31
Welcome Randy Rhea Founder of Eagleware & Elanix [email protected] © 2013 Agilent Technologies, Inc.
Welcome
Randy Rhea
Founder of Eagleware & Elanix
© 2013 Agilent Technologies, Inc.
Webcast:
Designing
Custom RF and Analog Filters
through Direct Synthesis
with examples from the new book
Synthesis of Filters: S/Filter Techniques
by Randy Rhea
(book available June 2014)
Slide 3
We'll Cover
• A two-slide review of the modern method
• The concept of transmission zeros (TZ’s) in filter design
• Finding the optimum extraction sequence
• The application of canonic, noncanonic, exact, and inexact transforms
• Examples of filters with L-C components, TEM-mode coaxial resonators
and quartz-crystals
Slide 3
Randy Rhea [email protected]
Slide 4
The Conventional Method
Slide 4
Randy Rhea
Most filter programs today use the modern method developed in the 1950’s.
Conventional designs of the modern method begin with a lowpass prototype
and scale the impedance and frequency to desired values. For highpass,
bandpass and bandstop, transformations are also applied.
Slide 5
Genesys Programs That Use Conventional Methods
Slide 5
Randy Rhea
The modern method is easy to apply. Genesys includes a variety of tools
for this, that are integrated into an environment with schematic entry,
layout, circuit-theory simulation and electromagnetic simulation. The
Genesys modules used for conventional filter design are:
• PASSIVE FILTER: lumped-element lowpass, highpass, bandpass and
bandstop filters in a variety of passband approximations and topologies.
• EQUALIZATION: designs all-pass group-delay equalizers for all filters
designed in the Genesys suite or for S-parameter data.
• ACTIVE FILTER: designs filters that use operational amplifiers and R-C
elements.
• MICROWAVE FILTER: a variety of distributed filters in a variety of
realization processes such as microstrip, stripline, slabline and others.
Genesys also includes tools for matching, signal control devices, mixers,
oscillators, phase-locked loops, transmission lines, and system design.
Slide 6
Direct Synthesis using Transmission Zeros
Slide 6
Randy Rhea
This webcast covers a more powerful technique - direct synthesis.
This technique uses the concept of transmission zeros (TZ’s).
@ Infinity
@ DC
L=73.89nH
L1
C=24.71pF
C2
C=39.83pF
C1
L=126.11nH
L2
Slide 7
Transmission Zeros in a Bandpass
Slide 7
Randy Rhea
How many TZ’s at DC and infinity are in this bandpass filter?
L=196.24nH
L1
C=38.76pFC1
L=138.8nH
L2
C=67.05pF
C3
C=202.78pF
C2
C=76.97pFC4
L=91.46nH
L3
C=26.62pFC5
C=35.76pF
C6
L=196.37nH
L4
C=53.29pFC7
Slide 8
Multiple Extraction Sequences
Slide 8
Randy Rhea
L=50.7nH
L1
C=68.8pF
C1
L=11.4nH
L2
C=237pF
C2
L=39.3nH
L3
C=53.3pF
C3
DC DC DC Inf Inf Inf
C=53.3pF
C1
L=39.3nH
L1
L=11.4nH
L2
ZO=50O C=305.8pF
C2
L=2.6nH
L3
C=1053.9pF
C3
S=4.4
P=1
T1
ZO=50O
Inf Inf DC DC DC Inf
L=50.7nH
L1
C=53.3pF
C1
L=174.7nH
L2
ZO=50OC=15.5pF
C2
L=50.7nH
L3
ZO=50O
C=53.3pF
C3
DC Inf Inf DC DC Inf
L=50.7nH
L1
ZO=50O
C=237pF
C2
L=8.8nH
L2
L=2.6nH
L3
C=1053.9pF
C3
C=68.8pF
C1
S=4.4
P=1
T1
ZO=50O
DC DC Inf Inf DC Inf
L=50.7nH
L1
DC Inf Inf Inf DC DC
ZO=50O
C=53.3pF
C1
L=174.7nH
L2
C=12pF
C2
L=1002nH
L3
C=3.5pF
C3
S=0.2
P=1
T1
ZO=50O
L=50.7nH
L1
C=53.3pF
C1
DC Inf DC DC Inf Inf
C=15.5pF
C2
L=225.4nH
L2
L=776.7nH
L3
C=2.7pF
C3
S=0.2
P=1
T1
ZO=50OZO=50O
All of these filters have three TZ’s at DC and three at infinity, and they have
the same response as the conventional bandpass at the upper left.
Slide 9
Arbitrary Specification TZ’s at DC and Infinity
Slide 9
Randy Rhea
The quantity of TZ’s at DC sets the low-side selectivity of a bandpass, while
the TZ’s at infinity sets the high-side. The conventional bandpass has an
equal quantity of TZ’s at DC and infinity. With synthesis, there is a choice.
3 TZ’s @ DC
3 TZ’s @ Infinity
1 TZ’s @ DC
5 TZ’s @ Infinity
Slide 10
Finite Transmission Zeros (FTZ’s)
• A Finite-Transmission Zero (FTZ) is a zero at a frequency between DC and infinity
•The Cauer-Chebyshev elliptic response places a specific quantity of FTZ’s at specific frequencies to achieve equal minimum attenuation in the stopband.
• Direct synthesis supports placing FTZ’s wherever they are required.
Slide 10
Randy Rhea
Slide 11
The S/Filter Module in Agilent Genesys
Slide 11
Randy Rhea
After you enter passband parameters and specify the placement of TZ’s,
the S/Filter program in Genesys finds the required synthesis polynomial,
extracts element values for all unique sequences and displays the
responses. You may interactively change entries as the response
updates. You then select from a list of multiple solutions, each with a
different schematic.
Slide 12
Filter Degree
• Each TZ at DC adds one reactor and increases the degree of the filter by one.
• Each TZ at infinity adds one reactor and increases the degree by one.
• Each finite TZ (FTZ) adds three reactors and increases the degree by two.
Slide 12
Randy Rhea
Slide 13
Example #1 - Arbitrary Placement of FTZ’s
Slide 13
Randy Rhea
L=180.82nH
L1
C=12.15pF
C1
L=504.3nH
L2
C=2.08pF
C2
C=4.65pF
C3
C=4.91pF
C4
L=290.67nH
L3
C=4.57pF
C5
C=7.1pF
C6
C=11.42pF
C7
L=180.82nH
L4
ZO=50Ω ZO=50Ω
Slide 15
Arithmetic Transmission Response Symmetry
Slide 15
[1] R. Rhea, HF Filter Design and Computer Simulation, SciTech Publishing, Raleigh, NC, 1994
[2] R. Rhea, “Exploiting Filter Symmetry”, Microwave Journal, March 2001, pp. 100-108.
Randy Rhea
The conventional bandpass has an equal quantity of TZ’s at DC and
infinity. This naturally results in higher selectivity below the passband than
above. This effect is more pronounced with increasing bandwidth. A ratio
of 3 TZ’s at infinity for each TZ at results in arithmetic response symmetry.
L=36.6nH
L1
C=73.14pF
C1
L=256.58nH
L2
C=9.34pF
C2
C=1.25pF
C3
C=0.58pF
C4
L=1561.52nH
L3
C=12.81pF
C5
L=182.88nH
L4
L=36.14nH
L1 C=73pF
C1
L=256.42nH
L2
C=10.29pF
C2
L=21.23nH
L3C=124.29pF
C3
L=150.61nH
L4
C=17.52pF
C4
Slide 16
Example #2 - A Generalized Symmetric Bandpass
Slide 16
Randy Rhea
L=185.96nH
L1
C=49.86pF
C1
C=36.19pF
C2
C=49.37pF
C3 L=123.77nH
L2
C=78.25pF
C6
L=185.99nH
L4
C=32.95pF
C7
L=89.56nH
L3
C=376.71pF
C5
C=14.14pF
C4
Slide 17
Integrated Network Transforms - Canonic
Slide 17
Randy Rhea
L=36.6nH
L1C=73.14pF
C1
L=256.58nH
L2
C=9.34pF
C2
C=1.25pF
C3
C=0.58pF
C4
L=1561.52nH
L3
L=182.88nH
L4
C=12.81pF
C5
L=36.6nH
L1
L=256.58nH
L2
C=73.14pF
C1
C=30.76pF
C2
C=14.24pF
C3
C=1.9pF
C4 L=1561.52nH
L3
C=12.81pF
C5
L=182.88nH
L4
S/Filter also integrates scores of network transforms for additional control
of the final schematic. Canonic transforms modify the topology without
adding additional components.
Slide 18
Non-Canonic Transforms
Slide 18
Randy Rhea
Other transforms increase the quantity of components but have other
desirable attributes, such as eliminating a transformer, improving values,
or creating all parallel or all series resonators.
L=32.47nH
L1
C=74.1pF
C1
L=4.05nH
L2
C=74.1pF
C3
L=32.47nH
L3
C=463.11pF
C2
C=26.16pF
C2
L=32.47nH
L2
C=23.88pF
C3
C=26.16pF
C4
L=32.47nH
L3
C=47.94pF
C5
C=47.94pF
C1L=32.47nH
L1
Slide 19
Norton Transforms
Slide 19
Randy Rhea
A cornerstone, and the basis of some of the other transforms in S/Filter,
are the Norton transforms.
SHUNT SERIES
Before Transform After Transform
1 : N
Zb
Za Zc
Z Za
Zb
Zc
Before Transform After Transform
1 : N
Z
ZN
Za
11
N
ZZb
ZN
NZc 2
1
N
ZZa
1
N
ZZb
1NN
ZZc
Slide 20
Inexact Transforms
Slide 20
Randy Rhea
The Norton, pi to tee, and other transforms are exact. S/Filter also
includes inexact but useful transforms. One such transform is the
Replace End Inverter with Capacitive L which is used to scale the
internal impedance of a filter.
Transform
C1
C2
Z in Z out
inoutinC ZZZX 1
1
21
2
2C
CinC
X
XZX
Slide 21
Coaxial Resonators
Slide 21
Randy Rhea
Another inexact transform is the Parallel LC to Ground to Grounded Stub.
This is used to design filters with ceramic-loaded TEM-mode resonators.
For example, a Standard Profile Trans-Tech coaxial resonator with 8800
material has a Zo of 9.5 ohms. This equates to an effective L of 2.12 nH at
910 MHz.
04ZL
L C
Transform
L=90°
Zo
Slide 22
Filters with TEM-Mode Ceramic Resonators
Slide 22
Randy Rhea
TEM-mode resonators are popular because of their high unloaded Q and
good temperature stability. These filters are easily designed using many
filter programs.
K=1
L=70.97mm
Z=10.42Ω
TL1
C=0.63pF
C2
K=1
L=73.7mm
Z=10.04Ω
TL2
C=0.48pF
C3
K=1
L=73.7mm
Z=10.04Ω
TL3
C=0.63pF
C4
K=1
L=70.97mm
Z=10.42Ω
TL4
C=1.78pF
C5
C=1.78pF
C1
Slide 23
Example #3
Slide 23
Randy Rhea
S/Filter adds the ability to specify FTZ’s in filters using coaxial
resonators. This example is a four-resonator filter with two FTZ’s
above the passband for exceptional high-side selectivity.
K=1
L=73.68mm
Z=9.89Ω
TL1
L=3.45nH
L1
C=6.73pF
C2
K=1
L=77.03mm
Z=9.46Ω
TL2
C=2.23pF
C1
C=0.7pF
C3
K=1
L=77.03mm
Z=9.46Ω
TL3
L=3.45nH
L2
C=6.73pF
C4
K=1
L=73.68mm
Z=9.89Ω
TL4
C=2.23pF
C5
Slide 24
Quartz-Crystal Resonators
Slide 24
Randy Rhea
Very-narrow bandwidth filters are often constructed with quartz-crystal
resonators which have exceptionally high unloaded-Q and high
effective inductance.
[1] R. Rhea, Discrete Oscillator Design: Linear, Nonlinear, Transient and Noise Domains,
Artech House, Boston, 2010
L=12.092mH
LmC=0.02273pF
Cm
R=11.6Ω
Rm
C=5.45pF
Co
Slide 25
Example #4
Slide 25
Randy Rhea
This example has four crystals and a bandwidth of 2 kHz.
Port_2
Port_1
C=127.51331pF
C2
C=160.23787pF
C4
C=144.65189pF
C6
Co=5.45pF
Cm=0.02273pF
L=12.092mH
R=11.6Ω
X1
Co=5.45pF
Cm=0.02273pF
L=12.092mH
R=11.6Ω
X2
Co=5.45pF
Cm=0.02273pF
L=12.092mH
R=11.6Ω
X3
Co=5.45pF
Cm=0.02273pF
L=12.092mH
R=11.6Ω
X4
Slide 26
Other Crystal Filter Examples in the Book
The new book includes several example quartz-crystal and ceramic
piezoelectric resonator filters design using synthesis
Randy Rhea
Slide 27
Matching
Slide 27
Randy Rhea
Genesys includes the Impedance Match which integrates numerous
lumped and distributed routines into one environment. This is the
best choice for difficult matching problems.
When the need is for a filter with some matching, S/Filter is effective.
L=30677.883nH
L1
C=59.02pF
C1
L=313.57107nH
L2
C=32912.06pF
C2
C=7002.93267pF
C3
L=20857.55656nH
L3
C=87pF
C4
ZO=34Ω
ZO=50Ω
Slide 28
Distributed Filters
Slide 28
Randy Rhea
S/Filter uses Richards transform for synthesis with arbitrary placement of
TZ’s and multiple extraction sequences, as was illustrated today for
lumped filters. S/Filter also integrates a variety of network transforms used
in distributed filters.
Slide 29
Summary
• Most filter design software uses the modern method which became
popular in the 1950’s
• The modern method has been applied to many filter types and is easy
to use.
• Direct synthesis is a more powerful method of filter design
• S/Filter integrates synthesis and network transforms into the Genesys
environment.
• The new book Synthesis of Filters: S/Filter Techniques was specifically
written to guide and illustrate the synthesis design process.
Slide 29
Randy Rhea
Slide 30
For More Info
Questions about this presentation or the book:
• email Randy Rhea: [email protected]
About Genesys:
• Genesys product page http://www.agilent.com/find/eesof-genesys
• USA Genesys Specialist, Rick Carter [email protected]
To obtain a free trial Genesys license with S/Filter:
• Go to http://www.agilent.com/find/eesof-genesys-evaluation
Slide 30
Randy Rhea
You are invited to our next webcast
Register for our live and recorded webcasts here:
www.agilent.com/find/eesof-innovations-in-eda
www.agilent.com/find/eesof-webcasts-recorded
Designing with 4G Modulated
Signals for Optimized
Multi-Standard Transceiver ICs
October 3 – 7AM & 10AM PT
Andy Howard
Senior Application
Engineer
Agilent EEsof EDA
Juergen Hartung
RFIC Product
Marketing &
Foundry Program
Manager
Agilent EEsof EDA
Thank you
Please complete the short survey following the end of this webcast.
