Yes, it appears to be correct, but it required a bit of work to check that correctness.

 

It is not true that you want to match source and load impedances in a filter. You want the impedance to be such that you get the desired characteristic; in this case maximally flat in the passband and less than or equal to some value in the transition band. Impedance matching is primarily done to transfer the maximum amount of power from the source to the load. In most filtering applications power transfer is irrelevant.

Hello there,

Well, i have to tell you i think that's the first time i ever heard that because filters are used all the time for matching purposes.
At these frequencies maybe, but add another cap for an input cap and guess what we end up with ... a Low Pass impedance matching filter

The way this was worded it sounded at first like they wanted to match the input and output impedance too, but that is only possible with a compromise without adding the second cap, but then we get a low pass filter that also matches input to output.

Maybe at 1kHz it would be a bit rare. At 100kHz and up more likely. But with these academic type problems you never know what they want.

 

@MrAI and @Papabravo , thank you both so much for your time and effort in helping understand this question. I'm going to trouble you again in the weeks to come before my exams. This week is maths and design so I will post maths questions. Self study requires alot of dedication. I try to tackle 2 subjects a week.
Thank you again and thanks to this website (help from people like you) and the internet I am managing fine.

 

Hello there,

Well, i have to tell you i think that's the first time i ever heard that because filters are used all the time for matching purposes.
At these frequencies maybe, but add another cap for an input cap and guess what we end up with ... a Low Pass impedance matching filter

The way this was worded it sounded at first like they wanted to match the input and output impedance too, but that is only possible with a compromise without adding the second cap, but then we get a low pass filter that also matches input to output.

Maybe at 1kHz it would be a bit rare. At 100kHz and up more likely. But with these academic type problems you never know what they want.

The problem with impedance matching in a typical lowpass filter is the large bandwidth you need to deal with. Maybe in a bandpass or a notch filter you have a better chance of of doing it without changing the filter characteristic. Adding a cap to a Butterworth filter is like riding on a see-saw, it may improve something, but at the expense of something else.

 

The problem with impedance matching in a typical lowpass filter is the large bandwidth you need to deal with. Maybe in a bandpass or a notch filter you have a better chance of of doing it without changing the filter characteristic. Adding a cap to a Butterworth filter is like riding on a see-saw, it may improve something, but at the expense of something else.

Hi again,

Yes i have to agree. There's a tradeoff, unless of course the expense is what else we needed in the design.
I am not entirely sure i would want to do it this way yet but, if we could have a low pass filter that was able to match the output impedance of an amplifier to say an antenna, and the waveform of the signal had higher harmonics (square wave perhaps) then there is a chance we might want to try to match at the required frequency while getting rid of the higher harmonics at the same time. I can say though that i never had to do this, at least not yet but i guess it is something that could be done. Maybe like the equivalent of a low pass filter combined with a matching network: the low pass to get rid of the high harmonics, and the matching network to match one Z to the other Z.
Just some thoughts