Design of planar filters. Planar Filters design 1.Selection of a proper low-pass prototype (filter order, passband ripple,...) 2.Computing corresponding.

Designof planar filters

Planar Filtersdesign

1. Selection of a proper low-pass prototype(filter order, passband ripple, ...)

2. Computing corresponding planar implementation(widths and lengths of microstrip segments)

Low-Pass Prototype Filter

Butterworth Low-Pass PrototypeLAR = 3.01 dB

Requirement LAS = 40 dB, ΩS = 2 rad/sn = 6.644 → 7-pole Butterworth prototype filter

Chebyshev Low-Pass Prototype

Requirement LAS = 40 dB, ΩS = 2 rad/sn = 5.45 → 6-pole Chebyshev prototype filter

Elliptic FunctionLow-Pass Prototype Filter

Low-Pass Prototype Filter with inverters

Frequency and Element Transformations

-6 -4 -2 0 2 4 6-8 8

-40

-30

-20

-10

-50

0

freq*2*pi

dB(S

(2,1

))dB

(S(1

,1))

0.2 0.4 0.6 0.80.0 1.0

-40

-30

-20

-10

-50

0

freq, Hz

dB(S

(2,1

))dB

(S(1

,1))

-1.0 -0.5 0.0 0.5 1.0-1.5 1.5

-0.8

-0.6

-0.4

-0.2

-0.0

-1.0

0.2

freq*2*pi

dB(S

(2,1

))dB

(S(1

,1))

0.90 0.95 1.00 1.05 1.100.85 1.15

-40

-30

-20

-10

-50

0

freq, GHz

0.2 0.4 0.6 0.80.0 1.0

-40

-30

-20

-10

-50

0

freq, Hz

dB(S

(2,1

))dB

(S(1

,1))

Low-Pass Transformation

High-Pass Transformation

Band-Pass Transformation

Band-Stop Transformation

Planar filtersstepped impedance

Microstrip segmentsinductance, capacity

– High impedance:

– Low impedance:

– Characteristic impedance:

efef

v w

hZ

120

0

lZx

gc

2sin

l

Z

B

gc

tan1

2

l

ZB

gc 2

sin1

lZ

x

gc

tan

2

Low-Pass Stepped Impedancedesign (1)• Requirements:

– Cutoff frequency: 1 GHz– Passband ripple: 0.1 dB– Impedance: 50 – Order: 3

• Chebyshev low-pass prototype (c = 1 rad/s):

– g0 = g4 = 1

– g1 = g3 = 1.0316

– g2 = 1.1474

Low-Pass Stepped Impedancedesign (2)

• Inductance:

• Capacity:

nH209,8Z

0

101 cg

gL

nH209,80

303 cg

gZL

pF652,31

200

2 cggZ

C

Low-Pass Stepped Impedancedesign (3)

• Substrate parameters:– Dielectric constant: 10.8– Substrate height: 1.27 mm

• Selection of characteristic impedances:– Input / output: 50 – Inductive segment: 93 – Capacitive segment: 24

Low-Pass Stepped Impedancedesign (4)

• Width of microstrip segments:see the 4th lecture

rr

rrZA

11.0

23.01

1

2

1

600

rZB

0

260

Low-Pass Stepped Impedancedesign (5)

• Width of microstrip segments:see the 4th lecture

22exp

exp8:52.1for

A

A

h

WA

rr

r BBBh

W

61.0

39.01ln2

112ln1

2

:52.1for A

Low-Pass Stepped Impedancedesign (6)

• Width of microstrip segments:

– Input / output: 1.1 mm– Inductive segment: 0.2 mm– Capacitive segment: 4.0 mm

Low-Pass Stepped Impedancedesign (7)

• Effective permitivity of segments:see the 4th lecture

1pro

121

1

2

1

2

1

h

W

Wh

rref

Newly:

1pro104,0

121

1

2

1

2

12

h

W

h

W

Wh

rref

Low-Pass Stepped Impedancedesign (8)

• Wavelength of segments:see the 4th lecture

efc

df

c

– Input / output: 112 mm– Inductive segment: 118 mm– Capacitive segment: 105 mm

Low-Pass Stepped Impedancedesign (9)

• High-impedance segment:

lZx

gc

2sin

l

Z

B

gc

tan1

2

Low-Pass Stepped Impedancedesign (10)

• Low-impedance segment:

l

ZB

gc 2

sin1

lZ

x

gc

tan

2

Low-Pass Stepped Impedancedesign (11)

mm04,11sin2 0

1

L

cgLL Z

Ll

C

gCcc l

ZC

2

sin1

0

• Length of segments:

L

gLLc lZL

2

sin0

mm75,9sin2 0

1 Cc

gCC ZCl

Low-Pass Stepped Impedancedesign (12)

gC

CC

gL

LLc

lZ

lZL

tan

2sin 00

• Correcting reactance and susceptance:

gL

L

LgC

C

cc

l

Z

l

ZC

tan

22sin

1

00

Low-Pass …design (13)

References

• HONG, J.-S., LANCASTER, M. J. Microstrip Filters for RF / Microwave Applications. New York: John Wiley and Sons. 2001. ISBN 0-4713-8877-7.