Hello there,
This is a very interesting topic to explore!
Here is my take on this,
Designing complex filter networks like Butterworth and Chebyshev filters using passive components involves several steps.
1. Butterworth Filters-
These filters are great because they have a very smooth response in the passband, meaning no ripples. They transition smoothly to the stopband.
You calculate the values of resistors, capacitors, and inductors based on the desired cutoff frequency and the order of the filter. The math involves Butterworth polynomials to ensure that smooth response.
2. Chebyshev Filters-
These filters can cut off frequencies more sharply than Butterworth filters, but they introduce ripples in the passband.
Here, you use Chebyshev polynomials to determine the component values. You can control the amount of ripple, which is a trade-off for the steeper roll-off.
Practically, components aren’t perfect. For example, a resistor might have a 1% tolerance, which can slightly change the filter’s performance. Components can change value with temperature, which can affect the filter’s stability. Getting the exact component values to achieve the desired response can be tricky. It often requires some trial and error and simulation. How you place the components on a circuit board can introduce additional effects that change the filter’s behavior. Sometimes, the exact values you need aren’t available, so you might need to combine components to get the right values.
Tools like SPICE can help you simulate the filter’s performance before you build it.
Designing these filters is a mix of theory and practical adjustments. You need to be precise with your component values and account for actual imperfections to get the desired frequency response.
You can refer to;
https://eng.libretexts.org/Bookshelves/ ... ev_Filters
https://www.analog.com/media/en/trainin ... apter8.pdf