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How do I design a bandpass filter with Chebyshev characteristics?

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yannik33

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How do I design a bandpass filter with Chebyshev characteristics?
My tutor gave me following specifications:

Bandpass
Chebyshev 2nd order with multifeedback
highpass, low pass= 2kHz/2kHz
ripple 1dB

I calculated the transfer function (the result is sth like this **broken link removed**)
but it is not possible to compare the coefficient. (because of the degree of the numerator).

My next idee was to apply "lowpass to bandpass transformation" ie transform a 1st order lowpass with Chebyshev characteristics to a bandpass.
But would that be the correct way? (It's necessary that the result is a band-pass with 2nd order, multi feedback bandpass and I don't know whether the circuit would be multi feedback)
What would be/ your approach for this problem?
thanks
 

Hi Yannik,

the specification of the filter is not clear to me:

* A 1st order lowpass can be transformed into a 2nd order bandpass. But such a transfer function can not be described as "Chebyshev approximation". For these lowest-order filters one can not discriminate between different approximations (Butterworth, Chebyshev,...).
* What is the meaning of the mentioned terms "highpass, lowpass=2kHz/2kHz" ?
* What do you mean with "....not possible to compare the coefficient"? A 2nd order bandpass function (with coefficients) always can be compared with a 2nd order filter function that is derived from the selected circuit configuration (in terms of R and C): In your case "multi-feeedback".
* Finally, did you hear already about filter design programs (available for free)?

---------- Post added at 18:57 ---------- Previous post was at 18:45 ----------

As an alternative, perhaps your tutor thinks of a bandpass consisting of a Chebyshev lowpass-highpass series combination.
However, in this case you get a 4th order bandpass and you need two opamps.
 

The problem is I have coefficients for a Tschebyscheff Coefficients for 1-dB Passband Ripple (**broken link removed** page 59) but this coefficients require a transfer function a la Ao/(ai s²+ bi + 1) but my transfer function is (Ao*s)/(ai s²+ bi + 1) and therefore to compare the ai from the data sheet is not possible with ai from my transfer fuction. (ai stands for sth Like R*C/wo or so)
 

I can just guess, that the problem means a 4th order bandpass, formed by cascading 2nd order low- and high-pass prototypes. This would be the only specification, where "2kHz/2kHz" makes sense and where also the Chebyshev ripple specification can be applied.
 

The problem is I have coefficients for a Tschebyscheff Coefficients for 1-dB Passband Ripple (**broken link removed** page 59) but this coefficients require a transfer function a la Ao/(ai s²+ bi + 1) but my transfer function is (Ao*s)/(ai s²+ bi + 1) and therefore to compare the ai from the data sheet is not possible with ai from my transfer fuction. (ai stands for sth Like R*C/wo or so)

If you are somewhat familiar with filter functions you know that a numerator that is constant (like Ao) belongs to a lowpass and an expression like Ao*s is the numerator of a second order bandpass function. Thus, a comparison of coeffficients makes not much sense.
 

Like I said that seems not to be a possible way.
 

Like I said that seems not to be a possible way.

Yannik, the classical way to design second order filter stages is to compare the coefficients of the theoretical transfer function (expressed by pole data) and the function derived from the selected circuit (expressed by parts values). However, in case of a bandpass both functions must belong to a bandpass. Surprise?
But, at first, you have to clarify what you want resp. need: A bandpass of 2nd or of 4th order?
 

2nd order,
Chebyshev 2nd order with multifeedback
highpass, low pass= 2kHz/2kHz
ripple 1dB
 

It has been previously explained, why a 2nd order bandpass (transfer function (Ao*s)/(ai s²+ bi + 1) ) can't have a ripple specification or Chebyshev characteristic. I still wonder, if my guess from post #4 is true.
 

2nd order,
Chebyshev 2nd order with multifeedback
highpass, low pass= 2kHz/2kHz
ripple 1dB

Yannik, it doesn`t make much sense to simply repeat the contents of your first posting.
If you really need help, you first must clarify the requirements because - as mentioned before - a 2nd order Chebyshev bandpass with ripple does NOT exist!
 
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    FvM

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I spoke with my tutor and it was an mistake.
Like you concluded his intention was an 2nd Order low-pass and an 2nd order high-pass. (that means an forth order band-pass filter).

I tried to design the low-pass filter but bode-plot doesn't look like a Chebyshev Filter.
There were a few requirements and I chose the capacitance of the capacitors.
It would be quite nice if you could take a look, thanks
**broken link removed**
 

I tried to design the low-pass filter but bode-plot doesn't look like a Chebyshev Filter.
There were a few requirements and I chose the capacitance of the capacitors.
It would be quite nice if you could take a look, thanks

Hi yannik, I think the only problem is the resolution of the magnitude response.
Most probably, everything is OK - however, you cannot detect a 1-dB change in amplitude.
Therefore, display only the range from zero to -10 dB or -20 dB (instead of 150 dB).

---------- Post added at 18:43 ---------- Previous post was at 18:31 ----------

Ohh, there seems to be a second problem: The frequency is to low (below 1 rad/sec). Recalculate the parts.
 
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    FvM

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In addition, I don't understand why you set the gain to a rather low value of 0.18. It's an independent parmeter of the MFB, I would usually start with a gain of 1, unless other parameters are required.

According to your bandpass design method, you'll face an additional gain reduction by cascading both filters.
 

Two Additional comments:
* Error: Remove wc from the denominator of the second transfer function
* Do you really want a resistor of 4.8E7 (48 Megaohms) ?
 

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