Lowpass Filter

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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

SolutionStart 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.

The normalized low-pass prototype element values are:

Zin = g0 = 1

L1 = g1 = 3.348931C2 = g2 = 0.711668

L3 = g3 = 3.348931Zout = g4 = 1

Figure 1: Low pass filter dialog



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 = L1ZC2 = C2

ZL2 = L2

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)

Now we will use series and shunt equivalent circuit nr 1 to convert the shunt capacitors into shuntstubs.

Figure 2: Low pass prototype filter

L1

C2

L3

1 1

Figure 3: Low pass filter after using Kuroda's Identities

C2

UE

Z0'C3

UE

Z0'C1

1 1

Z0' = 4.3489

C1 = 0.7701

C2 = 0.7116C3 = 0.7701

Figure 4: Series and shunt equivalent circuits dialog



After de-normalization to Z0 = 50 Ω we get the following low pass filter using ideal transmissionlines:

Figure 7: ADS circuit of the low pass filter using ideal transmission lines

Figure 5: Normalized low pass stub filter. All lengths are λ/8.

1

1.2985 1.29851.4053

4.3489 4.3489 1

Figure 6: De-normalized low pass stub filter. All lengths are λ/8.

50Ω

64.9 Ω 64.9 Ω70.3 Ω

217.4 Ω 217.4 Ω50Ω

S_Param

SP1

Step=.05 GHzStop=7.0 GHz

Start=2.0 GHz

S-PARAMETERS

TLIN TL2

F=4 GHz

E=45Z=217.4 Ohm

TLIN

TL3

F=4 GHz

E=45Z=64.9 Ohm

TLIN

TL4

F=4 GHz

E=45Z=70.3 Ohm

TLIN TL1

F=4 GHz

E=45Z=217.4 Ohm

TLIN

TL5

F=4 GHz

E=45Z=64.9 Ohm

Term

Term2

Z=50 Ohm

Num=2

Term

Term1

Z=50 Ohm

Num=1



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.

m1freq=dB(S(2,1))=-2.984

4.000GHz

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.52.0 7.0

-50

-40

-30

-20

-10

-60

0

freq, GHz

B

S

2 , 1

m1

m1freq=dB(S(2,1))=-2.984

4.000GHz



W =5.08 mmW = 0.11 mm

L = 2.89 mm

W = 0.11 mm

L = 2.89 mm

W = 3.37 mmL = 2.72 mm

W = 3.37 mmL = 2.72 mm

W = 2.94 mm

L = 2.73 mm

W =5.08 mm

Figure 9: Microstrip linecalculator dialog



Figure 11: ADS simulation of the low pass filter using microstrip lines

m1freq=

dB(S(2,1))=-3.128

4.000GHz

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.52.0 7.0

-50

-40

-30

-20

-10

-60

0

freq, GHz

d B ( S ( 2 , 1

) )

m1

m1freq=

dB(S(2,1))=-3.128

4.000GHz

Figure 10: ADS circuit of the low pass filter using microstrip lines

S_Param

SP1

Step=.05 GHzStop=7.0 GHzStart=2.0 GHz

S-PARAMETERS

VARVAR1

w3=2.76w2=.07w1=3.17l3=6.92l2=7.37l1=6.89

EqnVar

MSUB

MSub1

Rough=0 mm TanD=0 T=35 umHu=1.0e+033 mmCond=1.0E+50Mur=1Er=2.2H=62 mil

MSub

MLIN TL4

L=l3 mmW=w3 mmSubst="MSub1"

MLIN TL7


MLIN TL6


MLIN TL1


MLIN TL3


Term Term2

Z=50 OhmNum=2

Term Term1

Z=50 OhmNum=1

Lowpass Filter

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