- #1

- 19

- 0

Say you have a circuit

Rp || L || C and you have a sine source and some load connected to it call it Re and you want to mesaure the gain. Vi being across the sine source, Vo being across the load resistor.

So you get somehing like this:

[tex]

H = \frac{V_o}{V_i} = \frac{R_e*R_p + R_e*j*w*L - R_e*w^2*L*C*R_p}{R_e*R_p + R_e*j*w*L - R_e*w^2*L*C*R_p + j*w*L*Rp}

[/tex]

So you take the derivative with respect to j*w and get something even uglier then that.

Set it equal 0 and solve for j*w and you get

[tex]

j*w = \frac{1}{\sqrt{L*C}}

[/tex]

But dont you actually want to solve for w? Not j*w? In which case if you solve for w you get a complex resonant frequency. Which to me makes no sense. And is wrong because I know the formula for the circuit in question is:

[tex]

w_o = \frac{1}{\sqrt{L*C}}

[/tex]

What did I over look?