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[SOLVED] Specify component values for a given gain at a given frequency

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dzafar

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Hello there,

Attached below is the question I am trying to solve.

3.4.png

(a) H(s) = 2sRC -- Is this correct? Does this mean the zero is at the origin? Is the '2' considered gain?
(b) I have no idea how to approach part b.. Help!

Same thing for the question below:

3.5.png

(a) H(s) = (1/RC)/s - considering R1C1 = R2C2 = RC
(b) I have no idea how to approach part b.. Help!

Thanks

- - - Updated - - -

For second image.. My attempt

(b) Putting s=jw => A(w) = (1/RC)/jw
converting to dB => A_dB = sqrt((1/RC)^2/w^2) = 1/RC/w
Substituting w = 100 and A_dB = 20 and letting C = 10nF => R = 50k ohm. Is this correct?

Thanks
 

Answer to question 1: Yes, the expression for H(s) is correct.
For part b you have nothing to do than to set s=jw=j*2Pi*100 and to solve for |H(jw)|=1.
 

dzafar said:
Hello there,

For second image.. My attempt

(b) Putting s=jw => A(w) = (1/RC)/jw
converting to dB => A_dB = sqrt((1/RC)^2/w^2) = 1/RC/w
Substituting w = 100 and A_dB = 20 and letting C = 10nF => R = 50k ohm. Is this correct?

Thanks
Click to expand...

Part a is correct in boh image 1 and image 2.
About part B, as suggested, just substitute s=jw and solve for the required gain (1 linear for the first circuit and 20dB for the second)

What is wrong is the conversion you did from dB to linear. You have to apply Glinear=(10^GdB/20). The ./20 is due to te fact that you have to consider a voltage gain.
So 20 dB gain mean a factor 10 of linear gain. Also w=2*pi*100 and not w=100 as you wrote.

Then the answers to questions b can be obtained by solving:

2*2*pi*100*R*C=1 circuit of image 1
1/(2*pi*100*R*C)=10 circuit of image 2
 

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