FILTER 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 (Chebyshev).
• Er = 2.2
• Thickness of dielectric = 62 mill
Solution
Start up the rf & microwave toolbox and select the low pass filter tool.
Then select, from the menu, 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
Figure 2: Low pass plot
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 3: 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 4: 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. Select tool Series and Shunt Circuit lines and calculate the line impedance's. See Figure 5.
Figure 5: Series and shunt
equivalent circuits dialog
1
4.3489
1.4053
1.2985
1
4.3489
1.2985
Figure 6: 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 64.9 Ω
217.4 Ω
217.4 Ω
70.3 Ω
50 Ω 64.9 Ω
Figure 7: 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
TL4
Z=70.3 Ohm
E=45
F=4 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
TL5
Z=64.9 Ohm
E=45
F=4 GHz
Term
Term2
Num=2
Z=50 Ohm
TLIN
TL2
Z=217.4 Ohm
E=45
F=4 GHz
Figure 8: 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 9: ADS simulation of the low pass filter using ideal transmission lines
Next step is to convert the ideal transmission lines to real microstrip lines.
Select tool Microstrip line Calculator and fill in the values for Er (2.2) and substrate height (62
mil).
Fill in a phase of 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 and length of the
microstrip lines.
Figure 10: Microstrip line calculator
dialog
W =5.08mm W1 = 3.22mm
L1 = 6.88mm
W2 = 0.11mm
L2 = 7.27mm
W2 = 0.11mm
L2 = 7.27mm
W3 = 2.8mm
L3 = 6.91mm
W =5.08mm W1 = 3.22mm
L1 = 6.88mm
Var
Eqn
S-PARAMETERS
S_Param
SP1
Start=1.0 GHz
Stop=7.0 GHz
Step=0.05 GHz
MLIN
TL2
Subst="MSub1"
W=W1
L=L1
Term
Term1
Num=1
Z=50 Ohm
MSub
VAR
VAR1
L1=6.88mm
L2=7.27mm
L3=6.91mm
W1=3.22mm
W2=.11mm
W3=2.8mm
MLIN
TL3
Subst="MSub1"
W=W3
L=L3
MLIN
TL1
Subst="MSub1"
W=W2
L=L2
MLIN
TL4
Subst="MSub1"
W=W1
L=L1
MSUB
MSub1
H=62 mil
Er=2.2
Mur=1
Cond=1.0E+50
Hu=1.0e+033 mm
T=0 mm
TanD=0
Rough=0 mm
Term
Term2
Num=2
Z=50 Ohm
MLIN
TL5
Subst="MSub1"
W=W2
L=L2
Figure 11: ADS circuit of the low pass filter using microstrip lines
m1
freq=4.000GHz
dB(S(2,1))=-3.400
m1
dB(lowpass_lc..S(2,1))
dB(S(2,1))
0
-10
-20
-30
-40
-50
-60
1
2
3
4
5
6
freq, GHz
Figure 12: ADS simulation of the low pass filter using microstrip lines.
Black: Plot of prototype filter (LC-network). Blue: Plot of microstrip filter.
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