As noted, the receiver output noise is the sum of the amplified signal source noise and the receiver's own noise, i.e.
With this in mind, we get:
.
From the expression it follows that always 
... Only the perfect receiver when 
then 
.
Attitude 
can be considered conventionally as the intrinsic noise of the receiver, converted to the input of the receiver or reduced to the input of the receiver. We denote:
,
.
Hence the reduced noise is:
Rated power of noise entering the input of the receiver from the output impedance of the signal source 
at a temperature 
, equals
,
where the value 
determined by the formula 
.
This amount is called the standard input noise. Then the reduced noise will be expressed as follows
Receiver noise temperature
Let us introduce the notation into the last formula:
.
This value is called the receiver noise temperature. With this in mind, we get
.
Let's define the physical meaning of the noise temperature. Let us express the noise at the output of a real receiver from the last formula as follows:
Now we express the noise at the output of an ideal receiver:
Comparing both expressions, we can give the following physical meaning to the concept of "receiver noise temperature". The receiver noise temperature is the temperature by which the temperature of the output resistance of the signal source must be increased 
so that the noise at the output of an ideal receiver is equal to the noise at the output of a real receiver.
Let us express the noise factor in terms of the noise temperature, for this we divide expression (2.2) by (2.3), we get:
.
The quantity 
is called the relative noise temperature of the receiver. Taking this notation into account, we finally obtain
.
2.3 Noise figure for series-connected four-port networks
To analyze the influence of the noise of individual stages of the receiver on its resulting noise figure, it is convenient to represent the receiver as a series connection of four-port networks (Figure 2.2), i.e.
Figure 2.2
Suppose the receiver consists of three stages, each of which has its own gain 
and your noise figure 
... We use the expression (2.1)
.
For the output noise of a three-stage receiver, we write
Similarly, for an ideal receiver, we have:
Substituting the numerator and denominator in the expression for 
and considering that
;
,
Similarly, you can get expressions for any number of stages. Conclusions:
1) The noise figure of a receiver is mainly determined by the noise of its first stages.
2) An amplifier with low intrinsic noise and high gain should be located at the receiver input.
3) The higher the gain of the first stage, the less influence subsequent stages have on the resulting receiver noise figure.
In addition, mathematically, it can be shown that for a passive two-port network, in which 
, the noise figure is
.
2.4 Sensitivity of pnu and its relationship with noise figure
Distinguish between limiting (or threshold) and real sensitivity of RP R U.
The limiting sensitivity is the minimum signal at the input of the receiver at which the ratio at the output of the receiver is 
is equal to one.
Real sensitivity (or noise-limited sensitivity) is the minimum signal at the input of the receiver, at which a given level of the useful signal is provided at the output of the receiver, at a given 
.
The limiting sensitivity is equal to the sum of the reduced noise of the receiver and the noise arriving at the input from the antenna, i.e.
,
where 
- antenna noise temperature;
is the relative noise temperature of the antenna.
However, for normal operation of the terminal device, it is necessary that 
it would be much more than one. Therefore, the real sensitivity is determined by the expression
,
,
where 
- coefficient of distinguishability.
To estimate the sensitivity of the receiver itself (without an antenna), use the formula at 
, i.e.
;
.
In all cases, the more 
, the more 
and the less (worse) the sensitivity of the receiver.
Page 3
Numerous reports on the development of cooled parametric amplifiers have been published in the literature. In particular, the results of studying the effect of diode cooling on the effective noise temperature of the amplifier are presented in the works. In fig. 11.4 shows the experimentally obtained dependences of the noise temperature of the amplifier on the temperature of diodes made of germanium, silicon and gallium arsenide.
Along with this, there are many cases when the actual noise significantly exceeds the noise calculated by these formulas. In order to avoid a discrepancy between experiment and calculation, the concepts of effective noise temperature or effective resistance (conductivity) are introduced instead of the corresponding real values. Such ideas are unsuccessful and even harmful, since although they make it possible to numerically reduce experience with calculation, they do not correspond to the essence of the matter, and therefore do not indicate the correct ways of dealing with noise.
In equation (5.26), noise figure is used to describe the noise performance of an amplifier. Equation (5.28) is an alternative (but equivalent) characteristic called effective noise temperature. Recall that the noise factor is a measurement relative to a reference. Noise temperature has no such limitation.
This separation is simply done with a circulator as shown in fig. 17.23, a. This also has the advantage that room-temperature receiver loading noises do not pass directly into the maser. In addition to the intrinsic noise temperature of the maser TNM, the effective noise temperature includes the following terms: TNR / gp, which takes into account the receiver noise; TLA, which takes into account the matched load noise reflected from the antenna; TLM due to noise passing between arms 2 and 4 of the circulator; TRM due to receiver pikes passing between arms 3 and 2 of aT0, determined by dissipative loss in the feeder between the antenna and the maser.
The differences between amplifier networks and line loss networks can be viewed in the context of the loss and noise mechanisms described earlier. However, in this case, too, the degradation will be expressed in terms of an increase in the noise figure or effective noise temperature.
For example, Petritz's theory leads to a law of the form v - 1 with deviations of 3 56 in almost a five-decade frequency range. Some flicker noise measurements have been made; Nichol found that at 45 MHz this noise could be larger than the shot noise and be significant at frequencies up to 1 GHz. These additional noise sources should be considered when analyzing the performance of point-contact diodes by referring such noise to the effective noise temperature.
Parametric amplifiers are most often used in TRRL equipment. They are devices in which a variable reactive element is used, in the capacity of which a parametric diode is used, which has the properties of a nonlinear capacitance and changes its reactance due to external energy sources. Since purely reactive elements do not have their own noise, the PU provide low noise levels, allowing the effective noise temperature of the receiver to be reduced to the required value of 100 - 150 K. They use the capacity of the p-th junction of the diode to store energy, and this capacitance is changed due to the supply from the pump generator (GN) of an alternating voltage, the frequency of which is higher than the frequency of the amplified signal.
For cryogenically cooled receivers of millimeter and submillimeter waves, the Rayleigh-Jeans approximation can give a significant error. Two formulas are used to determine the effective noise temperature of a heat source when quantum effects are to be taken into account.
Taking the effective gas temperature to be 500 K, for the Ne n Doppler broadened line (9.9), we find that the amplifier bandwidth is 315 MHz, and from formula (9.20) we find the total output noise power per mode 12 3 10 - 9 W. Formula (9.6) gives that the effective noise temperature in this case is 8550 K, while the ideal value of this value is 6120 K.
The temperature range for commercial systems is usually between 30 and 150 K. The disadvantage of using noise factors for such low noise networks is that all the values \u200b\u200bobtained are close to unity (0 5 - 15 dB), which creates certain difficulties when comparing devices. For space communications applications, a reference temperature of 290 K is not as appropriate as for terrestrial applications. The effective input noise temperature is simply compared to the effective noise temperature of the source. In general, applications involving low noise devices are best described using effective temperature rather than noise factor.
A circulator is used to implement the single-arm version of the amplifier. In amplifiers of this kind, diodes with sharp, smooth and point-contact junctions are used. Output capacities are equal to 5 - 500 mt, above these values \u200b\u200bsaturation occurs; within this power range, the gain-bandwidth product increases. The effective noise temperature usually does not exceed 300 K; within certain limits, the noise temperature can be reduced by using a higher pump power.
In fig. 4.11 is a graph that compares the noise properties of different types of amplifiers. It follows from the graph that the noise temperature of crystal mixers increases very rapidly with increasing frequency and at / 300 MHz exceeds 1000 K. Circuits of high-frequency amplifiers on triodes have a lower noise temperature. However, with an increase in the frequency of amplified vibrations, it also increases very rapidly. The effective noise temperature of the tunnel diode amplifiers remains practically constant (Te 800 K) up to a frequency of / 6000 MHz. Parametric amplifiers (PA) have a noise temperature close to 100 K. For comparison, the figure shows the noise temperature of some noise sources.
The receiving path consists of a series of cascades connected in series, performing various functions. These are amplifiers, connecting passive paths, filters, mixers, etc. All stages are characterized by the power transmission ratio as the ratio of the signal power at the output of the stage to the power of the signal at its input, including mixers, whose input signal is at one frequency and at the output at another. If the transmission coefficient of the stage does not change when the signal power at its input changes, then we will assume that it is in the linear mode. Likewise, if the series-connected cascades of a path are in linear mode, then the entire path is called a linear path. The consequence of this property is that for a linear path, the ratio of the signal power to the noise power at the input and at the output is the same.
In the general case, the characteristic (amplifier, mixer, etc.) is shown in Fig. 5. The abscis axis shows the value of the signal power at the input of the stage - P in. The ordinate is the value of the cascade transfer coefficient - K.
At a certain value of the input power P sat. there is a decrease in the transmission coefficient by DK The power level of the signal at the input of the stage, at which a decrease in the transmission coefficient by the value of DK is observed, is called the saturation level of the stage.
DK is set, depending on the purpose of the path, equal to 0.1 dB, 0.5 dB, 1.0 dB, 3 dB or another value. With a given permissible criterion for reducing the transmission coefficient of the cascade, it is considered that the cascade operates in a linear mode until the signal power at its input exceeds the value of P sat.
For passive stages (filters built on passive elements, feeder and waveguide paths), the transmission coefficient does not depend on one signal power. The combustion effect of passive cascades is not considered in this case.
All stages generate noise, the power of which at the output of the stage can be calculated using the following formula:
,
where 
- Boltzmann constant; - the equivalent noise temperature of the noise at the output of the stage; - the frequency band of the cascade, which is limited by selective elements to the frequency band in which the signal spectrum is concentrated.
Equivalent noise temperature of the cascade input is the noise temperature at which 
- the noise power supplied to the input of the ideal (non-noisy) stage, having passed through the ideal stage with the gain K, would form at its input the noise power equal to. Then 
... Hence:.
For active stages or devices (amplifier, mixers, receivers, etc.), the passport data contains the value of the equivalent noise temperature of the input of the stage or device. For large values \u200b\u200bof the noise power in the passport for such cascades or devices, the value N is given - the noise figure (a dimensionless value expressed in times). The relationship between the noise figure and the equivalent noise temperature of the device inlet is given by:
, where is the ambient temperature, usually at normal temperature.
From the general theory of radio engineering circuits, the total transmission coefficient of series-connected n stages (in the absence of mismatch and saturation) and the equivalent noise temperature at the input of series-connected n cascades are calculated using the following formulas:
;
where: 
- transmission coefficients of the first, second, ..., n-th cascades, respectively;
- equivalent noise temperatures at the inlet of the respective stages.
Here the data transfer coefficients are at times, and the equivalent noise temperatures are in Kelvin.
For passive elements (waveguide, feeder path, etc.), the generated noise power at the path output is calculated from the following expression.
Effective noise temperature
The effective noise temperature of the antenna or AFD is introduced as a parameter of the receiving antenna when receiving weak microwave signals by analogy with sources of thermal noise.
In the study of microwave radio receivers, the effective noise temperature of the noise source (in degrees Kelvin) is introduced as a coefficient linking the noise power and the bandwidth:
,
where is the Boltzmann constant
The effective noise temperature, which characterizes the power of all external interference, is conventionally called the noise emission temperature. It is usually calculated by introducing the concept of brightness temperature of interference sources. The area of \u200b\u200bthe surface of the source of interference has a temperature if the intensity of interference generated by it is equal to the intensity of radio emission of the corresponding area of \u200b\u200ba black body with temperature and the same spatial configuration as the source of interference. Intensity - it is the spectral power density of the emitting body surface coming out through a unit area into a unit solid angle.
For a completely black body: 
.
The receiving antenna receives only that part of the power that is radiated by the area (elementary area on the radiating surface) into a solid angle resting on the area equal to the effective area of \u200b\u200bthe antenna. Thus, the spectral power density of the radiation from the area at the input of the receiver matched to the antenna is:
where is the solid angle at which the radiating area is visible from the antenna ()
Because the interference fields coming from different parts of the radiating surface are statistically independent, then the total spectral power density of the interference at the input of the receiver is determined by summing in all directions from the antenna to the parts of the radiating surface:
Total noise power:
Noise temperature:
The value depends not only on the antenna parameters, but also on the intensity of the distribution of external interference sources.
Antenna's intrinsic noise is determined by the antenna loss resistance, the temperature of which must be considered equal to the ambient temperature - the physical temperature of the antenna. Taking into account losses, the equivalent circuit of the antenna as a generator of noise emf is shown in the figure, where the noise temperature is assigned, which is different from the ambient temperature.
External noise and noise due to antenna losses are statically independent, so you need to add their rms values:
or ,
where is the effective noise temperature of the antenna.
After transformation we have:
,
,
where is the antenna efficiency.
A similar technique takes into account noises due to losses in the feeder together with the various devices included in it:
where is the efficiency of the transmission line, is the physical temperature of the transmission line (feeder), is the power transmission coefficient of the antenna circuit without taking into account the losses in the antenna and the line. Here the antenna is matched with the feeder, but the receiver is not ().
Receiver-feeder mismatch is often used to reduce noise in the receiver input circuit while realizing the ultimate sensitivity in the microwave range.
Internal noise is the noise of the active resistance of the antenna loss Tlos (loss) and the noise of the active resistance of the loss of the feeder Tf. Their level depends on the frequency to the extent that active losses in the antenna and feeder depend on it.
feeder thermal noise Tf
Knowing the loss of the feeder in dB, it is easy to calculate it using the formula Tf \u003d To (1 - efficiency), where To is the temperature of the medium (feeder) in gr. Kelvin. For this, the known feeder losses must be converted from dB to efficiency and a calculation must be made. For example, with a feeder loss of 1 dB, its efficiency is 0.89. At 17 ° C this feeder will have a noise temperature Tf \u003d 290 (1 - 0.89) \u003d 32 °.
tlos antenna thermal noise
It can also be calculated from the known losses in the antenna material. Antenna made of ideal material does not make noise. From real - it makes noise to the extent that its loss resistance is a part of the antenna RADIATION resistance. By choosing a power point and a matching device together with R emit. and R loss is also reduced to the INPUT impedance of the antenna.
The dB loss in a real material antenna can be determined from the difference in gain between an ideal and real material antenna. Converting db into the ratio of values \u200b\u200band subtracting from unity, we obtain the share of R losses in R radiation. or R input. Multiplying the share of R losses by the ambient temperature in ° Kelvin, we obtain T noise R losses or T loss with an accuracy more than sufficient for normal VHF antennas.
For example, a 50 ohm antenna made of an ideal material has a gain of 13 dB, and of aluminum 12.81 dB. A difference of 0.19 dB corresponds to a U or R ratio of 0.9783. 1.0 - 0.9783 \u003d 0.0217 is the share of losses. With R input 50 ohms, the loss resistance reduced to the input will be 0.0217 x 50 \u003d 1.085 ohms. If the temperature of the medium is taken as 290 ° Kelvin, then T loss will be: 290 ° K x R / Rin. In our case, this will be 290 x 1.085 / 50 \u003d 6.3 ° K.
It is easier to calculate with sufficient accuracy. From the decibel table, we find the numerical value of the gain difference, subtract 1 and multiply by 290 °. In our example, 0.19 dB \u003d 1.022. In this case, Tlos will be equal to 290 (1.022-1) \u003d 6.4 °. The table below calculates Tlos for the commonly present losses in pure aluminum VC antennas, made in MMANA. Taking into account the feeder losses, the effective temperature Tlos at the receiver inlet will be equal to Tlos x the feeder efficiency.
Conversion table for antenna gain differences calculated for ideal material and pure aluminum in Tlos
EXTERNAL NOISE AFS
External noise is noise received by the antenna from noise sources in the external space in the same way as the wanted signal. Such sources are the thermal noise of the earth Tz or Tearth (earth - earth), technogenic noise Tm and cosmic noise (noise of the sky) Tk or Tsky (sky - the sky). Obviously, the total external noise of the APS will depend both on the noise temperature of these sources and on the diagram and position of the antenna relative to these sources, and therefore it cannot be normalized. thermal earth noise T earth
Strictly speaking, the noise temperature of Tearth is equal to its physical temperature T times 1 - Ф, where Ф is the reflection coefficient of the earth's surface, which in turn depends on the tilt angle, electrical properties of the earth's surface and the polarization of the antenna. But on the VHF bands, as a rule, the Rayleigh condition is fulfilled, the surface of the earth is considered rough, the reflection from it is diffuse, F tends to 0, and Tearth tends to the physical temperature of the earth, which is usually taken in calculations to be 290 ° K. The level of thermal noise of the earth depends little on frequency.
technogenic noise TT
The noise of electrical devices, from household appliances, computer networks to power lines, electric vehicles and industrial. enterprises. The level can be very different, from 0 ° K in a deserted area without rail, pipeline and electrical communications within a radius of 100 km, to thousands and tens of thousands of degrees in business centers of cities and industrial zones. Or simply if a neighbor has a Chinese charger or power supply unit connected to the network without a noise filter. With increasing frequency, the intensity of technogenic noise decreases, but not as fast as we would like.
sky noise Tsky
As can be seen on the Tsky sky map for a frequency of 136 MHz, its various regions have very different noise temperatures Tsky, from 200 ° to 3000 ° K. At 430 MHz, the noise temperature of the same regions is 15 times lower on average. The noise temperature Tsky is not constant over time, it depends on solar activity. In addition, Tsky also includes the noise of the disk of the Sun, Moon, planets, which are also variable and very different in time.
ESTIMATION OF APS NOISE TEMPERATURE
The evaluation methodology is well described by DJ9BV and F6HYE in the journal “DUBUS” -3 / 1992. The translation of this article, Assessing the quality of the EME system, can be read on the VHF portal The author of the translation is Nikolay Myasnikov, UA3DJG.
TOTAL AFS NOISE TEMPERATURE
The antenna noise temperature Ta at the feeder inlet is the arithmetic sum of the noise temperatures of internal and external noise sources. The APS noise temperature at the receiver input is also the arithmetic sum of the antenna noise temperature Ta, taking into account its losses in the feeder and the noise temperature Tf of the feeder itself. Tafs \u003d Ta x efficiency + Tf. The TF of a particular feeder can be calculated in advance by its attenuation and does not participate in the calculations below, only Ta of the antenna or antenna system (stack) is considered below.
CALCULATION OF ANTENNA NOISE TEMPERATURE
There are several methods for calculating Ta. For example, one of them is given:
In a number of cases, it turns out to be convenient to determine the antenna noise temperature through the scattering coefficients β i. The dissipation factor in the transmission mode is the ratio of the fraction of the power contained within a given solid angle to the total power emitted by the antenna. Usually, the total and differential scattering coefficients are distinguished. The total dissipation factor represents the ratio of the total power radiated by the antenna to the side and trailing lobes of the antenna pattern to the total radiated power. Naturally, the total scattering coefficient is the sum of the differential coefficients β i.
If, for example, the space surrounding the antenna is divided into three regions: 1) the main lobe region,. 2) the region occupied by the lobes of the front half-space (with respect to the antenna aperture), 3) the rear half-space region, then the effective noise temperature of the antenna, without taking into account ohmic losses, can be determined through the scattering coefficients from the expression Ta \u003d T 1 (1 - β) + T 2 β 2 + T 3 β 3, where T 1 is the average brightness temperature of the medium within the main lobe of the diagram; T 2 is the average brightness temperature of the noise radiation received by the side lobes in the region of the front half-space relative to the antenna opening; T 3 is the average brightness temperature of the noise radiation in the back half-space; β is the total scattering coefficient of the antenna outside the main lobe of the pattern; β 2, β 3 are the scattering coefficients, respectively, in the front and rear hemispheres β 1 \u003d β 2 + β 3 The total noise temperature of the antenna, taking into account the ohmic losses in the transmission line, is equal to: Ta y \u003d Ta η + Ty \u003d T 1 (1 - β) η + T 2 β 2 η + T 3 β 3 η + T 0 (1 - η). Thus, the noise temperature of the antenna depends not only on the intrinsic characteristics of the antenna (β, η), but also on the temperature of the external noise radiation (T 1, T 2, T 3). Therefore, depending on the orientation of the antenna, its noise temperature will change.
In the above method, there is no specific parameter or their complex by which one can compare the antennas with each other and make a choice. The reason is the variability of the noise temperature of external sources and its dependence on the position of the antenna relative to them. I. Goncharenko DL2KQ writes about this on his forum.
Question:
Are there formulas for calculating Ta, G / Ta, T los. Why is this data calculated only by YA324, but not MMANAGAL?
Answer:
The noise temperature of the antenna (aka Ta) came to us from radio astronomy. Ta is calculated as the product of the space noise density (solar flux unit, sfu) S (1S \u003d 10-22 W s / m2) by the effective aperture area A, divided by two Boltzmann constants 2 k (where k \u003d 1.380662 10-23). Replacing the area of \u200b\u200bthe aperture through the formula connecting it with Ga (see, for example, clause 3.1.7 in the second part of "HF and VHF"), and simplifying, calculating the degrees and constants, we get: Ta \u003d SG λ² / 3.47, where: S - sfu dimensionless, today's value (see eg Geophysical Alerts); G - times (not in dB); λ - in meters.
As you understand, having the G calculated in the program (both maximum and current, in an arbitrary direction along the vector), it is not difficult to calculate Ta, G / Ta, Tlos. Let's do it in GAL-ANA. Why not done in MMANA-GAL? Because the free MMANA-GAL was made by us for our personal (and possibly erroneous) idea of \u200b\u200bwhat is understandable and convenient in antenna calculations. In the opinion mentioned, using the temperatures of the feeder and antenna is an inconvenient thing. See for yourself: the Tlos formula includes the variable temperature of the surrounding space, To, and the Ta formula, the variable solar flux unit, which depends on the Sun. As a result, Tlos and Ta walk on the weather. Is it convenient to use such floating parameters? Of course, you can enter some standard-average To and S. But this is not yet standardized, which is why in different publications some are in the forest, some for firewood. the answer was written on 1/24/2007, at 8:11
Radio amateurs have adopted a method for calculating the noise properties of an antenna as the ratio G / T, where G is the antenna gain and Ta is its noise temperature. The gain G is quite definite, and the noise level Ta is determined only for T los, the rest of the components depend on variable external noise sources and the orientation of the antenna relative to them, therefore, they must be agreed in advance.
The orientation of the antenna or a stack of them relative to the ground is taken as the position of the antenna in horizontal polarization with a maximum tilt angle relative to the horizon (elevation) of 30 °
The external conditions, T sky noise and T ground noise, are assumed to be uniformly distributed over the upper and lower hemispheres around the antenna. For T sky noise at 144 MHz, the temperature is taken to be 200 °, and at 432 MHz, 15 °. The noise of the earth on both bands is assumed to be 1000 °.
The results of calculating the G / T antennas in 2 x 2 stacks are presented in table VE7BQH.
CONTACT NOISE
There is also a source of noise that programs do not know about, and radio amateurs sometimes forget - contact noise. Contact noise is directly proportional to the magnitude of the current, the power density decreases with increasing frequency (1 / f), but under certain conditions on VHF it can reach a value that interferes with even local communications. This is the noise of variable points of contact in antennas with a mechanical connection of elements, traverse, metal fasteners to each other. Threaded connection, pressing, crimping with a clamp, tight fit of the tube into the tube, HF plug - everywhere there is a galvanic contact not over the entire surface, but at several points. Despite their many, any slightest impact breaks some points of contact and forms others. Impact means displacement from the wind, change in size with a change in temperature, the process of surface corrosion, breakdown by HF voltage of the oxide film and its recovery during reception, "stray currents" of the power grid and electrostatics, etc. As a result, with reliable contacts from the point of view of an electrician, the current path and the antenna geometry are constantly changing. Rustles and crackles arising from this are usually attributed to external interference. The bolted connection between the vibrator and the cable is made of dissimilar metals and fully has these disadvantages. In VC antennas, in which the vibrator and the gamma matcher are fastened by crimping the strip, the same reasons at 145 MHz are possible, and at 1296 MHz will inevitably lead to instability and deterioration of the antenna parameters.
Literature (and they are also links sites where you can download them):
1 - Modern problems of antenna-waveguide technology Collection of articles of the USSR Academy of Sciences
2 - Handbook of radio amateur - shortwave S.G.Bunin, L.P. Yaylenko
3 - Methods of suppression of noise and interference in electronic systems G. Ott
4 - Handbook on radio relay communication ed. Borodich S.V.
5 - Kaplan elementary radio astronomy
6 - Radioastronomy J. Kraus
