NTIA Redbook Calculations

0169-EX-CN-2019 Text Documents

AeroTEC Inc.

2019-04-26

Link Budget Calculations
Equipment
 Part                               Description                                       Gain or Loss
 L1/L2GPSA-T                        Active Roof Antenna                               40dBm
 L1/L2GRRKPA-T                      Passive Antenna. dBi depends on angle             3 dBi to -6 dBi
 RRKAMP                             Line Amplifier                                    30 dBm
 RG214/U                            Cabling                                           10.3 dB per 100ft
Formulas
The formula for the maximum EIRP in dBm as given in NTIA Redbook 8.3.27.f:

                         𝑃 π‘‡π‘šπ‘Žπ‘₯ = 𝑃𝑅 + 20 log10 𝑓 + 20 log10 (30 + 𝑑) − 27.55
Where: PTmax is the maximum permissible EIRP in dBm
       PR is the power received at 30 meters from the building (-140 dBm/24 Mhz)
       f is the frequency in MHz
       d is the distance between the radiator and the closest exterior wall of the building in meters.



The formula for the system’s radiated broadcast power in dBm is:

                                         𝑅𝑝 = 𝐺𝑅 + 𝐿𝐢 + 𝐺𝐴 + 𝐺𝑃 + 𝑅𝐴

Where: Rp is the radiated power in dBm
       GR is the gain provided by the roof antenna
       LC is the loss caused by cable and adapters
       GA is the gain from the reradiating amplifier
       Gp is the gain provided by the passive antenna
       RA is the average receive power for a given frequency in North America


Installation
The installation environment is a 56 x 54 meter rectangle as shown in this drawing:




The radiating antenna is suspended 15 meters above the ground in the center of the hangar. The
nearest wall is 27 meters away (54/2). In order to comply with NTIA regulations, the received signal
power must be less than -140 dBm at a range of 57 meters from emissive antenna. Please note that
emissive antenna is aiming down at the floor of the hangar.

Proof
First, we will compute the radiated power that this system will provide for the L1 and L2 signals.

The radiated power at the emissive antenna can be obtained by summing the gains and losses of the
broadcast system as shown in the formula section.

                                         𝑅𝑝 = 𝐺𝑅 + 𝐿𝐢 + 𝐺𝐴 + 𝐺𝑃 + 𝑅𝐴

For the L1 signal we will set:
        GR as 40dBm for the gain provided by the roof antenna
        LC as -2dBm for the loss caused by cable and adapters
        GA as 30 dBm for the gain from the reradiating amplifier
        Gp as -5 dBi for the gain provided by the passive antennai
        RA as -130 dBm for the average receive power for L1 in North America

                                   𝑅𝑝 = 40 − 2 + 30 − 5 − 130 = −67 π‘‘π΅π‘š


For the L2 signal we will set
        GR as 40dBm for the gain provided by the roof antenna
        LC as -2dBm for the loss caused by cable and adapters
        GA as 30 dBm for the gain from the reradiating amplifier
        Gp as -6 dBi for the gain provided by the passive antenna ii
        RA as -132 dBm for the average receive power for L2 in North America

                                   𝑅𝑝 = 40 − 2 + 30 − 6 − 132 = −70 π‘‘π΅π‘š

Now that we have the radiated power levels, we can compute the maximum allowed power level per
NTIA Redbook 8.3.27.f for L1 and L2:

                         𝑃 π‘‡π‘šπ‘Žπ‘₯ = 𝑃𝑅 + 20 log10 𝑓 + 20 log10 (30 + 𝑑) − 27.55
For L1, Let:
         PR = -140dBm
         f = 1575 MHz
         d= 27

             𝑃 π‘‡π‘šπ‘Žπ‘₯ = −140 + 20 log10(1575) + 20 log10 (30 + 27) − 27.55 = −68.5 π‘‘π΅π‘š
For L2, Let:
         PR = -140dBm
         f = 1227 MHz
         d= 27

             𝑃 π‘‡π‘šπ‘Žπ‘₯ = −140 + 20 log10(1227) + 20 log10 (30 + 27) − 27.55 = −70.6 π‘‘π΅π‘š

Results
    Signal               Max Allowed Power           Computed Power              Difference
    L1                   -68.5 dBm                   -67 dBm                     1.5 dBm
    L2                   -70.6 dBm                   -70 dBm                     0.6 dBm

By this analysis, both signals will be slightly above the required power level at a range of 30 meters. This
issue will be rectified by the inclusion of a 3 dBm fixed RF attenuator between the roof antenna and
repeater amplifier.



i
   At an antenna height of 15 meters and a measurement distance of 57 meters, we create a right triangle to
estimate the minimum angle between the emissive antenna and isotropic measurement antenna. Considering that
the average measurement antenna will be held at least 1 meter above the ground, we can reduce the effective
height of the emissive antenna to 14 meters.
                                                          14
                                             πœƒ = π‘‘π‘Žπ‘›−1 ( ) = 13.8°
                                                          57
The datasheet for the L1/L2GRRKPA-T specifies a gain of -5 dBi at 10° for the L1 frequency.
ii
   The datasheet for the L1/L2GRRKPA-T specifies a gain of -6 dBi at 10° for the L2 frequency.



Document Created: 2019-04-26 11:42:31
Document Modified: 2019-04-26 11:42:31

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