10.55: Starting with the Figure 10.
31(b) circuit configuration, design a 3rd order
Chebyshev bandstop filter for a 50 Ω system. The stopband is to be from 900 MHz to
1100 MHz with 3 dB of ripple allowed. Plot the insertion loss.
Setup: This is similar to Example
10.17.
Solution:
Assuming 3 dB of ripple, from Table
10.3 we have:
g1 = g3 = 3.3487, and g 2 = 0.7117.
(see Figure P10.31(b)) Figure 10.31(b)
Now we perform the impedance
g2
transformation: L1 ' = L3 ' = g1 R = 167.4, and C2 ' =
= 0.01423
R
The frequency transformation is performed using Table 10.4, where L1 ' is transformed
(a) (b)
Fig. P10.55 a&b
into a parallel circuit containing L1 '' and C1 '' . C2 ' is transformed into a series circuit
containing L2 '' and C2 '' . This is shown in Figure P10.55(a). To perform the
transformation, we calculate BWω and wo:
BWω = 2π ( 200MHz )
ωo = 2π ( 900MHz )(1100MHz ) = 2π ( 995MHz )
We then have:
1 1
C1 '' = = = 4.75 pF
BWω L1 ' 2π ( 200 x106 ) (167.4 )
BWω L1 ' 2π ( 200 MHz )(167.4 )
L1 '' = = = 5.39nH
ω ( 2π ) ( 995MHz )
2 2 2
o
Written by Stuart M. Wentworth. Copyright John Wiley and Sons 2007
1 1
L2 '' = = = 55.9nH
BWω C2 ' 2π ( 200MHz )( 0.01423)
BWω C2 ' 2π ( 200 x106 ) ( 0.01423)
C2 '' = = = 0.458 pF
ωo2 ( 2π ) ( 995MHz )
2 2
To plot the insertion loss using ML1055, we use the impedances shown in Figure
P10.55(b), given as
j −j
Z 2 = jω L2 ''− , Z1 = jω L1 ''
ωC2 '' ωC1 ''
We also define Z3 as the impedance seen by the voltage v1: Z 3 = Z 2 ( R + Z1 ) .
⎛ R ⎞ ⎛ Z3 ⎞
Now we can find the voltage ratio relations: vLF = ⎜ ⎟ v1 , and v1 = ⎜ ⎟ vs .
⎝ R + Z1 ⎠ ⎝ Z 3 + R + Z1 ⎠
v
Combining, and realizing vL = vs/2, we arrive at: L =
( R + Z1 )( R + Z1 + Z3 ) .
vLf 2 RZ 3
⎛ v ⎞
The insertion loss is then: IL = 20 log ⎜ L ⎟ .
⎜ vLf ⎟
⎝ ⎠
This is plotted by ML1055 in Figure P10.55(c).
% MLP1055
%
% Design N=3 band-stop filter, 3 dB ripple.
%
clc;clear
R=50;
flo=900e6;fhi=1100e6;
BW=2*pi*(fhi-flo);
wo=2*pi*sqrt(flo*fhi);
g1=3.3487;g2=.7117;
L=g1*R;C=g2/R;
C1=1/(BW*L);
L1=BW*L/((wo^2));
C2=BW*C/((wo^2));
L2=1/(BW*C);
f=.8:0.001:1.2; %f in GHz
w=2*pi.*f*1e9;
Z2=j.*(w.*L2-1./(w.*C2));
Written by Stuart M. Wentworth. Copyright John Wiley and Sons 2007
Z1=parallel(j.*w.*L1,-j./(w.*C1));
Z3=parallel(Z2,R+Z1);
A=((R+Z1).*(R+Z1+Z3))./(2.*R.*Z3);
IL=20*log10(abs(A));
plot(f,IL)
grid on
xlabel('frequency (GHz)')
ylabel('IL (dB)')
title('N=3 Band-Stop Filter: 900-1100 MHz')
axis([0.8 1.2 0 50])
Fig. P10.55c
Written by Stuart M. Wentworth. Copyright John Wiley and Sons 2007
