# how to write a complex transfer function

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John on 20 Feb 2024
Commented: Paul on 20 Feb 2024
how should i write followinG transfer function (tf) in the form of nuemrator and denominator in MATAB
-10.45 s^3 - 10.53 s^2 - 0.2246s
-----------------------------------------
s^2 + 1.2116 s - 0.1087 - 0.0909i
following is not working as it returns S^3 in the denominator, but i need s^2 in denominator :
numerator = [-10.45 -10.53 -.2246 0];
denominator = [0 1 1.2116 -.1087 -.0909j];
sys = tf(numerator,denominator);

Sam Chak on 20 Feb 2024
Ensure no space in .
numerator = [-10.45 -10.53 -.2246 0];
denominator = [0 1 1.2116 -.1087-.0909j];
sys = tf(numerator, denominator)
Warning: The numerator or denominator of this transfer function has complex-valued coefficients.
sys = -10.45 s^3 - 10.53 s^2 - 0.2246 s --------------------------------- s^2 + 1.212 s - (0.1087+0.0909i) Continuous-time transfer function.
John on 20 Feb 2024
Thanks, it worked
Paul on 20 Feb 2024
Or use commas to separate the array elements, then no need to worry about spacing
numerator = [-10.45 , -10.53 , -.2246 0];
denominator = [0 , 1 , 1.2116 , -.1087 - .0909j];
sys = tf(numerator, denominator)
Warning: The numerator or denominator of this transfer function has complex-valued coefficients.
sys = -10.45 s^3 - 10.53 s^2 - 0.2246 s --------------------------------- s^2 + 1.212 s - (0.1087+0.0909i) Continuous-time transfer function.