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Figure 55 Butterworth Filter Design
The value of a for any filter order n can be solved manually or easily using the Matlab buttap
command that will solve the poles and gain of any Butterworth filter as is shown below:
[z,p,k] = buttap(n)
Where: z = [];
p = exp(sqrt(-1)*(pi*(1:2:2*n-1)/(2*n)+pi/2)).';
k = real(prod(-p));
Each high pass filter in this particular system has a transfer function:
H ( s) =
V0
=
Vi
s2
2
1
s +
s+
R2 C
R1 R2 C 2
Eq. 8
2
Although the Butterworth high pass filter will often amplify noise signals within the pass
band, the effect of noise at frequencies higher than 1GHz is nullified by Bluetooth’s ability to
constantly change from one transmitting frequency to another within the ISM radio band, or
“frequency hop”. Each time a Bluetooth device transmits a packet of information it immediately
jumps to another frequency within the band and instructs the receiving end to jump to that same
frequency. A common Bluetooth device will “hop” frequencies approximately 1,600 times per
second between the 79 1-MHz RF
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