how can we find the amount of capacitors for the third order chebyshev Gm-C filter?

[arashbarghi20]

how can we find the value of capacitors for the third order chebyshev Gm-C filter?



could you help me please that how should I find the amount of capacitors for this tunable third order chebyshev filter?

thanks

 

[LvW]

I suppose, you know that the capacitor values depend on the desired frequency range (which we don`t know).
More than that, such a filter circuit can be described by it`s transfer function. And this transfer function leads to design formulas.
I am sure, the book or paper you have derived the circuit from contains this function also.

 

[arashbarghi20]

I suppose, you know that the capacitor values depend on the desired frequency range (which we don`t know).
More than that, such a filter circuit can be described by it`s transfer function. And this transfer function leads to design formulas.
I am sure, the book or paper you have derived the circuit from contains this function also.

Thanks a lot for your answer. actually, I need to know more. the transfer function is the picture that I bring. the title of paper is (A 23.4 mW 68 dB Dynamic Range Low Band CMOS Hybrid Tracking Filter for ATSC Digital TV Tuner Adopting RC and Gm-C Topology). from the equation of transfer function, how can we calculate the amount of capacitors?

thanks

 

[LvW]

At first, you need VALUES for the 3 capacitors, correct? (not the "amount").
Furthermore, if you compare the second part of the transfer function (second order denominator) with the GENERAL 2nd order lowpass transfer function you get the following relations:

wp^2=gm1*gm2/C2*C3
wp/Qp=gm2/C3

wp: pole frequency of complex pole pair, Qp=corresponding quality factor.

The first part of the transfer function belongs to a simple first order RC-lowpass with wp=wo=1/R1C1.

The values for wp, Qp and wo depend on your particular requirements (design tables for Chebyshev responses 3rd order)

 

[arashbarghi20]

thanks again for your help. would you tell me what is the difference between wp and wo, and which one shows the cutoff frequency? because with the value of the capacitors in the paper, I could calculate Fp from Wp 160MHz and Fo from Wo 97MHz. now I cannot understand what is Wp and Wo.

thanks

 

[LvW]

As mentioned in my last post,
wp=pole frequency.
(each stage has its own pole frequency, which are chosen so that the cascade of both stages results in the desired overall cutoff frequency).

If wo is the desired cut-off frequency for the cmplete third-order filter, you can use filter tables to denormalize the given numbers.
However, first you need the allowed ripple for the Chebyshev response (typical values in dB are 0.1, 0.5, 1 or 3).
Remark: For Chebyshev filters the cutoff frequency normally is specified according to these ripple values (that means: not necessarily at the -3dB points).

 

[arashbarghi20]

thanks again, I re-calculate the wp and wo and find same value for them.

 

[LvW]

thanks again, I re-calculate the wp and wo and find same value for them.

What does this mean? Your 3rd order circuit (consisting of two stages) has TWO (different) pole frequencies.
And both certainly differ from the overall cut-off frequency. How is your cut-off frequency defined and how much ripple is allowed for your Chebyshev response?

 

[arashbarghi20]

Re: how can we find the value of capacitors for the third order chebyshev Gm-C filte

I calculate Wp and Wo. In the paper the values for capacitors C1=5pf C2=19pf and C3=36pf were given at 100 MHz . So, after re-calculation both wp and wo, Fp=97MHz and Fo=160MHz. Now, How should I know which one is my frequency? would you tell me please what do you mean by (how much ripple is allowed for your Chebyshev response?)

my equation is F=W/2Π
Fo= first stage
Fp= second stage

Thanks

 

[LvW]

Re: how can we find the value of capacitors for the third order chebyshev Gm-C filte

would you tell me please what do you mean by (how much ripple is allowed for your Chebyshev response?)

arashbarghi20, you have the task to design a filter having a Chebyshev response.
For my opinion, you should AT LEAST try to find out what a Chebyshev filter is - that means: What is the characteristic of the transfer function and what are the describing parameters (in comparison to other responses like Butterworth,...). Then you will be able to answer your own question about "ripple".

 

[arashbarghi20]

Re: how can we find the value of capacitors for the third order chebyshev Gm-C filte

yes I know that, would you introduce a reference(book or paper) to me to increase my acknowledge about the answer of my question?