Methods to place Satellite into Geostationary orbit

Methods to place Satellite into Geostationary orbit

 

There is a considerable amount of expertise and technology used to ensure that satellites enter their orbits in the most energy efficient ways possible. This ensures that the amount of fuel required is kept to a minimum; an important factor on its own because the fuel itself has to be transported until it is used. If too much fuel has to be used then this increases the size of the launch rocket and in turn this greatly increases the costs.

Many satellites are placed into geostationary orbit, and one common method (1st method) of achieving this is based on the Hohmann transfer principle. This is the method use when the Shuttle launches satellites into orbit. Using this system the satellite is placed into a low earth orbit with an altitude of around 180 miles. Once in the correct position in this orbit rockets are fired to put the satellite into an elliptical orbit with the perigee at the low earth orbit and the apogee at the geostationary orbit as shown. When the satellite reaches the final altitude the rocket or booster is again fired to retain it in the geostationary orbit with the correct velocity.

as shown in the fig the perigee of the transfer orbit intersects the LEO orbit.This point is 1st pro-grade burn i.e rocket thrust (called delta V) in the same direction as of orbit and transferred to elliptical orbit i.e Hohmann Transfer orbit or Geostationary Transfer orbit.

at half of the transfer orbit is apogee point which intersects the geostationary orbit after that point satellite starts to fall i.e we have to fire our thrust in the same direction of the orbit which is 2nd pro-grade burn to remain in the geostationary orbit.

( 2nd method )Although now-a-days almost all the county uses Expandable Launch vehicle which directly place satellite into geostationary transfer Orbit without using LEO. ( PSLV , GSLV is expendable launch vehicle use by India)

But hohmann Transfer orbit is very useful for interplanetary travel (travels to diffrent planets by including one more method called gravity Assist )

America NASA’s Space shuttle and Russia’s Soyuz are Partial reusable launch vehicle to carry payloads to LEO orbit (ISS is in LEO orbit) while PSLV GSLV (india), Ariane 5 (ESA),Proton M (Russia) are expandable launch vehicle i.e non reusable vehicle.

no true reusable launch system is currently in use.

Fourier Transform

Fourier Transform

 

Fourier Transform  is a very powerful tool that can able to convert any Time Domain Signal (periodic / non periodic) as a function of  Frequency called Frequency Domain.

we can also convert from frequency domain to time domain by inverse fourier transform.

 

Here, w = 2.pi.f

F(w) is called as Fourier Transform & f(t) is called as Inverse Fourier Transform.

The time domain description tells you what sound you hear every instant, while the frequency domain description tells you, roughly,what instruments are involved in the ways & how they are played.

 

one of the most important properties of the Fourier transformation is that it converts calculus i.e differentiation and integration into algebra i.e multiplication and division. This underlies its
application to linear ordinary differential
equations and further to partial differential equation

Fourier Transform has many Application in many fields of science such as 

Signal Analysis,Image Processing,Sound Filtering/Digital Filter-high pass low pass band pass etc,Data Compression,Solving Linear Partial Differential Equations,Communication,Optics,Geology,Astronomy,Antenna Designing and many moreand many
more.

 

 

in fact
any field of physical science that uses sinusoidal signals, such as
engineering, physics, applied mathematics, and chemistry.

let’s take an example :-

Fig 1

lets observe fig 2 by looking at time domain we can’t determine the frequency of resultant sound wave signal but by taking the transformation we can say that it contains three harmonic frequency of 50Hz,100Hz and 150Hz. similarly by taking the transformation of modulated signal at the receiver one can able to determine the carrier frequency and information signal frequency.

Fig 2

in modulation process i.e while signal is passing through the channel,noise is superimposed on the signal.by  taking the Fourier transformation we can suppress the noise signal by designing the filter.that is the use of filter in signal processing.we can able to eliminate the unwanted frequency (particular or band of frequency ) by designing high pass, low pas , band pass filter. click here

 

Square

Sawtooth

Pulse

 

above fig shows how many harmonics of sine wave are used to approximate/generate the square wave,saw tooth & pulse.

 

 

Fourier Series

Fourier Series

I found that  almost all the books of DSP have a chapter dedicated to Fourier theory, all describing some crazy looking weird formulas and one can be easily lost in  the mathematics behind that. But basic idea behind all the horrible formulas is very simple & even  fascinating :-Any Periodic function can be represented as sum of sine and cosine wave this representation is known as Fourier series named in the honor of Jean Baptiste Joseph Baron Fourier.

Fourier series is given by :-

where,

n = 1 , 2 , 3 , … and T is the period of function f(t). 

a_n and b_n are called Fourier coefficients and are given by

 

now lets we want to represent Square wave in the form of sine & cosine wave.

periodic square wave function f(t) defined by
 

here suppose T = 6 (approx)

now lets find coefficient a₀ which is  DC value 

 

 

 

a₀ = 0  

 

i.e our waveform will oscillation either side of 0 = horizontal axis X line. 

 

now  lets find coefficient a_n which is Even Part 

 

 

 

 

 

 

 

 

 

 

a_n = 0 

 

i.e our waveform will not contain any of cosine Part (even) 

 

now, lets find coefficient b_n which is Odd Part 

Note that cos (n pi) may be written ascos (n pi) = (-1)ⁿ

and that b_n = 0 whenever n is even.

The given function f(t) has the following Fourier series
 

 

 

so, our waveform contains only of sum of sine function i.e odd part.

 

now put N=1 and observer the waveform, 

 

we got 1st harmonic of sine wave also called fundamental harmonic. 

now put n=2  

at 2nd harmonic we observe no change in the waveform because our function is zero when ( i.e bn = 0) whenever n is even 

 

now put n=3

 

its a addition of 1st harmonic + 3rd harmonic(shown in black at centre) = resultant red waveform

 

n=4 which is even so there is no change in waveform

 

 

n=5 note we are closer to approximation of square wave

 

 

n=29 we have almost approximated the square wave

 

 

Note :- fourier series is used when function is continuous and periodic.

Interfaces in GSM

Interfaces
in GSM

 

BSS subsystem consist of :-

 

1. A Interface
2. Ater Interface
3. Abis Interface
4. Um Interface

 

 

A Interfaces
:-

 

At MSC uses
PCM30(8000 samples/second) or E1 links to carry the data to and from transcoder. Suppose 4-E1 links
between MSC – Transcoder.

 

1 E1 = 32ch

4 E1=128ch

 

Each channel is of 64kbps.

128*64 = 8.192Mbps

but out of 128 channel only 120 is used (8 for signalling i.e 2 from each E1 link)

so there are 120 channel available for Traffic.

Ater interface :-

as shown above Ater interface consist of 32 channel.

but remember CH0 & CH16 is not converted into 16 kbps i.e it is transparent.

so total of 120 sub channel (30*4) each of 16Kbps.

Abis interface & Um interface:-

2 channel from Abis interface are mapped to 8 timeslot of TDMA Frame.

here in fig it is mapped at full rate of 16kbps but its depends on vendor equipment configuration.one can also use 32kbps or 64kbps. i.e Abis interface is proprietory.

So,maximum 15 TRX = 15 ARFCN = 15*8 timeslots =120 user calls can be handled by 1 BTS with 1 E1.

but if all the channels are used for voice then there wouldn’t be any channel for signaling.so, signaling information is carried over in specific Abis timeslots of 64kbps each,or in 16kbps sub timeslots to atleast 1 TRX per cell.

Signaling CAS & CCS

        Signaling 

In today’s world Two types of signaling is used:-

1.        CAS – Channel
   Associated Signaling
2.        CCS – Common
   Channel Signaling

 

In CAS,signaling bits are associated inside the voice channel i.e.
no dedicated channel for signaling also called in band signaling.

T – Carrier CAS

 

T1 in CAS à
24 voice channel (1.544Mbps)

 

Basic single channel rate is 64 kbps also called DS0. (as per
sampling theorem sampling rate should be twice the maximum frequency of the
signal. We know that human voice range is 4Hz – 4kHz of frequency so to
reproduce the signal we must sample it twice i.e. 2*4KHz=8KHz=8000  sample/sec
& each channel is of 8 bits so channel rate is 8000*8=64Kbps)

So, T1 contains 24 DS0 voice channel in CAS. but all channel
is used for voice so  how can we obtain
the singling. Here is the concept CAS in T1 use every last bit (Least Significant
Digit)of each channel of every 6^th frame for signaling (not total
channel but only a bit).this is known as robbed bit signaling or RBS.

fig1 T1 CAS

Note one thing here ,we know that T1 is of 1.544 Mbps.

lets calculate 24ch*8bits=192bits

192bits*8000samples = 1536 Kbps=1.536 Mbps so how come its 1.544 Mbps.

here, is the conclusion we use 1 bit for framing at the end of each frame so, its 192+1=193bits and 193bits*8000samples=1544 Kbps=1.544 Mbps which is our T1 Line.

8000 samples means each frame is repleted 8000 times to obtain 1.544Mbps T1 line.T1 CAS uses two types of framing :-

Super Frame sends 12 frame at a time.in SF we get 2 bits A,B for signaling

Extended Super Frame 24 frame at a time.in ESF we get 4 nits A,B,C,D for signaling.

The meaning of these bits depends on what type of signaling is used on the channel.The most common types of signaling are loop start,ground start and E&M.

Loop Start

Ground Start

E&M

E – Carrier CAS

 

E1 in CAS à  30 voice channel + 2  dedicated signalling channel (2.048 Mbps)E1 CAS has :-

• CH1 dedicated channel for framing
• CH17 for signaling
• CH2-16 & CH18-32 are dedicated for voice

why is it called CAS even if it uses dedicated channel for signaling ? answer is E1 CAS uses same signaling type as that of T1 CAS as shown in below fig.

so, E1 CAS is compatible with T1 CAS.one can able to convert E1 to T1 or vice-versa.

T – Carrier CCS & E – Carrier CCS

T1 in CCS à  23 voice channel + 1 signaling channel (1.544Mbps)

T1 in CCS uses 1 dedicated channel for signaling which operates at 64Kbps.

E1 in CCS à  30 voice channel + 2  dedicated signalling channel (2.048 Mbps)

E1 in CCS uses 1 dedicated channel for signaling(ch 17 in our diagram above) & 1 dedicated for sync purpose ch 1 (which is neither bearer(voice) ch nor data ch(signaling))

so, what is new in CCS ? answer is instead of using bits (A,B,C,D) CCS uses packets for exchanging short messages for signaling i.e it uses protocol for communication on signaling channel (64kbps)

some of the available protocols are ISDN & SS7(signaling system 7).

note here applications/protocols such as SS7 have the flexibility to define any of channel as signaling channel.