Help with proving a transfer function?

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SUMMARY

The discussion centers on proving a transfer function using impedance in a circuit. The user initially states that Zout equals Z2 in parallel with Z3, leading to the expression Z2Z3/(Z2 + Z3). The correct transfer function H(s) is derived as H(s) = Zout/Zg = Z2Z3/(Z1Z2 + Z1Z3). The voltage division principle is applied to find the equivalent impedance across Vo, resulting in Zo = (Z2Z3)/(Z2 + Z3), and the total impedance seen by the source is Zi = Zo + Z1. The clarification sought involves understanding the relationship Zi = Zo + Z1 in the context of voltage division.

PREREQUISITES
  • Understanding of transfer functions in control systems
  • Familiarity with impedance and complex numbers
  • Knowledge of voltage division in electrical circuits
  • Basic concepts of parallel and series circuits
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  • Study the derivation of transfer functions in electrical engineering
  • Learn about voltage division and its application to AC circuits
  • Explore the concept of equivalent impedance in series and parallel configurations
  • Investigate the use of Laplace transforms in circuit analysis
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Electrical engineering students, circuit designers, and anyone involved in analyzing and designing electrical circuits using transfer functions and impedance calculations.

Chandasouk
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http://img195.imageshack.us/i/89020004.jpg/

I cannot get the Z2Z3 to appear in the bottom.

I'm saying Zout = Z2 || Z3 so that gives Z2Z3/Z2+Z3 and Zg = Z1

Then H(s) = Zout/Zg = Z2Z3/Z1Z2+Z1Z3

What am I doing wrong?
 
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You can attack this problem using voltage division. You can get the equivalent impedence across Vo and then divide it by the total impedence seen by the source, Vg.

So:

The voltage seen by Vo:
Zo = (Z3)(Z2)/(Z3+Z2)

The voltage seen by Vg:
Zi = Zo + Z1

So when you divide Zo/Zi and simplify you get the correct answer. Hope that helps! Let me know if you need further explanation.
 
Can you explain why Zi = Zo + Z1? I always thought voltage division was

Vn = Vtotal(Rn/Rtotal)

Where V is voltage and R is resistance. In our case, we would just replace the R's with Z's for impedances but I'm still not sure how you got Zi = Zo + Z1 from that
 

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