Capítulo 1. El cambio de preferencias en el agente económico
1.2. El contenido empírico de la racionalidad
1.2.1. Las bases de la coherencia
With the most of the local propagation aspects modelled, it is now possible to determine a shielding budget for on-site RFI. The shielding budget will function as a tool to determine if a noise-source is harmful to the nearest receiver. This will be done using the SARAS levels seen in Eq. 6.5.1 as a reference. The calculations for this example will be done to the nearest, out of the core, MeerKAT-receiver not shielded by Losberg (See Fig. 6.15).
SARAS = −17.2708 log10(f ) − 192.0714 (6.5.1)
where
• f is the frequency in MHz, less than 2000 MHz • SARAS is the maximum tolerable level in dBm/Hz
Using the models in Eq. 6.2.4, 6.3.1 and 6.4.1 a shielding level can be calculated from either inside the KAPB, outside the KAPB and outside the KAPB not shielded by the berm. This is possible by just changing the way the equations are handled. The shielding levels for each of the three mentioned scenarios can be seen, as an example, in Fig. 6.16. In the ”outside KAPB” case
CHAPTER 6. PROPAGATION AND SHIELDING MEASUREMENTS 106 Shield d rg 7 M M B K B Losberg
Figure 6.15: Google Earth satellite map showing the location of the KAPB and berm relative to the nearest MeerKAT receiver.
the RFI is placed close to the living quarters at a height of 2 m to simulate the use of a laptop. Similarly in the ”Not shielded by berm” case the RFI is moved into the field region removing the berm obstruction. Here the distance and height is kept the same as the previous case. With this prediction, it can be seen that RFI inside the KAPB has at least 150 dB (200 MHz) shielding to the closest MeerKAT receiver. This shielding represents an unshielded RFI source inside the building. Equipment placed in a shielded compartment would benefit from shielding additional to that calculated in these models. Assuming an RFI source with a bandwidth of 12.5 kHz, the maximum allowable signal, according to SARAS, can be seen in Fig. 6.16b for a source located inside the KAPB.
A step-by-step procedure for obtaining the overall shielding as in the ex- amples will be explained. It should first be noted that these models were only tested between 260 MHz and 930MHz. Also, a noise source inside the KAPB is assumed to radiate, after shielding has been applied, at a height of 5.5 m from the centre of the KAPB. Berm shielding is assumed for propagation per- pendicularly over its centre. In the case where berm shielding is applied, the source height for the ground-loss equation is taken as the height of the berm where the ground is approximated as a flat earth. Finally, propagation from outside the KAPB does not take into account obstacles such as containers, sheds and other on-site buildings.
• Step 1: If the RFI source is inside the KAPB continue to Step 2, oth- erwise take LKAP B = 0 and skip to step 6.
• Step 2: Calculate the shielding LKAP B delivered in the direction of the
CHAPTER 6. PROPAGATION AND SHIELDING MEASUREMENTS 107 200 300 400 500 600 700 800 900Frequency [MHz] 120 130 140 150 160 170 180 190 Shielding [dB]
Comparing Shielded Areas to Receiver M59
Inside KAPB
Living Quarters
Open Field
(a) Shielding in areas
200 300 400 500 600 700 800 900Frequency [MHz] −45 −40 −35 −30 −25 −20 −15 −10
Maximum transmit power [dBm]
Maximum transmit level at 12.5kHz bandwidth
For Receiver M59
For Receiver M60
(b) Maximum transmit level
Figure 6.16: Shielding to nearest MeerKAT receiver (M59) from inside KAPB, outside KAPB and outside KAPB not shielded by the berm. Height for the outside RFI positions were kept at 2 m high 70 m from the foot of the berm. In (b) the maximum allowable signal transmitted, from inside the KAPB, can be seen graphed using (a).
• Step 3: Calculate the berm shielding LBerm with Eq. 6.4.1. Here v
(Eq. 6.5.5) is calculated using a simplified form of v in Eq. 6.4.1. v = 1.34xr− 12.62hr+ 176.62 xr+ 80 r 80.45 + d2 λd2 (6.5.2) where
– λ is the wavelength of the RFI
– hr is the height of the receiver above ground
– xr = xtot − 80 which is now the distance from the berm to the
receiver
– xtot is the distance from the KAPB to the receiver
– d2 =p(xr)2+ (14 − hr)2
– d2 can be approximated as xr when xr >> 14
• Step 4: Calculate the ground loss LGround using Eq. 6.5.3 which is a
simplified form of Eq. 6.3.1. LGround = L50 = 10 log10 13hr (xtot− 80)2 2 40 f 2! (6.5.3) where
CHAPTER 6. PROPAGATION AND SHIELDING MEASUREMENTS 108
The two-ray model (Eq. 6.3.2) can also be used for a worst-case shielding scenario leading to Eq. 6.5.4. Keep in mind that the latter equation is only valid for distances beyond the two-ray model critical distance.
LGround = 10 log10 13hr (xtot− 80)2 2 (6.5.4) • Step 5: Continue to step 11
• Step 6: If the Berm is located between the RFI source and the receiver continue to the next step, otherwise take LBerm = 0 and skip to step 10
• Step 7: Calculate the berm shielding LBerm with Eq. 6.4.1. Here v
(Eq. 6.5.5) is calculated using a simplified form of v in Eq. 6.4.1 with variable source position and height.
v = xr(14 − hs) − xs(14 − hr) xr− xs s 2(d1+ d2) λd1d2 (6.5.5) where
– hs is the height of the RFI source from the ground
– xs= −(xsb+ 20)
– xsb is the distance from the RFI source to the foot of the berm
– d1 =p(xs)2+ (14 − hs)2
• Step 8: Calculate the ground loss LGround in the same manner as in
Step 4.
• Step 9: Continue to step 11.
• Step 10: Calculate the ground loss LGround using Eq. 6.5.6 which is
similar to Eq. 6.3.1. LGround= 10 log10 hshr x2 tot 2 40 f 2! (6.5.6) Or use the two-ray model in Eq. 6.5.7 for the worst-case shielding sce- nario. Keep in mind that the latter equation is only valid for distances beyond the two-ray model critical distance.
LGround = 10 log10 hshr x2 tot 2 (6.5.7)
CHAPTER 6. PROPAGATION AND SHIELDING MEASUREMENTS 109
• Step 11: Calculate the total shielding using Eq. 6.5.8.
Stotal = LKAP B + LBerm+ LGround (6.5.8)
• Step 12: Calculate the SARAS level PSarasfor the given frequency from
Eq. 6.5.1.
• Step 23: Calculate the maximum transmit level Pmax using Eq. 6.5.9.
Pmax = PSaras+ Stotal (6.5.9)
Using these empirically-based models along with the steps laid out in this section, it is now possible to calculate the amount of buffer available between the on-site noise sources and the SARAS reference levels. For an on-site RFI Engineer, this could be used as a tool to determine the severity of RFI sources. Therefore, sources exceeding the maximum transmit level can be flagged. While sources well below the maximum transmit level can be left in place to save resources.