SATELLITE LINK DESIGN CHAPTER 3
Basic Transmission Theory
The fundamental to the understanding of sat comm syst. These will include all the parameters such as:
Flux density EIRP Power received Power transmit System noise temperature Carrier to noise power ratio
Flux Density Isotropic Source
Area A (m2)
EIRP = Pt Gt Distance R (m) Flux density F (W/ m2)
Transmitting source radiate power Pt uniformly in free space. At distance R from the source, the flux density crossing the surface of a sphere with radius R is given by (ideal antenna):
F = Pt/ (4πR2)
W/m2
Flux Density For Real Antenna
Real antenna are directional It has gain G(θ) = the ratio of power per unit solid angle radiated in a direction θ to the average power radiated per unit solid angle.
G(θ) = P(θ)/ (P0/4π)
G= 4 π Ae/ λ2
Where:
,
G = η (πD/ λ)2
P(θ) = power radiated per unit solid angle by the antenna P0 = total power radiated by the antenna G(θ) = the gain of the antenna at an angle θ θ = boresight direction
Continued
Flux density for real antenna in the direction of boresight at distance R meter where G(θ) at angle θ = 0º
F = PtGt/ (4πR2)
W/m2
Where:
PtGt = Effective isotropic radiated Power The combination of tx power and antenna gain in terms of equivalent isotropic source with power radiating uniformly in all directions.
Continued
Antenna with physical aperture area of Ar m2 The energy incident on aperture is reflected away from the antenna and some is absorbed by lossy components This reduction in efficiency is describe as an effective aperture Ae Where:
Ae = η Ar
m2
η = aperture efficiency - all losses between the incident wavefronts and the antenna output port. (diffraction effect, feeder loss, blockage)
Power Received
For ideal antenna, the power received: Pr = F x Ae watts
Pr = Pt Ae / (4πR2) watts For real antenna, the power received: Pr = Pt Gt Ae / (4πR2)
Where :
Ae = η Ar
m2
Continued
Rearrange the equation: Pr = (Pt Gt Ae )/ (4πR2)…………. (i) G= (4 π Ae)/ λ2……………………………………(ii)
Subs (ii) in (i)
Pr = (Pt Gt Gr )/ (4πR/ λ)2 = power received in any radio link
Lp = (4πR/ λ)2 =path loss / free space loss =the way energy spread out as an emwave travels away from any transmitting source in 3 dimensional space.
Continued
There are other losses need to be considered:
Losses in atmosphere, rain, water vapor Losses in the antenna, miss pointing, feeder loss
Rewrite the equation:
Pr = EIRP + Gr – Lp – Lo
dBW
Example 1
A sat at a distance of 40000 km from a point on the earth’s surface radiates a power of 10 w from an antenna with a gain of 17 dB in the direction of the observer. Find the flux density at the receiving point and the power received by an antenna at this point with an effective area of 10 m2.
Example 2
A geostationary satellite at a distance of 37000 km operates at a frequency of 14 GHz. It radiates power from an antenna with a gain of 16 dB. The flux density at receiving point is 2.86 x 10-14 W/m2 in the direction of boresight. The receiving antenna has a physical aperture of 40 m2 with efficiency of 55%. Calculate: i) the power transmit by the transmitter from the sat to the e/s in dB. ii) the EIRP of the sat in dB iii) the received gain by e/s in dB iv) the path loss during transmission in dB v) the received power at e/s in dB
System Noise
Arises from the random thermal motion of electrons in various resistive and active devices in the receiver. Thermal noise also generated in the lossy components of antenna. The available noise power from a thermal noise source is given by:
Pn = kTB
Where:
T = noise temp B = noise bandwidth K = 1.38 x 10-23 J/K = Boltzmann constant
Continued
The noise power per unit bandwidth is termed as the noise power spectral density, N0. N0 = Pn/ B = kT The noise temp is directly related to the physical temp of the noise source but is not always equal to it.
Example 3
An antenna has a noise temp of 35 k and is matched into receiver which has a noise temp of 100 k. calculate: i) ii)
the noise power density the noise power for a bandwidth of 36 MHz
Antenna Noise
Antenna operating in the receiving mode introduce noise into sat circuit. The antenna noise can be classified into 2 groups: Sky noise
The microwave radiation which is present throughout the universe. Originate from matter in any form at finite temp. Rainfall introduce attenuation, therefore it degrades transmission.
Antenna loss
Add to the noise received as radiation The total antenna noise temp is in the sum of equivalent noise temp of all these sources.
Amplifier Noise Temperature Amplifier
Tant
G, T1
N0, in
N0, out
Figure 1
The input noise energy coming from the antenna is:
N0,in = kTant
The output noise energy:
N0,out = G k (Tant + T1)
The total noise referred to the i/p is simply:
N0,in = k (Tant + T1) = N0,out / G
Continued Tant N0, 1
Amp 1
Amp 2
G1, T1
G2, T2
N0, 2
N0, out
Figure 2
The noise energy of amp 2 referred to its own i/p:
N0,2 = kT2
The noise i/p to amp 2 from the preceding stages:
N0,in2 = G1 k (Tant + T1)
Thus the total noise energy referred to amp2 i/p:
N0,in2 = G1 k (Tant + T1) + kT2
Continued
The total noise referred to the i/p is :
N0,1 = k [Tant + T1 + (T2/G1)] = N0,2/ G1
System noise temp may defined as Ts by: N0,1 = kTs Ts = [Tant + T1 + (T2/G1)] Ts = [Tant + T1 + (T2/G1) + (T3/G1 G2) ]
Example 4
Suppose we have 4 GHz receiver with the following gains and noise temp: Tant = 25 k TRF = 50 k Tm = 500 k TIF = 1000k
i) ii) iii)
GRF = 23 dB GIF = 30 dB
Calculate the syst noise temp assuming that the mixer has a gain Gm = 0 dB Recalculate the syst noise temp when the mixer has a 10 dB loss How can the noise of temp of the receiver be minimized when the mixer has a loss of 10 dB?
Noise Factor
In defining the noise factor of an amp, the source is taken to be room temp, denoted by T0 (290 k). The i/p noise from such a source is kT0. The o/p from the amp is: N0, out = FGkT0
Continued
Relationship between noise temp and noise factor:
Thus:
Te = noise temp of the amp Tant = T0 = the source at room temp
GK (T0 + Te) = FGKT0 Te = (F -1)T0
The noise figure (f) is simply noise factor (F) expressed in dB.
f = 10 log F
F2 1 F3 1 FN 1 F F1 .. G1 G1G2 G1G2...GN 1
Example 5
An LNA is connected to a receiver which has a noise figure, f= 12 dB. The gain of the LNA is 40 dB and its noise temp is 120 k. calculate the overall noise temp referred to the LNA input.
Example 6 i)
ii)
Calculate the equivalent noise temperature for a noise figure of 5 dB and 5.6 dB. Assume the environmental temperature is 300 K. For equivalent noise bandwidth of 15 MHz and total noise power of 0.0357 pW, determine the noise density and equivalent noise temp. OCT 2004
Overall System Noise Temperature Tant
LNA
Cable
Receiver
G1, T1
Loss L:1
F
Figure 3 shows the cable is after the LNA
Figure above shows a typical rx antenna syst. Applying the previous sections yields for the syst noise temp referred to the i/p:
(L 1)T 0 L(F 1)T 0 Ts Tant T1 G1 G1
Continued
Tant
Cable
LNA
Receiver
Loss L:1
G1, T1
F
Figure 4 shows the cable is before the LNA
Thus the equation:
L(F 1)T 0 Ts Tant (L 1)T 0 LT1 G1
Example 7 i)
ii)
For the syst shown in fig 3, the receiver noise figure is 12 dB, the cable loss is 5 dB, the LNA gain is 50 dB and its noise temp is 150k. The antenna noise temp is 35 k. Calculate the noise temp referred to the input. Repeat the calculation when the system of fig 3 is arranged as shown in fig 4.
Example 8
A receiving syst consists of an antenna having a noise temperature of 60 K, feeding directly into LNA. The amplifier has a noise temperature of 120K and gain of 45 dB. The coaxial feeder between the LNA and the main receiver has a loss of 2 dB and the main receiver has a noise figure of 9 dB. Calculate the syst noise temp referred to input.
Carrier To Noise Ratio
A measure of the performance of a sat link. Carrier power to noise power Link budget calculation Denoted by C/N or C/N0 which equivalent to PR/PT. C EIRP Gr Losses k Ts Bw N C Gr EIRP Losses k N0 Ts C Gr A0 m BO k RFL N0 Ts
Example 8
In a link calculation of 2 GHz, the free space loss is 206 dB, the antenna pointing loss is 1 dB and the atmosphere absorption is 2 dB. The receiver G/T ratio is 19.5 dB/K and the receiver feeder losses are 1 dB. The EIRP is 48 dBW. Calculate the carrier to noise spectral density ratio.
Uplink
The uplink of sat cct is the one in which the e/s is transmitting the signal and the sat is receiving it.
(C/N0)u = EIRPe/s + (G/T)s – FSL - losses - k (C/N0)u = Ae +Ψ m+ (G/T)s – RFL - k
Where: Ae + Ψ
m=
EIRPe/s – FSL - losses + RFL
Example 9
An uplink operates at 14 GHz and the flux density required to saturate the transponder is -120 dB (W/M2). The free space loss is 207 dB and the other propagation losses amount to 2 dB. Calculate the e/s EIRP required for saturation assuming clear sky conditions. Assume RFL is negligible.
Input Backoff
When a number of carriers increased in TWTA, the operating point must be backoff to a linear region of the transfer characteristic to reduce the effects of IM distortion. Suppose the saturation flux density for a single carrier operation is known. Input backoff will be specified for multiple carrier operation referred to the single carrier saturation level. The e/s EIRP will have to be reduced by the specified backoff (BO).
Example 10
An uplink at 14GHz requires a saturation flux density of -91.4 dBW/M2 and an input backoff of 11 dB. The sat G/T is -6.7 dB/K and receiver feeder loss amount to 0.6 dB. Calculate the carrier to noise density ratio.
Downlink
The sat transmitting the signal and the e/s is receiving it.
(C/N0)d = EIRPs + (G/T)e/s – FSL - losses - k (C/N)d = EIRPs + (G/T)e/s – FSL - losses – k Bw
Output Backoff
When i/p BO is employed, a corresponding o/p BO must be allowed in the downlink transmission. The relationship between IBO and OBO in decibels is:
OBO = IBO – 5 dB
Example 11
A satellite tv signal occupies the full transponder bandwidth of 36 MHz and it must provide a C/N ratio at the destination e/s of 22 dB. Given that the total transmission losses are 200 db and te destination e/s (G/T) ratio is 31 dB/K. calculate the satellite EIRP required.
Example 12
The specified parameter for a downlink are sat saturation value of EIRP 25 dBW. OBO is 6 dB; FSL is 196 dB; other losses 1.5 dB and e/s (G/T) 41 dB/K. Calculate the C/N0 at the e/s.
Example 13
A multiple carrier circuit operates in the 6/4 GHz band with the following characteristic. Uplink Saturation flux density -67.5 Ae -37 IBO 11 G/T -11.6 Downlink Satellite EIRP 26.6 OBO 6 FSL 196.7 G/T 40.7 k -228.6 Calculate C/N0 for both links and the total C/N0 for the transmission.
