-The analog part of the link budget, which is the title of this episode, covers what we called system resources. But what are these resources? Remember week 2. We mentioned a few laws, satellite communication laws. We talked about the rectangle law which mentions the energy dedicated to communication. We also talked about the distance law which specifies that when distance is doubled, four times more energy is required to send the signal. Finally, we mentioned the parabolic antenna law which says that the bigger an antenna, the more focused in a given direction the signal is. System resources group all this: antenna size and energy dedicated to communication. This illustration shows an uplink between a terminal and the satellite. For now we will focus on this case before considering the end-to-end link budget that will include the uplink, the satellite and the downlink. We will consider a simplifying assumption. The terminal on the illustration has only one satellite transponder that is entirely used for it. Remember the terminal architecture we previously saw. For the analog link budget, we will only consider the transmitter and antenna parts, that is to say everything after the modulator circled in blue here. In the case we are considering, the transmitter is directly located in the antenna head. Let us see this again. Let us have a look at the power of the signal received by the satellite. Power is nothing else than energy per time unit. It is expressed in watts but here we will use dBWs for easier calculations. dBW are simply a scale change compared to watts. This scale change has several benefits. It allows expressing small and large values without having to consider a huge amount of 0s and potentially making mistakes. This is shown on the right of the screen. Then, when power is multiplied by a certain factor, which is what an amplifier does, in dBW it does not require a multiplication but a simple sum. This is due to the definition of dB which has a logarithmic base as illustrated in the lower right corner. All I am saying is that we will count in dBW instead of watts for simplicity. But the same physical phenomenon is measured. Let us start with the transmitter located here in the satellite head. It transmits a certain power called PTX. At this stage, the power received by the satellite would equal the transmitted power. Of course this is not true since we are overlooking everything that happens to the signal afterwards. This is specified in the formula by the ellipsis, reminding us that it is incomplete. We already knew it thanks to the parabola formula. The parabolic reflector will concentrate the transmitted power in a given direction causing a gain effect which is a multiplication factor. Remember that now for a given frequency or wavelength, the bigger the parabolic antenna, the higher the gain. This is shown in the formula calculating the maximum gain of a parabolic reflector. Here we do not use the frequency but the wavelength which is simply the ratio between the speed of light and the frequency. As is frequent in engineering, there is a price to pay. The bigger the antenna, the narrower the power beam, so the antenna is harder to point towards the target. We will call EIRP, or equivalent isotropically radiated power, the power sent into space toward the satellite. In fact it corresponds to the transmitter power amplified by the parabolic antenna. Remember the square of the distance law. We understood that when a signal traveled, it got tired or, technically speaking, attenuated and dispersed. This is expressed in the LFS formula which represents the attenuation as a function of the distance and wavelength. This is what we call the attenuation in free space. You must know that going through atmospheric gases, rain or snow, also adds some attenuation. These attenuations can be represented as the opposite of a gain. We will call it Luplink, losses on the uplink. For a geostationary satellite in the Ku band, here I consider a 14-GHz frequency, we can count a 205 dB and more attenuation. Most of it is due to the 36 000-kilometer journey. To tell the truth, this way of representing space-free attenuation does not represent the physical phenomena. In particular, this representation assigns a frequency selectivity to free-space routes that is actually linked to the reception antenna. But by representing it this way, we get a simple mathematical form, commonly accepted, and the global result is perfectly acceptable. The signal eventually reaches the satellite. Thanks to a phenomenon identical to that of the terminal antenna, it is amplified by the reception antenna of the satellite and can potentially undergo a small attenuation due to devices, connection cables after the satellite antenna for example. All of this is summed up in the term GRX. We finally get the full formula which allows the power received by the satellite to be calculated. It should be noted that, compared to what has been sent, there is not much left. We understand why the satellite payload includes many cascade amplifiers. These steps are done for the link budget of the uplink, but they can also be done for the downlink. In that case, we will consider that the transmitter is the satellite payload and we will measure the transmitted power just before the transmission antenna.