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#### crazyboy

##### Newbie level 6
Hello everyone,

I doing a simple receiver noise power calculation. The system consists of an antenna with Low noise amplifier and subsequent attenuation and gain stages.There are no mixing stages. I managed to find out the equivalent Noise Figure(NF) of entire system using Friss-Noise figure formula and arrived a value of 9dB.

Calculating the receiver Noise power using the formula Pr = NF*k*T*G I'm getting a Noise floor around -120 dBm/Hz.

Here's are my doubt's:

1. Is the inclusion of G (Gain of chain) is valid ? because in some articles they didn't mentioned about it.

2. Also if its inclusion is valid, then I have to sum up the gain of attenuators (in chain) as well ? or simply the gains of amplifiers only ?

The above calculation which i did is treating the attenuation of attenuator with negative gain and summing up all the gains in system chain. If I omit the gain summation of attenuators I'm arriving at a value of -74 dBm/Hz. So which value I have to consider as the Noise Floor of my system ?

3. The final stage of system is connected to an analyzer. So if i want to find out the minimum detectable power, I have to multiply one of above values with Noise Bandwidth Pr(min) = NF*k*T*G*B Watts. So my another question is which band width I have to consider here? whether it is the RBW / VBW of Analyser or I have to calculate the cascaded -3dB bandwidth of receiver chain?

Hello everyone,
Here's are my doubt's:

1. Is the inclusion of G (Gain of chain) is valid ? because in some articles they didn't mentioned about it.

2. Also if its inclusion is valid, then I have to sum up the gain of attenuators (in chain) as well ? or simply the gains of amplifiers only ?

The above calculation which i did is treating the attenuation of attenuator with negative gain and summing up all the gains in system chain. If I omit the gain summation of attenuators I'm arriving at a value of -74 dBm/Hz. So which value I have to consider as the Noise Floor of my system ?

3. The final stage of system is connected to an analyzer. So if i want to find out the minimum detectable power, I have to multiply one of above values with Noise Bandwidth Pr(min) = NF*k*T*G*B Watts. So my another question is which band width I have to consider here? whether it is the RBW / VBW of Analyser or I have to calculate the cascaded -3dB bandwidth of receiver chain?

1) Yes you need to include the net gain.
2) Yes this will be the sum of all the elements - positive and negative.
3) The noise floor of the spectrum analyzer will be proportional to the RBW. In addition though, your spectrum analyzer will have a somewhat high noise figure (20-30 dB is typical).

Also see the attachment, it has some good tips on using the spectrum analyzer.

#### Attachments

• Agilent - AN1286-1 8 Hints for better SA measurements.pdf
725.2 KB · Views: 69
• tony_lth and crazyboy

Points: 2

### tony_lth

Points: 2
1) Yes you need to include the net gain.
2) Yes this will be the sum of all the elements - positive and negative.
3) The noise floor of the spectrum analyzer will be proportional to the RBW. In addition though, your spectrum analyzer will have a somewhat high noise figure (20-30 dB is typical).

Also see the attachment, it has some good tips on using the spectrum analyzer.

All above answers are correct. It seems to me that you are confused with two basic concepts:

1. To define the signal-to-noise ratio, usually both signal and noise power is defined at receiver INPUT.
You can simplify estimating the input noise power by using the "dBm" formula for INPUT noise power:
Pn = -174 + NF +10 log BW, the power is then in dBm.

2. To estimate bit error rate, the signal and noise power is calculated at receiver OUTPUT to a detector or demodulator. Then you must apply receiver gain, and instead of S/N, the ratio Eb/No is used to estimate BER for a particular signal modulation used.

- - - Updated - - -

Finally, if you use a spectrum analyzer to evaluate the noise or signal power, then the receiver bandwidth is reduced by this instrument. There are two parameters for bandwidth in a spectrum analyzer: the RF bandwidth (RBW) before its detector (this counts in measuring the noise power ), and the video bandwidth (VBW) which is applied AFTER its detector, to reduce the noise effects and allow the periodic signal to be measured, free of noise.

• crazyboy

### crazyboy

Points: 2
Thanks a lot for replies My final goal is to specify the receiver noise power (Watts/Hz or Volts^2/Hz) of my complete system (including analyzer). Since I don't know the exact Noise figure of my analyzer I did a small test on my analyzer.

I adjusted my Analyzer settings as follows : VBW=RBW=300kHz, Sweep time = 100ms, span = 120MHz (these are my regular observation settings) with above settings and input as 50 Ohm load, I read out the Noise floor as -76 dB m on the display panel. Using this formula Pn = -174 + NF +10 log BW, I did a reverse calculation (BW=300kHz, Pn=-76dB m) and got the Noise Figure of my analyzer as 43 dB!!! So the Noise of analyzer is -128 dB m/Hz.

After including the Noise Figure of analyzer in final calculation(Friss-Formula) the receiver Noise of system is close to same value -120 dB m/Hz. Is it right or I messed up any where ? Also after converting to linear scale the Noise is 9.18 *10^-16 Watts / Hz. Is this value same as Volts^2/Hz or do I need to multiply with any proportionality constant?

Check your attenuation setting as well, that will increase the noise figure of the spectrum analyzer. Typically it defaults to at least 10 dB, you may have to go into manual mode to lower it to zero.

Your result seems reasonable though. The G+NF of your device under test is ~54 dB, so the spectrum analyzer NF of 43 dB will only have a small impact.

• crazyboy

Points: 2