Simple transfer function - algebra giving me problems

  • Thread starter trickae
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  • #1
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Homework Statement



Find a transfer function: [tex]\frac{V_o(s)}{V_i(s)} = \frac{Z_2 (s)}{-Z_1(s)}[/tex]

Homework Equations



[tex]Z_1(s) = R_1 + \frac{1}{C_1s}[/tex]
[tex]Z_2(s) = \frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}[/tex]


final solution should be:
[tex]G(s) = \frac{V_o(s)}{V_i(s)} = \frac{C_1C_2R_1R_2s^2 + (C_2R_2 + C_1R_2 + C_1R_1)s + 1}{C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1}[/tex]

The Attempt at a Solution



- Give me a second i'm still typing up the latex commands

[tex]G(s) = \frac{V_o(s)}{V_i(s)}= \frac{-\frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}}{R_1 + \frac{1}{C_1s}}[/tex]

[tex] = -\frac {\frac{R_2}{C_2s}}{(R_2 + \frac{1}{C_2s})(R_1 + \frac{1}{C_1s}) }[/tex]

[tex] = \frac{-R_2}{(C_2s)(R_2 + \frac{1}{C_2s})(R_1 + \frac{1}{C_1s})} [/tex]

[tex]= \frac{-R_2(C_1C_2s)}{(C_2s)(C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1)}[/tex]

[tex]=\frac{-R_2(C_1)}{(C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1)}[/tex]
which is no where near the solution.
 
Last edited:

Answers and Replies

  • #2
83
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I misread the problem - apologies - the transfer function for a Non inverting amplifer is in the form

[tex]\frac{Z_1(s) + Z_2(s)}{Z_1(s)}[/tex] - now i get the right answer
 
  • #3
809
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I misread the problem - apologies - the transfer function for a Non inverting amplifer is in the form

[tex]\frac{Z_1(s) + Z_2(s)}{Z_1(s)}[/tex] - now i get the right answer

hehe good. Cause I quickly did it, and definitely did not get the "answer".

I feel bad for you typing all of that up in Latex. Probably took a few ;)
 

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