 This is a free online tool to calculate the cascaded noise figure. This tool supports the 4 cascaded amplifiers.

Created by Commontools | Updated on: June 23, 2022

Aggerate Noise Figure (in linear term):
Aggerate Noise Figure (in dB):

 Module1 Noise Figure in dB : Module1 Gain in dB : Module2 Noise Figure in dB : Module2 Gain in dB : Module3 Noise Figure in dB : Module3 Gain in dB : Module4 Noise Figure in dB : Module4 Gain in dB :

## Introduction

The noise figure calculator determines the noise figure, a measurement of a device's contribution to the overall noise of the system in which it is installed. Using this information, you can choose how much noise is produced in that system.

In the following article, we define the words noise factor and noise figure, which are similar but differ slightly in how they are calculated. To calculate the degradation of signal-to-noise ratio (SNR) in a system like this, we utilize the latter, for instance, in the noise figure of the cascaded amplifier formula.

Read on to discover more about the noise figure formula and the real-world uses of noise figures in various walks of life.

## What do noise factor and noise figure mean?

The signal-to-noise ratio (SNR) is referred to as the noise figure, and the noise figure is the common logarithm of the input to output SNR ratio. This ratio gauges how strong the desired signal is about how much background noise is tolerable. Similar in concept but not using logarithms is the noise factor.

Any undesired disruption that degrades the signal's quality and interferes with the transmission of texts, graphics, audio, and video can be categorized as noise. Therefore, if you want to increase a system's performance, researching its noise component is essential.

## Definitions of noise figure and noise factor

The noise factor and figure measure the worsening of the signal-to-noise ratio.

When we calculate the value using a linear equation, the result is a noise factor, but when we use a common logarithm, the result is a noise figure.

The total noise figure of such a system is known as a cascaded noise figure when many devices are connected in a sequential or cascaded fashion.

### Noise figure calculator

Depending on the situation in front of you, the noise figure calculator enables you to calculate the noise figure's value in various methods. The calculator offers four different calculation types, each of which has a unique formula that you must use to calculate the noise value based on your inputs.

## The computation techniques are:

1. The signal-to-noise ratios;

2. The signal-to-noise ratios in decibels (dB);

3. Convert from noise factor to noise figure; and

## Noise figure formula & calculation

Using the diagram above, it is possible to determine the noise figure formula from the conditions described above.

$$N=10\log_{10}\left(\frac{S_iN_i}{S_oN_o}\right)$$

Where

Si is the signal at the input

Ni is the noise at the input

So is the signal at the output

No the noise at the output

For instance, if the signal to noise ratio was 4:1 at the input and 3:1 at the output, the noise factor would be 4/3 and the noise figure would be 10 log (4/3) or 1.25 dB. As an alternative, the noise figure can be easily calculated if the signal to noise ratios are given in decibels. This is because two integers are divided by subtracting their logarithms. In other words, the circuit would have a noise figure of 13 - 11 or 2 dB if the signal to noise ratio was 13 dB at the input and only 11 dB at the output.

## What exactly is gain, and how is the gain of a cascaded circuit determined?

The gain in electronics refers to the amount that a two-port circuit (typically an amplifier) enhances a signal's power or amplitude from the input to the output port.

The ratio of the output signal power to the input signal power determines an amplifier's power gain. The gain is frequently stated in decibels (dB gain). For example, the following formula determines an amplifier's power gain in dB units.

## Applications

When working with weak signals, noise in a circuit is a crucial factor to consider. Although you can partially eradicate it, noise in electronic communication systems is undesirable. It is the designer's responsibility to ensure that each component's noise contribution to the circuit is minimal enough to prevent noticeably degrading the signal-to-noise ratio.

The system's total noise figure determines the minimum magnitude of a signal you may recognize in the presence of noise. This indicates that the lowest possible noise level is required to ensure the best performance from a system. We can determine a device's noise contribution by looking at its noise figure. For example, the noise figure of an ideal amplifier is 1, as the signal-to-noise ratio for both its input and output is infinity. However, a true amplifier will add its noise to the signal in addition to amplifying the noise at its input. As a result, the amplifier's output has a lower noise figure and a lower signal-to-noise ratio.

## Measurements of noise performance

There are several approaches to specify a radio receiver's noise performance. The most visible is the signal-to-noise ratio, and there is also a SINAD (Signal to Noise And Distortion). In addition, other metrics, such as Bit Error Rate and others, can assess sensitivity performance.

However, because noise figures may be applied to both the entire system and individual components of it, it has emerged as one of the more crucial parameters linked to radio receiver performance.

The noise figure can be used to analyze the various components and create an overall figure.

Noise affects all frequencies and is brought in by circuitry components like electronic parts. As a result, the component selection can significantly affect how well the circuit handles noise.

Thermal noise makes up the majority of radio receiver circuit noise, but not all of it. Due to this, some specialized applications, such as radio astronomy, may require input circuits to be cooled to shallow temperatures in order to eliminate thermal noise. In addition, these applications require extremely low noise levels in order to detect tiny signals.

While thermal noise is the primary source of noise, there are other mechanisms that contribute to noise as well. These mechanisms must be taken into account when designing an RF circuit in order to select circuit configurations, electronic components, and design strategies that will minimize overall noise.

## Basics of noise factor and noise figure

In essence, the measurement evaluates the amount of noise that the system as a whole or each component of the system introduces. This could, for instance, be an RF amplifier or a radio receiver. If the system were flawless, there would be no noise added to the signal as it moved through it, and the signal-to-noise ratio at the output and input would be the same.

This is not the case, as we are all aware, and additional noise is always present. SNR, or signal-to-noise ratio, is worse at the output than at the input, according to this statement.

## Two fundamental figures can be employed:

Noise factor: To calculate the noise factor, divide the SNR at the input by the SNR at the output. The noise factor is always more than one since the SNR at the output will always be worse or lower. Specifications mentioning the noise factor are uncommon.

Noise figure: it is a parameter that is frequently used to specify and describe radio receivers and the components that makeup receiver systems. The noise figure is just the noise factor stated in decibels and employs a logarithmic scale.

## Noise figure for cascaded stages

A typical radio receiver will have the input tuner, an RF amplifier, maybe an RF attenuator, an RF mixer, and so forth. This is true of all RF circuit designs.

The total noise figure and, thus, the noise performance of the entire RF circuit design will tend to be defined in the initial stages.

Consider a two-stage RF circuit design. The input noise will be equal to kTB, and the gains G1 and G2 for each stage will amplify this noise. There will be noise from the first stage, which the second stage will amplify, and then there will be noise from the second stage. Because they are not associated, the noise powers can be summed.

Calculating the impact of the noise performance of several stages on the total noise figure is frequently important as part of the RF design process.

$$NF_{system}=NF_1+\frac{NF_2-1}{G_1}+\frac{NF_3-1}{G_1G_2}+...$$

Where: NF = Noise Figure for a System or for Stage 1, Stage 2, or Stage 3, as indicated by the Subscript

G stands for the gain for the step indicated by the subscript.

The first stage is the one that has the biggest impact on the noise figure for the entire RF circuit design, according to the noise figure formula for series or cascaded stages.

## Noise figure measurement

There are several approaches to measuring the noise figure of an element used in a radio communications system. There are numerous test instruments available. In actuality, the available test tools might dictate the procedure that is utilized.

1. A particular noise figure meter could be offered in some labs for measuring noise levels. These test instruments are produced by numerous manufacturers, and they offer a quick, simple, and precise noise figure measurement. If one is available, noise figure analyzers are an excellent choice since they offer a very rapid and simple way to determine the noise figure of an object. In addition, they are accurate.

The measurements only require that the noise figure meter be connected to the input and output of the circuit being tested. The test is started, the test instrument is set up, and the results are presented. A straightforward yet reliable test.

1. Noise figure measurements with a spectrum analyzer: Using a spectrum analyzer, noise figure measurements are very simple. Some of these test instruments are equipped with built-in processes that let you measure noise levels. There are two basic ways to measure noise figures, and both of them can make use of a spectrum analyzer. The gain method and the Y method are their names.

## Examples of noise figures

Diverse pieces of equipment used for various radio communications systems will have quite different requirements.

A common HF radio receiver used by professionals or amateurs may have a noise figure of 15 dB or higher and still perform quite effectively. Due to the high degree of atmospheric noise, a higher performance level is not required. Even at frequencies about 30 MHz, when the spectrum is on the verge of VHF, interference levels can still be high enough not to require very high levels of noise performance since atmospheric noise at these frequencies can be very high.

The noise figure of a receiver utilized for narrow band applications at VHF or above, however, may be 3 or 4 dB. A noise figure of about 1 dB is typical for some narrow band RF amplifiers. It's noteworthy to note that even the best wide-band VHF/UHF receivers for professionals may only have a noise figure of 8 dB or less. These radio receivers could be utilized for radio reception, radio communications, or spectrum monitoring.

The noise figure of a receiver utilised for narrow band applications at VHF or above, however, may be 3 or 4 dB. A noise figure of about 1 dB is typical for some narrow band RF amplifiers. It's noteworthy to note that even the best wide-band VHF/UHF receivers for professionals may only have a noise figure of 8 dB or less. These radio receivers could be utilised for radio reception, radio communications, or spectrum monitoring.

Applications like radio astronomy at frequencies extending into the UHF region of the spectrum and beyond require particularly high levels of performance.

## Conclusion

The noise figure is a very practical parameter to utilize because it can tell you how well certain system components perform in terms of noise. Through the usage of noise figures, it is also possible to determine a system's overall performance by knowing the noise figures and gain levels of each component. As a result, it is simple to compute and optimize the system noise figure. Noise statistics are frequently stated in the overall specification of radio communications equipment used for commercial or amateur radio applications.

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