EXAMPLE 1:
Low-Pass Filter Design Using Stubs
Design a low-pass filter for fabrication using microstrip lines.
The specifications are:
• cutoff frequency of 4 Ghz
• third order
• impedance of 50 Ω
• 3 dB equal-ripple characteristic.
• Er = 2.2
• Thickness of dielectric = 62 mill
Solution
Start up the rf & microwave toolbox and select the low pass filter tool.
Then select filter type Chebyshev and g-values as output.
Choose the shunt filter configuration.
Fill in the filter specifications and tab the Calculate button.
Figure 1: Low pass filter dialog
The normalized low-pass prototype element values are:
Zin = g0 = 1
L1 = g1 = 3.348931
C2 = g2 = 0.711668
L3 = g3 = 3.348931
Zout = g4 = 1
The next step is to use Richard's transformation to convert series inductors into series stubs, and
shunt capacitors to shunt stubs. According to this transformation all lengths for the stubs are λ/8.
ZL1 = L1
ZC2 = C2
ZL2 = L2
L1
L3
1
C2
1
Figure 2: Low pass prototype filter
We will use Kuroda's identity nr 2 to convert the series elements into shunt elements.
Select tool Filter Design and the tab button Kuroda's Identities.
Fill in the values for Z0 (Zin, Zout) and L (L1,L3)
1
C1
UE
UE
Z0'
Z0'
C2
1
Z0' = 4.3489
C1 = 0.7701
C2 = 0.7116
C3 = 0.7701
C3
Figure 3: Low pass filter after using Kuroda's Identities
Now we will use series and shunt equivalent circuit nr 1 to convert the shunt capacitors into shunt
stubs.
Figure 4: Series and shunt
equivalent circuits dialog
1
4.3489
1.4053
1.2985
1
4.3489
1.2985
Figure 5: Normalized low pass stub filter. All lengths are λ/8.
After de-normalization to Z0 = 50 Ω we get the following low pass filter using ideal transmission
lines:
50 Ω 217.4 Ω
64.9 Ω
217.4 Ω
70.3 Ω
50 Ω 64.9 Ω
Figure 6: De-normalized low pass stub filter. All lengths are λ/8.
S-PARAMETERS
S_Param
SP1
Start=2.0 GHz
Stop=7.0 GHz
Step=.05 GHz
TLIN
TL3
Z=64.9 Ohm
E=45
F=4 GHz
Term
Term1
Num=1
Z=50 Ohm
TLIN
TL1
Z=217.4 Ohm
E=45
F=4 GHz
TLIN
TL4
Z=70.3 Ohm
E=45
F=4 GHz
TLIN
TL2
Z=217.4 Ohm
E=45
F=4 GHz
TLIN
TL5
Z=64.9 Ohm
E=45
F=4 GHz
Term
Term2
Num=2
Z=50 Ohm
Figure 7: ADS circuit of the low pass filter using ideal transmission lines
m1
freq=4.000GHz
dB(S(2,1))=-2.984
m1
0
-10
dB(S(2,1))
-20
-30
-40
-50
-60
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
freq, GHz
Figure 8: ADS simulation of the low pass filter using ideal transmission lines
Next step is to convert the ideal transmission lines to microstrip lines.
Select tool Microstrip Calculator and fill in the values for Er (2.2) and substrate height (62 mil).
Fill in a phase 0f 45 deg (λ/8) and F is the cutoff frequency (4Ghz)
Leave all other parameters to default.
Fill in the desired impedance of the transmission lines and synthesize the width an length of the
microstrip lines.
Figure 9: Microstrip line
calculator dialog
W =5.08 mm W = 3.37 mm
L = 2.72 mm
W = 0.11 mm
L = 2.89 mm
W = 0.11 mm
L = 2.89 mm
W = 2.94 mm
L = 2.73 mm
W =5.08 mm W = 3.37 mm
L = 2.72 mm
Var
Eqn
S-PARAMETERS
S_Param
SP1
Start=2.0 GHz
Stop=7.0 GHz
Step=.05 GHz
MSub
MLIN
TL4
Subst="MSub1"
W=w3 mm
L=l3 mm
MLIN
TL3
Subst="MSub1"
W=w1 mm
L=l1 mm
Term
Term1
Num=1
Z=50 Ohm
VAR
VAR1
l1=6.89
l2=7.37
l3=6.92
w1=3.17
w2=.07
w3=2.76
MLIN
TL1
Subst="MSub1"
W=w2 mm
L=l2 mm
MSUB
MSub1
H=62 mil
Er=2.2
Mur=1
Cond=1.0E+50
Hu=1.0e+033 mm
T=35 um
TanD=0
Rough=0 mm
MLIN
TL7
Subst="MSub1"
W=w1 mm
L=l1 mm
Term
Term2
Num=2
Z=50 Ohm
MLIN
TL6
Subst="MSub1"
W=w2 mm
L=l2 mm
Figure 10: ADS circuit of the low pass filter using microstrip lines
m1
freq=4.000GHz
dB(S(2,1))=-3.128
m1
0
dB(S(2,1))
-10
-20
-30
-40
-50
-60
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
freq, GHz
Figure 11: ADS simulation of the low pass filter using microstrip lines
7.0