# Transfer Function of Linear two port system

• doublemint
In summary, the conversation discusses solving for the transfer function of a circuit. The first step is finding V_out at the resistor using the given equation. Then, the transfer function is determined using the Fourier transform and the boundaries provided. After rearranging the equation, A, B, a, and w1 are determined by comparing the two transfer functions, but there is confusion about the value of 'a'.
doublemint
So I am suppose to solve for the transfer function of the circuit i have attached.

First I would find the V_out at the resistor. This is done by V_in=I(jwL + 1/jwC + R)
Then the transfer function is: H(f) = V_out/V_in = R/(jwL + 1/jwC + R)

Now I need to find the transfer function by using the Fourier transform.
Given the boundaries:
h(t) : 0 for t<0
e^(-at)(Acos(w1)t + Bsin(w1)t) for t>=0

so I have done the FT of h(t) to find H(f) = $\frac{-A(a+2jf\pi)-2Bf\pi}{4\pi^2f^2 - 4\pi jaf-(a^2+4\pi^2f^2_1)}$

rearranging the equation from the beginning:
H(f) = $\frac{\frac{wR}{L}}{jw^2 - j\frac{1}{LC} + \frac{wR}{L}}$

now when i try to compare the two transfer functions to determine A, B, a, and w1, I cannot seem to determine what 'a' is because it conflicts..

Does anyone see what I did wrong?
DM

Forgot to upload the circuit diagram...

#### Attachments

• circuit.jpg
5.1 KB · Views: 399

## 1. What is a transfer function?

A transfer function is a mathematical representation of the relationship between the input and output of a linear two port system. It describes how the output of the system changes in response to changes in the input.

## 2. How is a transfer function calculated?

A transfer function is calculated by taking the Laplace transform of the system's differential equations. It can also be determined experimentally by measuring the input and output signals of the system and using the ratio of the two to calculate the transfer function.

## 3. What is the significance of the poles and zeros in a transfer function?

The poles and zeros of a transfer function are important because they determine the stability, frequency response, and time response of the system. The poles represent the points where the transfer function becomes infinite, and the zeros represent the points where the transfer function becomes zero.

## 4. How can the transfer function be used to analyze a system?

The transfer function can be used to analyze a system by examining its frequency response, stability, and time response. It can also be used to design controllers and filters for the system to achieve desired performance.

## 5. What is the difference between a transfer function and an impulse response?

A transfer function describes the overall behavior of a system, while an impulse response describes the output of the system when an impulse (or delta function) is applied as the input. The transfer function can be calculated from the impulse response, but the reverse is not possible.

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