Contents

**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

**Formula**

**PSD = Ps/BW**

## How to calculate Spectral Density

- 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 a spectrum analyzer for instance is -161 dBm/Hz. The lower this number the more sensitive the instrument. 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.