**Noise figure in the communication system:**

The noise figure in the communication system is, viz.

**1. Signal to noise ratio:**

Calculating the equivalent noise resistance of an amplifier, receiver, or device can serve one of two purposes, or sometimes both. The first objective is the comparison of two types of equipment in the evaluation of their performance. The second is the comparison of noise and signal at the same point to ensure that the noise is not excessive. In the second case, and also when it is difficult to obtain an equivalent resistance to noise, the signal/noise ratio S/N is usually used. It is defined as the ratio between the signal power and the noise power at the same point. Therefore

Equation (2-10) is a simplification that applies whenever the resistance through which the noise develops is the same as the resistance through which the signal develops, and this is almost invariable. Naturally, an effort is made to keep the signal to noise ratio as high as possible under a given set of conditions.

**2. Definition of the Noise Figure in the Communication System:**

For comparison of receivers or amplifiers operating at different impedance levels, the use of an equivalent noise resistance is misleading. For example, it is difficult to quickly determine if a receiver with an input impedance of 50 Ω and R_{equation}= 90 Ω is better, from the noise point of view, than another receiver whose input impedance is 300 Ω and R_{equation}= 400Ω. By the way, the second receiver is the best, as we will see. Instead of equivalent noise resistance, a quantity known as the communication system noise figure, sometimes called noise figure, is defined and used. The noise figure F is defined as the ratio of the signal-to-noise power delivered to the input terminals of a receiver or amplifier to the signal-to-noise power delivered to the output or load resistor. That's why

One can immediately see that a practical receiver will generate some noise and the S/N will deteriorate as it moves towards the output. Consequently, in a practical receiver, the output S/N will be less than the input value, and therefore the noise figure will exceed 1. However, the noise figure will be 1 for an ideal receiver, which has no own noise. Thus, we have the alternative definition of a noise figure, which states that F is equal to the S/N of an ideal system divided by the S/N at the output of the receiver or amplifier under test, both operating at the same temperature during the Same time. bandwidth and powered by the same source. Also, both must be linear. The noise figure can be expressed as a real ratio or in decibels. The noise figure in the communication system of practical receivers can be kept below a few decibels down to frequencies in the lower gigahertz range by proper choice of the first transistor, combined with proper circuit design and low-noise resistors. . At frequencies higher than this, similarly low noise values (lower, in fact) can be achieved by devices that use or are relatively independent of the transit time effect.

**3. Calculation of the noise figure:**

The noise figure in the communication system can be calculated for an amplifier or receiver in the same way, treating them as a whole. Each is treated as a four-terminal network with an input impedance R_{t}, an output impedance R_{UE}, and a general voltage gain A. It is fed by a source (antenna) of internal impedance R_{a}, which may or may not be equal to R_{t}as circumstances warrant. A block diagram of this four-terminal network (with the supply that feeds it) is shown in Figure 2-4.

The calculation procedure can be divided into several general steps. Each is now displayed, followed by the number of the corresponding equation(s) below:

- Determine the input power of the signal P
_{mi}(2-12, 2-13). - Determine the noise input power P
_{they}(2-14, 2-15). - Calculate the input signal-to-noise ratio S/N
_{UE}of the relationship of P_{mi}mi pag_{they}(2-16). - Determine the output power of the signal P
_{so}(2-17). - write p
_{No}so that the power output of the noise is determined later (2-18). - Calculate the signal to noise ratio of output S/N
_{o}of the relationship of P_{so}mi pag_{No}(2-19). - Compute the generalized form of the noise figure from steps 3 and 6 (2-20).
- Calculate P
_{No}by R_{equation}if possible (2-21, 2-22), and substitute F into the general equation to get the actual formula (2-23, 2-24) or determine P_{No}of the measure (2-3, 2-25, 2-26) and substitute to obtain the formula of F (2-27, 2-28, 2-29).

From Figure 2-4 it is seen that the input voltage and power of the signal will be

Also, the noise input voltage and power will be

The input signal/noise ratio will be

The intensity of the output signal will be

Noise power output can be difficult to calculate. For now, it can be written simply as

The output signal to noise ratio will be

Finally , the general expression for the Noise Figure in the Communication System is

Note that equation (2-20) is only an intermediate result. A real formula for F can now be obtained by substituting the output noise power, or by knowing or measuring the equivalent noise resistance.

**4. Equivalent noise resistance noise figure:**

As derived from Equation (2-7), the equivalent noise resistance of an amplifier or receiver is the sum of the input termination resistance and the first stage equivalent noise resistance, together with the input noise resistances. the previous stages referred to the Forbidden. . Put another way, we see that all these resistances add up to R_{t}, giving a concentrated resistance which is then said to concentrate all the "noise" at the receiver. Now the rest are supposed to be silent. All of this applies here, with the small exception that these noise resistors must now be added to the parallel combination of R_{a}y R. S._{t}. To correlate the noise figure and the equivalent noise resistance, it is convenient to define R'_{equation}, which is a noise resistor that does not incorporate R_{t}and which is given by

The equivalent total noise resistance for this receiver will now be

The equivalent noise voltage generated at the input of the receiver will be

Since the amplifier has an overall voltage gain of A and can now be treated as noiseless, the noise output will be

When Equation (2-22) is substituted into the general Equation (2-20), the result is an expression for the Noise Figure in the Communication System in terms of the equivalent noise resistance, that is,

From Equation (2-23) it can be seen that if the noise is minimal for any given value of antenna resistance R_{a}, the reason (R_{a}+R_{t})/D_{t}must also be a minimum, so that R_{t}must be much greater than R_{a}. This is a situation that is very often explored in practice and can now be applied to Eq. (2-23). Under these incompatible conditions, (R_{a}+R_{t})/D_{t}approaches unity, and the formula for the noise figure reduces to

This is a very important relationship, but it must be remembered that it only applies under incompatible conditions. Under combined conditions (R_{t}= R_{a}) or when the mismatch is not severe, Equation (2-23) should be used instead.

Note that if a "noise equivalent resistance" is given without further comment on the noise figure calculations, it can be assumed to be R'_{equation}.

**5. Measurement noise figure:**

The previous section showed how the noise figure can be calculated if the equivalent noise resistance is easy to calculate. When this is not feasible, as in transit time conditions, it is possible to carry out measurements that lead to the determination of the Noise Figure in the Communication System. A simple method using the diode noise generator is often employed. It is shown in Figure 2-5 in the form of a circuit block.

Equation (2-3) gave the formula for the exact plate noise current of a vacuum tube diode, and it can now be used. As shown, the anode current is controlled via the potentiometer which varies the filament voltage, and this is how the noise trigger current is adjusted.

The output capacitance of the diode and its associated circuitry resonates at the receiver's operating frequency through the variable inductance, so it can be ignored. The noise generator output impedance will now be simply R_{a}. The noise voltage supplied to the input of the receiver by the diode will be given by

The noise generator is connected to the receiver (or amplifier) under test, and the noise output power of the receiver is measured with zero diode plate current, that is, with thediodeboard voltage supply disconnected. The diode plate voltage source is now turned on and the filament pot is adjusted so that the diode plate current begins to flow. It is further adjusted until the noise power developed in R_{UE}is twice the noise power in the absence of diode plate current. The plate current at which this happens, i_{pag}, is measured with the milliamnieter and recorded. The extra noise power output is now equal to the normal noise power output, so the latter can be expressed in tennis diode plate current. Now we have

As already described, Eq. (2-26) can be substituted into Eq. (2-20).

This does

Assuming once more that the system is incompatible and R_{t}≫ R_{a},Equation (2-27) simplifies to

If the above procedure is repeated from the beginning for a system under the corresponding conditions, it can be shown that Eq. (2-28) applies exactly to that system, rather than simply being a good approximation, as it is here. Such a result emphasizes the measurement value of the noise diode.

As a final simplification, we substitute into Equation (2-28) the values of the various constants it contains. This includes the standard temperature at which these measurements are taken, which is 17 °C or 290 K. This provides a frequently quoted formula:

where R_{a}is measured in ohms and I_{pag}me amps.