Canadian TV, Computing and Home Theatre Forums banner
21 - 34 of 34 Posts

·
Registered
Joined
·
419 Posts
To perform modal solutions (S-parameters, or Z-matrix, or VSWR) for antennas which contain transmission lines (2-bay antennas, all kind of LPDA) your engine should support correct simulations of transmission lines.

Let say, some LPDA design have TR line Zo=158 Ohm (dimensions and spacing between boom pipes gives Zo=158)

Round shape wire with diameter=X, produce Zo=158 Ohm when spacing (tip-to-tip) is also X. Spacing center-to-center is 2*X.

MMANA-GAL treat this line as R=109.7 +j46.23 Ohm (VSWR158=1.65) and this VSWR is random value depending on length
Code:
*
600.0
***Wires***
4
0.0,    0.001,    0.0,    0.2,    0.001,    0.0,    0.001,    -1
0.0,    -0.001,    0.0,    0.2,    -0.001,    0.0,    0.001,    -1
0.0,    -0.001,    0.0,    0.0,    0.001,    0.0,    0.001,    -1
0.2,    -0.001,    0.0,    0.2,    0.001,    0.0,    0.001,    -1
***Source***
1,    0
w3c,    0.0,    1.0
***Load***
1,    1
w4c,    1,    158.0,    0.0
***Segmentation***
800,    80,    2.0,    2
***G/H/M/R/AzEl/X***
0,    0.0,    0,    50.0,    120,    60,    0.0
This behaviour prevent NEC2 engines from correct simulation of far field. Power distribution in phased array antennas significantly influence their radiation pattern. Broken transmission line broke both far-field solutions and modal solutions for S-parameters. Neither radiation patten, nor Z-matrix are correct.

Since NEC2-based engines do not support transmission lines, 4NEC2 added support for virtual transmission lines (special description card).

LPDA designs in 4NEC2 always use such approach to be able to solve far-fields at least
 

·
Registered
Joined
·
75 Posts
Discussion Starter · #22 ·
Yurii Pylypenko

Thank you for taking your time when modeling this antenna.
MQ6938 HDTV 2x Array of 4-Bay BowTie @ 300 Ohm @ UHF TV 470-700 MHz
I am encouraged to build it.
Since NEC2-based engines do not support transmission lines, 4NEC2 added support for virtual transmission lines (special description card).

LPDA designs in 4NEC2 always use such approach to be able to solve far-fields at least
For that reason there is always the doubt if an antenna with a transmission line will work correctly in a real construction.
The virtual transmission line in 4nec2 from what I read does not interaction with the antenna elements, so there is still the doubt of those parameters.
 

·
Registered
Joined
·
419 Posts
The virtual transmission line in 4nec2 from what I read does not interaction with the antenna elements, so there is still the doubt of those parameters.
2 most strong interactions which occur in LPDA:
1) boom correction for element (dipole) length. Nature of this effect is the same as in Yagi with metal boom, but quantitive estimations are not identical. It's very easy to assign sweep variable $k=1 +-0.05 to element length and choose best Gain/SWR curve in 3D modelling CAE. I do not know how to do this without 3D CAE. Even for classical Yagi this is the only practical method for frequencies higher than VHF. Quantitive BCF models were developed only for limited geometry combinations.

2) interaction with magnetic field of 2-wire symmetrical line (2 booms). If booms are close enough (typical scenario for 50 Ohm or 75 Ohm LPDA), this E-fields of each boom are thightly coupled, no radiation occurs, magnetic field decrease very fast and doesn't influence much on elements.
Typical 75 Ohm LPDA has Zo=105 Ohm transmission line. Here are magnetic flux lines


But in higher impedance LPD A (e.g. 200 Ohm), especially on higher frequencies (up to 1 GHz and over), electrical distance between boom pipes is big (measured in lambda). Oversized symmetrical transmission line can also have other than TEM modes, more radiation and more interaction with dipoles. For 75 Ohm LPDA <700 MHz it's not an issue.
Here is example of oversize boom separation:

It produces strong H-fields, distort radiation pattern and you cannot model this antenna in MMANA or 4NEC2.

Next example: LogAnt win32 calculator support MMANA export.
Here is example of UHF TV 300 OHm (for Guanella 4:1 balun) LPDA design
LogAnt -> MMANA -> HFSS -> DIY & measure with VNA

MMANA, HFSS and VNA agree on VSWR.
At 630 MHz MMANA show 125 Ohm resonance. HFSS and VNA confirm this value
[SPOILER="LPDA"]





[/SPOILER]
this is not example of good antenna design (VSWR is bad, it is in fact 150 Ohm design, not 300 Ohm), but proof how MMANA, HFSS and VNA give the same value
 

·
Registered
Joined
·
75 Posts
Discussion Starter · #27 ·
Reference LPDA website:
Channel 7-13 Log Periodic Antenna Design
Antenna File for 4nec2.
Code:
CM  Created by LPCAD 3.57 on 07-01-2021
CM 
CM  F1 =  160.09 MHz, FH =  220 MHz, Number of LP elements =  12
CM  TAU-L =  0.95 TAU-S =  0.95 SIGMA = 0.18000 L/D =  138.4391
CM  Input Z =  85 ohms, Feeder Z =  101 ohms
CE 
GW 1 21   0.000     -17.305   0.000    0.000    17.305   0.000    0.125
GW 2 21   12.460    -16.440   0.000    12.460   16.440   0.000    0.125
GW 3 19   24.296    -15.618   0.000    24.296   15.618   0.000    0.125
GW 4 19   35.541    -14.837   0.000    35.541   14.837   0.000    0.125
GW 5 17   46.223    -14.095   0.000    46.223   14.095   0.000    0.125
GW 6 17   56.372    -13.390   0.000    56.372   13.390   0.000    0.125
GW 7 15   66.013    -12.721   0.000    66.013   12.721   0.000    0.125
GW 8 15   75.171    -12.085   0.000    75.171   12.085   0.000    0.125
GW 9 13   83.872    -11.480   0.000    83.872   11.480   0.000    0.125
GW 10 13   92.138    -10.906   0.000    92.138   10.906   0.000    0.125
GW 11 11   99.991    -10.361   0.000    99.991   10.361   0.000    0.125
GW 12 11  107.451     -9.843   0.000   107.451    9.843   0.000    0.125
GS 0 0 0.0254
GE 0 0 0.
EK
EX 0 12 6 00 1. 0.
FR 0  11 0 0  174 6
TL 1 11 2 11  -101 0. 0. 0. 0. 0.
TL 2 11 3 10  -101 0. 0. 0. 0. 0.
TL 3 10 4 10  -101 0. 0. 0. 0. 0.
TL 4 10 5 9  -101 0. 0. 0. 0. 0.
TL 5 9 6 9  -101 0. 0. 0. 0. 0.
TL 6 9 7 8  -101 0. 0. 0. 0. 0.
TL 7 8 8 8  -101 0. 0. 0. 0. 0.
TL 8 8 9 7  -101 0. 0. 0. 0. 0.
TL 9 7 10 7  -101 0. 0. 0. 0. 0.
TL 10 7 11 6  -101 0. 0. 0. 0. 0.
TL 11 6 12 6  -101 0. 0. 0. 0. 0.
RP 0 1 360 1500 90. 0. 0. 1. 0. 0.
FR 0  11 0 0  174 6
RP 0 360 1 1500 -90. 0. 1. 1. 0. 0.
EN
 

·
Registered
Joined
·
75 Posts
Discussion Starter · #28 ·
Drawing of antennas in DXF format.
Colorfulness Photograph Product Black Rectangle

Here you have several types of antennas drawn in LibreCAD.
To view the drawings, use LibreCAD or another CAD program of your choice, which allows you to import files in DXF format.
Website: LibreCAD - Free Open Source 2D CAD

VHF-1
14-Element VHF-TV Yagi, CM_3617B_v1_inch, Korner_19.3_TV_VHF, Stellar-Labs_dim-inch.
VHF_1.zip

UHF-1
91_XG, CM_4228HD_V1, CM_4251, DB4e_inch, DB8e_inch, Log_Yagi_l6pu66, Yagi_UHF_470-608, Korner19_UHF_TV_v1, Korner29_UHF_TV_v2.
UHF_1.zip

VHF & UHF antennas
DAT-BOOS_mix_LR, HD_Stacker, W7698P.
VHF_UHF.zip
 

·
Registered
Joined
·
6 Posts
dear "Jope" thank you for the work done! I looked at your previous work. I was wondering what diameter of the elements you will use when simulating the UHF range.
 

·
Registered
Joined
·
75 Posts
Discussion Starter · #31 · (Edited)
vova. gumerov
I was wondering what diameter of the elements you will use when simulating the UHF range.
It is recommended that the element diameters be limited to between 0.001 and 0.02 wavelengths. At the current Design Frequency, 440.000 Hz, this is 0.027" (0-1/32") to 0.536" (0-17/32"), or 0.681 mm to 13.627 mm. The idea here is to keep the diameter small in relation to the element length. Thus, as frequency increases, the useful element diameter decreases.
At a design frequency of 584 MHz
wavelengths = 0.5136986301 m

(0.5136986301×0.001)÷1
0.000513699 m = 0.51 mm
(0.5136986301×0.02)÷1
0.010273973 m = 10.27 mm

Reference website:
VHF/UHF Yagi Antenna Design - K7MEM
 

·
Registered
Joined
·
75 Posts
Discussion Starter · #32 ·
Antennas Website Reference:
Sumtech Home Page

A 14-element Parabeam antenna for VHF Band 3.
Antenna File for MmanaGal.
Code:
VHF_Band _III_PB205
*
198.5
***Wires***
26
0.0,    -0.261,    0.0,    0.0,    0.261,    0.0,    0.006,    -1
0.0,    0.261,    0.0,    0.11695,    0.261,    0.28947,    0.006,    -1
0.11695,    0.261,    0.28947,    0.11695,    -0.261,    0.28947,    0.006,    -1
0.11695,    -0.261,    0.28947,    0.0,    -0.261,    0.0,    0.006,    -1
0.0,    0.261,    0.0,    0.11695,    0.261,    -0.28947,    0.006,    -1
0.11695,    0.261,    -0.28947,    0.11695,    -0.261,    -0.28947,    0.006,    -1
0.11695,    -0.261,    -0.28947,    0.0,    -0.261,    0.0,    0.006,    -1
0.204,    -0.2895,    0.0,    0.204,    0.2895,    0.0,    0.006,    -1
0.465,    -0.2895,    0.0,    0.465,    0.2895,    0.0,    0.006,    -1
0.726,    -0.2895,    0.0,    0.726,    0.2895,    0.0,    0.006,    -1
0.987,    -0.2895,    0.0,    0.987,    0.2895,    0.0,    0.006,    -1
1.294,    -0.2895,    0.0,    1.294,    0.2895,    0.0,    0.006,    -1
1.601,    -0.2895,    0.0,    1.601,    0.2895,    0.0,    0.006,    -1
1.908,    -0.2895,    0.0,    1.908,    0.2895,    0.0,    0.006,    -1
2.238,    -0.2895,    0.0,    2.238,    0.2895,    0.0,    0.006,    -1
2.568,    -0.2895,    0.0,    2.568,    0.2895,    0.0,    0.006,    -1
2.898,    -0.2895,    0.0,    2.898,    0.2895,    0.0,    0.006,    -1
3.26,    -0.2895,    0.0,    3.26,    0.2895,    0.0,    0.006,    -1
3.622,    -0.2895,    0.0,    3.622,    0.2895,    0.0,    0.006,    -1
-0.295,    -0.261,    0.0,    -0.295,    0.261,    0.0,    0.006,    -1
-0.295,    0.261,    0.0,    -0.295,    0.261,    0.2895,    0.006,    -1
-0.295,    0.261,    0.2895,    -0.295,    -0.261,    0.2895,    0.006,    -1
-0.295,    -0.261,    0.2895,    -0.295,    -0.261,    0.0,    0.006,    -1
-0.295,    0.261,    0.0,    -0.295,    0.261,    -0.2895,    0.006,    -1
-0.295,    0.261,    -0.2895,    -0.295,    -0.261,    -0.2895,    0.006,    -1
-0.295,    -0.261,    -0.2895,    -0.295,    -0.261,    0.0,    0.006,    -1
***Source***
1,    0
w1c,    0.0,    1.0
***Load***
0,    0
***Segmentation***
800,    80,    2.0,    2
***G/H/M/R/AzEl/X***
0,    15.0,    4,    300.0,    120,    60,    0.0
A 52-element Multibeam antenna for VHF Band 3.
Antenna File for MmanaGal.
Code:
VHF_Band _III_MB205
*
198.5
***Wires***
116
0.0,    -0.24,    0.0,    0.0,    0.24,    0.0,    0.008,    -1
0.0,    0.24,    0.0,    0.0,    0.24,    0.0365,    0.008,    -1
0.0,    0.24,    0.0365,    0.0776,    0.24,    0.2386,    0.008,    -1
0.0776,    0.24,    0.2386,    0.0776,    -0.24,    0.2386,    0.008,    -1
0.0776,    -0.24,    0.2386,    0.0,    -0.24,    0.0365,    0.008,    -1
0.0,    -0.24,    0.0365,    0.0,    -0.24,    0.0,    0.008,    -1
0.0,    0.24,    0.0,    0.0,    0.24,    -0.0365,    0.008,    -1
0.0,    0.24,    -0.0365,    0.0776,    0.24,    -0.2386,    0.008,    -1
0.0776,    0.24,    -0.2386,    0.0776,    -0.24,    -0.2386,    0.008,    -1
0.0776,    -0.24,    -0.2386,    0.0,    -0.24,    -0.0365,    0.008,    -1
0.0,    -0.24,    -0.0365,    0.0,    -0.24,    0.0,    0.008,    -1
0.148,    -0.1845,    0.0,    0.148,    0.1845,    0.0,    0.008,    -1
0.411,    -0.137,    0.0,    0.411,    0.137,    0.0,    0.008,    -1
0.342,    0.0418,    0.0413,    0.342,    0.1535,    0.153,    0.008,    -1
0.342,    0.1535,    0.153,    0.342,    0.4375,    0.153,    0.008,    -1
0.342,    0.0418,    -0.0413,    0.342,    0.1535,    -0.153,    0.008,    -1
0.342,    0.1535,    -0.153,    0.342,    0.4375,    -0.153,    0.008,    -1
0.342,    -0.0418,    -0.0413,    0.342,    -0.1535,    -0.153,    0.008,    -1
0.342,    -0.1535,    -0.153,    0.342,    -0.4375,    -0.153,    0.008,    -1
0.342,    -0.0418,    0.0413,    0.342,    -0.1535,    0.153,    0.008,    -1
0.342,    -0.1535,    0.153,    0.342,    -0.4375,    0.153,    0.008,    -1
0.648,    0.0418,    0.0413,    0.648,    0.1535,    0.153,    0.008,    -1
0.648,    0.1535,    0.153,    0.648,    0.4375,    0.153,    0.008,    -1
0.648,    0.0418,    -0.0413,    0.648,    0.1535,    -0.153,    0.008,    -1
0.648,    0.1535,    -0.153,    0.648,    0.4375,    -0.153,    0.008,    -1
0.648,    -0.0418,    -0.0413,    0.648,    -0.1535,    -0.153,    0.008,    -1
0.648,    -0.1535,    -0.153,    0.648,    -0.4375,    -0.153,    0.008,    -1
0.648,    -0.0418,    0.0413,    0.648,    -0.1535,    0.153,    0.008,    -1
0.648,    -0.1535,    0.153,    0.648,    -0.4375,    0.153,    0.008,    -1
0.945,    0.0418,    0.0413,    0.945,    0.1535,    0.153,    0.008,    -1
0.945,    0.1535,    0.153,    0.945,    0.4375,    0.153,    0.008,    -1
0.945,    0.0418,    -0.0413,    0.945,    0.1535,    -0.153,    0.008,    -1
0.945,    0.1535,    -0.153,    0.945,    0.4375,    -0.153,    0.008,    -1
0.945,    -0.0418,    -0.0413,    0.945,    -0.1535,    -0.153,    0.008,    -1
0.945,    -0.1535,    -0.153,    0.945,    -0.4375,    -0.153,    0.008,    -1
0.945,    -0.0418,    0.0413,    0.945,    -0.1535,    0.153,    0.008,    -1
0.945,    -0.1535,    0.153,    0.945,    -0.4375,    0.153,    0.008,    -1
1.242,    0.0418,    0.0413,    1.242,    0.1535,    0.153,    0.008,    -1
1.242,    0.1535,    0.153,    1.242,    0.4375,    0.153,    0.008,    -1
1.242,    0.0418,    -0.0413,    1.242,    0.1535,    -0.153,    0.008,    -1
1.242,    0.1535,    -0.153,    1.242,    0.4375,    -0.153,    0.008,    -1
1.242,    -0.0418,    -0.0413,    1.242,    -0.1535,    -0.153,    0.008,    -1
1.242,    -0.1535,    -0.153,    1.242,    -0.4375,    -0.153,    0.008,    -1
1.242,    -0.0418,    0.0413,    1.242,    -0.1535,    0.153,    0.008,    -1
1.242,    -0.1535,    0.153,    1.242,    -0.4375,    0.153,    0.008,    -1
1.539,    0.0418,    0.0413,    1.539,    0.1535,    0.153,    0.008,    -1
1.539,    0.1535,    0.153,    1.539,    0.4375,    0.153,    0.008,    -1
1.539,    0.0418,    -0.0413,    1.539,    0.1535,    -0.153,    0.008,    -1
1.539,    0.1535,    -0.153,    1.539,    0.4375,    -0.153,    0.008,    -1
1.539,    -0.0418,    -0.0413,    1.539,    -0.1535,    -0.153,    0.008,    -1
1.539,    -0.1535,    -0.153,    1.539,    -0.4375,    -0.153,    0.008,    -1
1.539,    -0.0418,    0.0413,    1.539,    -0.1535,    0.153,    0.008,    -1
1.539,    -0.1535,    0.153,    1.539,    -0.4375,    0.153,    0.008,    -1
1.864,    0.0418,    0.0413,    1.864,    0.1535,    0.153,    0.008,    -1
1.864,    0.1535,    0.153,    1.864,    0.4375,    0.153,    0.008,    -1
1.864,    0.0418,    -0.0413,    1.864,    0.1535,    -0.153,    0.008,    -1
1.864,    0.1535,    -0.153,    1.864,    0.4375,    -0.153,    0.008,    -1
1.864,    -0.0418,    -0.0413,    1.864,    -0.1535,    -0.153,    0.008,    -1
1.864,    -0.1535,    -0.153,    1.864,    -0.4375,    -0.153,    0.008,    -1
1.864,    -0.0418,    0.0413,    1.864,    -0.1535,    0.153,    0.008,    -1
1.864,    -0.1535,    0.153,    1.864,    -0.4375,    0.153,    0.008,    -1
2.189,    0.0418,    0.0413,    2.189,    0.1535,    0.153,    0.008,    -1
2.189,    0.1535,    0.153,    2.189,    0.4375,    0.153,    0.008,    -1
2.189,    0.0418,    -0.0413,    2.189,    0.1535,    -0.153,    0.008,    -1
2.189,    0.1535,    -0.153,    2.189,    0.4375,    -0.153,    0.008,    -1
2.189,    -0.0418,    -0.0413,    2.189,    -0.1535,    -0.153,    0.008,    -1
2.189,    -0.1535,    -0.153,    2.189,    -0.4375,    -0.153,    0.008,    -1
2.189,    -0.0418,    0.0413,    2.189,    -0.1535,    0.153,    0.008,    -1
2.189,    -0.1535,    0.153,    2.189,    -0.4375,    0.153,    0.008,    -1
2.522,    0.0418,    0.0413,    2.522,    0.1535,    0.153,    0.008,    -1
2.522,    0.1535,    0.153,    2.522,    0.4375,    0.153,    0.008,    -1
2.522,    0.0418,    -0.0413,    2.522,    0.1535,    -0.153,    0.008,    -1
2.522,    0.1535,    -0.153,    2.522,    0.4375,    -0.153,    0.008,    -1
2.522,    -0.0418,    -0.0413,    2.522,    -0.1535,    -0.153,    0.008,    -1
2.522,    -0.1535,    -0.153,    2.522,    -0.4375,    -0.153,    0.008,    -1
2.522,    -0.0418,    0.0413,    2.522,    -0.1535,    0.153,    0.008,    -1
2.522,    -0.1535,    0.153,    2.522,    -0.4375,    0.153,    0.008,    -1
2.874,    0.0418,    0.0413,    2.874,    0.1535,    0.153,    0.008,    -1
2.874,    0.1535,    0.153,    2.874,    0.4375,    0.153,    0.008,    -1
2.874,    0.0418,    -0.0413,    2.874,    0.1535,    -0.153,    0.008,    -1
2.874,    0.1535,    -0.153,    2.874,    0.4375,    -0.153,    0.008,    -1
2.874,    -0.0418,    -0.0413,    2.874,    -0.1535,    -0.153,    0.008,    -1
2.874,    -0.1535,    -0.153,    2.874,    -0.4375,    -0.153,    0.008,    -1
2.874,    -0.0418,    0.0413,    2.874,    -0.1535,    0.153,    0.008,    -1
2.874,    -0.1535,    0.153,    2.874,    -0.4375,    0.153,    0.008,    -1
3.226,    0.0418,    0.0413,    3.226,    0.1535,    0.153,    0.008,    -1
3.226,    0.1535,    0.153,    3.226,    0.4375,    0.153,    0.008,    -1
3.226,    0.0418,    -0.0413,    3.226,    0.1535,    -0.153,    0.008,    -1
3.226,    0.1535,    -0.153,    3.226,    0.4375,    -0.153,    0.008,    -1
3.226,    -0.0418,    -0.0413,    3.226,    -0.1535,    -0.153,    0.008,    -1
3.226,    -0.1535,    -0.153,    3.226,    -0.4375,    -0.153,    0.008,    -1
3.226,    -0.0418,    0.0413,    3.226,    -0.1535,    0.153,    0.008,    -1
3.226,    -0.1535,    0.153,    3.226,    -0.4375,    0.153,    0.008,    -1
3.671,    0.0418,    0.0413,    3.671,    0.1535,    0.153,    0.008,    -1
3.671,    0.1535,    0.153,    3.671,    0.4375,    0.153,    0.008,    -1
3.671,    0.0418,    -0.0413,    3.671,    0.1535,    -0.153,    0.008,    -1
3.671,    0.1535,    -0.153,    3.671,    0.4375,    -0.153,    0.008,    -1
3.671,    -0.0418,    -0.0413,    3.671,    -0.1535,    -0.153,    0.008,    -1
3.671,    -0.1535,    -0.153,    3.671,    -0.4375,    -0.153,    0.008,    -1
3.671,    -0.0418,    0.0413,    3.671,    -0.1535,    0.153,    0.008,    -1
3.671,    -0.1535,    0.153,    3.671,    -0.4375,    0.153,    0.008,    -1
4.124,    0.0418,    0.0413,    4.124,    0.1535,    0.153,    0.008,    -1
4.124,    0.1535,    0.153,    4.124,    0.4375,    0.153,    0.008,    -1
4.124,    0.0418,    -0.0413,    4.124,    0.1535,    -0.153,    0.008,    -1
4.124,    0.1535,    -0.153,    4.124,    0.4375,    -0.153,    0.008,    -1
4.124,    -0.0418,    -0.0413,    4.124,    -0.1535,    -0.153,    0.008,    -1
4.124,    -0.1535,    -0.153,    4.124,    -0.4375,    -0.153,    0.008,    -1
4.124,    -0.0418,    0.0413,    4.124,    -0.1535,    0.153,    0.008,    -1
4.124,    -0.1535,    0.153,    4.124,    -0.4375,    0.153,    0.008,    -1
-0.242,    -0.3055,    0.0,    -0.242,    0.3055,    0.0,    0.008,    -1
-0.242,    0.3055,    0.0,    -0.242,    0.3055,    0.279,    0.008,    -1
-0.242,    0.3055,    0.279,    -0.242,    -0.3055,    0.279,    0.008,    -1
-0.242,    -0.3055,    0.279,    -0.242,    -0.3055,    0.0,    0.008,    -1
-0.242,    0.3055,    0.0,    -0.242,    0.3055,    -0.279,    0.008,    -1
-0.242,    0.3055,    -0.279,    -0.242,    -0.3055,    -0.279,    0.008,    -1
-0.242,    -0.3055,    -0.279,    -0.242,    -0.3055,    0.0,    0.008,    -1
***Source***
1,    0
w1c,    0.0,    1.0
***Load***
0,    0
***Segmentation***
800,    80,    2.0,    2
***G/H/M/R/AzEl/X***
0,    15.0,    4,    300.0,    120,    60,    0.0
 

·
Registered
Joined
·
6 Posts
Thanks for the clarification. I understood the pattern with the diameters of the elements by studying the file you sent. Your work is very informative!
 
21 - 34 of 34 Posts
Top