validation of a method for predicting anechoic chamber ... · 02.. 51mm# t 1 8 , are shown in table...

31IEEE AntEnnAs & ProPAgAtIon MAgAzInE a u g u s t 2 0 1 8 1045-9243/18©2018IEEE

Vince Rodriguez

Indoor antenna ranges must have the walls, floor, and ceiling treated with a radio-frequency (RF) absorber. The normal incidence performance of the absorber is usually provided by the manufacturer of the material—but the bistatic or off-angle performance must also be known. Recently, a polynomial approximation was introduced to predict the reflected energy from a pyramidal absorber.

In this article, these approximations were used to forecast the quiet zone (QZ) performance of several anechoic cham-bers. The predictions were compared with full-wave analyses performed in CST Suite. In addition to the comparison of the predictions with analyses that use a different numerical method, comparisons were made against actual measurements of the QZ effectiveness of anechoic chambers. Measurements taken per the free-space voltage standing wave ratio (VSWR) method were compared with the estimates that use the poly-nomials presented in [1]. The results show that the polynomial

approximations can be used to give a fairly accurate indication of the QZ performance of anechoic chambers.

RF ABSORBER APPROXIMATIONAn RF absorber is used in indoor ranges to reduce reflection from certain areas of the range to create a free-space condition for testing. The absorber’s pyramidal shape helps the electro-magnetic wave penetrate into the material, where it is trans-formed into thermal energy and dissipated. In most absorber applications in indoor ranges, it is important to know not only the material’s normal incidence reflectivity (where the absorber performance is optimized) but also the bistatic reflectivity for oblique angles of incidence. In [1], a polynomial approximation was developed to provide a prediction of the reflected signal from a pyramidal absorber of a given thickness t for a given angle of incidence .i The resulting polynomial has the follow-ing form:

,

R dB C t C t C t C tC t C t0 1 2

23

3

44

55

i i i

i i

= + + +

+ +

^ ^^

^^

^ ^h hh

hh

h h (1)

Digital Object Identifier 10.1109/MAP.2018.2839895Date of publication: 19 June 2018

Validation of a Method for Predicting Anechoic Chamber Performance

A technique that uses polynomial approximations for RF absorber reflectivity.

©istockphoto.com/max_xie

32 IEEE AntEnnAs & ProPAgAtIon MAgAzInE a u g u s t 2 0 1 8

where t is the electrical thickness (in terms of wavelengths) of the pyramids and i is the angle of incidence. By thickness of absorber or pyramid—the common usage in the anechoic range industry—we understand the height of the material applied to the interior surfaces of the range. The polynomial is valid for . t0 25 18# # and .0 85c c# #i The coefficients of the polynomial in (1) are a function of the thickness ,t which has no units, as it is the number of wavelengths at a given frequency. The coefficients’ values are given by another set of equations. The zeroth-order coefficient is given by the following expression:

. . .C t e54 98 55 21 .o t0 7744= - + -^ h (2)

This equation is an approximation of the normal incidence per-formance of the absorber, which is .0ci =

The rest of the coefficients in (1) were approximated by polynomials of a maximum seventh order. In general, the coef-ficients in (1) have the following form:

.

C A A t A t A t

A t A t A t A ton 1 2

23

3

44

55

66

77

= + + + +

+ + + + (3)

The choice of the seventh order may not be the best approach, as a high number of significant figures are required for the An values. However, it simplifies the overall set of

equations when compared with the approximation presented in [2]. Tables 1 and 2 show the values of the coefficients for the polynomials that describe the coefficients in (1). The values for the frequencies where the absorber material is between a quarter of a wavelength and 1.8 wavelengths, that is, for

. . ,t0 25 1 81#m m are shown in Table 1, while the coefficients for t2 181 #m m are found in Table 2.

From these equations, a set of curves can be obtained to show the reflectivity of the absorber in decibels versus the angle for different absorber thicknesses (Figure 1). Using (1)–(3), together with the geometry of the chamber and knowledge of the radiation pattern of the illuminating antenna, it is possible to estimate the highest level of reflected energy arriving in the QZ. That is known as the QZ level and indicates the quality of the chamber and provides an estimate of the expected measure-ment errors.

SIMPLIFIED RAY-TRACING APPROACHThe presented approach is intended for rectangular anechoic chambers. As will be shown, the approach is valid not only for far-field measurement ranges but also for near-field and com-pact ranges. The necessary input parameters are the internal size of the anechoic chamber (its length, width, and height); the thickness of the absorber used on the side walls, floor, ceiling,

TABLE 1. THE COEFFICIENTS FOR (4): 0.25λ ≤ t ≤ 1.8λ.C1 C2 C3 C4 C5

A0 −6.32E+00 7.69E−01 −2.69E−02 3.51E−04 −1.55E−06

A1 7.23E+01 −8.66E+00 3.02E−01 −3.94E−03 1.74E−05

A2 −3.23E+02 3.84E+01 −1.33E+00 1.74E−02 −7.71E−05

A3 7.31E+02 −8.67E+01 3E+00 −3.92E−02 1.74E−04

A4 −9.18E+02 1.09E+02 −3.76E+00 4.92E−02 −2.19E−04

A5 6.42E+02 −7.63E+01 2.63E+00 −3.44E−02 1.54E−04

A6 −2.34E+02 2.78E+01 −9.58E−01 1.26E−02 −5.62E−05

A7 3.43E+01 −4.10E+00 1.41E−01 −1.85E−03 8.30E−06

TABLE 2. THE COEFFICIENTS FOR (4): 2λ < t < 18λ.C1 C2 C3 C4 C5

A0 −1.39E+00 2.03E−02 7.63E−04 −2.42E−05 1.63E−07

A1 3.07E+00 −2.45E−01 7.31E−03 −8.18E−05 3.08E−07

A2 −1.23E+00 1.17E−01 −3.86E−03 4.79E−05 −2.01E−07

A3 1.77E−01 −1.86E−02 6.46E−04 −8.34E−06 3.61E−08

A4 −1E−02 1.23E−03 −4.53E−05 5.99E−07 −2.62E−09

A5 4.92E−05 −2.29E−05 1.05E−06 −1.46E−08 6.34E−11

A6 1.51E−05 −8.66E−07 2.01E−08 −2.36E−10 1.10E−12

A7 −3.96E−07 3.08E−08 −9.25E−10 1.18E−11 −5.35E−14

33IEEE AntEnnAs & ProPAgAtIon MAgAzInE a u g u s t 2 0 1 8

and end wall; and the size of the QZ and the distance from its center to the source antenna.

There are some recommended rules for sizing a rectangular anechoic chamber. Some of these are given in [2]–[4]. A typi-cal rectangular anechoic chamber is depicted in Figure 2. The chamber has an internal length L and height .H The internal width W of the chamber is usually the same as the height, but this is not always the case, as discussed in [2] and [4].

A simple model can be made in which only the first-order reflections are considered. This is quite basic, but the goal is to achieve a simplified approach to estimate the performance of an anechoic chamber. The first-order reflections will be the energy reflected from the end wall behind the QZ and the reflections from the specular point on the side walls, ceiling, and floor. It is assumed that the source antenna has a front-to-back ratio high enough so that the absorber on the end wall behind the source will reflect a level much lower than the other reflections.

From the chamber’s dimensions, the angle of incidence onto the absorber on the ceiling, floor, and side walls can be calcu-lated using basic trigonometry. This angle i is the one used in (1) to estimate the reflected energy. For the end wall behind the QZ, (2) provides the level of energy reflected. It should be noted that this approach does not take into account the size of the QZ. A more rigorous approach would be to check the angle of inci-dence onto the absorber treatment for rays that go to the edges of the QZ, as shown in Figure 3. The angle of incidence for the ray incident on the center of the QZ is given by

,tan H t2

2PL

1i =-

- f p (4)

while for the ray incident on the top of the QZ, the angle of inci-dence is given by

.tanH t2 2

QZPL

top1i =

- -

-

f p (5)

For the ray incident on the bottom of the QZ, as shown in Fig-ure 3, the angle of incidence is given by

.tanH t2 2

QZPL

bottom1i =

- +

-

f p (6)

Notice that, if the QZ diameter is much smaller than the size of the range, the angles are quite close in value. Using (4) provides one with an average of the angles of incidence.

Another factor determining the level of reflected energy entering the QZ is related to the level of energy incident on the side walls compared to the direct path between the source antenna and the QZ. Figure 3 shows that the level of the field toward the specular point is about 5 dB lower than the level of the direct ray to the QZ.

The final factor is the additional path loss as the waves propagate. The difference between the reflected path and the

direct path will add some losses to the absorber reflectivity and the source radiation pattern difference. The path difference given by the QZ location versus the back wall is given by the distance S in Figure 3. It should be noted that, when modeling compact ranges using this approach, the plane wave created by the compact range reflector will not attenuate as it propagates along the axis of the chamber.

COMPARISON WITH FULL-WAVE MODELSIn the previous section, an extremely simple approach for modeling a rectangular anechoic range was presented. How good is this model? Is it good enough for estimating the per-formance of an anechoic range? To answer these questions, two rectangular ranges were modeled using this methodology, and the performance was compared to the computations from

0–5

–10–15–20–25–30–35–40–45–50–55–60

Ref

lect

ivity

(dB

)

0 5 10 15 2025 3035 4045 50 55 60 65 70 75 80 85Angle of Incidence (°)

0.25 λ0.3 λ0.4 λ0.5 λ0.6 λ0.7 λ

0.8 λ0.9 λ1.0 λ1.2 λ1.4 λ1.5 λ

1.6 λ1.8 λ2.0 λ2.5 λ3.0 λ3.5 λ

4.0 λ4.5 λ5.0 λ5.5 λ6.0 λ7.0 λ

8.0 λ9.0 λ10.0 λ15.0 λ

Computed Data (Forced to Have a Minimum of –55 dB)and Polynomial Curve Fit

FIGURE 1. Some plots from (1) of the reflectivity of the RF absorber.

H PL

S

t

QZ

θφ

L

FIGURE 2. The geometry of a rectangular anechoic range. :PL path length.


a full-wave model. CST was chosen to model the chambers. This is not such an efficient method, as the required computer resources limit the highest frequency that can be computed for a given range.

A 400-MHz SPHERICAL NEAR-FIELD RANGEFor a spherical near-field range, a chamber with inside dimen-sions of 10.40 m wide by 11.78 m long and 12.8 m high was chosen. The QZ was 3.66 m in diameter. The distance from the center of the QZ to the open-ended waveguide (OEWG) source antenna was 4.57 m. The side walls were treated with absorber 1.22 m (48 in) in thickness, with the rest of the surfaces covered with absorbing material 0.9 m (36 in) thick. The angle of inci-dence onto the walls was 33° and 24.4° for the ceiling and floor (see Table 3).

The effects of the illuminating OEWG were approximately −2 dB to −5 dB lower than the direct path. The levels depended on the polarization. Figure 4 shows the pattern for a typi-cal OEWG at the lowest, middle, and highest frequencies of operation. For analysis, we can use the highest level of −2 dB. If we add the additional path loss, we end up with a highest reflectivity level of −44 dB, equivalent to an amplitude ripple of ±0.057 dB (see Table 4).

The chamber model was built within CST. The absorber material properties were the same as those used in [1]. Fig-ure 5 shows the chamber model, including the location of the QZ at the center of the apparatus. The chamber was analyzed at 400 MHz, and the field distribution was obtained at two orthogonal planes. The planes cut the chamber in half in the vertical and the horizontal planes. In Figure 6, the horizontal plane is shown for the vertical and horizontal polarization of the source antenna.

90OEWG Pattern

80 7060

5040

30

20

10

–10

–20

–30

–40–50

–60

–80 –70–90–100–110

–120–130

–140

–150

–160

–170

180

170

100

0–12–10 –8 –6 –4 –2

H-Plane CenterE-Plane CenterH-Plane LowE-Plane LowH-Plane HighE-Plane High

FIGURE 4. The typical patterns for an OEWG. Note that the level illuminating the side walls, ceiling, and floor can be between −2 and −9 dB depending on the orientation of the probe.

–90 –75–60

–45

–30

–15

0–5–1

0–1

5–2

0–2

5

15

30

4560

7590105120

135

150

165

180

–165

–150

–135–120

–105

φ

θ

PL QZ

S

t

L

H-PlaneE-Plane

Antenna Pattern

FIGURE 3. A pattern of the source antenna superimposed on the chamber diagram, showing that the level of energy toward the specular point is lower than the level of the direct ray along the PL.

TABLE 3. THE REFLECTIVITY OF THE ABSORBER PER (1).

Thickness θ = 0° θ = 24.4° θ = 33°

.t 1 22m= −34 −35 −32

.t 1 63m= −39 −40 −39


From the data, we can arrive at the field distribution in the QZ and along the three main axes of the sphere: the longitudi-nal, the horizontal transverse, and the vertical transverse. The data can then be fitted with a second-order polynomial, and the ripple riding on that polynomial can be determined. From the ripple, the reflectivity in the QZ can be estimated.

In Figure 7, the ripple for a longitudinal scan of the QZ is shown. A similar plot can be produced choosing the transverse

0

–3

–6

–9

–12

–15

–18

–15–10

–50

510

1515 10

5 0–5 –10

–15

x (ft)

y (ft)

y (f

t)

E-F

ield

(dB

)

0

–3

–6

–9

–12

–15

–18

–15–10

–50

510

1515 10

5 0–5 –10

–15

x (ft)

x (ft)

y (ft)

E-F

ield

(dB

)

0–0.5

–1.5

–2.5–2

–3.5–3

–4.5–4

–5

–1

–5–5.5

–6.5

–7.5–7

–8.5–8

–9.5–9

≤ –10

≥ –1.4–1.44–1.48–1.52–1.56–1.6–1.64–1.68–1.72–1.76≤ –1.8

–6

181614121086420

–2–4–6–8

–10–12–14–16–18

–18

–16

–14

–12

–10 –8 –6 –4 –2 0 2 4 6 8 10 12 14 16 18

y (f

t)

x (ft)

181614121086420

–2–4–6–8

–10–12–14–16–18

–18

–16

–14

–12

–10 –8 –6 –4 –2 0 2 4 6 8 10 12 14 16 18

–1.48

–1.7

2

–1.7

2

–1.76–1.8 –1.56 –

1.6–1.44 –1.48–1.72

–1.68–1.8

–1.7

6

–1.6

4

–1.6

–1.56

–1.72

–1.76

–1.8

–1.52–1.48

–1.6

–1.64–1.68

–1.56–1.52

–1.4

8

–1.64

–1.68

–1.44

–1.52 –1.8

–1.76

–1.44–1.52 –1.56

–1.6

–1.64

–1.8

–1.4

4

–1.44

–1.43

–1.56

–1.52–1.56

–1.6

–1.64

–1.68

–1.72

–1.76

–1.8

–1.72

–1.76–1.68

–1.64

–1.6

–1.48 –1

.52

–1.68

(a) (b)

FIGURE 6. The field distribution at 400 MHz inside the chamber for the two principal polarizations: (a) horizontal (z polarized) and (b) vertical (i polarized).

y

z

x

FIGURE 5. The chamber model with one wall removed for clarity. The transparent sphere is the QZ. To the left of the sphere is the OEWG.

TABLE 4. THE REFLECTIVITY AT 400 MHz.

Frequency (GHz)

Source Antenna Directivity (dB)

QZ Level (dB)

Amplitude Ripple (dB)

0.4 GHz 8 dB −44 ±0.057 dB


axis of the QZ on the horizontal plane. Figure 8 shows the plot with the ripple riding on the second-order polynomial fit. While the longitudinal plot showed a largest ripple of 0.055 dB peak to peak for the vertically polarized field, the transverse horizontal scan shows a much smaller 0.025-dB peak to peak for the vertically polarized OEWG. The vertical transverse scans shown in Figure 9 show a rip-ple of 0.026 dB.

The ripples for the horizontally polarized OEWG were all much smaller for the scans on the horizontal planes. For the vertical scans, the horizontally polarized OEWG showed the larger ripple. In the horizontal scans of the QZ, the ripple is mainly from the side walls. The lateral walls are treated with thicker absorber, and, with the OEWG vertically polarized, there is a higher level of energy illuminating the side walls, but it is attenu-ated. Figure 6 shows this effect. When the scan is vertical, the floor and the ceiling are the contributing reflectors. The hori-zontally polarized OEWG sends less energy to the ceiling and floor versus the vertically polarized OEWG.

From the ripple levels taken from the transverse scans in Figures 8 and 9, the reflectivity on the QZ could be estimated to be about −51 dB. The longitudinal scan in Figure 7 shows a larger ripple of ±0.055 dB, equivalent to a reflectivity of −44 dB. This maximum value of the reflectivity at the QZ is the same

that was predicted by the simple ray tracing of the predictions using (1) that are shown in Table 4.

A 700-MHz LARGE INDOOR FAR-FIELD RANGEFor the far-field range, a chamber with inside dimensions of 12 m wide by 22 m long with a height of 12 m was chosen. The chamber was ana-lyzed assuming a standard gain horn (SGH) as the source antenna. The range geometry is as follows: there is 1-m-thick absorber on the receiv-er end wall. On the two lateral

walls, 1.5-m-thick absorber was used. The same absorber was used on the floor and ceiling. The QZ diameter was 2 m, and the QZ was placed 3 m from the end wall. The PL was set to 18.5 m, and the frequency to be analyzed was 700 MHz. The angle of incidence onto the side wall, floor, and ceiling absorber was 64°. A reflectivity of −21.41 dB is given by (1), with the additional path loss of 0.8 dB for the reflected path. For the back wall, (2) gives us a −44-dB level, with an additional 2 dB of path loss. The nominal 15.5-dB SGH, a model MI-210-0.49, has a directivity of 16.8 dB at 700 MHz, and it reduces the energy illuminating the side walls by approximately −12 dB for both planes. Following the analysis described in the previous section, the estimated, expected levels are noted in Table 5.

Figure 10 shows the chamber model for the full-wave analysis. The figure depicts a view of the model with one wall

Computed Results Horizontal PolarizationSecond-Order Polynomial FitComputed Results Vertical PolarizationSecond-Order Polynomial Fit

–1.2

–1.25

–1.3

–1.35

–1.4

–1.45

–1.5

–1.55

–1.6–1.65

–1.7

–1.75

–1.8

–1.85

–1.9–6 –5 –4 –3 –2 –1 0 1 2

y (ft)

E-F

ield

(dB

)

3 4 5 6

Ripple ≈ 0.055 dB(Peak to Peak)

FIGURE 7. A longitudinal scan at 400 MHz.

–1.4

–1.45

–1.5

–1.55

–1.6

–1.65

–1.7

–1.75

–1.8–6 –4 –2 0 2

x (ft)

E-F

ield

(dB

)

4 6


Ripple ≈ 0.025 dB(Peak to Peak)

FIGURE 8. A transverse horizontal scan at 400 MHz.

Comparisons with measured performance also showed the approach to be valid in predicting the performance of rectangular anechoic chambers.


removed for clarity. Two views are shown: one looking toward the QZ and another toward the SGH that illuminates the cham-ber. Notice that the model shows flat absorber behind the QZ on the floor, ceiling, and side walls, and that there has been no spe-cial treatment on the edges of the anechoic room, which are exposed bare metal.

The chamber was analyzed and the field distribution obtained at 700 MHz in the two orthog-onal planes of symmetry of the anechoic chamber. Figure 11 shows the field distribution in the anechoic chamber in these two planes. The typical pattern of the SGH is evident in these distributions.

As was done for the near-field range analyzed in the sec-tion “A 400-MHz Spherical Near-Field Range,” the field along the three main axes of the spherical QZ was plotted and a second-order polynomial fit obtained. The ripple rid-ing on the second-order approximation was calculated, and from it the reflectivity of the QZ was obtained. Figure 12 shows the longitudinal scan of the QZ, with a 0.22-dB peak-to-peak ripple equivalent to a −38-dB level.

Figure 13 shows the transverse scan along the vertical axis of the QZ. The ripple is 0.26 dB peak to peak, which is equivalent to a −36.4-dB reflectivity. The trans-verse scan along the horizontal axis shows a similar peak-to-peak ripple of 0.2 dB, which is equivalent to a reflectivity of −39 dB. The data are shown in Figure 14, indicat-ing that the highest reflectivity is in the −36.4-dB range. This value is

extremely close to the analysis based on (1), which estimated a reflectivity level of −34.21 dB.

COMPARISON WITH MEASUREMENTSTo further verify the analysis approach introduced in the “Sim-plified Ray-Tracing Approach” section, an existing chamber was analyzed, and the results of the analysis were compared with measurements done per the free-space VSWR method in [5]. The anechoic chamber was 18 m long by 11.5 m wide and 11.5 m in height. The QZ was a 1-m-diameter sphere. The PL was 12 m. All surfaces were treated with pyramids that were 1.82 m (72 in) long, except for the wall behind the source antenna, which was treated with pyramids 1.22 m (48 in) long. The chamber was

(a)

(b)

FIGURE 10. A model of the large far-field chamber: views toward (a) the QZ and (b) the SGH that illuminates the chamber.

TABLE 5. THE QZ LEVELS PER THE SIMPLIFIED MODEL.

Frequency (GHz)

Source Antenna Directivity (dB)

QZ Level (dB)

Amplitude Ripple (dB)

0.70 15.5 −34.21 ±0.17

–1.4

–1.45

–1.5

–1.55

–1.6

–1.65

–1.7

–1.75

–1.8–6 –4 –2 0 2

z (ft)

E-F

ield

(dB

)

4 6


Ripple ≈ 0.026 dB (Peak to Peak)

FIGURE 9. A transverse vertical scan at 400 MHz.

The results further validated the use of the equations introduced in [1] for the prediction of pyramidal absorber reflectivity.


measured at 100 MHz, 400 MHz, 4 GHz, and 12 GHz. An Elec-tro-Metrics Biconical-Log Hybrid model EM-6917-1 was used to illuminate the chamber from 100 MHz to 1 GHz. A Scientific Atlanta SA-12-3.9 SGH was used for the 4-GHz measurement, and an SA-12-12 SGH was used for the 12-GHz measurement. Table 6 shows the manufacturers’ gain specifications for these antennas at the frequencies of the measurements.

The antenna pattern was estimated assuming a square aperture with a TE01 illumination using the equations for TE01 apertures shown in [6]. The size of the aperture was adjusted to provide a pattern with the same directivity as the

antenna gain indicated by the manufacturer. The estimated patterns are shown in Figure 15, and they add a level of uncer-tainty to the QZ level estimate. This is especially the case for 100 and 400 MHz since the actual directivity of the antenna is not known. Based on the geometry, the absorber thickness, and the estimated patterns, the reflectivity levels in Table 7 were computed using simple ray tracing and (1).

The chamber was measured per the free-space VSWR meth-od, so the QZ was scanned in the horizontal plane along the lon-gitudinal and transverse axes with the probe antenna oriented at different angles. The ripple patterns obtained were used to obtain

240

192

144

96

48

–48

–96

–144

–192

–240–408 –360 –312 –264 –216 –168 –120 –72 –24 24 72 120 168 216 264 312 360 408

0

Length of Chamber (in)

Horizontal Plane (Vertically Polarized Horn)W

idth

of C

ham

ber

(in)

≥ –30–31–32–33–34–35–36–37–38–39–40–41–42–43–44–45–46–47–48–49

240

192

144

96

48

–48

–96

–144

–192

–240–408 –360 –312 –264 –216 –168 –120 –72 –24 24 72 120 168 216 264 312 360 408

0

Length of Chamber (in)

(a)

(b)

Vertical Plane (Vertically Polarized Horn)

Hei

ght o

f Cha

mbe

r (in

)

≥ –30–31–32–33–34–35–36–37–38–39–40–41–42–43–44–45–46–47–48–49

50 –41 –42

–44 –49

–46 –43

–45–4

4 –43

–45

–41

–35 –37–31

–47

–33 –46

–49

–48

–42

–44

–50

–34–36

–38

–45

–31 –32

–39–40

–49

–41

–47–48–50–46–48 –47

–37 –38

–35

–32–31

–33

–34

–35

–37

–40

–36

–38

–43

–39

–39

–42

–40

–36

–33–34

–46 –41 –44 –43 –48

–47

–49

–44

–48 –50

–39

–35

–34–37

–47

–45

–44

–36

–32

–31–33–32

–38

–42

–46

–49–45–47

–37–35

–40

–41

–50

–45

–36

–35

–34 –33

–31–32

–40–38

–41

–43

–48–50–3

9 –49

–46

–42

–36–33–34

–39–37–38–42

–43

–40

FIGURE 11. The field distributions at 700 MHz in the large far-field range in the (a) horizontal and (b) vertical planes. Note the SGH pattern of the source antenna.


the reflectivity of the QZ, as described in [7]. Figure 16 shows some pictures of the measurement of the anechoic chamber.

Table 8 presents the measured levels for the anechoic chamber per the free-space VSWR approach. These results show excellent agreement with the predictions from the meth-od that uses (1). The biggest disagreement is at 100 MHz. It should be noted that there are some issues with the method presented in [5], as was recently reported in [8]. In this par-ticular case, the QZ was 1 m in diameter. Hence, at 100 MHz, the QZ was / .3m This seems to be too small to be able to measure a full cycle of the ripple because of reflected energy. Thus, the measured data may lack a peak or a valley of the ripple or possibly both. The effect when analyzing the measured

Computed FieldSecond-Order Polynomial Fit

–33.4

–33.6

–33.8

–34

–34.2

–34.4

–34.6

–34.8–350 –340 –330 –320 –310 –300 –290 –280 –270

Longitudinal Axis of Chamber (in)

Ele

ctric

Fie

ld M

agni

tude

(dB

Rel

ativ

e to

Hig

hest

Lev

el in

Cha

mbe

r)

0.22 dB (Peak to Peak)

FIGURE 12. A longitudinal scan of the 2-m QZ for the large far-field range at 700 MHz.


–33.6–33.65

–33.75–33.7

–33.8–33.85

–33.95–33.9

–34–34.05

–34.15–34.1

–34.2–34.25

–34.35–34.3

–34.4–34.45

–34.55–34.5

–34.6

–40

–34

–28

–22

–16

–10 –4 2 8 14 20 26 3832

Location Along the QZ (in)

Fie

ld M

agni

tude

(dB

Rel

ated

to H

ighe

st L

evel

in C

ham

ber)


FIGURE 13. A transverse scan (along the vertical axis) of the 2-m QZ for the large far-field range at 700 MHz.


–33.6–33.65

–33.75–33.7

–33.8–33.85

–33.95–33.9

–34–34.05

–34.15–34.1

–34.2–34.25

–34.35–34.3

–34.4–34.45

–34.55–34.5

–34.6–40 –32 –24 –16 –8 0 8 16 24 4032

Location Along the QZ (in)

Fie

ld M

agni

tude

(dB

Rel

ated

to H

ighe

st L

evel

in C

ham

ber)


FIGURE 14. A transverse scan (along the horizontal axis) of the 2-m QZ for the large far-field range at 700 MHz.

0

–5

–10

–15

–20

–25

–30

Nor

mal

ized

Pat

tern

(dB

)

–35

–40

–450 10 20 30 40 50 60 70 80 90

θ (°)

Maximum of E- and H-Planes 1-dB DirectivityMaximum of E- and H-Planes 6-dB DirectivityMaximum of E- and H-Planes 18-dB DirectivityMaximum of E- and H-Planes 24.7-dB Directivity

FIGURE 15. The assumed patterns used for the analysis of the measured chamber.

TABLE 6. THE SOURCE ANTENNA GAIN.

Antenna Frequency Nominal Gain

EM-6917-1 100 MHz 1 dBEM-6917-1 400 MHz 6 dBSA-12-3.9 4 GHz 18 dBSA-12-12 12 GHz 24.7 dB


data is that a smaller ripple may be assumed, so the measured reflectivity may be lower than the actual reflectivity. At the other measured frequencies, where the QZ is larger in terms of the number of wavelengths, the results were very close, given the approximation used for the source antenna pattern.

CONCLUSIONSThe results presented show that the simplified ray-tracing approach together with the equations introduced in [1] provide a good approach to estimating the performance of an anechoic chamber. This approach was validated by comparing it to esti-mates from full-wave analysis performed using commercially available packages. Comparisons with measured performance also showed the approach to be valid in predicting the perfor-mance of rectangular anechoic chambers. The results further validated the use of the equations introduced in [1] for the pre-diction of pyramidal absorber reflectivity.

AUTHOR INFORMATIONVince Rodriguez ([email protected]) is with NSI-MI Technologies, Suwanee, Georgia. His research interests include

anechoic range design and the applications of numerical tech-niques to antenna measurements.

REFERENCES[1] V. Rodriguez and E. Barry, “A polynomial approximation for the prediction reflected energy from pyramidal RF absorbers,” in Proc. 38th Annu. Symp. Antenna Measurement Techniques Association, Oct. 2016, pp. 155–160.[2] V. Rodriguez, “Basic rules for anechoic chamber design, Part 1: RF absorber approximations,” Microw. J., vol. 59, no. 1, pp. 72–86, 2016.[3] L. Hemming, Electromagnetic Anechoic Chambers: A Fundamental Design and Specification Guide. Piscataway, NJ: IEEE Press, 2002.[4] V. Rodriguez, “Basic rules for anechoic chamber design, Part 2: Com-pact ranges and near field measurements,” Microw. J., vol. 59, no. 2, pp. 80–90, 2016.[5] R. E. Hiatt, E. F. Knott, and T. B. Senior, “A study of VHF absorbers and anechoic rooms,” Univ. Mich., Ann Arbor, MI, Rep. 5391-1-F, Feb 1963.[6] W. Stutzman and G. Thiele, Antenna Theory and Design, 2nd ed. New York: Wiley, 1998.[7] B. Tian, “Free space VSWR method for anechoic chamber electromagnetic evaluation,” in Proc. 30th Annu. Symp. Antenna Measurement Techniques Asso-ciation, Nov. 2008, pp. 524–529.[8] Z. Chen, Z. Xiong, and A. Enayati, “Limitations of the free space VSWR measurements for chamber validation,” in Proc. 38th Annu. Symp. Antenna Measurement Techniques Association, Oct. 2016, pp. 144–148.

(a) (b)

FIGURE 16. Two pictures of the testing of the chamber. (a) A large Yagi is used to scan the QZ at 100 MHz, seen from the side wall of the chamber. (b) A horn is used to scan at 12 GHz, as seen from the source wall.

TABLE 7. THE PREDICTED REFLECTIVITY.

FrequencyQZ Reflectivity

Amplitude Ripple

100 MHz −11 dB ±2.84 dB400 MHz −27 dB ±0.38 dB4 GHz −55 dB ±0.02 dB12 GHz −55 dB ±0.02 dB

TABLE 8. THE MEASURED REFLECTIVITY.

FrequencyMeasured QZ Reflectivity

Predicted QZ Reflectivity

100 MHz −16.79 dB −11 dB400 MHz −30.88 dB −27 dB4 GHz −57.63 dB −55 dB12 GHz −52.62 dB −55 dB

validation of a method for predicting anechoic chamber ... · 02.. 51mm# t 1 8 , are shown in table...

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