This tool converts from Error Vector Magnitude (EVM) to Signal-to-Noise Ratio (SNR).

In order to calculate SNR the following are required:

**EVM**(use this tool to convert from dB to %)_{%}**Peak-to-Average Power Ratio**(PAPR). Use the table below to find the PAPR of a modulated signal.

**Formula**

**SNR = – [PAPR + 20 * Log _{10} (^{EVM}% / _{100})]**

**Example EVM to SNR calculation**

If you want to calculate the SNR for a QPSK waveform for instance, use the PAPR value of **1.76 dB** from the table below in the calculator above.

For a **1%** EVM, the SNR is **38.24 dB**. As the EVM increases the SNR degrades and at a certain point it will become difficult to demodulate the signal.

**Background**

**Error Vector Magnitude (EVM)** is a metric used to quantify the distortion and impairment in a transmitted signal.

It is mainly used in communication systems and more specifically in the area of modulation and demodulation.

EVM measures the difference between the ideal or desired transmitted signal and the actual received signal. This difference is calculated in terms of both amplitude and phase.

EVM is usually expressed in percentage and a lower EVM value indicates a higher quality and accuracy of the transmitted signal.

There are several factors that can contribute to EVM, such as

- Amplifier non-linearity,
- Phase noise
- Amplitude distortion
- Receiver noise figure

By measuring and analyzing the EVM of a transmitted signal, RF systems engineers can evaluate the performance of the system and identify any potential problems or areas of improvement. Overall, EVM is a crucial parameter in evaluating the performance and quality of modulation and demodulation systems.

**Peak-to-Average-Power-Ratio Values **

Below is a table of PAPR values for different modulation formats. These can be used in the calculator.

Waveform | PAPR (dB) |
---|---|

Sine Wave | 3.01 |

Full-wave rectified sine | 3.01 |

Half-wave rectified sine | 6.02 |

Triangle wave | 4.77 |

PWM signal | 10*log_{10}(T/dT) |

QPSK | 1.76 |

8-PSK | 3.3 |

π⁄4-DQPSK | 3 |

OQPSK | 3.3 |

64-QAM | 3.7 |

-QAM | 4.8 |

WCDMA downlink carrier | 10.6 |

OFDM | 12 |

GMSK | 0 |

Gaussian noise | |

Periodic chirp | 3.01 |

**Orthogonal Frequency-Division Multiplexing** (OFDM) has a high PAPR of 12 dB relative to a Sine wave with a PAPR of only 3 dB. For a fixed value of EVM, the SNR will be lower for OFDM than for a sine wave.

The table below shows a comparison for 1% EVM

Waveform | PAPR | SNR (dB) |
---|---|---|

Sine | 3 | 37 |

Half wave Rectified Sine | 6 | 34 |

OFDM | 12 | 28 |