[SOLVED] 1st order Pass-Band Active Filter

[zionico90]

Hi guys,

I have an exercise which ask to design a suitable 1st order pass-band active filter in order to satisfy the attached specification. My understanding of the exercise is the following:

- I have to use two 1st order filter in cascade (LP+HP filter) in order to have the 20dc/decade slope
- I assume that f=22 kHz is the -3dB cut-off frequency
- For the design I assume that the 12dB gain is the one specified at fc=22 kHz, so the LP and HP filter have been design to have a gain of 12 dB + 3dB

In annex the picture of the designed circuit and the achieved frequency response. Do you think that am I correct? My understanding is that it is not possible to realize a filter with the specified shape because a certain rounding is not possible to avoid. What do you think?

Thanks!

 

[barry]

There seems to be a bit of confusion here. First, a band pass filter generally has a bandwidth specified; you seem to be trying to design a filter with zero bandwidth. That doesn't mean it's invalid, just that your specification is a little hazy.

You can't be +9db and +12dB and the same time. That's the law. The -3dB point is at the same point where you're trying to establish maximum gain; you can't have it both ways.

I THINK (and this is only guessing because you didn't post the actual question) you want 12dB of gain in the passband so that at 22kHz you'll be at 9dB, i.e., -3dB down.

 

[crutschow]

You circuit is more of a notch type filter with a slow roll-off rather than a bandpass filter, since you only mention one frequency.

 

[FvM]

I would designate the filter as first order low-pass/high pass combination. The simulated frequency characteristic is correct, the simplified sharp edge shape isn't. "First order band-pass" usually describes a band-pass with one complex pole pair, not the present circuit with real poles.

 

[crutschow]

..........
I THINK (and this is only guessing because you didn't post the actual question) you want 12dB of gain in the passband so that at 22kHz you'll be at 9dB, i.e., -3dB down.

The graph he posted shows a desired peak gain of 12dB, so he should design for 18dB of DC gain if the -3dB point of both the low-pass and high-pass filter is 22kHz.

 

[zionico90]

Thanks for your answers, i fully agree, the specification is not hazy. I report here the full text of the exercise:

- To Design a First Order Notch filter as in figure, using the minimum number of Op-Amp.

 

[barry]

Not to quibble, but that's not a notch filter; it's an inverse notch.

 

[crutschow]

Not to quibble, but that's not a notch filter; it's an inverse notch.

Yes, I was standing on my head. ;-)

 

[zionico90]

I agree, this doesn't make sense! That's the reason why a supposed to design a band-pass filter :bang:

 

[FvM]

I don't exactly understand the problem.

The designed high-pass/low-pass combination basically meets the given specification (as good as a first order filter can).

You need to understand that the idealized transfer function with sharp edge can't be realized by a real first order circuit.

 

[zionico90]

Yes, basically my question is if my understanding of the problem is correct and if it is possible to realize something better than what I have already designed.

Thanks

 

[barry]

Yes, basically my question is if my understanding of the problem is correct and if it is possible to realize something better than what I have already designed.

Thanks

I think you've met the requirements as best as you can. It's not a real-world problem. A real-world problem would be a little bit better defined. Maybe your professor has never actually designed a filter...

 

[zionico90]

Thanks! Solved, it can be closed.