Finding a Transfer Function using Laplace

In summary, the individual is attempting to determine the transfer function and draw a Bode plot for a circuit using Laplace equations. They have provided their equations and rearranged them to solve for the transfer function, but are unsure if their result is correct. They also suggest checking the math for the capacitor impedance.
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I'm trying to find the Transfer function of the circuit below so that I can draw the Bode plot for it. I chose to use Laplace because I think it made it a little simpler.
7hRIx.png


My equations so far:

KVL of Left Loop: EQUATION1
Vs=I1(900+1800)-900I2

KVL of Right Loop: EQUATION2
0=((2E6)/s+400+900)I2-900I1

EQUATION3
Vo=I2*(2E6)/s

Rearranging EQUATION2 gives:
I1=(1/900)((2E6)/s +1300)I2
Substitute this back into EQUATION1 to get Vs in terms of I2 and s.

When I do:
H(s)= Vo/Vs
I get:
H(s)= 5000/(3(s+5000))

Which I'm pretty sure is wrong.
 
Last edited:
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  • #2
I think you'll want to check the math for your capacitor impedance; 1/(50E-6) is not 2E6.
 

1. How do you find the transfer function using Laplace?

The transfer function can be found by taking the Laplace transform of the input and output signals and then dividing the output by the input.

2. What is the purpose of finding the transfer function using Laplace?

The transfer function allows for the representation of a system's input-output relationship in the frequency domain, making it easier to analyze and design control systems.

3. What type of systems can be analyzed using Laplace transform?

Laplace transform can be used to analyze linear time-invariant (LTI) systems, which are systems that have constant parameters and exhibit linear behavior.

4. How do you interpret the poles and zeros of a transfer function?

The poles of a transfer function represent the locations in the complex plane where the output signal becomes infinite, while the zeros represent the locations where the output signal becomes zero. These locations can provide insight into the stability and behavior of the system.

5. Are there any limitations to using Laplace transform for finding transfer functions?

One limitation is that Laplace transform can only be used for LTI systems, and it may not accurately represent the behavior of non-linear or time-varying systems. Additionally, it requires the system to have a finite number of poles and zeros, which may not always be the case.

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