Error Vector Magnitude using RMS Voltage Calculator

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Frequency Modulation

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Fundamentals of Analog Communications

Sideband and Frequency Modulation

✖Rms Voltage of the Signal is a measure of the effective voltage level of the signal over a certain period of time.ⓘ Rms Voltage of the Signal [V_rms]			+10% -10%
✖Number of Error Vectors is the count of vectors that are drawn between each measured point and its ideal position.ⓘ Number of Error Vectors [N]			+10% -10%
✖Magnitude of Each Error Vector is a measure of the absolute size or length of the error in a vector space.ⓘ Magnitude of Each Error Vector [e_j]			+10% -10%

✖Error Vector Magnitude Using Rms Voltage to represent the deviation of the constellation points from their ideal positions.ⓘ Error Vector Magnitude using RMS Voltage [EVM₁]

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Formula

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Error Vector Magnitude using RMS Voltage

Formula

`"EVM"_{"1"} = (1/"V"_{"rms"})*sqrt((1/"N")*sum(x,1,"N",("e"_{"j"})^2))`

Example

`"1.52381"=(1/"5.25V")*sqrt((1/"9")*sum(x,1,"9",("8m")^2))`

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Error Vector Magnitude using RMS Voltage Solution

STEP 0: Pre-Calculation Summary

Formula Used

Error Vector Magnitude Using Rms Voltage = (1/Rms Voltage of the Signal)*sqrt((1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2))
EVM₁ = (1/V_rms)*sqrt((1/N)*sum(x,1,N,(e_j)^2))
This formula uses 2 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
sum - Summation or sigma (∑) notation is a method used to write out a long sum in a concise way., sum(i, from, to, expr)

Variables Used

Error Vector Magnitude Using Rms Voltage - Error Vector Magnitude Using Rms Voltage to represent the deviation of the constellation points from their ideal positions.
Rms Voltage of the Signal - (Measured in Volt) - Rms Voltage of the Signal is a measure of the effective voltage level of the signal over a certain period of time.
Number of Error Vectors - Number of Error Vectors is the count of vectors that are drawn between each measured point and its ideal position.
Magnitude of Each Error Vector - (Measured in Meter) - Magnitude of Each Error Vector is a measure of the absolute size or length of the error in a vector space.

STEP 1: Convert Input(s) to Base Unit

Rms Voltage of the Signal: 5.25 Volt --> 5.25 Volt No Conversion Required
Number of Error Vectors: 9 --> No Conversion Required
Magnitude of Each Error Vector: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

EVM₁ = (1/V_rms)*sqrt((1/N)*sum(x,1,N,(e_j)^2)) --> (1/5.25)*sqrt((1/9)*sum(x,1,9,(8)^2))

Evaluating ... ...

EVM₁ = 1.52380952380952

STEP 3: Convert Result to Output's Unit

1.52380952380952 --> No Conversion Required

FINAL ANSWER

1.52380952380952 ≈ 1.52381 <-- Error Vector Magnitude Using Rms Voltage

(Calculation completed in 00.004 seconds)

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Error Vector Magnitude using RMS Voltage

Go Error Vector Magnitude Using Rms Voltage = (1/Rms Voltage of the Signal)*sqrt((1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2))

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Error Vector Magnitude using RMS Voltage Formula

What is the purpose of calculating the Error Vector Magnitude using RMS Voltage?

The constellation can also provide a quantitative measure of the impairments that corrupt the signal. Representing the deviation of the constellation points from their ideal
positions, the “error vector magnitude” (EVM) is such a measure. To obtain the EVM,
a constellation based on a large number of detected samples is constructed and a vector is
drawn between each measured point and its ideal position. The EVM is defined
as the rms magnitude of these error vectors normalized to the signal rms voltage.

How to Calculate Error Vector Magnitude using RMS Voltage?

Error Vector Magnitude using RMS Voltage calculator uses Error Vector Magnitude Using Rms Voltage = (1/Rms Voltage of the Signal)*sqrt((1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2)) to calculate the Error Vector Magnitude Using Rms Voltage, The Error Vector Magnitude using RMS Voltage formula is used to represent the deviation of the constellation points from their ideal position. Error Vector Magnitude Using Rms Voltage is denoted by EVM₁ symbol.

How to calculate Error Vector Magnitude using RMS Voltage using this online calculator? To use this online calculator for Error Vector Magnitude using RMS Voltage, enter Rms Voltage of the Signal (V_rms), Number of Error Vectors (N) & Magnitude of Each Error Vector (e_j) and hit the calculate button. Here is how the Error Vector Magnitude using RMS Voltage calculation can be explained with given input values -> 1.52381 = (1/5.25)*sqrt((1/9)*sum(x,1,9,(8)^2)).

FAQ

What is Error Vector Magnitude using RMS Voltage?

The Error Vector Magnitude using RMS Voltage formula is used to represent the deviation of the constellation points from their ideal position and is represented as EVM₁ = (1/V_rms)*sqrt((1/N)*sum(x,1,N,(e_j)^2)) or Error Vector Magnitude Using Rms Voltage = (1/Rms Voltage of the Signal)*sqrt((1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2)). Rms Voltage of the Signal is a measure of the effective voltage level of the signal over a certain period of time, Number of Error Vectors is the count of vectors that are drawn between each measured point and its ideal position & Magnitude of Each Error Vector is a measure of the absolute size or length of the error in a vector space.

How to calculate Error Vector Magnitude using RMS Voltage?

The Error Vector Magnitude using RMS Voltage formula is used to represent the deviation of the constellation points from their ideal position is calculated using Error Vector Magnitude Using Rms Voltage = (1/Rms Voltage of the Signal)*sqrt((1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2)). To calculate Error Vector Magnitude using RMS Voltage, you need Rms Voltage of the Signal (V_rms), Number of Error Vectors (N) & Magnitude of Each Error Vector (e_j). With our tool, you need to enter the respective value for Rms Voltage of the Signal, Number of Error Vectors & Magnitude of Each Error Vector and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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