# dBm/Hz to nV/SQRT Hz Calculator

This tool converts dBm per Hz to nV per root(Hz) or nV/√(Hz).

🔄 nV/√(Hz) to dBm/Hz

## Formula

The formula below shows how dBm/Hz can be converted to noise with units nV/sqrt(Hz)

V/(√Hz) = √((10dBm/Hz/10)*Z*0.001)

nV/(√Hz) = √((10dBm/Hz/10)*Z*0.001)*109

where Z is the impedance

## Background

dBm stands for deciBel referenced to 1 milliwatt. It is an absolute unit of power. The Power expressed per unit frequency (Hz) is referred to as Power Spectral Density. Units are dBm/Hz or Watt/Hz.

The plot below shows the Noise Spectral Density of an operational amplifier. Noise spectral density is simply the PSD of noise. This varies with frequency and as per the data sheet, the value at 1 kHz is 55 nV/√Hz.

The important things to note from the plot is that the noise is not flat across the entire frequency range. It’s relatively stable up to around 300 Hz with small variation up to 1 kHz.

This noise is referred to as Johnson-Nyquist noise ( also known as thermal noise floor) and an important consideration when modeling the effect of the op-amp in a receiver circuit, for instance. The calculator on this page converts from dBm/Hz which can be measured using RF instruments to voltage noise density.

## Example Application and Use

A spectrum analyzer provides amplitude measurement in terms of dBm with an associated resolution bandwidth. Typical RBW can be 30 kHz for instance. Use this calculator to find the dBm value in a 1 Hz RBW (also known as dBm/Hz).

dBm/Hz can be converted to nV/√Hz using the calculator on this page.

As an example, -150 dBm/Hz converts to 7.07 nV/√Hz.

In this calculation the default impedance value of 50 ohm is used but it can be changed to any value.

As well, the units can be changed to any of the following:

• nV/√Hz
• uV/√Hz
• mV/√Hz
• V/√Hz

dBm/Hz can be converted to dBm by integrating over a specified bandwidth. The calculator assumes that the value is constant with frequency. In the above Operational Amplifier example, this applies up to about 300 Hz. But after that it’s not uniform.

## Notes

 In this post, the author has derived the result taking readings from a spectrum analyzer. The results show that -156 dBm/Hz = 3.544 nV/Root Hz – same as what you get when you use the calculator.

 This application note discusses the input voltage noise of an op amp.