Calculate transfer function magnitude, phase, dB, and cutoff from real/imaginary parts or RC/RL filter frequency, R, C, and L values.

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Magnitude Of Transfer Function Formula

The following formula is used to calculate the magnitude of the transfer function.

|T(jω)| = √((G² + B²))

Variables:

  • |T(jω)| is the linear magnitude of the transfer function (an output/input ratio for like quantities)
  • G is the real part of the transfer function
  • B is the imaginary part of the transfer function
  • j is the imaginary unit; ω is angular frequency (rad/s), with ω = 2Ï€f for frequency f in Hz

To calculate the magnitude of the transfer function, square the real part of the transfer function and the imaginary part of the transfer function. Add these two results together and then take the square root of the sum. The square root gives linear magnitude. For amplitude gain, the level in decibels is 20 log10 of that magnitude; magnitude alone does not establish stability.

What is the Magnitude Of Transfer Function?

The magnitude of a transfer function, in the field of control systems engineering, refers to the absolute value of the output signal in relation to the input signal. It is a measure of how much the system amplifies or attenuates the input signal. This is typically represented as a function of frequency, with the magnitude often expressed in decibels. The magnitude describes gain versus frequency; magnitude alone does not establish stability.

How to Calculate Magnitude Of Transfer Function?

The following steps outline how to calculate the Magnitude Of Transfer Function.

  1. First, determine the real part of the transfer function (G).
  2. Next, determine the imaginary part of the transfer function (B).
  3. Next, use the formula |T(jω)| = √((G^2 + B^2)) to calculate the magnitude of the transfer function.
  4. Finally, calculate the magnitude of the transfer function.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

real part of the transfer function (G) = 3

imaginary part of the transfer function (B) = 4