Hello,
I wonder if someone could suggest a good source of information, either in print form or online is fine, for understanding a particular negative feedback circuit as it applies to shaping an EQ response. In other words I would like to learn how it functions (I have a good idea of the basics) and what the mathematics are for determining component values and how to change them to achieve different requirements. This is the circuit I'm interested in:
I wonder if someone could suggest a good source of information, either in print form or online is fine, for understanding a particular negative feedback circuit as it applies to shaping an EQ response. In other words I would like to learn how it functions (I have a good idea of the basics) and what the mathematics are for determining component values and how to change them to achieve different requirements. This is the circuit I'm interested in:
It is much more easy and convenient for analyzing the circuit with LTspice simulation. There are many tutorial videos at YouTube.
Johnny
Johnny
Just Googling "active filter design" should turn up a lot of resources.
A couple of examples:
https://www.tinaja.com/ebooks/afcb.pdf
https://gctjaipur.wordpress.com/wp-content/uploads/2015/08/continuous-time-active-filter-design.pdf
Also, often it is assumed that the reader is familiar with the Laplace Transform. Some possible resources, if needed (basically, it is used to reduce problems involving differential equations into algebra problems):
https://www.sjsu.edu/me/docs/hsu-Chapter 6 Laplace transform.pdf
https://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_Ch32.pdf
A couple of examples:
https://www.tinaja.com/ebooks/afcb.pdf
https://gctjaipur.wordpress.com/wp-content/uploads/2015/08/continuous-time-active-filter-design.pdf
Also, often it is assumed that the reader is familiar with the Laplace Transform. Some possible resources, if needed (basically, it is used to reduce problems involving differential equations into algebra problems):
https://www.sjsu.edu/me/docs/hsu-Chapter 6 Laplace transform.pdf
https://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_Ch32.pdf
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It's actually pretty simple ... in theory. As you've undoubtedly found if you read Lipshitz' paper, the math gets hairy in a hurry. But in theory the feedback network is "just" a voltage divider:
Pardon the mirror image for Z1. So now you can derive the divider ratio as:
Vout/Vin = Z2/(Z1+Z2)
Trouble arises because Z1 depends on frequency and that makes the math a bit complicated. It should be no trouble to play with the divider in a simulator and get some understanding that way, though. Keep in mind that the frequency response of the amplifier overall will be approx. 1/ß, so (Z1+Z2)/Z2, assuming you have sufficient forward gain.
If you're new to circuit simulation, I suggest learning QSpice. I'm thinking LTspice has become abandonware now that the author is with Qorvo.
Tom
Pardon the mirror image for Z1. So now you can derive the divider ratio as:
Vout/Vin = Z2/(Z1+Z2)
Trouble arises because Z1 depends on frequency and that makes the math a bit complicated. It should be no trouble to play with the divider in a simulator and get some understanding that way, though. Keep in mind that the frequency response of the amplifier overall will be approx. 1/ß, so (Z1+Z2)/Z2, assuming you have sufficient forward gain.
If you're new to circuit simulation, I suggest learning QSpice. I'm thinking LTspice has become abandonware now that the author is with Qorvo.
Tom