# Calculating power over a frequency band

• newenglandguy
In summary, the noise power is 1.38 x 10-20 x 293 x 106 = 4 x 10-12milliwatts per MHz = -114 dBm per MHz. The total power over a certain bandwidth can be calculated by integrating power over that bandwidth.

#### newenglandguy

I am interested in taking a measurement with a Spectrum Analyzer from an amplifier circuit I'm putting together and am interested in calculating the total power over a certain bandwidth. Is is just a matter of taking all the readings in dBm, converting to watts and then taking the RMS values taken from the Spectrum Analyzer across my band of interest? The only power into the amplifier will be the noise power. The amplifier has 45 dB gain.

I understand some Spectrum Analyzers have an option that allows you to measure this directly, but the Spectrum Analyzer I have access to does not have this functio

Thanks

I will guess that the noise power is about -111 dBm per MHz**., including 3 dB noise figure, and 45 dB gain to get -66 dBm per MHz. You don't need to convert to watts. Just use dBm.

Bob S

** the noise power is kTB where k= 1.38 x 10-20 millijoules per deg kelvin, T=293 kelvin, and B(bandwidth in Hz)= 1 MHz

So noise power is 1.38 x 10-20 x 293 x 106 = 4 x 10-12milliwatts per MHz = -114 dBm per MHz.

Add 3 dB noise figure to get -111 dBm per MHz

Bob - thanks for the reply. That's noise power, but once I hook up the amplifier, I'll get some trace that represents the output noise power versus frequency. How do I calculate total power over that bandwidth? Say I have the following readings versus F1 - F2:

-55.6 dBm, -55.7 dBm, -56.2 dBm, -57.2dBm, -57.8 dBm, -56.9 dBm.

I guess thr question I have is how I integrate (think that's the right term) power over that bandwidth?

Thanks

Do you know the frequency resolution of the analyzer? Presumably, values of -55.6 dBm (i.e. 2.75 nW), etc. correspond to the energy contained within the window around the frequency to which the analyzer is tuned. The size of the window is either adjustable or can be found in the manual.

hamster143 - I want to get the Noise Floor of the Spectrum Analyzer down to -65 dBm or lower, and I planned on setting the Resolution Bandwidth (RBW) and the Video Bandwidth (VBW) to 30 KHz.

newenglandguy said:
hamster143 - I want to get the Noise Floor of the Spectrum Analyzer down to -65 dBm or lower, and I planned on setting the Resolution Bandwidth (RBW) and the Video Bandwidth (VBW) to 30 KHz.
If you back-terminate the input to the spectrum analyzer with a good matched resistor, the noise level should be in the range -114 to -111 dBm per MHz bandwidth (not per MHz resolution). See my post #2.

Bob S

## 1. What is power over a frequency band?

Power over a frequency band refers to the amount of energy or signal present in a specific range of frequencies. This can be calculated by measuring the amplitude or intensity of the signal at each frequency within the band and summing them together.

## 2. How is power over a frequency band calculated?

To calculate power over a frequency band, you first need to have a frequency spectrum of the signal. This can be obtained through various methods such as Fourier transform. Then, the power at each frequency within the band is determined by squaring the amplitude or intensity value. Finally, the power values are summed together to obtain the total power over the frequency band.

## 3. What are some applications of calculating power over a frequency band?

Calculating power over a frequency band is commonly used in signal processing and analysis. It can help in identifying dominant frequencies in a signal, detecting noise or interference, and determining the bandwidth of a signal. It is also used in fields such as telecommunications, audio engineering, and radio astronomy.

## 4. How does the width of the frequency band affect the calculated power?

The width of the frequency band can greatly impact the calculated power. A narrower band will result in a more precise measurement of the power at a specific frequency, while a wider band may provide a more general overview of the signal's power distribution. It is important to choose the appropriate band width based on the specific application and goals of the analysis.

## 5. Can power over a frequency band be affected by external factors?

Yes, power over a frequency band can be affected by external factors such as noise, interference, and filtering. These factors can alter the amplitude or intensity values of the signal at certain frequencies, therefore impacting the calculated power. It is important to consider and account for these external factors in the analysis and interpretation of the results.