# Power Spectral Density PSD Calculator

The PSD can be computed by taking the ratio of the signal power to bandwidth.

To compute the Power spectral density, enter

• Signal power Ps in either Watt/Milliwatt/Microwatt/Nanowatt OR dBm
• Bandwidth BW in GHz/MHz/kHz/Hz

PSD = Ps/BW

## Example Calculation

• A total power of 10 Watt across bandwidth of 1 kHz results in a PSD of 10/1000 = 0.01 W/Hz.
• Watt can be converted to dBm and 0.01 Watt is equivalent to 10 dBm.
• The PSD is therefore 10 dBm/Hz.

Starting with a dBm value instead. For instance 30 dBm across a bandwidth of 20 kHz.

• The dBm value is first converted to Watt. 30 dBm = 1 Watt
• The next step is do divide Watt by the bandwidth as above. 1 Watt/20 kHz = 0.00005 Watt/Hz
• Finally convert Watt back to dBm to give -13 dBm/Hz.

Note that the dBm value cannot be divided by the bandwidth. It has to be converted to a linear value before dividing the two numbers.

## Background

Power Spectral Density (PSD) is a mathematical tool used to analyze signals in terms of their frequency content. It represents the distribution of power across different frequency components of a signal and as a function of frequency or bandwidth.

Unit for PSD is Watt/Hz or dBm/Hz.

PSD provides valuable information about the strength and distribution of different frequency components in a given signal.

### What’s the difference between Power Spectrum and Power Spectral Density?

While power spectrum focuses on the magnitude of the signal in the frequency domain, PSD considers the power per unit frequency.

### Where is PSD used?

PSD is used to describe the noise floor of a spectrum analyzer. The units are dBm/Hz. The normalized quantity is called the Displayed Average Noise Level or DANL.

The DANL of the Siglent Spectrum Analyzer for instance is -161 dBm/Hz. The lower this number the more sensitive the analyzer. A sensitive analyzer is able to detect very weak RF signals.

## Related Calculators

Thermal noise power depends on the bandwidth and temperature. If the bandwidth is 1 Hz, then it is the power spectral density of noise or noise spectral density.

SNR (in dB) is the difference between the PSD and the noise density.