GW Instek GRF-3300 User Manual
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.
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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.
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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.
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