RLC Transfer Function for Voltage Across the Capacitor

[dashkin111]

Homework Statement

We have a series RLC circuit with x(t) as the voltage source. We are to find the frequency response function H(w) from the input x(t) to the output y(t)=Vc(t) - ie the voltage across the capacitor.

Homework Equations

The Attempt at a Solution

My answer is:

$$H(\omega) = \frac{1}{1+j \omega R C - \omega ^{2} L C }$$

I just got it from doing the impedance of the capacitor over the total impedance. First does this look correct?

My second question arises in a more "general" approach of going at transfer function problems. Do I always just do the impedance part we are looking at divided by the impedance of the whole circuit?

 

[mjsd]

Homework Statement

We have a series RLC circuit with x(t) as the voltage source. We are to find the frequency response function H(w) from the input x(t) to the output y(t)=Vc(t) - ie the voltage across the capacitor.

Homework Equations

The Attempt at a Solution

My answer is:

$$H(\omega) = \frac{1}{1+j \omega R C - \omega ^{2} L C }$$

I just got it from doing the impedance of the capacitor over the total impedance. First does this look correct?

yes.

My second question arises in a more "general" approach of going at transfer function problems. Do I always just do the impedance part we are looking at divided by the impedance of the whole circuit?

not entirely sure what you mean by "general" approach; but it usually depends on the circuit

 

[piercas]

I cannot provide a specific response to a specific content without knowing the context and background information. However, I can provide a general explanation about the RLC transfer function for voltage across the capacitor.

The RLC circuit is a type of electrical circuit that contains a resistor (R), an inductor (L), and a capacitor (C) in series. In this circuit, the voltage source (x(t)) is connected to the resistor, and the output voltage (y(t)) is measured across the capacitor. The transfer function, H(\omega), represents the relationship between the input and output signals in the frequency domain.

To find the transfer function for the voltage across the capacitor, we can use the concept of impedance. The impedance of a capacitor is given by 1/(j\omega C), where j is the imaginary unit and \omega is the angular frequency. The total impedance of the circuit is the sum of the individual impedances of the resistor, inductor, and capacitor. Therefore, the transfer function for the voltage across the capacitor can be calculated by taking the impedance of the capacitor over the total impedance of the circuit.

In the general approach to finding transfer functions, the impedance method can be applied to any circuit. However, the specific steps may vary depending on the type of circuit and the desired output. It is important to understand the underlying principles and concepts of impedance and transfer functions in order to apply them effectively in different situations.

In conclusion, the RLC transfer function for voltage across the capacitor is a valuable tool in analyzing and designing electrical circuits. It can be calculated using the impedance method and can provide insights into the behavior of the circuit in the frequency domain.