The desired answer for the transfer function is in the photo below. Solve for the following using the given circuit. The subject is second order lti system: Passive Low Pass Filter RC Circuit. 1.) Solve for the transfer function (without the values just like in the photo below) using circuit/nodal analysis, after getting the transfer function. Solve for the poles and identify what kind of response. (Damping response, overdamped response, underdamped response, etc.) After identifying the response, apply step input and inverse laplace. 2.) Solve for the transfer function with values by simply substituting the values of the components. 3.) Solve for the Voltage Out of the Circuit.
Transfer function
A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.
Convolution Integral
Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.
This is a review question, therefore it is not graded.
The desired answer for the transfer function is in the photo below. Solve for the following using the given circuit.
The subject is second order lti system: Passive Low Pass Filter RC Circuit.
1.) Solve for the transfer function (without the values just like in the photo below) using circuit/nodal analysis, after getting the transfer function. Solve for the poles and identify what kind of response. (Damping response, overdamped response, underdamped response, etc.) After identifying the response, apply step input and inverse laplace.
2.) Solve for the transfer function with values by simply substituting the values of the components.
3.) Solve for the Voltage Out of the Circuit.
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