- #1
topcat123
- 78
- 1
Homework Statement
Derive the transfer function for both circuits [tex]\frac{V_{out}}{V_{in}}[/tex] sketch Bode plots for each circuit (amplitude and phase)
Homework Equations
[tex]Z_c=\frac{1}{j{\omega}C}~and~{\omega}_C=\frac{1}{RC}[/tex]
The Attempt at a Solution
We can treat this as a potential divider using the impedances of the resister and caps.
using the Equation for the first circuit (Low pass active)[tex]\frac{V_{out}}{V_{in}}=\frac{Z_c}{Z_R+Z_C}[/tex][tex]Z_R=R[/tex]
sustituting for ZC and ZR
[tex]\frac{V_{out}}{V_{in}}=\frac{\frac{1}{j{\omega}C}}{R+\frac{1}{j{\omega}C}}[/tex]Multiply though by [tex]j{\omega}C[/tex] gives[tex]\frac{V_{out}}{V_{in}}=\frac{1}{j{\omega}RC+1}[/tex]
substituting for RC with wC
[tex]\frac{V_{out}}{V_{in}}=\frac{1}{j\frac{\omega}{\omega_C}+1}[/tex]
I am not sure how to implement the gain function, I think it is just a case of multiplying by
[tex]G=\frac{R_2}{R_1}[/tex]
as this is negative feed back [tex]\frac{V_{out}}{V_{in}}=\frac{-G}{j\frac{\omega}{\omega_C}+1}[/tex]
Am I on the right lines.
As for the BODE plot when the filter is at cutoff frequance the phase shift will be -45 deg at -3dB with a roll of of 20dB per dec?
All help will be apreciated
Thanks