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EXPERIMENT NO. 1
AIM: To design third and fifth order Butterworth and Chebyshev Low Pass Filter.
DESIGN SPECIFICATION
1. PLR = 3 dB
2. Frequency = 5 GHz
3. Impedance = 50 Ω
DESIGN STEPS
1. Butterworth LPF
LAR = 3dB
=2=3.1415 10
/
a) N=3
g = 2 − (1.1)
g = 1.0 ; = 0 (1.2)
g = 2 − = 2 = 1 ; = 1 g
= 2 4 1
6 = 2 36 = 2 ; = 2
g = 2 6 16 = 2 56 = 1 ; = 3 Value of capacitance and inductance are
C 1= g = 795.8
L= g = 3.979
C 3= g = 795.8
b)
N=5
g = 2 2 12 g = 1.0 ; = 0 g = 2 2 110 = 2
10 = 0 . 6 1 8 ; = 1
g = 2 4 110 = 2 310 = 1. 618 ; = 2
g = 2 6 1
10
= 2 5
10
= 2 ; = 3 g = 2 8 110 = 2 710 = 1. 618 ; = 4
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g = 2 1 0 110 = 2 910 = 0. 618 ; = 5
Value of capacitance and inductance are
C 1= g
= 491.8
L= g = 3.219 C 3=
g = 1.592 L=
g = 3.219 C 5=
g = 491.8 2. Chebyshev LPF
LAR = 3dB =2=3.1415 10/ a)
N=3
=1.0 , = 2 , = 4−−− ℎ = 2,3 … … …
= 2 12 ℎ = 1,2… … … = + ( ) ℎ = 1,2 … … … = {ℎ( 17.37)} = ℎ ( 2)
≥
cosh− √ 10/ 110/ 1
cosh−
= 2 16 =6 = 0 . 5 ; = 1
= 4 16 =36 = 1 ; = 2
= 6 16 =56 = 0 . 5 ; = 3
= {ℎ( 317.37)} =1.766
= ℎ (1.766
6 ) = 0.298
= 0.298 + 3 = 0.839
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= 0.298 + (23 ) = 0.839 = 0.298 + (33 ) = 0.088
= 1.0 ; = 0
= 2 = 3.349 ; = 1 = 4 = 0.7118 ; = 2 = 4 = 3.349 ; = 3 Value of capacitance and inductance are
C 1= g = 2.665
L
= g
= 1.416
C 3= g = 2.665
b) N=5
=1.0 , = 2 , =4−−− ℎ = 2,3… … …
= 2 12 ℎ = 1,2… … …
= + ( ) ℎ = 1,2 … … … = {ℎ( 17.37)} = ℎ ( 2)
≥cosh− √ 10/ 110/ 1
cosh−
= 2 1
10 =
10 = 0 . 3 0 9 ; = 1
= 4 110 = 310 = 0. 809 ; = 2 = 6 110 =
510 = 1 ; = 3
= 8 110 =710 = 0 . 8 0 9 ; = 4
= 1 0 110 =96 = 0 . 3 0 9 ; = 5
= {ℎ( . 5
17.37)} =1.766
= ℎ (1.76610 ) = 0.1775
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Figure 1.1 3rd Order Butterworth Low Pass Filter
2. Butterworth LPF (N=5): The 5th Order Butterworth Low Pass Filter Using PUFF
is shown in the Figure 1.2.
Figure 1.2 5th Order Butterworth Low Pass Filter
3. Chebyshev Filter (N=3): 3rd Order Chebyshev Low Pass Filter Using PUFF is
shown in the Figure 1.3.
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Figure 1.3 3rd Order Chebyshev Low Pass Filter
4. Chebyshev LPF (N=5): 5th Order Chebyshev Low Pass Filter Using PUFF is
shown in the Figure 1.4.
Figure 1.4 5th Order Chebyshev Low Pass Filter
5. Butterworth LPF (N=3): 3rd Order Butterworth Low Pass Filter circuit Using
QUCS is shown in the Figure 1.5 and its plot is shown in the Figure 1.6.
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Figure 1.5 3rd
Order Butterworth Low Pass Filter Circuit
Figure 1.6 Plot for 3rd Order Butterworth Low Pass Filter
6. Butterworth LPF (N=5): 5th Order Butterworth Low Pass Filter Using QUCS is
shown in the Figure 1.7 and its plot is shown in the Figure 1.8.
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Figure 1.7 5th Order Butterworth Low Pass Filter Circuit
Figure 1.8 Plot for 5th Order Butterworth Low Pass Filter
7. Chebyshev LPF (N=3): 3rd Order Chebyshev Low Pass Filter Using QUCS is
shown in the Figure 1.9 and its plot is shown in the Figure 1.10.
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Figure 1.9 3rd Order Chebyshev Low Pass Filter Circuit
Figure 1.10 Plot for 3rd Order Chebyshev Low Pass Filter
8. Chebyshev LPF (N=5): 5th Order Chebyshev Low Pass Filter Using QUCS is
shown in the Figure 1.11 and its plot is shown in the Figure 1.12.
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Figure 1.11 5th Order Chebyshev Low Pass Filter Circuit
Figure 1.12 Plot for 5th Order Chebyshev Low Pass Filter
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RESULTWe have designed and analysed third and fifth order Butterworth and Chebyshev Low
Pass Filter using PUFF and QUCS. Chebyshev LPF designed and simulated values are
shown in Table 1.1.
Specification Order Cut off
frequency
(GHz)
Insertion loss
(dB)
Centre
frequency
(GHz)
Return loss
(dB)
Ripple
(dB)
Designed N=3 5 3 5
20
3
N=5 5 3 5 20 3
Simulated N=3 4.9749 2.974 5.33 18.131 2.99
N=5 4.9749 2.603 5.13 47.013 2.99
Table 1.1 Chebyshev LPF designed and simulated values.
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