in the frequency band of interest, that is, high frequency antennas and a higher bandwidth

impulse generator. The drawbacks of performing a high-frequency analysis of chambers using this

test method are increased data requirements and lower sensitivity. The fact that higher

frequencies are being generated and analyzed requires higher oscilloscope sample rates, which

translates to more data. Increasing the bandwidth to 10 GHz results in a tenfold increase in the

amount of data. Lower sensitivity results from the limited availability of high-speed highamplitude impulse generators. Broad bandwidth generally implies low spectral energy content

within any given passband, and measurements beyond approximately 10 GHz are not currently

feasible given our existing measurement capabilities. Given the promising nature of transient

measurement techniques, other related time-domain methods are being developed to overcome

these difficuhies.

17
Several recommendations which would improve the reliability of the measurements can be

made. To improve the accuracy of our estimate of Q, it is important to reduce o,. Careful

examination of eq (18) demonstrates the effect of changing any of the major parameters. The

values of F( ^Z)) change very slowly for decays of D greater than 20 dB, thus the variance is 10

dominated by the cubic term, and the best way to reduce the variance is to increase the

measurement time. Unfortunately, the exponential decay of the signal means that sensitivity of the

system decreases as we observe events farther away from the original impulse. If the oscilloscope

is well calibrated, it may be possible to increase the sensitivity or averaging factor for later records

and still be able to accurately recombine the records, but a thorough system analysis would be

needed before the results could be considered reliable. Through the course ofthis investigation, other questions which we hope to answer in the

near fijture were raised. The effect of antenna type used in the measurements needs to be

evaluated to see if commercially available antennas can be used instead of custom-made TEM

horn antennas. This would make the technique more practical for industrial use and allow

measurement of smaller facilities which are unable to hold a 1.2 m antenna.

The effect of absorbing material placed inside the chamber must also be evaluated. It is

possible that this could result in nonlinear decay characteristics, as seen in acoustical

measurements [22], or decay times that are too short to measure accurately. If the technique is

applicable in loaded cavities, it may be possible to apply it to measurements such as aircraft

immunity [21] and other high-cost applications.

This measurement technique has shown substantial advantages over the traditional

methods for low-frequency analysis of reverberation chambers. The fact that these measurements

can be performed without a mechanical stirrer or paddle means that a cavity can be evaluated

before a mechanical stirrer is installed. By comparing the results before and after the installation

of a mechanical stirrer, we can measure any degradation caused by the installation. Similarly, we

can evaluate the effect of any change to the chamber, such as placing a test device or additional

antennas into the chamber, as it is made. The effect of using a metallized paint or adding a zinc

coating to walls can be easily measured before the work is completed, possibly saving time, effort,

and money.

18
6. References

[I] Crawford, M.L.; Koepke, G.H. Design, evaluation, and use of a reverberation chamber

for performing electromagnetic susceptibility/vulnerability measurements. Nat. Bur.

Stand. (U.S.) Tech. Note 1092; 1986 April. 139 p.

[2] Hatfield, M.O.; Bean, J.L.; Freyer, G.J.; Johnson, D.M. Repeatability of mode-stirred

chamber measurements. Proc. IEEE Intl. Symp. on EMC: 485-490; 1994.

[3] Hill, D.A.; Camell, D.G.; Cavcey, K.H.; Koepke, G.H. Radiated emissions and immunity

of microstrip transmission lines: theory and measurements. Natl. Inst. Stand. Technol.

Tech. Note 1377; 1995 June. 32 p.

[4] Page, J. Stirred mode reverberation chambers for EMC emission measurements and radio

type approvals or organised chaos. EEE Intl. Conf on Electromagnetic Compatibility:

313-320; 1994.

[5] Corona, P.; Latmiral, G.; Paolini, E. Performance and analysis of a reverberating enclosure

with variable geometry. IEEE Trans. Electromag. Compat., EMC-22: 2-5; 1980.

[6] Hill, D.A. Electronic mode stirring for reverberation chambers. IEEE Trans. Electromag.

Compat., EMC-36: 294-299; 1994.

[7] Loughry, T. A. Frequency stirring: an alternative approach to mechanical mode-stirring

for the conduct of electromagnetic susceptibility testing. Phillips Laboratory, PL-TR—91-

1036; 1991.

[8] Pierce, AD. Acoustics - An Introduction to its Physical Principles and Applications.

New York: McGraw-Hill; 1981.

[9] Vorlander, M., Bietz, H. Comparison of methods for measuring reverberation time.

Acustica, 80: 205-215, 1994.

[10] Watson, R.B. The modulation of sound decay curves. J. Acous. Soc. Am. 18: 119-129;

1946.

[I I] Morse, P.M.; Bolt, R. H. Sound waves in rooms. Rev. Mod. Phys. 16: 69-150; 1944.

[12] Jackson, J.D. Classical Electrodynamics. New York: John Wiley & Sons, Inc.; 1975.

[13] Liu, B.H.; Chang, DC; Ma, M.T. Eigenmodes and the composite quality factor of a reverberating chamber. Nat. Bur. Stand. (U.S.) Tech. Note 1066, 1983 August. 46 p.

19
[14] HUl, DA.; Ma, M.T.; Ondrejka, A.R.; Riddle, B.F.; Crawford, M.T.; Johnk, R.T.

Aperture excitation of electrically large, lossy cavities. IEEE Trans. Electromag. Compat.

36: 169-178; 1994.

[15] Carin, L.; Felsen, L.B. Wave-oriented data processing for frequency- and time-domain

scattering by nonuniform truncated arrays. IEEE Antennas Propagat. 36: 29-43; 1994.

[16] Cohen, L. Time-frequency distributions—a review. Proc. IEEE, 77: 941-981; 1989.

[17] Lim, J.S.; Oppenheim, A.V. Advanced topics in signal processing. New Jersey: Prentice

Hall; 1988.

[18] Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; Vetterling, W.T. Numerical Recipes in C~

The art of scientific computing. New York: CambridgeUniversity Press; 1988.

[19] Schroeder, M.R. New method of measuring reverberation time. J. Acoust. Soc. Am. 37:

409-412, 1965.

[20] Davy, J.L. The variance of impulse decays. Acustica 44: 51-56, 1980.

[21] Johnk, R.T.; Ondrejka, A.R. Time-domain measurements of the reverberation

characteristics and shielding effectiveness of a small aircraft. URSI National Radio

Science Meeting: 127,1994.

[22] Knudsen, V.O.; Delsasso, L.P.; Leonard, R.W. Reverberation-room acoustics-effects of

various boundary conditions. J. Acoust. Soc. Am. 42: 953-965, 1967.

20
Paddle

ControllaReverberation

Chamber

Paddle

Transmitting

Antenna

Receiving

Antenna

ti&maicy

Synmesizei

Bi-directional

Coupler

Computer

Figure 1. Traditional measurement configuration.

21
Paddle

Controller

Reveri>eration *

Note: Paddle was removed

for our measurement

Transmitting

Antenna

Receiving

Antenna

Pulse

Generator

Sampling

Oscilloscope

Computer

Figure 2. Proposed NIST time-domain measurement configuration.

22
0.2

0.1

0)

O)

(0

0.0

-0.1

-0.2

owm^ wmii nid i ii I

2 3 4

Time (|us)

Figure 3. Sampled impulse response of NIST chamber.

23
%

o

Q-

>

'i—

a:

500 MHz

Manning Window

N=5000

12 3 4

Time (iis)

Figure 4. Effect of tapered window on processed results.

24
(D

I

Q.

I

(D

a:

500 MHz Manning Window

N=10 000

2 3

Time (|is)

Figure 5. Effect of window size on processed results.

25
o

Q-

>

(D

500 MHz N=500

Manning Window

Averaging Decay

Span Time

^ 100 ns 557 ns

10 ns 557 ns

ns 554 ns

Time (\is)

6

Figure 6. Time averaged results.

26
i

o

>

JO

3 GHz N=500

Manning Window

A=100ns

Time (^s)

Figure 7. Noise floor of the measurement system.

27
i

Q.

>

(D

a:

500 MHz N=500

Manning Window

Averaging Decay

Bandwidth Time

500 MHz 590 ns

250 MHz 561 ns

150 MHz 551ns

50 MHz 554 ns

2 3 4

Time (jis)

Figure 8. Results of frequency averaging with a short time window.

28
i

QI

500 MHz N=5000

Manning Window

Averaging Decay

Bandwidth Time

- 105 MHz 547 ns

55 MHz 569 ns

25 MHz 633 ns

5 MHz 646 ns

2 3 4

Time (ins)

Figure 9. Results of frequency averaging with a long time window.

29
i

o

CL

CD>

<D a:

500 MHz N=500

Manning Window

T=549 ns

2 3 4

Time (jus)

Figure 10. The Integrated Impulse Response Method (short time window).

30
§ - Ol

I

(D

500 MHz N=10 000

Manning Window

T=589 ns

2 3

Time (^s)

6

Figure 11. The Integrated Impulse Response Method (long time window).

31
800 -n

600

E

p 400

s

Q

200 —

N=500

Integrated Impulse Response Method

200 400 600 800

Frequency (MHz)

1000

Figure 12. Calculated decay times versus frequency.

32
100 000

10 000

%

(0

CO o

1000

100

200

Maximum Q (Traditional Method)

Average Q (Time-domain Method)

N=500

Integrated Impulse Response Method

400 600 800

Frequency (MHz)

1000

Figure 13. Comparison of Q estimates using traditional and time-domain methods.

33
%

o

CL

0)

>

JO

a:

T=373 ns Q=469

200 MHz N=500

Manning Window

T=586 ns Q=736

2 3 4

Time (^s)

Figure 14. Strange behavior at 200 MHz. (Multiple decay rates?)

34
10 000^

Average Q (Traditional Method)

CO U-

(0

O

1000

100

_L. Average Q (Time-domain Method)

with estimated uncertainty

N=500

200 400 600

Frequency (MHz)

800 1000

Figure 15. Estimated accuracy of time-domain Q measurement method.

35

r.S. GOVKRNMKNT PRINTING OFFICK I •t«-ft-77«-« 1 1'«00 I <



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