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1
EKT 441MICROWAVE COMMUNICATIONS
CHAPTER 5:
MICROWAVE FILTERS
PART II
2
f2
Filter Realization Using Distributed Circuit Elements (1) Lumped-element filter realization using surface mounted inductors and
capacitors generally works well at lower frequency (at UHF, say < 3 GHz). At higher frequencies, the practical inductors and capacitors loses their intrinsic
characteristics. Also a limited range of component values are available from manufacturer. Therefore for microwave frequencies (> 3 GHz), passive filter is usually realized
using distributed circuit elements such as transmission line sections. Here we will focus on stripline microwave circuits.
3
Zo
Zo
Filter Realization Using Distributed Circuit Elements (2) Recall in the study of Terminated Transmission Line Circuit that a
length of terminated Tline can be used to approximate an inductor and capacitor.
This concept forms the basis of transforming the LC passive filter into distributed circuit elements.
Zo
Zo
Zc ,
l
L
Zc ,
l
C
4
Filter Realization Using Distributed Circuit Elements (3)
This approach is only approximate. There will be deviation between the actual LC filter response and those implemented with terminated Tline.
Also the frequency response of distributed circuit filter is periodic. Other issues are shown below.
How do we implement series Tlineconnection ? (only practical forcertain Tline configuration)
Connection physicallength cannot beignored atmicrowave region,comparable to
Thus some theorems are used to facilitate the transformation of LCcircuit into stripline microwave circuits.Chief among these are the Kuroda’sIdentities (See Appendix)
Thus some theorems are used to facilitate the transformation of LCcircuit into stripline microwave circuits.Chief among these are the Kuroda’sIdentities (See Appendix)
Zo
Zo
5
More on Approximating L and C with Terminated Tline: Richard’s Transformation
Zc ,
l
L jLLjljZZ cin tanZin
LZ
l
c tan
(3.1.1a)
Zc ,
l
CZin jCCjljYY cin tan
CY
l
cZc
1
tan (3.1.1b)
For LPP design, a further requirment isthat:
1tan cl (3.1.1c)8
2 1tan cc
ll
Wavelength atcut-off frequency
6
More on Approximating L and C with Terminated Tline: Richard’s Transformation
7
Kuroda’s Identities
As taken from [2].
122 1ZZ
n
Z1
l
21Z Z2/n2
l
nZ1
Z2
l
221
Znn2Z1
l
1Z
Z2
l
21
n
ZZ2/n2
l
1Z
1: n2
Z1
l
221
Znn2Z1
l
21Z
n2: 1
Note: The inductor representsshorted Tline while the capacitorrepresents open-circuit Tline.
8
Example 5.7 – LPF Design Using Stripline
Design a 3rd order Butterworth Low-Pass Filter. Rs = RL= 50Ohm, fc = 1.5GHz.
Step 1 & 2: LPP
Zo=1
g1 1.000H
g3 1.000H
g2 2.000F
g4
1
Length = c/8for all Tlinesat = 1 rad/s
500.0000.21
9
Example 5.7 – LPF Design Using Stripline
Design a 3rd order Butterworth Low-Pass Filter. Rs = RL= 50Ohm, fc = 1.5GHz.
Step 3: Convert to Tlines using Richard’s Transformation Length = c/8for all Tlinesat = 1 rad/s
500.0000.21
Z0=1 Z0=1
Z0=0.5
10
Z0=1 Z0=1
Z0=0.5
UE UE
Z0=1 Z0=1
Example 5.7 Cont…
Length = c/8for all Tlinesat = 1 rad/s
Step 4: Add extra Tline on the series connection Extra T-lines
11
Example 5.7 Cont…
Step 5: apply Kuroda’s 1st Identity.
Similar operation isperformed here
Z0=1 Z0=1
Z0=0.5
UE UE
Z0=1 Z0=1
Step 6: apply Kuroda’s 2nd Identity.
12
Example 5.7 Cont…
After applying Kuroda’s Identity.
Length = c/8for all Tlinesat = 1 rad/s
Since all Tlines have similar physicallength, this approach to stripline filterimplementation is also known as Commensurate Line Approach.
Since all Tlines have similar physicallength, this approach to stripline filterimplementation is also known as Commensurate Line Approach.
Z0=0.5
Z0=2 Z0=2
Z0=2 Z0=2
13
Example 5.7 Cont…
Length = c/8for all Tlines atf = fc = 1.5GHz
Zc/Ω /8 @ 1.5GHz /mm W /mm 50 13.45 2.8525 12.77 8.00100 14.23 0.61
Microstrip line using double-sided FR4 PCB (r = 4.6, H=1.57mm)
Step 5: Impedance and frequency denormalization.
Z0=25
Z0=100 Z0=100
Z0=100 Z0=100
14
Example 5.7 Cont…
Step 6: The layout (top view)
15
Example 5.8
Design a low pass filter for fabrication using microstrip lines. The specifications are: cutoff freq of 4 GHz, third order, impedance of 50 ohms and a 3dB equal ripple characteristics
g1 = 3.3487 = L1
g2 = 0.7117 = C2
g3 = 3.3487 = L3
g4 = 1.0000 = RL
16
Example 5.8 (cont)
17
Example 5.8 (cont)
18
Example 5.8 (cont)
19
Example 5.8 (cont)
20
Kuroda’s Identities
As taken from [2].122 1ZZ
n Note: The inductor representsshorted Tline while the capacitorrepresents open-circuit Tline.
1Z
2
2
n
Z2
1
n
Z2Z
2
2Zn1Z
2Z 1
2Zn
21
Kuroda’s Identities
As taken from [2].122 1ZZ
n Note: The inductor representsshorted Tline while the capacitorrepresents open-circuit Tline.
2
2
n
Z2
1
n
Z
2:1 n
1
2Zn
2
2
1
Zn
1:2n
1Z
2Z
2Z 1
Z
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