Transfer function from a Z = a - i * b number.

In summary, someone is trying to find a transfer function for a circuit where after a deduction of the impedance, they have found the output to input voltage relation as Vout/Vin = 2 - 3i. They would appreciate help or a link to a document that explains how to convert a function expressed in rectangular form into s functions.
  • #1
Arif1996
3
0
I have a circuit where after a deduction of the impedance, I have found the output to input voltage relation as Vout/Vin = 2 - 3i

Can anyone please let me know how can I can convert it to s functions (such as G(s) = 1/1+s) in Matlab so that I can get a transfer function?

I would appreciate help, or a link to a document if that is preferred.
 
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  • #3
Thanks..but i swear to God..i have read those...i think i am missing a very small little connection...2 - 3i is supposed to be a resistor and capacitor in series..R and C...and now just have to convert that into s domain...i guess..i would need some more reading...once i have the numerater and denominator, i can just use the MATLAB function to find the transfer function...as i said...it's been a while since i have done this and just trying to peak some brain from a person who deals with this on a daily basis...

not trying to be slacker...i will resolve as time progress...
 
  • #4
a capacitor is 1/sC and a resistor is R. An inductor is sL. So a series RC is R + 1/sC or you could say it is R + 1/jwC (I use j instead of i) which is R -j/wC

The impedance of a capacitor is 1/2πfc which is the same as saying 1/wC.
 
  • #5
yes..you are absolutely correct..:-)...i am a bit suspicious about the frequency and the reason trying to see...if i am missing something while writing the TF...i will most likely take care of this on the coming week and your explanation really helped a lot...much appreciated...
 

1. What is a transfer function?

A transfer function is a mathematical representation of the input-output relationship of a system. In the context of Z = a - i * b numbers, the transfer function describes how the complex number Z transforms the input (a) into the output (b) through the operation of subtraction and multiplication by the imaginary unit i.

2. How is a transfer function calculated from a Z = a - i * b number?

The transfer function can be calculated by dividing the output (b) by the input (a), resulting in a complex number of the form Z = -i * (b/a). This is because dividing by a complex number is equivalent to multiplying by its complex conjugate, which in this case is -i.

3. What does the transfer function tell us about a system?

The transfer function provides insight into the behavior and characteristics of a system. It can reveal information such as stability, frequency response, and overall performance. By analyzing the transfer function, we can gain a better understanding of how the system processes and transforms inputs into outputs.

4. Can a transfer function be used to design a system?

Yes, a transfer function can be used in system design. By manipulating the transfer function, we can adjust the characteristics of the system, such as its frequency response or stability, to meet our desired specifications. This allows us to optimize the performance of the system for a given input.

5. How is a transfer function related to other representations of a system?

A transfer function is closely related to other representations of a system, such as differential equations or block diagrams. In fact, the transfer function is often derived from these other representations and can be used as a tool to analyze and solve them. However, the transfer function offers a simpler and more intuitive way to understand the behavior of a system, making it a valuable tool in many scientific fields.

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