butterworth filter experiment

8/19/2019 Butterworth Filter Experiment

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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



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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



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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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butterworth filter experiment

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