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Dynamic Analogue IC Design

Lab 2: Ladder Filter Design

Student Name: Mark Lennon

Lecturer Name: Mark Norton

Date: 11/12/08

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Filter 1

Objective:To design a fourth-order, Butterworth, bandpass filter with a center frequency of

3kHz and a bandwidth of 600Hz

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Filter Conversions:

To convert a low pass filter to a band pass filter the following transformations must take place:

Where:

L = Inductance

C = Capacitance

Wa = (W2 W1) / W2 = (f2 f1) / f2

Wb = (W2 W1) / W1 = (f2 f1) / f1

F1 = Lower -3db frequency

F2 = Upper -3db frequency

W1 = 2 * pi * f1

W2 = 2 * pi * f2

Component Scaling:

The components must then be scaled as follows:

L => (L*R) / W2

C => C / (W2*R)

R => R*R

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Layout of the 4th

order bandpass filter.

Overall graph showing the 4th

order band pass filter with centre frequency of 3kHz and a

bandwidth of 600Hz

1k 3k 10k

Frequency (Hz)

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

VoltageMagnitude(dB)

vdb(vout)

vdb(vinac)

Band_Pass

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Zoomed in graph of the 4th

order band pass filter with centre frequency of 3kHz and a

bandwidth of 600Hz. We can see the lower and upper -3db (taken as -2.98db in this graph)

frequencies are at 271kHz and 3.29kHz respectively. Thus, the bandwidth of the circuit form

this graph can be seen to be 580Hz. This is slightly lower than the desired 600Hz. This is caused

by two reasons. The first is that the components used have been slightly rounded and will lead

to inaccuracies. Also, the -3db was only measured as -2.98db (the closest I could get on the

graph). If it was taken at a value of -3db then the difference between the lower and upper -3db

frequencies would be larger leading to a larger bandwidth.

The centre frequency can also be measured by taking the midpoint of 3.29kHz and

2.71kHz. This is (3.29k+2.71k)/2 = (6k)/2 = 3kHz.

So, for the circuit designed the following values were obtained:

Ideal Measured

Centre Frequency: 3kHz 3kHz

Bandwidth: 600Hz 580Hz

Thus, this circuit meets the specified performance goals.

2.8k 3.2k

Frequency (Hz)

-20

-15

-10

-5

VoltageMagnitude(dB)

vdb(vout)

-9.07

x1= x2= dx=2.71k 3.29k 576.91 y1= y2= dy=-6.20 -9.18 -2.98Band_Pass

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Netlist:

********* Simulation Settings - Parameters and SPICE Options *********

LInductor_1 vinac N_14 20.3mH

LInductor_2 N_13 Gnd 580uH

LInductor_4 Vout Gnd 1.4mH

RResistor_1 Vin vinac 100 TC=0.0, 0.0

RResistor_2 Gnd Vout 100 TC=0.0, 0.0

vvinac Vin Gnd 2.5 AC 1 0.0

CCapacitor_1 N_14 N_13 140nF

CCapacitor_2 N_13 Gnd 4.9uF

LInductor_3 N_13 N_5 49mH

CCapacitor_3 N_5 Vout 58nF

CCapacitor_4 Vout Gnd 2.3uF

********* Simulation Settings - Analysis section *********

.ac dec 10k 1k 10k

********* Simulation Settings - Additional SPICE commands *********

.print ac vdb(vout)

.end

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Filter 2

Objective:To design a fifth-order, Chebyshev, bandstop filter with a center frequency of

5.25GHz and a bandwidth of 20MHz

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Filter Conversions:

To convert a low pass filter to a band stop filter the following transformations must take place:

Where:

L = Inductance

C = Capacitance

Wa = (W2 W1) / W2 = (f2 f1) / f2

Wb = (W2 W1) / W1 = (f2 f1) / f1

F1 = Lower -3db frequency

F2 = Upper -3db frequency

W1 = 2 * pi * f1

W2 = 2 * pi * f2

Component Scaling:

The components must then be scaled as follows:

L => (L*R) / W2

C => C / (W2*R)

R => R*R

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Layout of the 5th

order bandstop filter.

Overall graph showing the 5th

order band pass filter with centre frequency of 5.25GHz and a

bandwidth of 20MHz

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Zoomed in graph of the 5th

order band stop filter with centre frequency of 5.25GHz and

a bandwidth of 20MHz. We can see the lower and upper -3db frequencies are at 5.14GHz and

5.36GHz respectively. Thus, the bandwidth of the circuit form this graph can be seen to be

22MHz. This is slightly higher than the desired 20MHz. This is caused by the fact that the

components used have been slightly rounded and will lead to inaccuracies.

The centre frequency can also be measured by taking the midpoint of 5.14GHz and

5.36GHz. This is (5.14G+5.36G)/2 = (10.5G)/2 = 5.25GHz.

So, for the circuit designed the following values were obtained:

Ideal Measured

Centre Frequency: 5.25GHz 5.25GHz

Bandwidth: 20MHz 22MHz

Thus, this circuit meets the specified performance goals.

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Netlist:

********* Simulation Settings - Parameters and SPICE Options *********

LInductor_1 vinac N_3 27.0701pH

LInductor_2 N_2 Gnd 36.456nH

LInductor_4 N_3 N_4 19.247pH

RResistor_1 N_1 vinac 50 TC=0.0, 0.0

RResistor_2 Gnd Vout 50 TC=0.0, 0.0

vvinac N_1 Gnd 2.5 AC 1 0.0

CCapacitor_1 vinac N_3 7.4587pF

CCapacitor_2 N_3 N_2 25.2223fF

LInductor_3 N_5 Gnd 36.456nH

CCapacitor_3 N_4 N_5 25.2223fF

CCapacitor_4 N_3 N_4 5.306pF

CCapacitor_5 N_4 Vout 7.4587pF

LInductor_5 N_4 Vout 27.0701pH

********* Simulation Settings - Analysis section *********

.ac dec 10000 1g 10g

********* Simulation Settings - Additional SPICE commands *********

.print ac vdb(vout)

.end