Often while dealing with signals in electronics and communication systems, we encounter distortion in signals due to noise. Noise is an unwanted disturbance that can attenuate our signal making it difficult to obtain the original signal. In this article, we will study the noise factor which is an important instrument used for measuring the quality of signals.

Later, we will understand the work behind calculating the noise factor. Through a diagram, we will also see the formula used for calculating noise factor with a physical understanding of the formula. Some solved examples have been provided to enhance the understanding of readers about the topic. We will look at the advantages, disadvantages, and applications of noise factors in the real world. In the end, we will conclude the article with some frequently asked questions that readers can refer to.

What is the Noise Factor?

The noise factor is a parameter used to compare the quality of received signals. We know that during the propagation of a signal, it can get affected by noises it encounters in the traveling medium. These noises can deteriorate the quality of the signal therefore, there was a need to introduce a parameter that can help in measuring the degradation of the signal due to noise. A lower noise factor indicates a better-performing device than a device with a higher noise factor.

Definition

Let us now see a formal definition of the noise factor :

Noise Factor is the ratio of the Signal to Noise Ratio at the input to the Signal to Noise Ratio at the output.

Working Principle of Noise Factor

Noise Factor is used to measure the quality of sound. Let us see the principle used behind calculating the noise factor.

Calculation of SNR: The main principle used for measuring noise figure is calculating the Signal to Noise ratio of devices. The SNR provides information regarding the ratio of the power of the signal to the power of the noise. This helps to analyse the power lost due to the presence of noise. The idea is to optimize the performance by minimizing the SNR of the device.

Calculation of Noise Figure or Noise Factor: Once we have measured the SNR, we can quantify the degradation of signal due to noise using a noise figure. It analyses the losses that would have occurred in signal during transmission due to components like amplifiers, speakers etc. These losses are measured and used to compare the quality of signals in various communication instruments.

Formula of Noise Factor

We have seen that the noise factor is the ratio of Signal to Noise Ratio at the input to the Signal to Noise Ratio at the output. Let us see this mathematically

Noise Factor(F)= SNR_in/SNR_out

where

F= (S_in/N_in)/(S_out/N_out) S_in = Signal level at input

N_in = Noise level at input

S_out = Signal level at output

N_out= Noise level at output

Let us compare the relationship between noise figure and noise factor. Since noise factor is linear equivalent of noise figure, we can write

Noise Factor(F)=10^NF/10

where NF is noise figure

Since noise factor is a ratio, it is a dimensionless quantity. The units of noise figure are decibels(db). Since the signal to noise ratio at the output will always be lower than the Signal to Noise ratio at the input, the Noise Factor is always greater than 1.

Construction of Noise Figure

Calculating the noise figure involves certain components which are given below. Let us see each component individually.

Noise Factor Construction

• Noisy Source : Initially a source is taken to generate a signal. The power associated with this signal is given by signal power S_i and noise power N_i. The SNR_in at this point is given by SNR=S_i/N_i where S_i and N_i denote the power associated with signal and noise respectively.
• Single Stage Amplifier : The source is continued by an amplifier which is used to amplify both the signal and the noise. It not only amplifies the signal and noise but also adds an additional noise which is denoted by N_a.
• Output: The final output is taken from the amplifier and the output SNR is calculated. For a Gain G of amplifier, we can write the output SNR_o as :

SNR_o= S_o/N_o= S_iG/(N_iG+N_a)

The noise factor can be denoted by

Noise Factor(F)= (S_i/N_i)/(S_iG/(N_iG+N_a))

∴ F= (N_iG+N_a)/N_iG

∴ F= (1+N_a/N_iG)

Solved Examples of Noise Factor

Example 1

If each stage had a gain of 10db and noise figure of 10db, and Noise Figure of 10db then the overall Noise Figure of two-stage cascade amplifier will be

For a cascaded system we can calculate the noise figure as

∴ F_n= F₁+ (F₂-1)/G₁+ (F₃-1)/G₁G₂ +………………………………….+(F_n-1)/(G₁G₂……….G_n)

For a two stage amplifier n=2

∴ F₂= F₁+ (F₂-1)/G₁

For each stage gain=10db and noise figure(F)= 10db

Overall noise figure F=10 + (10-1)/10 =10.9 db

Example 2

The noise figure of a device is 2. If input SNR is 30db ,what will be the output SNR?

Using our knowledge we know that noise figure is the ratio of input to output SNR

∴ Noise Figure(NF)= SNR_in/SNR_out

NF(in db)= SNR_in(in db) -SNR_out(in db)

∴ NF(in db)=10 log₁₀^(NF)= 3db

On putting the values

we get

3db=30db- SNR_out(in db)

∴ SNR_out=27db

Advantages of Noise Factor

let us see the advantages of noise factor:

• Noise Factor helps to analyse the signal quality. A lower noise factor indicates that the signal is less degraded. This eventually leads to higher signal quality in devices and a higher SNR means signal is more degraded.
• A low noise figure helps to make the system more reliable. This is done by reducing the errors per bit in digital communication system. This an even yield higher accuracy.
• Noise Factor is used in appliances that have low sensitivity. Signals with low SNR are quite useful since they help to detect weaker signals.
• The introduction of noise factor helps to design an optimal system. Components that have low noise figures are used to form a complete system to improve the overall performance of the system.
• A lower noise factor can lead to wider dynamic range. This wider dynamic range allows us to handle a wider range of amplitudes with degrading the signal quality.

Disadvantages of Noise Factor

let us see the disadvantages of noise factor:

• An increased Noise factor indicates a degraded signal. Systems that have higher noise factor indicate that the quality of the signal is poor mainly due to enhanced noise.
• Calculation of noise factor can be complex sometimes. This is mainly complex in case of cascaded systems because interconnected components can complicate the calculations.
• Noise Factors method becomes unreliable because noise factor is temperature sensitive. With an increase in temperature, the Noise factor increases which impacts the whole system by degrading its performance.
• Noise Factor can only provide information about certain components. Due to lack of versatility it can be a challenging task to obtain system information from noise factor.
• Noise Factor is a theoretical concept therefore it might not accurately describe the real-world situation. Real-world involves certain important factors like environmental conditions which are ignored while calculating noise factor.

Applications of Noise Factor

let us see the applications of noise factor

• Noise Factor is used in telecommunication system to calculate the effect of noise in a signal system. It is used for analysing and optimally designing communication systems like satellites, fibre optics.
• Noise Factor is used in radio and television broadcasting. Here noise factor is used to obtain high-quality audio and video signals. This is helpful in broadcasting systems.
• Noise Factor is used in medical imaging in hospitals. This involves using them in MRI and ultrasound to minimize noise and obtain accurate images for medical purposes.
• Noise Factor is used for scientific purposes in different instruments like spectrometers and detectors,. Scientists minimize noise to obtain accurate data for scientific predictions.
• Noise Factor is used in remote sensing like in weather monitoring and sensors. Even here noise factor contributes by minimizing the errors due to noise and obtaining accurate forecasting data.

Conclusion

We have seen how noise plays a significant role in telecommunication. The quality of signal is greatly affected by noise generated during the transmission of the signal and noise factor is a parameter that was introduced in this article to analyse the quality of signal.

We have already studied how to study noise factor and even seen the formulas associated with the calculation of noise factor. Some solved examples have been provided which help readers to grasp the concept well. We have also discussed what are the advantages and disadvantages of calculating noise factor of devices. Readers are advised to go through the FAQs section in-case of any doubts.

Noise Factor – FAQs

What is the difference between noise factor and noise figure?

The noise factor is the ratio of the output signal-to-noise ratio to the input signal-to-noise ratio. Noise figure is a logarithmic representation of the noise factor, expressed in decibels (dB).

What is the relation between signal to noise ratio and noise factor?

Noise factor is the ratio of the output signal-to-noise ratio to the input signal-to-noise ratio. Mathematically Noise Factor(F)= SNR_in/SNR_out

Does temperature have an effect on noise factor?

Yes the temperature does impact the noise factor. The noise factor increases as temperature increases making the signal worse with increased noise.