2 added 561 characters in body edited Apr 27 '17 at 17:33 Phiteros 4,76111 gold badge1616 silver badges3636 bronze badges When discussing radio antennae, radio astronomers usually describe things in terms of temperatures. We can convert between power and temperature simply by multiplying (or dividing) by Boltzmann's Constant: $$P=k_BT$$. We define the antenna's System Temperature, $$T_{sys}$$, as the sum of all the temperature contributing factors. The most important contributor to $$T_{sys}$$ is the source temperature, $$T_{A}$$. Sometimes this temperature is just the temperature of a blackbody, but for non-thermal sources we use brightness temperature: $$T_b=\frac{S_\nu \lambda^2}{2k_B\theta_s^2}$$ where $$S_\nu$$ is the source flux density, $$\lambda$$ is the wavelength, and $$\theta_s^2$$ is the angular size of the object. In the case of a spacecraft, $$\theta_s^2$$ would be the angular size of the spacecraft's antenna beam: $$\theta=k\frac{\lambda}{d}$$ where $$k$$ is a coefficient dependent on the geometry of the dish. Other sources of temperature come from the spillover from the ground, ambient sky temperature, and the antenna itself. So how do we get rid of those contributions? The answer: calibration. When we observe a source, be it a spacecraft or a quasar, in order to determine the amplitude of the actual signal we are receiving, we calibrate by looking at a source of known flux density. Usually this is done in radio astronomy by first observing a bright point source near to our target. Some telescopes utilize a calibrator device that emits a known flux. For a spacecraft, it is probably even simpler: the engineers will know the power the signal is being transmitted with, the beam size, and the source distance. From that they can easily calculate the brightness temperature. Once we know what kind of flux we should be getting from our source, we can easily subtract away the unwanted temperature components. They will still add some noise to our signal, as our calibrations can never be perfect. However, they will not completely swamp our signal. Alternatively, instead of looking at an absolute flux calibrator, if you're looking at a point-source (like a spacecraft), you can simply calibrate by pointing your beam off-source. By assuming that your noise is gaussian in nature, it will be the same both on-source and slightly off it. You can rapidly switch between the beams, and subtract your off-source beam from your on-source beam. This will leave you with the signal from your source itself. This is known as Dicke Switching. Now, why do we cool the receivers so much? The answer is that we are seeking to decrease the receiver temperature, $$T_{R}$$. The antenna's receiver contains amplifiers to gain up the signal. The receiver temperature is given by: $$T_R=T_{G,1}+\frac{T_{G,2}}{G_1}+\frac{T_{G,3}}{G_1G_2}+...$$ where $$T_{G,n}$$ is the temperature of the nth amplifier and $$G_n$$ is the gain of the nth amplifier. As long as you are gaining your signal up by a few orders of magnitude at each step, each successive amplifier contributes practically nothing to the overall receiver temperature. Therefore, your biggest contribution is the first amplifier. If we were to leave the receiver out in the open, this would add a whopping 300 K to our signal, a contribution that we cannot simply calibrate away. However, by cooling it to ~4 K, you eliminate the majority of the noise that would come from your receiver. As the above website notes, when using Dicke switching, you end up doubling your receiver temperature, which is another reason they seek to cool the receivers by such a great amount. Source: Tools of Radio Astronomy by Wilson, Rohlfs, and Huttemeister, 5th ed. When discussing radio antennae, radio astronomers usually describe things in terms of temperatures. We can convert between power and temperature simply by multiplying (or dividing) by Boltzmann's Constant: $$P=k_BT$$. We define the antenna's System Temperature, $$T_{sys}$$, as the sum of all the temperature contributing factors. The most important contributor to $$T_{sys}$$ is the source temperature, $$T_{A}$$. Sometimes this temperature is just the temperature of a blackbody, but for non-thermal sources we use brightness temperature: $$T_b=\frac{S_\nu \lambda^2}{2k_B\theta_s^2}$$ where $$S_\nu$$ is the source flux density, $$\lambda$$ is the wavelength, and $$\theta_s^2$$ is the angular size of the object. In the case of a spacecraft, $$\theta_s^2$$ would be the angular size of the spacecraft's antenna beam: $$\theta=k\frac{\lambda}{d}$$ where $$k$$ is a coefficient dependent on the geometry of the dish. Other sources of temperature come from the spillover from the ground, ambient sky temperature, and the antenna itself. So how do we get rid of those contributions? The answer: calibration. When we observe a source, be it a spacecraft or a quasar, in order to determine the amplitude of the actual signal we are receiving, we calibrate by looking at a source of known flux density. Usually this is done in radio astronomy by first observing a bright point source near to our target. Some telescopes utilize a calibrator device that emits a known flux. For a spacecraft, it is probably even simpler: the engineers will know the power the signal is being transmitted with, the beam size, and the source distance. From that they can easily calculate the brightness temperature. Once we know what kind of flux we should be getting from our source, we can easily subtract away the unwanted temperature components. They will still add some noise to our signal, as our calibrations can never be perfect. However, they will not completely swamp our signal. Now, why do we cool the receivers so much? The answer is that we are seeking to decrease the receiver temperature, $$T_{R}$$. The antenna's receiver contains amplifiers to gain up the signal. The receiver temperature is given by: $$T_R=T_{G,1}+\frac{T_{G,2}}{G_1}+\frac{T_{G,3}}{G_1G_2}+...$$ where $$T_{G,n}$$ is the temperature of the nth amplifier and $$G_n$$ is the gain of the nth amplifier. As long as you are gaining your signal up by a few orders of magnitude at each step, each successive amplifier contributes practically nothing to the overall receiver temperature. Therefore, your biggest contribution is the first amplifier. If we were to leave the receiver out in the open, this would add a whopping 300 K to our signal, a contribution that we cannot simply calibrate away. However, by cooling it to ~4 K, you eliminate the majority of the noise that would come from your receiver. Source: Tools of Radio Astronomy by Wilson, Rohlfs, and Huttemeister, 5th ed. When discussing radio antennae, radio astronomers usually describe things in terms of temperatures. We can convert between power and temperature simply by multiplying (or dividing) by Boltzmann's Constant: $$P=k_BT$$. We define the antenna's System Temperature, $$T_{sys}$$, as the sum of all the temperature contributing factors. The most important contributor to $$T_{sys}$$ is the source temperature, $$T_{A}$$. Sometimes this temperature is just the temperature of a blackbody, but for non-thermal sources we use brightness temperature: $$T_b=\frac{S_\nu \lambda^2}{2k_B\theta_s^2}$$ where $$S_\nu$$ is the source flux density, $$\lambda$$ is the wavelength, and $$\theta_s^2$$ is the angular size of the object. In the case of a spacecraft, $$\theta_s^2$$ would be the angular size of the spacecraft's antenna beam: $$\theta=k\frac{\lambda}{d}$$ where $$k$$ is a coefficient dependent on the geometry of the dish. Other sources of temperature come from the spillover from the ground, ambient sky temperature, and the antenna itself. So how do we get rid of those contributions? The answer: calibration. When we observe a source, be it a spacecraft or a quasar, in order to determine the amplitude of the actual signal we are receiving, we calibrate by looking at a source of known flux density. Usually this is done in radio astronomy by first observing a bright point source near to our target. Some telescopes utilize a calibrator device that emits a known flux. For a spacecraft, it is probably even simpler: the engineers will know the power the signal is being transmitted with, the beam size, and the source distance. From that they can easily calculate the brightness temperature. Once we know what kind of flux we should be getting from our source, we can easily subtract away the unwanted temperature components. They will still add some noise to our signal, as our calibrations can never be perfect. However, they will not completely swamp our signal. Alternatively, instead of looking at an absolute flux calibrator, if you're looking at a point-source (like a spacecraft), you can simply calibrate by pointing your beam off-source. By assuming that your noise is gaussian in nature, it will be the same both on-source and slightly off it. You can rapidly switch between the beams, and subtract your off-source beam from your on-source beam. This will leave you with the signal from your source itself. This is known as Dicke Switching. Now, why do we cool the receivers so much? The answer is that we are seeking to decrease the receiver temperature, $$T_{R}$$. The antenna's receiver contains amplifiers to gain up the signal. The receiver temperature is given by: $$T_R=T_{G,1}+\frac{T_{G,2}}{G_1}+\frac{T_{G,3}}{G_1G_2}+...$$ where $$T_{G,n}$$ is the temperature of the nth amplifier and $$G_n$$ is the gain of the nth amplifier. As long as you are gaining your signal up by a few orders of magnitude at each step, each successive amplifier contributes practically nothing to the overall receiver temperature. Therefore, your biggest contribution is the first amplifier. If we were to leave the receiver out in the open, this would add a whopping 300 K to our signal, a contribution that we cannot simply calibrate away. However, by cooling it to ~4 K, you eliminate the majority of the noise that would come from your receiver. As the above website notes, when using Dicke switching, you end up doubling your receiver temperature, which is another reason they seek to cool the receivers by such a great amount. Source: Tools of Radio Astronomy by Wilson, Rohlfs, and Huttemeister, 5th ed. 1 answered Apr 27 '17 at 5:22 Phiteros 4,76111 gold badge1616 silver badges3636 bronze badges When discussing radio antennae, radio astronomers usually describe things in terms of temperatures. We can convert between power and temperature simply by multiplying (or dividing) by Boltzmann's Constant: $$P=k_BT$$. We define the antenna's System Temperature, $$T_{sys}$$, as the sum of all the temperature contributing factors. The most important contributor to $$T_{sys}$$ is the source temperature, $$T_{A}$$. Sometimes this temperature is just the temperature of a blackbody, but for non-thermal sources we use brightness temperature: $$T_b=\frac{S_\nu \lambda^2}{2k_B\theta_s^2}$$ where $$S_\nu$$ is the source flux density, $$\lambda$$ is the wavelength, and $$\theta_s^2$$ is the angular size of the object. In the case of a spacecraft, $$\theta_s^2$$ would be the angular size of the spacecraft's antenna beam: $$\theta=k\frac{\lambda}{d}$$ where $$k$$ is a coefficient dependent on the geometry of the dish. Other sources of temperature come from the spillover from the ground, ambient sky temperature, and the antenna itself. So how do we get rid of those contributions? The answer: calibration. When we observe a source, be it a spacecraft or a quasar, in order to determine the amplitude of the actual signal we are receiving, we calibrate by looking at a source of known flux density. Usually this is done in radio astronomy by first observing a bright point source near to our target. Some telescopes utilize a calibrator device that emits a known flux. For a spacecraft, it is probably even simpler: the engineers will know the power the signal is being transmitted with, the beam size, and the source distance. From that they can easily calculate the brightness temperature. Once we know what kind of flux we should be getting from our source, we can easily subtract away the unwanted temperature components. They will still add some noise to our signal, as our calibrations can never be perfect. However, they will not completely swamp our signal. Now, why do we cool the receivers so much? The answer is that we are seeking to decrease the receiver temperature, $$T_{R}$$. The antenna's receiver contains amplifiers to gain up the signal. The receiver temperature is given by: $$T_R=T_{G,1}+\frac{T_{G,2}}{G_1}+\frac{T_{G,3}}{G_1G_2}+...$$ where $$T_{G,n}$$ is the temperature of the nth amplifier and $$G_n$$ is the gain of the nth amplifier. As long as you are gaining your signal up by a few orders of magnitude at each step, each successive amplifier contributes practically nothing to the overall receiver temperature. Therefore, your biggest contribution is the first amplifier. If we were to leave the receiver out in the open, this would add a whopping 300 K to our signal, a contribution that we cannot simply calibrate away. However, by cooling it to ~4 K, you eliminate the majority of the noise that would come from your receiver. Source: Tools of Radio Astronomy by Wilson, Rohlfs, and Huttemeister, 5th ed.