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ELCT564 Spring 2013


ELCT564 Spring 2013 Chapter 8: Microwave Filters * * ELCT564 ELCT332 ELCT564 ELCT564 ELCT564 ELCT564 Filters * * ELCT564 Two-port circuits that exhibit selectivity to ... – PowerPoint PPT presentation

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Title: ELCT564 Spring 2013

ELCT564 Spring 2013
Chapter 8 Microwave Filters
  • Two-port circuits that exhibit selectivity to
    frequency allow some frequencies to go through
    while block the remaining
  • In receivers, the system filters the incoming
    signal right after reception
  • Filters which direct the received frequencies to
    different channels are called multiplexers
  • In many communication systems, the various
    frequency channels are very close, thus requiring
    filters with very narrow bandwidth high out-of
    band rejection
  • In some systems, the receive/transmit functions
    employ different frequencies to achieve high
    isolation between the R/T channels.
  • In detector, mixer and multiplier applications,
    the filters are used to block unwanted high
    frequency products
  • Two techniques for filter design the image
    parameter method and the insertion loss method.
    The first is the simplest but the second is the
    most accurate

Periodic Structures
Bloch Impedance
Terminated Periodic Structures
Symmetrical network
Analysis of a Periodic Structure
Consider a periodic capacitively loaded line, as
shown below. If Zo50 O, d1.0 cm, and Co2.666
pF, compute the propagation constant, phase
velocity, and Bloch impedance at f3.0 GHz.
Assume kk0.
Image Parameter Method
Constant-k Filter
m-derived section
Composite Filter
Summary of Composite Filter Design
Example of Composite Filter Design
Design a low-pass composite filter with a cutoff
frequency of 2MHz and impedance of 75 O, place
the infinite attenuation pole at 2.05 MHz, and
plot the frequency response from 0 to 4 MHz.
Insertion Loss Method
Filter response is characterized by the power
loss ratio defined as
Where G(?) is the reflection coefficient at the
input port of the filter, assuming the the output
port is matched.
Low-pass Band-pass filter
Insertion Loss
Filter Responses
Maximally Flat, Equal Ripple, and Linear Phase
Maximally Flat Provides the flattest possible
pass band response for a given complexity.
Cutoff frequency is the freqeuncy point which
determines the end of the pass band. Usually,
where half available power makes it
through. Cut-off frequency is called the 3dB
Equal Ripple or Chebyshev Filter Power loss is
expressed as Nth order Chebyshev polynomial TN(?)
TN(x) cos (Ncos-1x), X 1
TN(x) cosh (Ncosh-1x), X 1
Much better out-of-band rejection than
maximally flat response of the same order.
Chebyshev filters are preferred a lot of times.
Filter Responses
Linear Phase Filters
  • Need linear phase response to reduce signal
    distortion (very important in multiplexing)
  • Sharp cut-off incompatible with linear phase
    design specifically for phase linearity
  • Inferior amplitude performance
  • If f(?) is the phase response then filter group

Filter Design Method
  • Development of a prototype (low-pass filter with
    fc1Hz and is made of generic lumped elements)
  • Specify prototype by choice of the order of the
    filter N and the type of its response
  • Same prototype used for any low-pass, band pass
    or band stop filter of a given order.
  • Use appropriate filter transformations to enter
    specific characteristics
  • Through these transformations prototype changes
    low-pass, band-pass or band-stop
  • Filter implementation in a desired from
    (microstrip or CPW)
  • use implementation transformations.

Maximally Flat Low-Pass Filter
g01,?c1, N1 to 10
Equal-Ripple Low-Pass Filter
g01,?c1, N1 to 10
Maximally-Flat Time Delay Low-Pass Filter
g01,?c1, N1 to 10
Filter Transformations
  • Impedance Scaling
  • Frequency Scaling for Low-Pass Filters
  • Low-Pass to High-Pass Transformation

Filter Implementation
  • Richards Transformation
  • Kurodas Identities
  • Physically separate transmission line stubs
  • Transform series stubs into shunt stubs, or vice
  • Change impractical characteristic impedances into
    more realizable ones

Design Steps
Lumped element low pass prototype (from tables,
Convert series inductors to series stubs, shunt
capacitors to shunt stubs
Add ?/8 lines of Zo 1 at input and output
Apply Kuroda identity for series inductors to
obtain equivalent with shunt open stubs with ?/8
lines between them
Transform design to 50O and fc to obtain
physical dimensions (all elements are ?/8).
Low-pass Filters Using Stubs
Design a low-pass filter for fabrication using
microstrip lines. The specifications include a
cutoff frequency of 4GHz, and impedance of 50 O,
and a third-order 3dB equal-ripple passband
  • Distributed elementssharper cut-off
  • Response repeats due to the periodic nature of

Bandpass and Bandstop Filters
A useful form of bandpass and bandstop filter
consists of ?/4 stubs connected by
?/4 transmission lines.
Bandpass filter
Stepped Impedance Low-pass Filters
  • Use alternating sections of very high and very
    low characteristics impedances
  • Easy to design and takes-up less space than
    low-pass filters with stubs
  • Due to approximations, electrical performance not
    as good applications where sharp cut-off is not

Stepped Impedance Low-pass Filter Example
Design a stepped-impedance low-pass filter having
a maximally flat response and a cutoff frequency
of 2.5 GHz. It is necessary to have more than 20
dB insertion loss at 4 GHz. The filter impedance
is 50 O the highest practical line impedance is
120 O, and the lowest is 20 O. Consider the
effect of losses when this filter is implemented
with a microstrip substrate having d 0.158 cm,
er 4.2, tand0.02, and copper conductors of 0.5
mil thickness.
Coupled Line Theory
Coupled Line Bandpass Filters
This filter is made of N resonators and
includes N1coupled line sections
dn ?g/4 (?ge ?go)/8
Find Zoe, Zoo from prototype values and
fractional bandwidth
From Zoe, Zoo Calculate conductor and slot width
N-order coupled resonator filter N1 coupled
line sections
Use 2 modes to represent line operation
Coupled Line Bandpass Filters
1. Compute Zoe, Zoo of 1st coupled line section
2. Compute eve/odd impedances of nth coupled line
3. Compute even/odd impedances of (N1) coupled
line section
4. Use ADS to find coupled line geometry in terms
of w, s, ße, ßo or eeff,e , eeff,o
5. Compute
Coupled Line Bandpass Filters Example I
Design a 0.5dB equal ripple coupledline BPF with
fo10GHz, 10BW 10-dB attenuation at 13 GHz.
Assume Zo50O.
From atten. Graph N4 ok But use N5 to have
Zo50 O
goge1, g1g51.7058, g2g41.229, g32.5408
Coupled Line Bandpass Filters Example II
Design a coupled line bandpass filter with N3
and 0.5dB equal ripple response. The center
frequency is 2GHz, 10BW Zo50O. What is the
attenuation at 1.8 GHz
Capacitively Coupled Resonator Filter
  • Convenient for microstrip or stripline
  • Nth order filter uses N resonant sections of
    transmission line with N1 capacitive gaps
    between then.
  • Gaps can be approximated as series capacitors
  • Resonators are ?g/2 long at the center frequency

Capacitively Coupled Resonator Filter
Design a bandpass filter using capacitive coupled
series resonators, with a 0.5 dB equal-ripple
passband characteristic. The center frequency is
2.0 GHz, the bandwidth is 10, and the impedance
is 50 O. At least 20 dB of attenuation is
required at 2.2GHz
Bandpass Filters using Capacitively Shunt
Bandpass Filters using Capacitively Shunt
Design a third-order bandpass filter with a 0.5
dB equal-ripple response using capacitively
coupled short-circuited shunt stub resonators.
The center frequency Is 2.5 GHz, and the
bandwidth is 10. The impedance is 50 O. What is
the resulting attenuation at 3.0 GHz?
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