Tan and ArcTan calculation

[baby_1]

Hello
Could you help me to solve this problem? i want to find w

 

[hakeen]

Hello Baby_1

the answer is w=10000*sqrt(230).

Hope helps.

Cheers

 

[godfreyl]

By trial and error, w = about 154000
I have no idea how to calculate it. What's this for?

 

[Baas Rietrot]

This looks like the start of a phase margin calculation.

Usually trail and error or plot it in MATLAB and read it off or use MATLAB's solve functions.

 

[godfreyl]

the answer is w=10000*sqrt(230).

How did you work that out?:???:
(I agree with the answer)

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This looks like the start of a phase margin calculation.

Oh, right - for poles at 10KHz, 100KHz and 200KHz.
I'd just use a simulator (or spreadsheet), but I'd still be interested to hear how Hakeen did the calculation.

 

[Baas Rietrot]

I would also want to know how hakeen did it, this might help to eliminate the tedious trail and error method.

Please post master hakeen:smile:

 

[baby_1]

Hello hakeen
it is completely right.
could you write the answer completely ? how did you find it ? it has a formula to solve these equation ?

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By trial and error, w = about 154000
I have no idea how to calculate it. What's this for?

i want to calculate an amplifier G.M(Gain Margin) and P.M(Phase margin)

 

[hakeen]

Hello

thanks for good posts, but I am not math-master.
Anyway, for solution two important things

1)arctan x + arctan y = arctan ( (x+y)/(1-x*y))
2)arctan(x) = -pi --> x=0

so think it is x=w/10^4 then

[arctan(x)+arctan(x/10)]+arctan(x/20) = -pi

so from 1&2

x= sqrt(230) and w= sqrt(230)*10^4

Hope helps.

Cheers

 

[karthick1987]

If you apply tan on both sides first

tan( arctan(w/10^4) + arctan(w/10^5) +arctan(w/2*10^5) ) = 0

then simple use tan ( A + B +C ) = tanA*tanB*tanC/(1-(tanA*tanB)-(tanA*tanB*tanC)) formula

Immediately you see that w = 0 is a solution or you get a cubic at the bottom

w^3/(10^4*10^5*2*10^5)/(1-(w^2/10^4*10^5)-w^3/(10^4*10^5*2*10^5)

hope it helps
K