How to derive the w/w0 result in the low-pass response in the fourth edition of Circuit Design Based on Operational Amplifiers and Analog Integrated Circuits...

sunboy25

How to derive the w/w0 result in the low-pass response in the fourth edition of Circuit Design Based on Operational Amplifiers and Analog Integrated Circuits... [Copy link]

I can calculate the second of the following two formulas, but I don't know how to get the value of the first one, 3.46a (w/w0=√1-1/2Q^2). Please give me some advice, "Circuit Design Based on Operational Amplifiers and Analog Integrated Circuits, Fourth Edition"

gmchen

I remember that the OP seemed to have asked a similar question in a previous post.

The solutions to this type of problem are similar, that is, write out the expression of the modulus of the transfer function, and then use w/w0 as the independent variable and the response of the transfer function as the dependent variable to find the extreme value. In the problem of this post, Q is a parameter. Finding the extreme value gives the expression of w/w0 at the extreme point, which is 3.46a. Substituting it back into the transfer function gives 3.46b.

sunboy25

gmchen posted on 2021-6-25 16:21 I remember that the host seemed to have asked a similar question in a previous post. The solutions to such problems are similar, that is, to write the model of the transfer function...

Master, I have posted the same thread before. After your explanation, the problem now is that I don't know how to find the extreme value, and I don't know how to calculate the modulus. Do you have any examples of finding extreme values? Just send me one, I will take a look, and I should know what's going on .

gmchen

sunboy25 posted on 2021-6-25 22:57 gmchen posted on 2021-6-25 16:21 I remember that the OP seemed to have asked a similar question in a previous post. The solutions to this kind of problem are...

If you have studied advanced mathematics in college, you should remember the method of finding extreme values: find the derivative and set it equal to zero.

If you can't even find the derivative, there's no way I can help you.

sunboy25

gmchen posted on 2021-6-26 09:32 sunboy25 posted on 2021-6-25 22:57 gmchen posted on 2021-6-25 16:21 I remember that the OP seemed to have asked a similar question in a previous post...

Thank you, great man. You are so awesome. You explained clearly what I wanted to confirm in just two sentences. What I wanted to confirm is whether this method works. Because I taught myself advanced mathematics, I am not sure how it is actually calculated.

jojoee

In this case, the transfer function of the filter is a complex function, so we must first list the expression of the complex modulus (amplitude), and the maximum value occurs at the point where the slope of the modulus function is 0.

It is enough to have the basic concept of complex numbers and the basic concept of finding extreme values in calculus. If you are not familiar with it, review the basic university mathematics. There are many videos on the Internet.