question about butterworth filters

Discussion in 'General Electronics Chat' started by hunterage2000, Mar 25, 2011.

1. hunterage2000 Thread Starter Senior Member

May 2, 2010
471
1
Can somebody tell me what the f is in the magnitude formula? I know Ho is the dc gain, fB is the 3db cut off frequency and n is the order.

2. hunterage2000 Thread Starter Senior Member

May 2, 2010
471
1
nobody know what f is then?

Apr 5, 2008
18,901
3,719
Hello,

Can you show the formulas?
The f will most probably be the frequency.
and fB the border frequency of the filter (-3dB point).

Bertus

4. hunterage2000 Thread Starter Senior Member

May 2, 2010
471
1
The attached is the formula and the question is:

Analyse the magnitude and phase characteristics of a 2nd order butterworth lowpass filter

Also forgot to mention that the cutoff frequency is 1000hz

• H0.pdf
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184.2 KB
Views:
15
Last edited: Mar 25, 2011

Apr 5, 2008
18,901
3,719
Hello,

The H0 is the passband gain.
When f = fB the gain will be
H0/sqr(1+(f/fB)^2n) =
H0/srq(1+1^2n) =
H0/sqr(2)=
H0/0.707 ,
wich is - 3dB.

Bertus

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40
6. hunterage2000 Thread Starter Senior Member

May 2, 2010
471
1
doesnt this mean all orders will give the same result? How would magnitude and phase be analysed then?

Apr 5, 2008
18,901
3,719
8. hunterage2000 Thread Starter Senior Member

May 2, 2010
471
1
looking at the graph on page 5 shows n= 1,4 and 10 and gives different results. so how does this apply to the formula when the magnitude is always 1/root2

Apr 5, 2008
18,901
3,719
Hello,

You mean this graph:

All the lines go through the same point at f/fB =1.
This is the -3 dB point.

Bertus

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10. hunterage2000 Thread Starter Senior Member

May 2, 2010
471
1
so magnitude for all orders is the same? just the question says analyse magnitudes of 2nd and 4th order.

Apr 5, 2008
18,901
3,719
Hello,

The magnitude is only the same for all at the - 3dB point.
Before and afther that point the values are diffetent as you can see in the graph.

Bertus

12. hunterage2000 Thread Starter Senior Member

May 2, 2010
471
1
so what is this formula used for? Can you explain what the magnitude and phase is for 2nd order as an example so I can try other orders