Noise Temperature. Concept of a Black Body

Transcription

1 Noise emperature In the last lecture, we introduced the Link Equation, which allows us to determine the amount of received power in terms of the transmitted power, the gains of the transmitting and receiving antennas, distance between the two antennas, and the wavelength of the transmitted signal. It appears in theory that no matter how low the received power at the receiving antenna is, the lowpower signals can always be amplified to any desired level making the amount of received power appear to be irrelevant. his is, however, not true because the limiting factor that determines whether the information contained in a transmitted signal can or cannot be retrieved is not how much signal power is received but how big is the ratio of the useful signal (what we call carrier power) to the amount of noise (what we call noise power). his ratio is called carrier to noise ratio or (C/N). We have studied how to evaluate the signal power at different stages of the satellite communication system, so now we will study how to evaluate the noise power at different stages of the satellite communication system. Concept of a Black Body he sources of noise are many in communication systems in general and in satellite communication systems in specific. For example, one of the sources of noise in satellite communication systems is radiated EM waves from the Sun, the moon, and Earth. Another source comes from surrounding electric and electronic equipment. One of the biggest sources of noise is electronic components of the satellite communication system itself. We will first consider the last source of noise and try to quantify the amount of noise that a satellite communication system generates resulting in the concept of Carrier/Noise Ratio. An electronic device generates noise as a result of the continuous movement and collisions of electrons with each other. he collisions of electrons generates noise in the form of a random electrical signal that has a very wide bandwidth with almost constant amount of power per Hz from 0 Hz to around 300 GHz. he amount of power a device generates per Hz is related to the temperature of the device in Kelvin (K). he higher the temperature of the device the more noise it generates and a device will generate no noise at all if its temperature is 0 K ( 273 C). he proportionality constant is know as Boltzmann constant (k = 1.391e 23 Joule/K). When a device such as an amplifier is manufactured, the manufacturer assigns to it a quantity called noise temperature or noise figure. Either of these quantities indicates the amount of noise that this device will introduce to its input signal at its specific operating temperature. For example, two different amplifiers that operate at the same temperature may introduce different amounts of noise to their respective input signals, indicating that the noise temperature (or noise figure) of the device that produces higher noise is higher than noise temperature (or noise figure) of the device that produces lower noise. he noise temperature of a device is defined as the temperature of a black body (a body that only generates noise and does not reflect it) that would result in that black body generating the same amount of noise power. It may appear that a device that operates at a temperature of 300 K, for example, would have a noise temperature of 300 K. In reality, with the advances in electronic

2 device manufacturing it is possible to manufacture amplifiers that have noise temperatures as low as 30 K ( 243 C) when operating at room temperatures and even higher without cooling these devices. In addition to this, generally the higher the operating frequency of the device is the higher its noise temperature. Concept of a Noise emperature When dealing with complicated electronic equipment, it is often useful to combine the noise that the different blocks individually generate into noise that is generated by the whole system as a block. For example, if a satellite transponder is built using an RF amplifier, a mixer, and a high power amplifier, each of which generates its own noise, we usually prefer to deal with the transponder as a single unit that generates an amount of noise that represents the combination of the three noise powers generated by the individual components. o do this, we refer the noise of a device to its input side as shown below: A Noisy Amplifier Model Input-Referred Noise with Noiseless Amplifier he above indicates that a noisy device (such as an amplifier) with a specific gain G can be represented by a similar noiseless device (the amplifier for example) with the same gain G but with an equivalent amount of thermal noise at its input. Now, if several devices (such as an RF amplifier, a mixer, and a high power amplifier) are place in series with each of them generating its own thermal noise, the noise signals of each can be placed at the input of each device and each of them is replaced by a similar noiseless device with the same original gain. he following is a block diagram of a satellite transponder showing the receiving antenna and the three main blocks up to the high power amplifier: his block diagram can be represented as shown below after including the thermal noise sources in each block (the signal or carrier is removed for simplicity since we are only interested in noise here):

3 By bringing the thermal noise of each block to its input, we change the above block diagram to the following one: he aim behind our discussion above is to combine all of the noise sources into a single source such that we get the following block diagram for the whole satellite transponder: We will see later how to combine all noise sources of a system into one equivalent source as shown above. hermal Noise he amount of available thermal noise that a device black body can provide to the next stage connected to it is given by the equation: where N = k d BN N is the available noise power in (W), k is the Boltzmann constant (=1.391*10 23 J/K), d is called the noise temperature of the device in (K), and that we are interested in (Hz). B N is the bandwidth of the noise

4 Notes: his noise power is available noise power from one block to the next block connected to it. he complete available power is delivered to the next block only if the input impedance of the block receiving the noise is matched to the output impedance of the block generating the noise. In electronic circuits, this is generally the case since impedances of different blocks are matched to insure that the maximum power of the desired signals are also transferred from one block to the next. he units of the left and right hand sides of the equation match J 1 K Hz= J = Watts K S. he amount of noise power is a function of the bandwidth of the noise. his noise bandwidth is always taken to the bandwidth of the desired signals to which the noise is added. his is logical because the bandwidth of filters in the system is usually set to be equal to the bandwidth of the desired signal that they process which means that the noise outside the band of the signal will also be filtered out by the same filters that filter the desired signal. System Noise ower and Noise emperature he aim now is to determine the amount of noise power that a system such as a satellite transponder generates knowing the different components of the transponder, their gains, and their noise temperatures. Consider the following system with different noise temperature as shown below: Now, we can represent the thermal noise of each block as a signal at the input of each block as: Noiseless RF Amplifier Noiseless Mixer Noiseless High ower Amplifier Ant = k Ant B N + + X + G RF G Mix G HA RF = Mix = HA = k RF B N k Mix B N k HA B N

5 he block diagram above can be reduced into a single block as shown below by bringing the different noises forward (remember that a signal after a block with gain G is equivalent to the signal divided by G before that block), and then collecting all gains of different blocks into a single gain (remember that several cascaded gains are combined by multiplying the gains by each other): he transponder noise rans becomes rans Mix HA = RF Expanding both sides of the above equation gives: k B k B k rans BN = k RF BN G G G Mix N HA N RF RF Mix Reducing the above equation gives by cancelling common quantities (i.e. k and B N ) we get: rans Mix HA = RF he gain of the complete transponder becomes: Grans = GRF GMix GHA Considering the whole system including the noise generated by the antenna itself as part of the system noise as shown below: his results in noise power and noise temperature given by and Mix HA Sys = Ant + RF

6 Mix HA Sys = Ant + RF Notes: Looking at the system noise power (and system noise temperature), it becomes obvious that for a system with blocks that have high gains that are much larger than 1, the noise power (and noise temperature) becomes dominated by the antenna noise power and RF stage noise power (the Antenna noise temperature and RF noise temperature). hat is, Sys Ant + RF and Sys Ant + RF For this reason, it is very important that the first block of the system (RF amplifier) be a low noise amplifier because its effect is extremely significant. In satellite systems, this block is usually called Low Noise Block (LNB). For a system with blocks that all have gains that are greater than 1 (all blocks amplify their signals), the effect of a block on the system noise power increases for earlier blocks compared to later blocks. For a block with a gain that is lower than 1 (a block that attenuates its input signals such as a mixer), the effect of the block that follows this attenuating block on the total noise of the system is more significant than the effect of the attenuating block itself. Noise Figure Another way of representing how much noise power a block generates is known as the Noise Figure (NF). he noise figure of a block is defined as the ratio of the output noise power of the block over the input noise power to the block. hat is: NF = Output Noise ower Input Noise ower he noise figure of a device is related to its noise temperature by the relation d ( ) = NF where 0 is the standard noise temperature (usually considered to be 290 K). he NF is sometimes expressed in db form as: NF (db) = 10 log 10 (NF (Linear) )