16 Microstrip Line Filters
309
16 MICROSTRIP LINE
FILTERS
Receiver
De-
Mod
Antenna Low-Pass
Filter
Antenna
Power
Amplifier
Low-Noise
Amplifier
Attenuator
Mixer
PLL
Phase Locked Loop
PLL
Pre-
Amplifier
Band-Pass
Filter
Mixer
Transmitter
Objectives
De-
Modulator
Modulator
Mod
Audio
Output
Audio
Input
1. Understand the basic concepts of microstrip line filters.
2. Learn how to design microstrip line filters.
3. Learn how to measure filter response.
* For generic filter and its applications, refer to Chapter 7.
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Theory
When the signal frequency is high, for example 3GHz, the wavelength no longer
becomes negligible as described in the generic circuit theory: in the example case, it
reaches 100mm in free space. In other words, higher frequency has shorter wavelength.
As the wave (signal) travels (flows) along the conductor, the phase of the voltage and
current changes significantly over the physical length of the conductor. Therefore the
conductor, which works as a short-circuit node in low frequency, now works as a
“distributed component” in high frequency. It is a completely different conception from
the standard circuit theory.
In this chapter we will introduce different methods to implement LPF, HPF and
BPF by using the transmission line technique. The general filter related theory has been
introduced in Chapter 7; here we will just focus on microstrip line filters.
16-1. Transmission Line Basics
Transmission line theory forms the basis of distributed circuits. For detailed study,
we should start from Maxwell’s equations, then move on to electromagnetic wave
analysis, and so on. In this section, we will give the very basic concept of transmission
line since introducing everything in this textbook is impossible.
The key difference between circuit theory and transmission line theory lies in
electrical size. The theory of circuit analysis assumes that the physical dimensions of a
network are much smaller than its electrical wavelength; the size of transmission lines
may be a fraction of single or several wavelengths. Thus we can say that a transmission
line is a distributed-parameter network where voltages and currents can vary in
magnitude and phase over the length of the network.
On the other hand, lumped elements in generic electronic circuit such as inductors
and capacitors are generally available only for a limited range of values and are difficult
to implement at microwave frequencies, where distance between filter components is not
negligible.
3
16 Microstrip Line Filters
311
16-1-1. Wave Propagation on a Transmission Line
The transmission line is often represented as shown in Figure 16-1.
),( tzi
),( tzv
z'
Figure 16-1, voltage and current definitions of a transmission line
z
In Figure 16-1, the voltage and current are not only functions of t (time) but also
functions of z (position), which means the voltage and current will change at different
positions (different spots of Z- axis). The equivalent circuit is shown in Figure 16-2.
),( tzi
),( tzv
zR'
zL'
zG'
zC'
c
z'
Figure 16-2, equivalent circuit of a transmission line
x R=series resistance per unit length, for both conductors, in :/m.
),( tzzi '
),( tzzv '
x L=series inductance per unit length, for both conductors, in H/m.
x G=shunt conductance per unit length, in S/m.
x C=shunt capacitance per unit length, in F/m.
The series inductance L represents the total self-inductance of the two conductors,
while the shunt capacitance C occurs due to the close proximity of the two conductors.
The series resistance R represents the resistance due to the finite conductivity of the
conductors, while the shunt conductance G occurs due to dielectric loss in the material
between the conductors R and G. A finite length of transmission line can be viewed as a
cascade of sections formed as in Figure 16-2.
From Figure 16-2, we define the traveling wave as:
z
)(
O
z
JJ
(16-1)
eVeVzV
O
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z
)(
O
z
JJ
(16-2)
eIeIzI
O
the complex propagation constant as:
(16-3)
))(( CjGLjRj
ZZEDJ
The characteristic impedance Zo can be defined as:
Vo
Io
J
LjRjLR
Z
(16-4)
CjG
Y
Zo
Vo
Io
From the electromagnetic theory, we know:
dz
X
U
dt
1
(16-5)
PH
where P is the permeability and H is permittivity of the medium. In free space, we
have
U
HPX
OO
For the transmission line, the phase velocity is
/1
U
is the relative permittivity, also known as dielectric constant of the medium
H
r
(substrate of the PCB).
We can find the wavelength as:
X
U
O
(16-7)
f
, (16-6)
HHPX
rOO
8
mc
u
, which is the speed of light..
sec/10998.2/1
3
and the wave number:
f
=2S/E (16-8)
E
O
where D is the attenuation constant, and E is the wave number.
16 Microstrip Line Filters
313
16-1-2. Lossless Line
16-1-3. Terminated Lossless Transmission Line
The above solution is intended for general transmission line including loss effects,
where the propagation constant and characteristic impedance are complex. However in
many practical cases, the loss of the line is very small and can be neglected, allowing
simplification of the above results. Setting R=G=0 in (16-3) gives the propagation
constant as:
(16-9)
LCjj
ZEDJ
(16-10)
LC
ZE
(16-11)
0
D
Figure 16-3 shows a lossless transmission line terminated by an arbitrary load
impedance Z
. This diagram illustrates the wave refection problem in transmission lines,
L
a fundamental property of distributed systems.
)(),( zIzV
I
L
E
Z
in
,OZ
V
Z
L
L
z
0
Figure 16-3
+
Assuming that a wave in the form V
- z
e
is generated from a source at Z < 0, we
0
can see that the ratio of voltage to current for such traveling wave is Z
impedance. But when the line is terminated in an arbitrary load Z
to current at the load must be Z
Thus, to satisfy this condition, a reflected wave must be
L.
L0,
, the characteristic
0
the ratio of voltage
excited with the appropriate amplitude.
The amplitude of the reflected voltage wave normalized to the amplitude of the
incident voltage wave is known as the voltage reflection coefficient *, expressed as:
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16-1-4. Special Cases of Terminated Lossless Lines
V
o
*
V
o
ZZ
OL
ZZ
OL
(16-12)
When load mismatch occurs, not all generated power is delivered to the
load. This “loss” is called Return Loss (RL), and is defined (in dB) as
* log20RL
dB (16-13)
*
SWR
V
V
max
min
1
1
(16-14)
*
The general form of the input impedance in Figure 16-3 is described as follows.
lj
ZZ
Oin
OL
lj
OL
lj
EE
)()(
eZZeZZ
OL
OL
lj
EE
)()(
eZZeZZ
Z
O
Z
O
OL
sincos
LO
ljZZ
E
tan
OL
ljZZ
E
tan
LO
ljZlZ
EE
(16-15)
ljZlZ
EE
sincos
When a line is terminated in a short circuit, ZL becomes ZL =0. From 16-15 Zin is:
(16-16)
ljZZ
E
tan
Oin
When a line is terminated in an open circuit, from 16-15 Zin is:
(16-17)
ljZZ
E
cot
Oin
When the line length is O/2:
3
(16-18)
ZZ
Lin
When the line length is O/4:
16 Microstrip Line Filters
315
16-1-5. Simulation Tools
16-1-6. Suggestions and Reference of Microstrip Line Filters
2
Z
O
(16-19)
Z
in
Z
L
Referring to 16-19 and redrawing Figure 16-3 as Figure 16-4, we get:
*
4/
O
Z
0
Z
1
R
L
Z
in
Figure 16-4
ZL is composed of a transmission line of characteristic impedance Zl and RL. In
order for * to become 0, we also need Zin=Zo. The 16-13 shows the characteristic
impedance as:
(16-20)
RZZ
LOl
Which is called Quarter-wave matching transformer.
The current simulation software tools are very useful for the designers, since they
can save lot of time for complicated calculations. Many tools are available meeting a
variety of demands. AppCAD developed by Agient (HP) is one of the tools for
calculating transmission line parameters, and it can be downloaded from the public
domain. The other software, like ADS and Momentum (by Agilent), MW Office (by
AWR), HFSS and Symphony (by Ansoft) etc., can simulate the design of a circuit so that
the designer can calculate the ideal results rapidly. Using the “Optimization” function in
the software, the circuit design can be automatically tuned to meet the target
specifications.
The suggested steps of implementing microstrip line filters are as follows.
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16-2-1. Design Example
4. Find the L, C values according to the standard filter theory.
5. Convert the L, C to microstrip lines.
6. Construct and simulate the filters.
7. Fine tune and modify the design until the goal is met.
8. Fabricate the filters.
When fabricating the RF circuit on the PCB, the substrate material is a key factor
for the success. Usually the FR4 material is not suited for frequencies above 1GHz
because of the following reasons: the dielectric constant is not uniform over the whole
material, the dielectric constant also varies according to frequency change, most circuit
board suppliers can guarantee dielectric constant within a range but not at a precise value,
etc. In practice, microwave substrate PCB such as ceramic and duroid
substrates is the
better choice for microwave applications. In our experiment, FR4 is chosen because it is
easier to obtain. The results may contain a margin of error, but the basic concept can
definitely be established.
The main theory reference of this chapter is the following textbook: ‘Microwave
Engineering’, by David, M. Pozar, Addison-Wesley Publish Company, Inc..
16-2. Stepped –Impedance Low Pass Filter
A common way to implement a low pass filter is to use alternating sections of very
high and very low characteristic impedance lines, which is referred to as stepped
–impedance, or hi-Z / low-Z filter.
Design a stepped-impedance type Butterworth low pass filter with cutoff
frequency at 2GHz and > 20dB attenuation at 3GHz. The input and output impedance are
both 50:. The PCB material is FR4 with dielectric constant 4.2 and thickness 1.2mm.
3
16 Microstrip Line Filters
317
16-2-2. Solution
Referring to Table 7-5, since Z/Zc=1.5 20dB attenuation is 20dB at 3GHz, the
order becomes 7. From Table 7-1, we find the normalized values of g1 to g8 as follows:
x g1=g7=0.4450
x g2=g6=1.2470
x g3=g5=1.8019
x g4=2.0000
x g8=1.0000
The equivalent circuit is illustrated in Figure 16-5.
C
1
We then convert the L, C value to electronic length by the following equations:
L=LRo/Z
E
E
L=CZ
, for inductor (16-21)
h
/Ro , for capacitor (16-22)
l
Ro is the filter impedance, E is the wave number,
the normalized values, Z
L
2
L
4
C
3
Figure 16-5
L
6
C
5
C
7
L is the line length, L and C are
and Zl are the highest and lowest line impedance, respectively.
h
According to Figure 16-3, g1, g3, g5 and g7 are capacitor sections in Z
g4 and g6 are inductor sections in Z
The PCB substrate is 1.2 mm thick, FR4 material, H
.
h
= 4.4. In order to make the
r
PCB fabrication realistic, the line widths are adjusted to 0.5mm for Z
and 5mm for Zl
h
, and g2,
l
before we start designing. The item left to be designed is the length of each section.
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Let’s start from the Z
sections which are capacitor sections including g1, g3, g5
l
and g7. By using the microstrip line calculation tool, when the line width is 5mm, Z
29.67:, wavelength O =78.847mm. According to 16-22, the first capacitor value is:
g1=C1=0.4450
We get
L
E
1=C1Zl
/Ro
=0.4450*29.67/50
=0.264 rads (16-23)
L
Combining 16.8 and 16.23, the line length of
and L
1
are:
7
=
l
L
=0.264/E
1
=0.264/(2S/O)
=0.264/(2S/78.847)
=3.31 mm.
By the same method, section 3 is:
L
=1.069 rads
E
3
L
=L
=13.4 mm.
3
5
The Z
(inductor) sections are also designed by the same method. By using the
h
calculation tool, Z
=101.73: and wavelength O = 86.087mm when the line width is
h
0.5mm. According to 16-21:
g2=L2=1.2470
We get
3
16 Microstrip Line Filters
319
EL
2=L2
Ro/Zh
=1.2470*50/101.73
=0.613 rads (16-24)
Combining 16-8 and 16-24, the line length of
L
=0.613/E
2
=86.087*0.613/(2*S)
=8.4 mm.
The section 4 is:
L
=0.983 rads
E
4
L
and L
2
is:
6
L
=13.5 mm
4
We have to consider another issue in addition to the filter itself. The transmission
line contains 50: impedance and is frequently put in front of the filter at both ends. Its
width is 2.3mm defined by the PCB structure. In addition, SMA terminals are attached to
the test module for external connection. The 2.3mm transmission line is too wide to be
directly connected to the SMA terminals, therefore an extra 1.6mm line section is
necessary for bridging them together.
Summarizing the above results, the entire filter is designed as in Figure 16-6.
x L1, L7: 5[3.3 mm
x L2, L6: 0.5[8.4 mm
x L3, L5: 5[13.4 mm
x L4: 0.5[13.5 mm
x Lo: 2.3[5 mm, for 50: transmission line
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16-2-3. Fine tune and Modification
x Lp: 1.6[8 mm, for SMA connector pin.
L
p
L
L
o
1
L
2
L
o
L
3
L
4
Figure 16-6
L
5
L
L
7
6
L
L
p
L
o
o
Just as mentioned in the previous section, the simulation tool is very useful and
important for microwave circuit design. We can simulate our design to check if the result
meets our design target. If not, we can do fine tuning and simulate again. By repeating this
fine tune and simulate step, we can make the design as close as possible to the design
target. In the above case, we find that the roll-off at fc=2GHz is 5dB more than we
expected from the simulation result. It could be caused by the extra sections of the
L
transmission line. Here we try to fine tune again by changing the
from 13.5mm to
4
10mm where the roll-off becomes 2.5dB but the attenuation at 3GHz becomes less than
20dB, which is a trade-off. Both simulation results are drawn in Figure 16-7.
0
-5
-10
-15
Insertion Loss (dB)
-20
-25
Stepped LPF
line4 = 13.5mm
line4 = 10mm
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Frequency (GHz)
Figure 16-7
In the experiment, we will take the 10mm case for measurement.
3
16 Microstrip Line Filters
321
16-3-1. Design Example
16-3-2. Solution
16-3. Coupled line Band Pass Filter
Coupled line filter is a good choice if we want to design a band pass filter in
microstrip form which requires bandwidth about less than 20%. Wider bandwidth filter
generally require tightly coupled lines, which are hard to fabricate.
We will design a coupled line filter with 0.5dB ripple, 2.4GHz center frequency,
15dB attenuation at 2GHz, and 10% bandwidth. The input and output impedance are both
50:. The PCB material is FR4 with dielectric constant of 4.2 and thickness of 1.2mm.
First, we need to decide the order of the filter.
§
w
1
wc
is the bandwidth ration and is equal to 0.1.
'
w
¨
¨
'
w
0
©
Referring to Figure 16-6, since
·
w
0
¸
¸
w
¹
2
11
§
¨
1.0
©
w
w
c
4.2
·
¸
2
4.2
¹
and attenuation is 15dB at 2GHz,
67.21
67.2167.3
the order (N) becomes 2. From Table 16-1, we find the normalized values of g1 to g3 as
follows:
x g1=1.4029
x g2=0.7071
x g3=1.9841
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322
0.5dB Ripple
Figure 16-6
N g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g11
1 0.6986 1.0000
2 1.4029 0.7071 1.9841
1.5963 1.0967 1.5963 1.0000
3
1.6703 1.1926 2.3661 0.8419 1.9841
4
5 1.7058 1.2296 2.5408 1.2296 1.7058 1.0000
1.7254 1.2479 2.6064 1.3137 2.4758 0.8696 1.9841
6
1.7372 1.2583 2.6381 1.3444 2.6381 1.2583 1.7372 1.0000
7
1.7451 1.2647 2.6564 1.3590 2.6964 1.3389 2.5093 0.8796 1.9841
8
9 1.7504 1.2690 2.6678 1.3673 2.7239 1.3673 2.6678 1.2690 1.7504 1.0000
1.7543 1.2721 2.6754 1.3725 2.7392 1.3806 2.7231 1.3485 2.5239 0.8842 1.9841
10
Table 16-1
3
16 Microstrip Line Filters
323
After that, we can use the follow equation to evaluate the even and odd mode of
the characteristic impedance.
'
S
JZ
10
2
g
1
'
S
JZ
0
N
2
JZ
10
N
>@
e
o
1
>@
1
gg
1
NN
'
S
2
gg
1
NN
JZJZZZ
JZJZZZ
we can get:
JZ
355.0
10
JZ
158.0
20
JZ
335.0
30
Z
e
10
Z
o
10
Z
e
20
Z
o
20
Z
e
30
Z
o
30
36.72
86.38
15.59
35.43
36.72
86.38
2
0000
2
0000
Due to the complexity of calculating the coupling coefficiency, we can use CAD
tools to find out the gap between coupling lines. The list below shows the results after the
calculation:
x
x
x
x
x
x
ll
ss
=17mm
l
2
=2.2mm
w
2
=1mm
s
2
=17.45mm
31
1.11.94mm
31ww
=0.26mm
31
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We still need to consider two issues: one is that the minimum practical distance is
0.5mm, and the other one that the impedance of pin connection lines is not 50 which
affects the filter frequency response. Therefore, after fine tuning, the final result becomes
as follows.
mmll
9.16
31
mmww
1.1
31
mmss
5.0
31
mml
17
2
mmw
2.2
2
mms
9.0
2
Summarizing the above result, we get:
x L1, L3=1.1x16.9mm, gap=0.5mm
x L2=2.2x17mm, gap=0.9mm
x Lo=2.3x5mm, for 50ȟ
x Lp=1.6x8mm, for pin connection
The entire filter is designed as Figure 16-7. The simulation results are shown in
Figure 16-8.
L
p
L
o
L
o
L
1
L
2
L
3
L
o
L
o
L
p
3
Figure 16-7
16 Microstrip Line Filters
325
16-4-1. Design Example
16-4-2. Solution
0
-5
-10
-15
Insertion Loss (dB)
-20
-25
2.0 2.2 2.4 2.6 2.8 3.0
Coupled Line BPF
before fine tune
after fine tune
Frequency (GHz)
Figure 16-8
Fine-tuned values were used for actual measurements.
16-4. Optimized High Pass Filter
There are several ways to design a high pass filter in microstrip form. In this
section, we will introduce an easy way to fabricate a high pass filter, which can also be
considered as a wideband band pass filter.
We will design a high pass filter with 0.1dB ripple and 1.5GHz cut off frequency.
The input and output impedance are both 50:. The PCB material is FR4 with dielectric
constant of 4.2 and thickness of 1.2 mm.
First, we assume that the pass band is from 1.5GHz to 4.7GHz.
§
¨
¨
-
©
Referring to Table 16-2, we choose
·
S
¸
3517.4
c
fGHz
¸
¹
-
q ou
cc
=
-
c
and N = 4, then y1, y12, y2 and y23
q35
become as follows:
x y1=0.4467
x y12=1.03622
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x y2=0.60527
x y23=1.01536
Figure 16-9 shows the structure of the filter.
n
2
3
4
5
ȏ
25Ʊġ
30Ʊġ
35Ʊ
25Ʊġ
30Ʊġ
35Ʊ
25Ʊġ
30Ʊġ
35Ʊ
25Ʊġ
30Ʊġ
35Ʊ
y
1
Ť
y
n
0.15436
0.22070
0.30755
0.19690
0.28620
0.40104
0.22441
0.32300
0.44670
0.24068
0.34252
0.46895
y
1,2
y
n-1,n
1.13482
1.11597
1.08967
1.12075
1.09220
1.05378
1.11113
1.07842
1.03622
1.10540
1.07119
1.02790
y
2
y
n-1
y
2,3
y
n-2, n-1
y
3
y
n-2
y
3,4
0.18176
0.30726
0.48294
0.23732
0.39443
0.60527
0.27110
0.43985
0.66089
1.10361
1.06488
1.01536
1.09317
1.05095
0.99884
0.29659
0.48284
0.72424
6
25Ʊġ
30Ʊġ
35Ʊ
10 y
y
1
T
c
0.25038
0.35346
0.48096
1.10199
1.06720
1.02354
0.29073
0.46383
0.68833
1.08725
1.04395
0.99126
Table 16-2
T
T
2
c
y
2,1
y
2
2
c
nny,1
y
1n
Short-circuited stub of electrical length
Figure 16-9
0.33031
0.52615
0.77546
y
n
1.08302
1.03794
0.98381
10 y
c
3
16 Microstrip Line Filters
327
Now we can use the following equations to evaluate the line impedance.
Z
Z
Z
0
i
y
Z
0
ii
1,
--
,
i
y
c
--
2,
1,
ii
c
We get:
Z
1
Z
12
Z
2
Z
23
93.111
25.48
16.82
24.49
And then we can use CAD tools to find out the real length and width of each
section.
23.11
1
1
12
12
2
2
23
23
mml
3762.0
mmw
189.21
mml
43.2
mmw
02.11
mml
867.0
mmw
22.21
mml
35.2
mmw
We still need to consider two issues: one is that the minimum practical distance is
0.5mm, and the other one is the cross section of each line. Therefore, after fine tuning, the
final result becomes as follows.
7.10
1
2
12
12
2
2
23
23
mml
8.0
mmw
2.21
mml
3.2
mmw
7.10
mml
1
mmw
2.21
mml
3.2
mmw
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Summarizing the above results, we get
x L1 =0.8x10.7mm,
x L12=2.3x21.2mm, gap=0.9mm
x L2=1x10.7mm
x L23=2.3x21.2mm
x Lo=2.3x5mm, for 50ȟ
x Lp=1.6x8mm, for pin connection
The end of L1 and L2 are grounded.
Figure 16-10 shows the design of the entire filter. The simulation results are
shown in Figure 16-11.
L
p
L
o
L
o
L
1
L
12
L
2
0
-10
-20
-30
Insertion Loss (dB)
-40
-50
0.0 0.5 1.0 1.5 2.0 2.5 3.0
L
23
Figure 16-10
Frequency (GHz)
L
2
Optimize HPF
after fine tune
before fine tune
L
12
L
L
1
L
p
L
o
o
3
Figure 16-11
Fine-tuned values were used for actual measurements.
16 Microstrip Line Filters
329
Questions
Question 1:
What is the possible factor, other than the design of the filter itself, that affects
implement the transmission line filter?
Question 2:
Describe how to limit the tolerance caused by connectors.
Question 3:
Describe how to choose the right PCB for implementing microstrip line filters.
3
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Experiments
Insertion Loss Measurement 1
Objective: Implement a microstrip low pass filter. Refer to Figure 16-12 or R-11
module in the GRF-3300.
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Figure 16-12 Microstrip line low pass filter
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9. Prepare the following items.
x GRF-3300, R-11 (Microstrip Low-Pass Filter) module
x N-SMA Adaptor x 2
x RF cable, 75cm x 2
x Spectrum Analyzer (SA)
10. Configure the SA as follows.
x Frequency span: Full Span
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x Resolution bandwidth (RBW): Auto
Step 1:
Step 2:
Span
BW
Figure 16-13 Spectrum analyzer configurations (GSP-830)
Full
Span
RBW
Auto/ Manu
RBW
Auto
11. Activate and adjust the Tracking Generator (TG) as follows.
x TG Reference level: 10dBm
x TG level: 0dBm
x TG reference value: 0dBm
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x TG output: on
x TG normalization: on
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Amplitude
Option TG
Option TG
Option TG
Option TG
Figure 16-14 TG configurations
12. Connect the SA and R-11 as follows.
x TG output – R-11 input
Ref
Level
IJ0 dBm
TG
Level
Ref
Value
TG
ON OFF
Normal
ON OFF
0 dBm
0 dBm
ON
ON
x R-11 output – SA RF input
TG Output
RF Input
RF I/P
RF O/P
N-SMA Adaptor x 2
75cm RF cable x 2
Figure 16-15 SA to R-11 connections
13. Turn on a marker in the SA, set the marker frequency to 3dB bandwidth of the filter,
and record the amplifier gain into Chart 16-1.
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Insertion Loss Measurement 2
Objective: Implement a microstrip line band pass filter. Refer to Figure 16-16 or
T-1 module in the GRF-3300.
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Figure 16-16 Microstrip line band pass filter
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Follow the same steps as in the “Insertion Loss Measurement 1” section but
change some items as follows.
x R-11 module T-1 module
x Chart 16-1 Chart 16-2
Insertion Loss Measurement 3
Objective: Implement a microstrip line high pass filter. Refer to Figure 16-17 or
T-6 module in the GRF-3300.
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Figure 16-17 Microstrip line high pass filter
Follow the same steps as in the “Insertion Loss Measurement 1” section but
change some items as follows.
x R-11 module T-6 module
x Chart 16-1 Chart 16-3
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Experiment Results
Insertion Loss Measurement
Chart 16-1 Measurement result of R-11 microstrip line low pass filter insertion loss
Chart 16-2 Measurement result of T-1 microstrip line band pass filter insertion loss
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Chart 16-3 Measurement result of T-6 microstrip line high pass filter insertion loss
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