Error Vector Magnitude using Average Power Calculator

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Frequency Modulation

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Fundamentals of Analog Communications

Sideband and Frequency Modulation

✖Average Signal Power refers to the average power carried by a signal over a specified period of time.ⓘ Average Signal Power [P_avg]			+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 Average Power to represent the deviation of the constellation points from their ideal positions.ⓘ Error Vector Magnitude using Average Power [EVM₂]

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Formula

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Error Vector Magnitude using Average Power

Formula

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

Example

`"4.266667"=(1/"15W")*(1/"9")*sum(x,1,"9",("8m")^2)`

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Error Vector Magnitude using Average Power Solution

STEP 0: Pre-Calculation Summary

Formula Used

Error Vector Magnitude Using Average Power = (1/Average Signal Power)*(1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2)
EVM₂ = (1/P_avg)*(1/N)*sum(x,1,N,(e_j)^2)
This formula uses 1 Functions, 4 Variables

Functions Used

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 Average Power - Error Vector Magnitude Using Average Power to represent the deviation of the constellation points from their ideal positions.
Average Signal Power - (Measured in Watt) - Average Signal Power refers to the average power carried by a signal over a specified 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

Average Signal Power: 15 Watt --> 15 Watt 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

EVM₂ = (1/P_avg)*(1/N)*sum(x,1,N,(e_j)^2) --> (1/15)*(1/9)*sum(x,1,9,(8)^2)

Evaluating ... ...

EVM₂ = 4.26666666666667

STEP 3: Convert Result to Output's Unit

4.26666666666667 --> No Conversion Required

FINAL ANSWER

4.26666666666667 ≈ 4.266667 <-- Error Vector Magnitude Using Average Power

(Calculation completed in 00.004 seconds)

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< 12 Frequency Modulation Calculators

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Go Overall Received Signal = (sum(x,1,Index Variable,Complex Valued Envelope*cos(Angle of Arrival)))*cos(Carrier Angular Frequency*Time Period of Signal)-(sum(x,1,Index Variable,Complex Valued Envelope*sin(Angle of Arrival)))*sin(Carrier Angular Frequency*Time Period of Signal)

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))

Error Vector Magnitude using Average Power

Go Error Vector Magnitude Using Average Power = (1/Average Signal Power)*(1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2)

Bandwidth with respect to Modulation Index of FM

Go Bandwidth of FM Wave = (2*Frequency Deviation)*(1+(1/Modulation Index in FM))

Bandwidth of FM by Carson Rule with Beta

Go Bandwidth of FM Wave = 2*(1+Modulation Index in FM)*Modulating Frequency

Frequency Sensitivity

Go Frequency Sensitivity = Frequency Deviation/Peak Amplitude of Message

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Go Frequency Deviation = Frequency Sensitivity*Peak Amplitude of Message

Bandwidth of FM wave by Carson Rule

Go Bandwidth of FM Wave = 2*(Frequency Deviation+Modulating Frequency)

Frequency Deviation provided Modulation Index

Go Frequency Deviation = Modulation Index in FM*Modulating Frequency

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Go Modulation Index in FM = Frequency Deviation/Modulating Frequency

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Error Vector Magnitude using Average Power Formula

What is the purpose of calculating Error Vector Magnitude using Average Power?

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. But in this method average signal power is used to calculate the error vector magnitude.

How to Calculate Error Vector Magnitude using Average Power?

Error Vector Magnitude using Average Power calculator uses Error Vector Magnitude Using Average Power = (1/Average Signal Power)*(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 Average Power, The Error Vector Magnitude using Average Power formula is defined as is used to represent the deviation of the constellation points from their ideal position and average signal power used to calculate the error vector magnitude. Error Vector Magnitude Using Average Power is denoted by EVM₂ symbol.

How to calculate Error Vector Magnitude using Average Power using this online calculator? To use this online calculator for Error Vector Magnitude using Average Power, enter Average Signal Power (P_avg), 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 Average Power calculation can be explained with given input values -> 4.266667 = (1/15)*(1/9)*sum(x,1,9,(8)^2).

FAQ

What is Error Vector Magnitude using Average Power?

The Error Vector Magnitude using Average Power formula is defined as is used to represent the deviation of the constellation points from their ideal position and average signal power used to calculate the error vector magnitude and is represented as EVM₂ = (1/P_avg)*(1/N)*sum(x,1,N,(e_j)^2) or Error Vector Magnitude Using Average Power = (1/Average Signal Power)*(1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2). Average Signal Power refers to the average power carried by a signal over a specified 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 Average Power?

The Error Vector Magnitude using Average Power formula is defined as is used to represent the deviation of the constellation points from their ideal position and average signal power used to calculate the error vector magnitude is calculated using Error Vector Magnitude Using Average Power = (1/Average Signal Power)*(1/Number of Error Vectors)*sum(x,1,Number of Error Vectors,(Magnitude of Each Error Vector)^2). To calculate Error Vector Magnitude using Average Power, you need Average Signal Power (P_avg), Number of Error Vectors (N) & Magnitude of Each Error Vector (e_j). With our tool, you need to enter the respective value for Average Signal Power, 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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