Cascaded Noise Figure Calculator

What is cascaded noise figure calculator?

Cascaded noise figure calculator is an online calculator. It receives the noise figure inputs (in dB) and power gain inputs (in dB) and accurately calculates the total noise figure and total gain of the cascaded circuit (for example, multistage-amplifier). This calculator has the capability to calculate the total noise figure and total gain of the cascaded circuit with 2 to 10 number of stages.

What is gain and how gain of the cascaded circuit is calculated?

In the electronics field, Gain is a measure of how much a two-port circuit (often an amplifier) amplifies the power or amplitude of a signal from the input to the output port.

The power gain of an amplifier is nothing but the ratio of output signal power to the input signal power. Often, the gain is expressed in the decibel unit (dB gain). The power gain of an amplifier in the dB unit is calculated by using the following formula.

If “n” number of devices are connected in the cascaded manner (for example, a multistage amplifier with n stage) and consider that 1, 2… nth stage has the power gain G1 dB, G2 dB….Gn dB. The total power gain of the cascaded circuit (multistage amplifier) is calculated by the following formula (i.e., the addition of individual power gain of the amplifier in dB).

For example, if a three-stage cascaded amplifier has individual power gain G1= G2=G3=10 dB, then the total power gain is:

GT = 10+10+10= 30 dB

What is noise figure and how noise figure of the cascaded circuit is calculated?

Noise figure (NF) and noise factor are the measures of degradation of the signal to noise ratio (SNR) as the signal pass through a circuit or a series (i.e., cascaded) circuits. The signal to noise (SNR) ratio is a ratio of signal power level to the noise power level. The SNR ratio more than 1:1 (greater than 0 dB) indicates more signal power than noise power. The SNR degradation occurs due to the external noise and internal noise (caused by the components of the cascaded circuit as the signal passes through).

The noise figure & noise factor is a number by which the performance of an amplifier or a radio receiver can be specified. A lower value of noise figure & noise factor indicating better performance of the amplifier.

Noise factor (F) is the ratio of signal-to noise ratio (SNRi) at input to the signal-to-noise ratio (SNRo) ratio at the output of a circuit/device.

The Noise figure (NF) is defined as decibel of Noise factor. i.e.,

If “n” number of devices are connected in the cascaded manner (for example, a multistage amplifier with n stage), then the total noise factor can be calculated by Friis formula as given below. Here, the noise factor (F) is the ratio of signal-to noise ratio (SNRi) at input stage to the signal-to-noise ratio (SNRo) ratio at the output stage of the multistage-amplifier.

Therefore, total noise figure,

From the formula, we can understand that the first amplifier of a multistage amplifier has a significant effect on the total noise figure; because the noise factor of the following stages is reduced by the stage gains. So, the first stage of the cascaded amplifier usually has a low noise figure and the noise figure requirements of other following stages usually more relaxed.

• Where:
• F- Total noise factor
• F1- Noise factor of the first stage
• F2-Noise factor of second stage
• F3- Noise factor of third stage
• Fn- Noise factor of nth stage
• NFT – Total noise factor
• G1 – Power gain of the first stage
• G2- Power gain of the second stage
• Gn- Power gain of the nth stage

Example problem:

Consider the three cascaded amplifier stages, each amplifier stage has a noise figure of 3 dB and power gain of 10 dB, then the calculation of total noise figure is given below.

Solution:

Internally, this calculator first converts the given noise figure (in dB) inputs to normal values (i.e., convert to noise factor F1, F2, &F3). After that, the total noise factor (F) is calculated for 3 stages as follows.

Therefore, total noise figure: NFT = 10 log10(F) = 10 log10(2.11) = 3.24 dB