Can you please help me to solve this assignment question

[naavid]

Dear Friends,

So far i didn’t get any clue how to solve this question, can you please help me on this?

A maximally flat low-pass filter is to be designed with a cut off frequency of 5.6GHz and a minimum attenuation of 20dB at 10GHz. How many filter elements are required?

 

[BigBoss]

This filter will be planar type e.g. stripline/microstripline/slotline etc.
Filter requirements will be very depended on substrate specifications which you intend to use.

 

[albbg]

The maximally flat response is obtained by the Butterworth topology. You can estimate the required order to meet your requirements independently from the implementation (lumped or distribuited components) starting from the theory. Of course actual implementation has to be choosen to minimize unwanted behaviour due to non-idealities.
You forgot to indicate the maximum attenuation can be tolerated in band. I can suppose here Amax(dB)=0.2 dB that in linear is Amax(lin)=10^(0.2/20)=1.0233.
The minimum attenuation at stop band ws=2•Π•10 GHz is Amin(dB)=20 dB --> Amin(lin)=10
The transfer function of a lowpass Butterworth filter is:

H(ws)=Ho/sqrt[1+岕(ws/wp)^(2•N)]

where Ho is the gain in DC, ws the stopband frequency, wp the pasbband frequency (in you case wp=2•Π•5.6 GHz), H(ws) is equal to 1/Amin(lin), N is the order and ε can be calculated from:

Amax(lin)=sqrt(1+ε²) --> ε²=[Amax(lin)²-1] --> ε²=(1.0233²-1)=0.0471

sing now the transfer function:

1/10=1/sqrt{1+0.0471•[(2•Π•10)/(2•Π•5.6)]^(2•N)}

that is;

10=sqrt{1+0.0471•(1.786)^(2•N)}

then:

100 = 1+0.0471•(1.786)^(2•N)

Solving with respect to N, I obtained 7 (the higher interger close to the calculated value).

 

[FvM]

I think, 3 dB attenuation at cut-off frequency should be assumed. A fourth order filter can still achieve the specification.

 

[BigBoss]

A fourth order filter can still achieve the specification.

Just curiosity..How you can make this statement since you don't know substrate specifications ??
I'm sure you won't use lumped elements for this filter at that frequency.

 

[naavid]

This is great help from side. Very nice of you, Thanks.

 

[FvM]

How you can make this statement since you don't know substrate specifications ??
I'm sure you won't use lumped elements for this filter at that frequency.

albbg has answered the point

You can estimate the required order to meet your requirements independently from the implementation (lumped or distribuited components) starting from the theory.

Practically, I can design a distributed butterworth low-pass with a filter design program.