Bode plot of transfer function

Mitchy190

Then I do not understand why the below is not correct

20*LOG10(SQRT(1+w/2127.659))

2127.659 = 1/RC

My bad,

20logg.pdf

cathode-ray

The only mistake you made in 20*LOG10(SQRT(1+w/2127.659)) is that you not squared the imaginary part. I wrote 20*LOG10(SQRT(1+(w*47E3*10E-9)^2) which is equal to 20*LOG10(SQRT(1+(w/2127.659)^2). I used the multiplication because 2127.659 is an approximated value and 47E3*10E-9 is the exact value.

Note: |a+jb|=sqrt(a^2+b^2)

Mitchy190

Ahh i see! Thanks for you help dude.

Managed to plot the phase response to I think.

What do you think?

phase1.pdf

cathode-ray

Im glad i could help :)

I saw your table and you made a mistake in the calculation of the argument. Given a complex number the argument is given by:

arg(a+jb)=arctan(b/a)

and given two complex numbers z1,z2 you have the following properties:

arg(z1*z2)=arg(z1)+arg(z2)
arg(z1/z2)=arg(z1)-arg(z2)

so applying this to the transfer function you get:

arg(H(jw))=arg(A)+arg(1+jwRC)-arg(1+jwR_3C)=0+arctan(wRC)-arctan(wR_3C)

In your table you should have then:

tan^-1(wRC) || -tan^-1(wR_3C)

Note:arctan and tan^-1 its the same

Mitchy190

Ahh yes! Thank you, I have corrected that (:

The formula in my table, for the actual column is =-arctan((ω/23404.235))

where,

23404.255 = 1/R_3*C

Mitchy190

Also I was just wondering, on my friends graph the phase starts to shift at 10 hertz and on my graph it starts to at 100 hertz?

Do you know which one is correct?

The formulas below show how I am working out mine:

ATAN(((w*R*C)))

-ATAN(w*4700*R3*C)

then,

ATAN(w*R*C) - ATAN(w*4700*R3*C) = arg(H(jw))