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Saturday, August 13, 2011

Cone Of Silence and Secant Correction .... demystified



If you are operating a Geostationary Satellite Earth station having an Az-El antenna mount then you may notice that when you move the antenna from away from peak signal - one axis at time - then El movement causes signal reduction faster than Az movement.


What I mean is that ( quantities are just illustrative .. they will vary from system to system ):

Signal strength = x dbm  becomes ( x -2 ) dbm when,
Elevation is moved thru 0.5 deg   or
Azimuth is moved thru 2 deg.

Azimuth - Elevation mount arrangement   
Why do you require this extra movement in Az as compared to El?

The phenomenon is simple Trigonometric result of Elevation axis being mounted over Azimuth axis ( as shown in the adjacent drawing ), so  when Az is moved the Elevation axis also rotates in Azimuth plane.  The Elevation axis on the other hand moves totally independently without affecting Az axis.

To understand the underlying facts we use the situation where the antenna is tracking Low Altitude satellites which generate 'paths' running nearly North-South due to Earth's rotation as shown in the next figure.




This leads to another phenomenon called as Cone of Silence.
This in turn necessitates Secant Correction in Azimuth axis during auto tracking.

The Cone of silence is a phenomenon resulting out of the geometrical mounting of one axis on top of another axis. The movement of the lower axis affects the upper axis pointing resulting in a non linear movement of the antenna ( which is mounted on upper axis ) beam w r t the movement of lower axis. It becomes therefore essential to provide a corrective mechanism in the lower axis servo electronics to compensate the non linearity.

The Secant Correction is a requirement resulting out of the above non linearity so that the autotrack gradients from tracking receiver are modified to suit the varying demand from the lower axis servo system at different positions of antenna in upper circuit.


Two of the most popular mounts of antenna are Elevation over Azimuth ( AZ-EL ) mount and X-Y mount.

For the present we will concentrate on Az-El mount.

To understand the requirements of very high velocity let's look at the earth station from exactly above the antenna ( Zenith ) direction. like in case of several passes of a real satellite and earth station depicted in the drawing below.





Notice that for the satellite pass which is far from Earth Station the Maximum Elevation is less ( for the grazing pas it is almost 0 deg ) while the Maximum Elevation is 90 deg for an overhead pass.






In the drawing below, we see the antenna from top. Let's analyze 3 passes A,B and C of a satellite . Pass C is a low Elevation pass while Pass A is a High Elevation pass. In each of the passes the satellite moves at a constant velocity and covers distance 1to2 , 2to3, ... in an equal period of time.




Observe the AZ angle rotation requirement for this distance 3 to 4 in all the three passes. We see that as the pass comes nearer to the station; the AZ angle that the antenna has to cover in that period increases rapidly. and ultimately for an exact overhead pass it approaches 180 degrees in almost no time ... or antenna has to travel at the speed that approaches infinity.

The mechanical limitations of antenna mount do not allow infinite speed and hence there is a limitation at which the antenna can move with maximum speed in AZ axis.

For example if the antenna can move at the maximum speed of 20deg per second then it will be able to track the satellite upto an elevation where the velocity requirement reaches 20 deg/sec. Exact Elevation at which this 20deg/sec AZ velocity is reached is a function of satellite height.

If a still higher elevation occurs then antenna starts lagging behind the satellite and may loose track if larger autotrack errors occur ( in fact after a certain amount of error buildup the error direction itself may change and will drive the antenna away from target at a great speed which may even cause damage to antenna system itself. ).

Thus the antenna in this example can't track passes above a certain Elevation. This zone ( conical in shape ) where antenna beam can't receive signal from satellite because of Az speed limitation is called Cone Of Silence.

We covered above the subject of Cone of Silence , which is a physical limitation of Elevation angle above which the station can't track satellite pass.

The geometry of mount calls for a certain correction which needs to be applied to AZ auto track servo even before it reaches cone of silence and now we will analyze that.

In the drawing below, O is the point where Elevation Axis passes through Az plane of antenna. OA is the diection of antenna beam when Elevation is 0 deg and OB is the beam direction when antenna elevation = EL. OA and OB and angle EL lie in a single plane passing through O and at a certain Az angle.





The spatial distance that the beam will move through when Az is rotated from a to a' with EL=0 deg is aa'.

Observe now the movement of beam when Elevation is =EL. We see that although the AZ axis has rotated through the same AZ angle aa', the beam would move through a smaller spatial distance bb' which is smaller than aa' and it can easily be deuced to be = aa'*cos(EL).

Which means that one has to rotate through more AZ angle if the same spatial distance ( equivalent to aa' ) when elevation =EL is to be covered and this this extra angular movement requirement is 1/cos(EL) or secant(EL).

In other words if the antenna has to autotrack properly over the entire hemisphere of antenna coverage then the Azimuth autotrack error needs to be multipled with secant(EL) to overcome the reduced equivalent error gradient at higher elevation.

This error modification is called as Secant Correction and can be introduced by various means: in olden days there were synchros which had secant potentiometers attached to them for multiplying the AZ error.

With digital electronics now the same can be applied easily using a suitable algorithm.

One of the most glaring effect on receiver is the change in doppler shift under such circumstances as shown in a sample image below. Note that the rate of change of doppler is highest at the tome of closest approach ( TCA in figure ) as indicated with the slope line.

A sample calculation of dynamic variations of different parameters during transit near Zenith is tabulated below for a typical satellite in a 630 kms orbit. Note that this is only one sided ( i.e. elevation going from 0 to 90 )..  the other side is a replica but in reverse order.


Sat. Ht. 630 Earth Rad. 6371
Tx.Freq. 8150 C 3.00E+10
Lambda 3.68
ELEVATION NADIR Angle SLR PATH LOSS NOISE VAR EXPECTED SIG VAR Path Loss Var C/N Var Range Rate Doppler
0 65.51 2902.47 -179.93 -4.01 -183.94 -11.01 -15.02
1 65.49 2793.41 -179.59 -2.8084 -182.40 -10.67 -13.48 109.06 2.964861
2 65.43 2688.63 -179.26 -2.49413 -181.76 -10.34 -12.84 104.78 2.848511
3 65.34 2588.13 -178.93 -2.31029 -181.24 -10.01 -12.32 100.50 2.732205
4 65.20 2491.88 -178.60 -2.17985 -180.78 -9.68 -11.86 96.25 2.616567
5 65.03 2399.84 -178.27 -2.07868 -180.35 -9.35 -11.43 92.04 2.502181
6 64.83 2311.94 -177.95 -1.99602 -179.95 -9.03 -11.03 87.90 2.389592
7 64.59 2228.10 -177.63 -1.92612 -179.56 -8.71 -10.64 83.84 2.279288
8 64.31 2148.22 -177.31 -1.86558 -179.18 -8.39 -10.26 79.88 2.171697
9 64.00 2072.18 -177.00 -1.81218 -178.81 -8.08 -9.89 76.04 2.067185
10 63.66 1999.86 -176.69 -1.76441 -178.46 -7.77 -9.54 72.32 1.966051
20 58.77 1450.38 -173.90 -1.45013 -175.35 -4.98 -6.43 549.48 14.93791
30 52.01 1124.00 -171.69 -1.2663 -172.95 -2.77 -4.03 326.38 8.872766
40 44.20 924.26 -169.99 -1.13586 -171.12 -1.07 -2.20 199.73 5.429851
50 35.80 797.85 -168.71 -1.03469 -169.74 0.21 -0.82 126.41 3.436568
60 27.07 716.86 -167.78 -0.95202 -168.73 1.14 0.19 80.99 2.201836
70 18.13 666.48 -167.15 -0.88213 -168.03 1.77 0.89 50.38 1.36955
80 9.09 638.83 -166.78 -0.82159 -167.60 2.14 1.32 27.66 0.751829
90 0.00 630.00 -166.66 -0.76819 -167.43 2.26 1.49 8.83 0.239947



Notice the doppler is constant upto 20 deg and then it increases to 14 KHz and drops to 0  KHz at zenith causing a high doppler RATE at Elmax.

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7 comments:

  1. Thank you for making this. You are correct, this subject seems to be quite illusive on the net. I did find some small stuff on it under "Antenna blind cone", but not like you presented here. This article was very useful.

    ReplyDelete
  2. Thanks Anthony to share your feelings.

    ReplyDelete
  3. The "cone of silence" is known as the keyhole.

    ReplyDelete
  4. thanks for the lucid explanation

    ReplyDelete
  5. I enjoyed reading your article :) PLease continue publishing helpful topics like this. Regards, from Let's get gadget, a company whose into selling
    magnet mount cb antenna

    ReplyDelete
  6. Thanks Steve for the encouraging words.

    ReplyDelete