# Receiver Sensitivity Calculator

Receiver sensitivity is the strength of the weakest signal that a radio receiver can detect and demodulate. It is specified in dBm, Watt or uV.

It is also referred to as Minimum Detectable Signal (MDS).

## How to Calculate Receiver Sensitivity

Use this tool is used to calculate the sensitivity. Enter the following:

• Temperature
• Bandwidth
• Receiver Noise Figure
• Signal to Noise ratio required to achieve the desired performance

## Receiver Sensitivity Formula

Receiver Sensitivity = 10 * log10 (kTB/(1 mW)) + NF + SNR

Where

• T – Temperature
• B – Bandwidth
• k – Boltzmann’s Constant 1.380649 × 10-23 m2 kg s-2 K-1
• NF – Noise Figure
• SNR – Signal-to-Noise ratio (sometimes referred to as Carrier-to-Noise Ratio)

### Noise Figure

Noise figure degrades the receiver sensitivity. Typically a low noise amplifier can be used to improve lower the minimum detectable signal level.

### Signal-to-Noise Ratio

As the complexity of the modulation increases the required SNR increases as well. FM for instance requires lower SNR than Bluetooth.

### Temperature

As the operating temperature increases, the noise power increases. This degrades the receiver sensitivity

### Bandwidth

The larger the bandwidth, the higher the noise power in the band of interest. This in turn degrades the receiver sensitivity.

## Example Receiver Sensitivity Calculation

At:

• Room temperature 27oC or 300 K,
• Signal bandwidth of 25 kHz,
• Receiver noise figure of 5 dB,
• Required SNR of 4 dB,

results in a receiver sensitivity or minimum detectable signal level of -121 dBm.

In other words, a signal has to be at least -121 dBm to be demodulated by the receiver.

## Bluetooth Receiver Sensitivity

Bluetooth signal has a bandwidth of 1 MHz and requires SNR of 15 dB for a Bit error rate of 0.1%.

Bluetooth requires that compliant devices must be able to achieve a minimum Receiver Sensitivity of -70 dBm. Using the calculator above, the noise figure can be as high as 29 dB.

In practice however the noise figure can be designed to be 8 dB or less. In this case the receiver can detect a signal as low as -90 dBm.