# Receiver Sensitivity Calculator (with practical examples)

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

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

It is an important parameter in wireless communication system planning. This is the target signal strength number that has to be achieved for the system to work.

## How to Calculate Receiver Sensitivity

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

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

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

Where

• T – Temperature
• B – Bandwidth
• k – Boltzmannâ€™s Constant 1.380649 Ã— 10-23 m2 kg s-2 K-1
• NF – Noise Figure
• SNR – Signal-to-Noise ratio (sometimes referred to as Carrier-to-Noise Ratio or CNR)

Receiver sensitivity can also be expressed as a function of Noise Floor:

### Noise Figure

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

### Signal-to-Noise Ratio

As the complexity of the modulation increases the required SNR increases as well. Frequency Modulation (FM) signals for instance require lower SNR than Bluetooth which is a more complex digital waveform.

### 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.

### What is maximum and minimum receiver sensitivity?

The sensitivity of a receiver depends on noise figure and signal to noise ratio based on the formula: 10 * Log10 (kTB/(1 mW)) + NF + SNR

While the SNR for a particular modulation scheme is fixed, the Noise Figure varies. It depends on the NF of the first LNA in the receive chain. The plot below shows the NF variation of an amplifier both with device voltage and frequency. It will also vary with temperature.

The maximum sensitivity corresponds to the highest value of noise figure while the minimum sensitivity depends on the lowest value of NF.

### What is the relationship between receiver sensitivity and bandwidth?

The sensitivity is given by the following equation:

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

As the bandwidth B increases, the sensitivity number increases and therefore the receiver becomes less sensitive. (E.g. when the receiver sensitivity goes from -90 dBm to -60 dBm, it has become less sensitive).

A ten fold increase in bandwidth – for example from 10 kHz to 100 kHz – reduces the sensitivity by 10 dB. Use this calculator to see the effect of 10*log(ratio) to dB.

To maximize the receiver’s ability to detect a signal it’s important to reduce the bandwidth as much as possible.

### How does Sensitivity impact Range?

Using the antenna distance calculator, a 3 dB improvement in sensitivity improves the range by over 40% in free space.

• Frequency of operation: 1 GHz
• Tx and Rx Antenna Gain: 10 dBi
• Transmit Power: +10 dBm
• Cable Loss: 3 dB

## How to Calculate Receiver Sensitivity

Here is an example 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 signal has a bandwidth of 1 MHz and requires SNR of 15 dB for a Bit error rate of 0.1%.

How to calculate Bit Error Rate

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 scenario the receiver will be able to detect a signal as low as -90 dBm.

## Communication System Design

Receiver sensitivity is typically defined in a standard. For instance, the table below from the 802.11ac standard shows the sensitivity of a Wi-Fi system and its dependence on coding, modulation, rate and bandwidth.

The table effectively informs the designer as to what the maximum Rx noise figure can be.

This information is used in conjunction with the Link Budget and Fade Margin to plan the design of a wireless communication system.

## Related Posts and Calculators

Use the following to convert from dBm to: