Circuits - Transfer function of this LRC circuit

In summary, a transfer function is a mathematical representation used to describe the relationship between input and output in a system, specifically in circuits. For an LRC circuit, the transfer function can be calculated using the Laplace transform and provides information on the circuit's response to different frequencies of input voltage. It can also be used to determine stability and frequency response. Changing the values of resistance, inductance, and capacitance will alter the transfer function, with effects such as decreasing output voltage amplitude and shifting resonant frequency. Additionally, the transfer function can be utilized in circuit design and analysis to select appropriate component values and predict circuit behavior.
  • #1
wcjy
73
10
Homework Statement
Given the following circuit with the inductor L1= 8(H). The transfer function between Vo(s) and Vs(s) can be described as:
$$\frac{V_o(s)}{V_s(s)} = \frac{1}{as^3+bs^2+cs+d}$$

Find a, b, c and d in this equation. Change the inductor by L1 by another inductor L2 = B(H) such that the system has a pole at S = -2/3. Find B
Relevant Equations
-
1617012351432.png

1617011617420.png
1617011638524.png
1617011649133.png
1617011656677.png


Got B = 9.

My school doesn't provide answers, hence could someone double check if my answers is right? Thanks!
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Looks good, but I think that you miscopied the constant 2 as a 3 in the final line of your derivation.
 
  • Like
Likes wcjy
  • #3
gneill said:
Looks good, but I think that you miscopied the constant 2 as a 3 in the final line of your derivation.
thank you so much!
 

FAQ: Circuits - Transfer function of this LRC circuit

What is a transfer function in relation to LRC circuits?

A transfer function is a mathematical representation of how a circuit responds to different frequencies of input signals. In the case of LRC circuits, the transfer function describes the relationship between the input voltage and the output voltage across the circuit.

How is the transfer function of an LRC circuit calculated?

The transfer function of an LRC circuit can be calculated by taking the ratio of the output voltage to the input voltage at each frequency. This can be done using Kirchhoff's laws and Ohm's law to determine the impedance of the circuit at each frequency.

What is the significance of the transfer function in LRC circuits?

The transfer function allows us to analyze the behavior of an LRC circuit and predict how it will respond to different input signals. It can also help us design circuits to achieve specific frequency responses.

How does the transfer function change with different values of resistance, inductance, and capacitance?

The transfer function of an LRC circuit is affected by changes in resistance, inductance, and capacitance. For example, increasing the resistance will decrease the amplitude of the output signal, while increasing the inductance will shift the frequency response to higher frequencies.

Can the transfer function of an LRC circuit be modified?

Yes, the transfer function of an LRC circuit can be modified by changing the values of the components or by adding or removing components from the circuit. This can be useful for achieving specific frequency responses or for filtering out unwanted frequencies.

Similar threads

Setting up an LRC series circuit with coupled coils
Replies
1
Views
1K
Power Dissipated By Resistor is LRC Circuit
Replies
3
Views
3K
Determining Inductance L in an LC Circuit
Replies
5
Views
849
LRC Series Circuit Voltage amplitude question.
Replies
4
Views
6K
Steady state circuit
Replies
7
Views
309
RLC Circuit Analysis -- Two sources and two switches
Replies
3
Views
1K
Changing capacitance effect on ripple in full rectification circuit
Replies
4
Views
2K
Calculation of current in driven series RLC circuit
Replies
8
Views
848
Finding the ODE that describes this circuit + find its transfer function
Replies
6
Views
2K
Determine Thevenin equivalent circuit.
Replies
1
Views
638

Hot Threads

Recent Insights

Back
Top