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**Bode Plot problem (Please check my work**

## Homework Statement

This is actually a circuits question. It required to find Vo(s) in a network with Vi(t) being 1V (so Vi(s) was 1/s). It then asked to plot the magnitude of Vo for a range of frequencies (from 100 to 1000Hz).

## The Attempt at a Solution

I did the question and had:

H(s)=Vo/Vi(s)=[tex]\frac{s(0.0004s+0.8)}{0.00006s^{2}+0.33s+1200}[/tex]

From which:

V(s)=[tex]\frac{0.0004s+0.8}{0.00006s^{2}+0.33s+1200}[/tex]

I factored out 6e-5 in the denominator and got:

V(s)=[tex]\frac{(20/3)*(s+2000)}{(s^{2}+5500s+20000000}[/tex]

Then,

V([tex]\omega[/tex])=[tex]\frac{0.00667*(j*\omega/2000+1)}{1-\omega^{2}/2e7+(2.75e-4)*j*\omega}[/tex]

So I figured there is one real zero at 2000, a complex pole with [tex]\omega_{n}[/tex] being 4472.1 rad/s and [tex]\zeta[/tex] of 0.61 [got this from 5500/2/[tex]\omega_{n}[/tex]].

There is also a DC gain of -20log(0.00667)=43.5 which kind of freaks me out because it's huge.

So the graph will be 43.5 at w=0. Then it will rise 20dB/dec from 2000rad/s until 4472 rad/s, after which it will decline at -20dB/dec.

Is this right?