What's your V(t)? Suppose that the transfer function is U(s) = 1/(s + 1). You need to deal with V(s)*U(s) if you expect to find the time domain response Vc(t) via Vc(s) = V(s)*U(s).alexmath said:Suppose R = C = 1 then the transfer function from the input voltage to the voltage across the capacitor is 1/ (s+1). So Vc(S) / V(S) = 1/(s+1). Getting back to time-domain: Vc(t) = V(t) * e^-t. What's wrong here? It should have been V(t) ( 1 - e^-t ). Thank you!
A transfer function is a mathematical representation of the relationship between the input and output of a system. It describes how a system responds to different input signals and is commonly used in control systems and signal processing.
Solving for the RC transfer function allows us to understand the behavior and characteristics of the system. It helps us determine the system's stability, frequency response, and other important properties that are essential for designing and analyzing systems.
In this case, the transfer function simplifies to a first-order low-pass filter with a cutoff frequency of 1 rad/s. The transfer function can be written as H(s) = 1 / (1 + s), where s is the complex frequency variable. To solve for the transfer function, you can use different techniques such as Laplace transform, Bode plot, or frequency response analysis.
Yes, the transfer function can be generalized for any values of R and C. The general transfer function for a first-order low-pass filter is H(s) = 1 / (1 + sRC), where RC is the time constant of the circuit. For R=C=1, the time constant is equal to 1 and the transfer function simplifies to H(s) = 1 / (1 + s).
The RC transfer function with R=C=1 has numerous applications in various fields such as electronics, telecommunications, and control systems. It is commonly used in audio amplifiers, power supplies, digital filters, and many other electronic circuits. It is also used in signal processing techniques such as noise reduction and signal conditioning.