Designing a chebyshev bandpass filter

Hi, I want to design a chebyshev bandpass filter of order 3, centre frequency of 10khz and bandwidth of 1khz, I'm also taking a band pass ripple of 1dB. Please I really need help on how to go about the calculations involved in the design (e.g filter transfer function) and how to design this filter itself. The only thing I could get is on the design of a chebyshev low pass filter and I know my way around that. Please I'm in a very tight corner here and I need a little help. Thanks

chris09 said:

Hi, I want to design a chebyshev bandpass filter of order 3, centre frequency of 10khz and bandwidth of 1khz, I'm also taking a band pass ripple of 1dB. Please I really need help on how to go about the calculations involved in the design (e.g filter transfer function) and how to design this filter itself. The only thing I could get is on the design of a chebyshev low pass filter and I know my way around that. Please I'm in a very tight corner here and I need a little help. Thanks

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At first, it has to be clarified if you need/want a passive or an active filter.
In the 2nd case (active) you have to decide which structure you want (cascade of lowpass/highpass or bandpass direct).
By the way: The order of a bandpass is defined by the order of the transfer functions denominator, which is either of order n=2,4,6,8...

LvW said:

At first, it has to be clarified if you need/want a passive or an active filter.
In the 2nd case (active) you have to decide which structure you want (cascade of lowpass/highpass or bandpass direct).
By the way: The order of a bandpass is defined by the order of the transfer functions denominator, which is either of order n=2,4,6,8...

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I need a passive filter and yes I missed that the order of a bandpass filter can only take even orders and that's because I have been working a lot with lowpass filters, in that case a 4th order will be needed.

Something like this?



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chris09 said:

calculations....

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Um, no. Inspired guesswork + trial and error = easier for me.

godfreyl said:

Something like this?



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Um, no. Inspired guesswork + trial and error = easier for me.

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You have gotten it solved, thanks a lot but shouldn't there be a source resistance? And please I will really need to know the calculations involved in obtaining the filter transfer function and the entire design, and what will be the value of the angular frequency w in the chebyshev polynomial Tn(w/wp) if wp=10.5khz? Another thing that gets me really confused is, what happens to the lower cutoff frequency? Thanks

Chris, it is not clear to me what your target is.
* If you need the transfer function of the particular circuit (as shown) you have to apply the classical formulas for network calculations (KCL, KVL, impedance divider).
* If you need - independent on a specific circuit - the transfer function, which satisfies your needs (bandwidth, center frequency, ripple/approximation) the calculation is more involved.
In this case you have to apply bandpass-lowpass-bandpass transformations.

Question: What do you mean with your last question (what happens...) ?

shouldn't there be a source resistance?

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Passive filters have to be designed for a specific combination of source and load impedance. It seems like the filter suggested by godfreyl (I didn't understand, if it's actually an exactly calculated Chebyshev BP with the said parameters?) uses Z1 = 0 and Z2 = 600 ohm, which would allow to implement the requested characteristic. In any case, there must be a resistive impedance part, either in source or load impedance, or both.

If you tell your impedance parameters, a lot of commercial or free filter design programs can calculate the filter elements according to your specification.

Or you can do it yourself by adjusting the parameters of the bandpass to make the transfer characteristic fit the chebyshev polynomial from literature.

chris09 said:

shouldn't there be a source resistance?

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The previous one had source impedance = zero.
This one has source impedance = load impedance = 50 Ohms.

I will really need to know the calculations involved

Click to expand...

Seems a bit masochistic, but if you really want to delve into the math try Googling "chebyshev filter design". Some useful looking stuff turns up.

Another thing that gets me really confused is, what happens to the lower cutoff frequency?

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Maybe it would be easier to think of it as a combination of a 2'nd order low-pass and a 2'nd order high-pass.

Why did you place a voltage divider? The filter can be implemented with 50 ohm matching as well.

FvM said:

Why did you place a voltage divider? The filter can be implemented with 50 ohm matching as well.

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I couldn't get the correct response with Zsource = Zload, without the extra resistor. There's no problem if Zsource << Zload.

Oh yes, I see. The Q of the symmetrical loaded filter would be too low to implement a Cheybshev characteristic.

Seems a bit masochistic, but if you really want to delve into the math try Googling "chebyshev filter design". Some useful looking stuff turns up.


Thank a lot, but the reason I need the calculations and certain values you used in yours (like stopband attenuation, as well as the Ws in the chebyshev function, Tn(Ws/Wp) where Wp is the passband frequency) is because I also need to simulate it with MATLAB.

Do I need to perform the computation as high pass and also as low pass filters or just as low pass filter then perform lowpass to bandpass transformation? Thank you very much

Hi Chris,
you have a clear specification: Order n=4, Fc=10 kHz, BW=1 kHz, Chebyshev ripple=1 dB.
If you need the corresponding transfer function (to be "masochistic"), I think you cannot avoid the following steps:

* Based on the specification, find the corresponding low pass, order n=2 (pole parameters, transfer function)
* Apply the lowpass-to-bandpass transformation and find the corresponding band pass poles (two conjugate pole pairs)
* As a result, you are able to write the band pass function (n=4)
* Now you have the choice either to split this function into two band pass stages (n=2) or into a highpass (n=2) and a lowpass (n=2).

The calculation needs some time - however, at first you should become familiar with the mentioned transformation (my recommendation: Some good textbooks on filter design).

Remark: This procedure applies to an active realization usimg opamps. In case of a passive realization (ladder topology) the calculation steps are different.

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Additional remark:
Of course, it is possible that a computer does all the calculation - if you need the transfer function only. In this case, you could feed a known circuit (like the one as proposed by godfreyl) into a symbolic analyzer program (e.g. SAPWIN).
This program calculates the transfer function - either in a general form (R, C, L) or in the specific form (with numbers, values) that corresponds with your specification.