View source for V&V Article 3: Modeling Broadband And Circularly Polarized Patch Antennas Using EM.Picasso

{{projectinfo|V&V|Modeling Broadband And Circularly Polarized Patch Antennas Using EM.Picasso|ART UWB title.png|In this article, a number of wideband and circularly polarized patch antenna designs are simulated in EM.Picasso, and the results are validated by the published data.|
*[[EM.Picasso]]
*Patch Antenna 
*Wideband Design
*Return Loss
*Voltage Standing Wave Ratio (VSWR)
*Circular Polarization (CP)
*Axial Ratio
|All versions| None }}

== Introduction ==

In this verification & validation (V&V) article, we will model a number of broadband patch antenna designs with both linear and circular polarization characteristics using [[EM.Cube]]'s Planar Module, also known as [[EM.Picasso]]. We will compare the simulation results with the published measured data.

==U-Slot Patch Antenna On Foam Substrate ==

The first broadband antenna design to be simulated is a probe-fed, rectangular patch on a thick foam substrate with a cut-out U-slot on it. The permittivity of the foam can be approximate to be equal to 1, i.e. equivalent to a grounded air substrate. The following table shows the substrate properties as well as the geometrical dimensions of the U-Slot patch antenna:

{| class="wikitable"
|-
! scope="col"| Parameter Name
! scope="col"| Value
! scope="col"| Units
|-
| Foam layer height (h<sub>1</sub>)
| 5
| mm 
|-
| Foam permittivity (&epsilon;<sub>r1</sub>)
| 1
| - 
|-
| Foam loss tangent (tan&delta;<sub>1</sub> @ 10GHz)
| 0
| - 
|-
| X
| 36
| mm 
|-
| Y
| 26
| mm 
|-
| F
| 13
| mm 
|-
| L<sub>x</sub>
| 12
| mm 
|-
| L<sub>y</sub>
| 20
| mm 
|-
| W<sub>x</sub>
| 2
| mm 
|-
| W<sub>y</sub>
| 2
| mm 
|-
| b
| 4
| mm 
|-
| r
| 0.65
| mm 
|}

<table>
<tr>
<td>
[[Image:ART UWB1.png|thumb|left|360px|Figure 1: Geometry of U-slot patch antenna on a foam substrate.]]
</td>
</tr>
</table>

In [[EM.Picasso]], the probe feed of the patch is modeled using a probe feed placed on a vertical PEC via of radius 0.6mm. For the planar MoM simulation, a center frequency of 4GHz and a frequency bandwidth of 4GHz were assumed, defining the range [2GHz &ndash; 6GHz]. Figure 2 shows the planar structure setup in [[EM.Picasso]].

<table>
<tr>
<td>
[[Image:ART UWB3.png|thumb|left|480px|Figure 2: The planar structure setup for the U-slot patch antenna in EM.Picasso.]]
</td>
</tr>
</table>

Figure 3 compares the real and imaginary parts of the input impedance of the patch antenna as simulated by [[EM.Picasso]] and the measured data presented by Ref. [1]. Figure 4 shows the simulated voltage standing wave ratio of the U-slot patch antenna as compared with the measured data given by the same reference.

<table>
<tr>
<td>
[[Image:ART UWB4.png|thumb|left|550px|Figure 3: Input impedance of the U-slot patch antenna over the range [2GHz – 6GHz]. Solid red line: EM.Picasso results for input resistance, solid blue line: EM.Picasso results for input reactance, orange symbols: measured input resistance presented by Ref. [1], and turquoise symbols: measured input reactance presented by Ref. [1].]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB5.png|thumb|left|550px|Figure 4: Voltage standing wave ratio (VSWR) of the U-slot patch antenna over the range [3.5GHz – 5.5GHz]. Solid line: EM.Picasso results, and symbols: measured data presented by Ref. [1].]]
</td>
</tr>
</table>

Figures 5 and 6 show the radiation pattern cuts at the YZ plane (E-Plane) and ZX plane (H-Plane), respectively. Figure 6 shows both co-polarized and cross-polarized components of the far field. Figures 5 and 6 also compare [[EM.Picasso]]'s results with the measured radiation pattern data presented by Ref. [1].

<table>
<tr>
<td>
[[Image:ART UWB7.png|thumb|left|480px|Figure 5: 2D E-plane radiation pattern of the U-slot patch antenna at f = 4.28GHz. Solid red line: EM.Picasso results, and magenta symbols: measured data presented by Ref. [1].]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB8.png|thumb|left|480px|Figure 6: 2D H-plane radiation pattern of U-slot patch at 4.28GHz. Solid blue line: EM.Picasso results for co-polarized far field component, solid red line: EM.Picasso results for cross-polarized far field component, turquoise symbols: Ref. [1] measured results for co-polarized far field component, and magenta symbols: Ref. [1] measured results for cross-polarized far field component.]]
</td>
</tr>
</table>

== Double U-Slot Patch Antenna On Foam Substrate ==

The next broadband antenna design to be simulated is a probe-fed, rectangular patch on a thick foam substrate with a cut-out double U-slot on it as shown in Figure 7. The following table shows the substrate properties as well as the geometrical dimensions of the double U-Slot patch antenna:

{| class="wikitable"
|-
! scope="col"| Parameter Name
! scope="col"| Value
! scope="col"| Units
|-
| Foam layer height (h<sub>1</sub>)
| 16.5
| mm 
|-
| Foam permittivity (&epsilon;<sub>r1</sub>)
| 1
| - 
|-
| Foam loss tangent (tan&delta;<sub>1</sub> @ 10GHz)
| 0
| - 
|-
| X
| 144
| mm 
|-
| Y
| 76
| mm 
|-
| F
| 40.5
| mm 
|-
| L<sub>x</sub>
| 41
| mm 
|-
| L<sub>y</sub>
| 49
| mm 
|-
| W<sub>x</sub>
| 3.5
| mm 
|-
| W<sub>y</sub>
| 3.5
| mm 
|-
| b
| 12.5
| mm 
|-
| P<sub>x</sub>
| 17
| mm 
|-
| P<sub>y</sub>
| 26
| mm 
|-
| r
| 3
| mm 
|}

<table>
<tr>
<td>
[[Image:ART UWB10.png|thumb|left|420px|Figure 7: Geometry of double U-slot patch antenna on a foam substrate.]]
</td>
</tr>
</table>

Ref. [3] presents measured data for the double U-slot patch antenna. However, not all geometrical dimensions are clearly specified. For this report, we assumed certain values of the parameters based on the visual inspection of the given drawing. Figure 8 shows the planar structure setup for the double U-slot patch in [[EM.Picasso]].

<table>
<tr>
<td>
[[Image:ART UWB12.png|thumb|left|550px|Figure 8: The planar structure setup for the double U-slot patch antenna in EM.Picasso.]]
</td>
</tr>
</table>

Figure 9 shows the return loss results of [[EM.Picasso]] for this antenna, where one can see an -10dB bandwidth of about 440MHz. Figure 10 shows the simulated voltage standing wave ratio of the double U-slot patch antenna as computed by [[EM.Picasso]] and compares it with the measured data given by reference [3]. 

<table>
<tr>
<td>
[[Image:ART UWB13.png|thumb|left|550px|Figure 9: Return loss of the double U-slot patch antenna computed by [[EM.Picasso]] over the range [1.2GHz &ndash; 2GHz].]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB11.png|thumb|left|550px|Figure 10: Voltage standing wave ratio (VSWR) of the double U-slot patch antenna over the range [1.2GHz &ndash; 2GHz]. Solid red line: [[EM.Picasso]] results, and orange symbols: measured data presented by Ref. [3].]]
</td>
</tr>
</table>

== L-Feed Patch Antenna on Foam Substrate ==

The next broadband antenna design to be simulated is a rectangular patch on a thick foam substrate with an L-shaped probe as shown in Figure 11. The following table shows the substrate properties as well as the geometrical dimensions of the L-feed patch antenna:

{| class="wikitable"
|-
! scope="col"| Parameter Name
! scope="col"| Value
! scope="col"| Units
|-
| Foam layer height (h<sub>1</sub>)
| 6.6
| mm 
|-
| Foam permittivity (&epsilon;<sub>r1</sub>)
| 1
| - 
|-
| Foam loss tangent (tan&delta;<sub>1</sub> @ 10GHz)
| 0
| - 
|-
| X
| 30
| mm 
|-
| Y
| 25
| mm 
|-
| L<sub>h</sub>
| 10.5
| mm 
|-
| L<sub>v</sub>
| 4.95
| mm 
|-
| D
| 2
| mm 
|-
| r
| 0.5
| mm 
|}

<table>
<tr>
<td>
[[Image:ART UWB15.png|thumb|left|480px|Figure 11: Geometry of L-feed patch antenna on a foam substrate.]]
</td>
</tr>
</table>

Reference [4] presents measured data for the L-feed patch antenna. In the fabricated antenna used for measurement, the inner conductor of the coaxial feed is bent at a 90&deg; angle such that its vertical arm has a height of Lv, while its horizontal arm, which is parallel to the surface of the patch, has a length of Lh. In [[EM.Picasso]], we modeled the coaxial probe with a vertical PEC via of radius r and height Lv, which is then transitioned to a horizontal PEC strip of length Lh. Figure 12 shows the planar structure setup for the L-feed patch in [[EM.Picasso]].

<table>
<tr>
<td>
[[Image:ART UWB16.png|thumb|left|480px|Figure 12: Planar structure setup for L-feed patch antenna in [[EM.Picasso]]. The patch is shown in mouse-over state.]]
</td>
</tr>
</table>

Figure 13 shows the return loss results of [[EM.Picasso]] for the L-probe patch antenna.

<table>
<tr>
<td>
[[Image:ART UWB17.png|thumb|left|550px|Figure 13: Return loss of the L-feed patch antenna computed by [[EM.Picasso]]..]]
</td>
</tr>
</table>

Figure 14 compares the real and imaginary parts of the input impedance of the L-probe patch antenna as simulated by [[EM.Picasso]] and the measured data presented by Ref. [4]. Figure 15 shows the simulated voltage standing wave ratio of the L-feed patch antenna as compared with the measured data given by the same reference.

<table>
<tr>
<td>
[[Image:ART UWB18.png|thumb|left|550px|Figure 14: Input impedance of the L-feed patch antenna over the range [3GHz &ndash; 6GHz]. Solid red line: [[EM.Picasso]] results for input resistance, solid blue line: [[EM.Picasso]] results for input reactance, orange symbols: measured input resistance presented by Ref. [4], and turquoise symbols: measured input reactance presented by Ref. [4].]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB19.png|thumb|left|550px|Figure 15: Voltage standing wave ratio (VSWR) of the L-feed patch antenna over the range [3GHz &ndash; 6GHz]. Solid line: [[EM.Picasso]] results, and symbols: measured data presented by Ref. [4].]]
</td>
</tr>
</table>

Figures 16 and 17 show the radiation pattern cuts in the YZ plane (E-Plane) and ZX plane (H-Plane), respectively. Figure 17 shows both co-polarized and cross-polarized components of the far field. Figures 16 and 17 also compare [[EM.Picasso]]'s results with the measured radiation pattern data presented by Ref. [4]. Figure 18 shows the directivity of the L-feed patch antenna on the foam substrate computed by [[EM.Picasso]]. It also compares the simulated data with the measured gain data presented by Ref. [4].

<table>
<tr>
<td>
[[Image:ART UWB20.png|thumb|left|480px|Figure 16: 2D E-plane radiation pattern of the L-feed patch antenna at f = 4.53GHz. Solid line: EM.Picasso results, and symbols: measured data presented by Ref. [4].]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB21.png|thumb|left|480px|Figure 17: 2D H-plane radiation pattern of the L-feed patch antenna at f = 4.53GHz. Solid blue line: [[EM.Picasso]] results for co-polarized far field component, solid red line: [[EM.Picasso]] results for cross-polarized far field component, turquoise symbols: measured data for co-polarized far field component presented by Ref. [4], and magenta symbols: measured data for cross-polarized far field component presented by Ref. [4].]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB22.png|thumb|left|480px|Figure 18: A comparison of directivity of the L-feed patch antenna on the foam substrate as computed by [[EM.Picasso]] (solid line), and the measured data for the gain of the antenna presented by Ref. [4] (symbols).]]
</td>
</tr>
</table>

== Circularly Polarized Probe-Fed Patch Antenna with Truncated Corners ==

Now we turn our attention to circularly polarized (CP) patch antenna designs. The first CP patch to be considered is a probe-fed rectangular patch with two opposite corner truncations as shown in Figure 19. This patch is located on a thin foam substrate, and as a result, it is not expected to provide a large bandwidth. The following table shows the substrate properties as well as the geometrical dimensions of the CP patch antenna:

{| class="wikitable"
|-
! scope="col"| Parameter Name
! scope="col"| Value
! scope="col"| Units
|-
| Foam layer height (h<sub>1</sub>)
| 1
| mm 
|-
| Foam permittivity (&epsilon;<sub>r1</sub>)
| 1
| - 
|-
| Foam loss tangent (tan&delta;<sub>1</sub> @ 10GHz)
| 0
| - 
|-
| X
| 28.6
| mm 
|-
| Y
| 28.6
| mm 
|-
| a
| 3.3
| mm 
|-
| D
| 8.2
| mm 
|-
| r
| 0.5
| mm 
|}

<table>
<tr>
<td>
[[Image:ART UWB25.png|thumb|left|360px|Figure 19: Geometry of the CP patch antenna with truncated corners on a foam substrate.]]
</td>
</tr>
</table>

Figure 20 shows the planar structure setup for CP patch antenna with truncated corners in [[EM.Picasso]].

<table>
<tr>
<td>
[[Image:ART UWB26.png|thumb|left|480px|Figure 20: Planar structure setup for the CP patch antenna with truncated corners in EM.Picasso.]]
</td>
</tr>
</table>

Figure 21 shows the return loss results of [[EM.Picasso]] for the CP patch antenna with truncated corners. Ref. [5] only provides the 10-dB return loss frequencies as shown in this figure. The simulated and measured 10-dB impedance bandwidths agree quite well.

<table>
<tr>
<td>
[[Image:ART UWB27.png|thumb|left|550px|Figure 21: Return loss of the CP patch antenna with truncated corners computed by [[EM.Picasso]]. The blue symbols shows the measured 10dB points as reported by Ref. [5].]]
</td>
</tr>
</table>

Figure 22 shows the 3D radiation pattern of the CP patch antenna with truncated corners computed by [[EM.Picasso]] at f = 4.92GHz. A figure of merit for the performance of a circularly polarized antenna is its axial ratio (AR). Figure 23 shows the computed axial ratio of the CP patch antenna with truncated corners as a function of elevation angle &theta; expressed in radians in the two principal YZ and ZX planes. Figure 24 shows the computed axial ratio of the CP patch antenna with truncated corners along the bore sight (&theta; = 0&deg;) over the frequency range [4.75GHz &ndash; 5.25GHz]. Ref. [5] only presents measured data for the AR &lt; 2 bandwidth of the CP antenna as shown in this figure.

<table>
<tr>
<td>
[[Image:ART UWB28.png|thumb|left|640px|Figure 22: 3D radiation pattern of the CP patch antenna with truncated corners computed by [[EM.Picasso]] at f = 5GHz.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB30.png|thumb|left|550px|Figure 23: Axial ratio (AR) of the CP patch antenna with truncated corners as a function of the elevation angle in the principal YZ and ZX planes.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB29.png|thumb|left|550px|Figure 24: Axial ratio (AR) of the CP patch antenna with truncated corners over the range [4.75GHz &ndash; 5.25GHz]. Solid line: [[EM.Picasso]] results, and symbols: measured data presented by Ref. [5] to represent the AR &lt; 2 bandwidth of the CP antenna. ]]
</td>
</tr>
</table>

== Circularly Polarized U-Slot Patch Antenna with Truncated Corners ==

The rectangular patch with truncated corners is a narrowband antenna. By increasing the foam thickness and cutting out a U-slot from the surface of the patch, one can increase the impedance bandwidth of the antenna as well as its axial ratio bandwidth. Figure 25 shows the geometry of the CP U-slot patch antenna with corner truncations. The following table shows the substrate properties as well as the geometrical dimensions of the CP U-Slot patch antenna:

{| class="wikitable"
|-
! scope="col"| Parameter Name
! scope="col"| Value
! scope="col"| Units
|-
| Foam layer height (h<sub>1</sub>)
| 6
| mm 
|-
| Foam permittivity (&epsilon;<sub>r1</sub>)
| 1
| - 
|-
| Foam loss tangent (tan&delta;<sub>1</sub> @ 10GHz)
| 0
| - 
|-
| X
| 28.6
| mm 
|-
| Y
| 28.6
| mm 
|-
| L<sub>x</sub>
| 12
| mm 
|-
| L<sub>y</sub>
| 14
| mm 
|-
| W<sub>x</sub>
| 1
| mm 
|-
| W<sub>y</sub>
| 1
| mm 
|-
| b
| 9.8
| mm 
|-
| a
| 7.7
| mm 
|-
| D
| 9.6
| mm 
|-
| r
| 0.5
| mm 
|}

<table>
<tr>
<td>
[[Image:ART UWB31A.png|thumb|left|360px|Figure 25: Geometry of CP U-slot patch antenna with truncated corners on a foam substrate.]]
</td>
</tr>
</table>

Figure 26 shows the project setup for the CP U-slot patch antenna with truncated corners in [[EM.Picasso]].

<table>
<tr>
<td>
[[Image:ART UWB31.png|thumb|left|480px|Figure 26: Planar structure setup for CP U-slot patch antenna with truncated corners in [[EM.Picasso]].]]
</td>
</tr>
</table>

Figure 27 shows the return loss results of [[EM.Picasso]] for the CP U-slot patch antenna with cut corners and compares the results to the measured data presented by Reference [6]. This reference reports a measured impedance bandwidth of 12.8% [3.66GHz &ndash; 4.16GHz]. [[EM.Picasso]] shows a slightly larger bandwidth up to 4.21GHz.

<table>
<tr>
<td>
[[Image:ART UWB32.png|thumb|left|550px|Figure 27: Return loss of the CP U-slot patch antenna with truncated corners. Solid line: [[EM.Picasso]] results, and symbols: measured data presented by Ref. [6].]]
</td>
</tr>
</table>

Figure 28 shows the 3D radiation pattern of the CP U-slot patch antenna computed by [[EM.Cube]] at the frequency 3.95GHz. Figure 29 shows the axial ratio of the U-slot patch antenna on the foam substrate computed by [[EM.Picasso]]. It also shows the measured axial ratio data presented by Ref. [6].

<table>
<tr>
<td>
[[Image:ART UWB33.png|thumb|left|640px|Figure 28: 3D radiation pattern of the CP U-slot patch antenna with truncated corners computed by [[EM.Picasso]] at f = 3.95GHz.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB34.png|thumb|left|550px|Figure 29: Axial ratio (AR) of the CP U-slot patch antenna with truncated corners over the frequency range [3.7GHz &ndash; 4.3GHz]. Solid line: [[EM.Picasso]] results, and symbols: measured data presented by Ref. [6].]]
</td>
</tr>
</table>

== Circularly Polarized L-Feed Patch Antenna with Truncated Corners  == 

Another method of achieving a broadband CP antenna is to use an L-feed in conjunction with a rectangular patch with truncated corners on a thick foam substrate. In this way, one can increase the impedance bandwidth of the antenna as well as its axial ratio bandwidth. Figure 30 shows the geometry of the CP L-feed patch antenna with corner truncations. The following table shows the substrate properties as well as the geometrical dimensions of the CP L-feed patch antenna:

{| class="wikitable"
|-
! scope="col"| Parameter Name
! scope="col"| Value
! scope="col"| Units
|-
| Foam layer height (h<sub>1</sub>)
| 7.5
| mm 
|-
| Foam permittivity (&epsilon;<sub>r1</sub>)
| 1
| - 
|-
| Foam loss tangent (tan&delta;<sub>1</sub> @ 10GHz)
| 0
| - 
|-
| X
| 28.6
| mm 
|-
| Y
| 28.6
| mm 
|-
| L<sub>h</sub>
| 10
| mm 
|-
| L<sub>v</sub>
| 6
| mm 
|-
| a
| 10
| mm 
|-
| D
| 3.3
| mm 
|-
| r
| 0.5
| mm 
|}

<table>
<tr>
<td>
[[Image:ART UWB40.png|thumb|left|480px|Figure 30: Geometry of the CP L-feed patch antenna with truncated corners on a foam substrate. ]]
</td>
</tr>
</table>

Figure 31 shows the project setup for the CP L-feed patch antenna with truncated corners in [[EM.Picasso]].

<table>
<tr>
<td>
[[Image:ART UWB41.png|thumb|left|480px|Figure 31: Planar structure setup for CP L-feed patch antenna with truncated corners in [[EM.Picasso]]. The patch is shown in mouse-over state.]]
</td>
</tr>
</table>

Figure 32 shows the return loss results of [[EM.Picasso]] for the CP L-feed patch antenna with truncated corners and compares the results to the measured data presented by Reference [6]. This reference reports a measured impedance bandwidth of 37% [3.47GHz &ndash; 5.05GHz]. [[EM.Picasso]]&rsquo;s return loss graph first reaches -10dB point at 3.71GHz, but it is rises slightly and crosses this threshold again at 4.2GHz and remain below -10dB up to 5.64GHz.

<table>
<tr>
<td>
[[Image:ART UWB42.png|thumb|left|550px|Figure 32: Return loss of the CP L-feed patch antenna with truncated corners. Solid line: [[EM.Picasso]] results, and symbols: measured data presented by Ref. [6].]]
</td>
</tr>
</table>

Figure 33 shows the 3D radiation pattern of the CP L-feed patch antenna with truncated corners computed by [[EM.Cube]] at the frequency 4.15GHz. Figure 34 shows the directivity of the CP L-feed patch antenna with truncated corners computed by [[EM.Picasso]]. It also shows the measured axial ratio data presented by Ref. [6].

<table>
<tr>
<td>
[[Image:ART UWB43.png|thumb|left|640px|Figure 33: 3D radiation pattern of the CP L-feed patch antenna with truncated corners computed by [[EM.Picasso]] at f = 4.15GHz. ]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:ART UWB44.png|thumb|left|550px|Figure 34: Axial ratio (AR) of the CP L-feed patch antenna with truncated corners over the range [3GHz &ndash; 6GHz]. Solid line: [[EM.Picasso]] results, and symbols: measured data presented by Ref. [6].]]
</td>
</tr>
</table>

== References ==

[1] K.F. Lee, K.M. Luk, K.F. Tong, S.M. Shum, T. Huynh, and R.Q. Lee, &ldquo;Experimental and simulation studies of the coaxially-fed U-slot rectangular patch antenna,&rdquo; IEE Proc. Microw. Antennas &amp; Propagat, Vol. 144, No. 5, pp. 354-358, 1997.

[2] K.F. Tong, K.M. Luk, K.F. Lee, and R.Q. Lee, &ldquo;A broadband U-slot rectangular patch antenna on a microwave substrate,&rdquo; IEEE Trans. on Antennas &amp; Propagat, Vol. 48, No. 6, pp. 954-960, 2000.

[3] Y.X. Guo, K.M. Luk, K.F. Lee, and Y.L. Chow, &ldquo;Double U-slot rectangular patch antenna,&rdquo; Electron Lett., Vol. 34, pp. 1805-1806, 1998.

[4] K.M. Luk, C.L. Mak, Y.L. Chow, and K.F. Lee, &ldquo;Broadband microstrip patch antenna,&rdquo; Electron Lett., Vol. 34, pp. 1442-1443, 1998.

[5] K.F. Lee and K.M. Luk, Microstrip Patch Antennas. Chapter 16, pp. 449-450, Imperial College Press, 2011.

[6] L.S. Steven Yang, K.F. Lee, A.A. Kishk and K.M. Luk, &ldquo;Design and study of wideband single feed circularly polarized microstrip antennas,&rdquo; Prog. In Electromagnetic Research, Vol. 80, pp. 45-61, 2008.

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