Part of Lecture series on EE321N, Power Electronics-I delivered by me during Fifth Semester of B.Tech. Electrical Engg., 2012
Z H College of Engg. & Technology, Aligarh Muslim University, Aligarh
Please comment and feel free to ask anything related. Thanks!
Use s parameters-determining_inductance_capacitancePei-Che Chang
1. Use s parameters-determining_inductance_capacitance
2. Relationship Between Common Circuits and the ABCD Parameters
3. Converts Z-parameters to S-parameters
4. Relationships Between Two-Port S and ABCD Parameters
5. Via and equivalent circuit
PARASITIC-AWARE FULL PHYSICAL CHIP DESIGN OF LNA RFIC AT 2.45GHZ USING IBM 13...Ilango Jeyasubramanian
• Analyzed and designed a single stage cascoded LNA with Q-based calculation for desired input matching, output matching, power gain, IIP3 and Noise figure, including all the parasitics in the on-chip and off-chip components using SpectreRF simulations.
• Synthesized the LNA layout for on-chip components with spiral inductor, MOS capacitor, MIM capacitor and Bond-pads with ESD protections.
• Our LNA exhibited a noise figure of 1.23dB, linear gain of 18.54 dB, IIP3 of -4.60dbm, S11 of -31.11db, S22 of -24.91db with the operating range between 2.4-2.5GHZ along with 10% variation tolerance.
Prof. Cuk invited talk at APEC 2011 plenary session to celebrate
35 years of his creation of this modeling and analysis method.
This talk was also recorded on video by IEEE.tv and can be viewed together. Here is a link to that video.
https://youtu.be/BLx57J2fF5w
Note: first few minutes of the video is Prof. Cuk's interview made after his presentation. This is thern followed by full 25 minutes presentation, which can be followed by the enclosed 67 slides.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
1. Chapter 4-1
Microwave Transistor Amplifier Design
Chien-Jung Li
Department of Electronics Engineering
National Taipei University of Technology
2. Department of Electronic Engineering, NTUT
Power Gain Equations
2 2
2
212 2
22
1 1
1 1
s LL
T
AVS in s L
P
G S
P S
2 2
2
212 2
11
1 1
1 1
s LL
T
AVS s out L
P
G S
P S
2
2
212 2
22
11
1 1
LL
p
in in L
P
G S
P S
2
2
212 2
11
1 1
1 1
sAVN
A
AVS s out
P
G S
P S
• Transducer Power Gain
• Operating Power Gain
• Available Power Gain
Transistor
[S]
sE
sZ
LZ
PAVNPAVS PLPin
Ms
interface interface
ML
2/45
3. Department of Electronic Engineering, NTUT
Example (I)
• Calculate the PAVS, Pin, PAVN, and PL
1 50Z
Input
Matching
Network
Output
Matching
Network
1 10 0E
2 50Z
0.5 120s in
out 0.4 90L
sZ inZ outZ LZ
S
11 12
21 22
0.6 160 0.045 16
2.5 30 0.5 90
S S
S
S S
Transistor S parameters:
12 21
11
22
0.627 164.6
1
L
in
L
S S
S
S
12 21
22
11
0.471 97.63
1
s
out
s
S S
S
S
2 2
2
212 2
22
1 1
9.43
1 1
s LL
T
AVS in s L
P
G S
P S
or 9.75 dB
3/45
4. Department of Electronic Engineering, NTUT
Example (II)
2
2
212 2
22
11
13.51
1 1
LL
p
in in L
P
G S
P S
or 11.31 dB
2
2
212 2
11
1 1
9.55
1 1
sAVN
A
AVS s out
P
G S
P S
or 9.8 dB
in AVS sP P M T p sG G Mand
9.43
0.698 1.56 dB
13.51
T
s
p
G
M
G
2 2
2
1 1
0.6983 1.56 dB
1
s in
s
s in
M
L AVN LP P M T A LG G Mand
9.43
0.9874 0.055 dB
9.55
T
L
A
G
M
G
2 2
2
1 1
0.9874 0.055 dB
1
L out
L
out L
M
2 2
1
1
10
0.25 W
8 8 50
AVS
E
P
R
0.25 W 0.1745 Win sP M
0.25 W 2.358 WL TP G
2.358 WL AVN LP P M 2.39 WAVNP
4/45
5. Department of Electronic Engineering, NTUT
Stability
12 21
11
221
L
in
L
S S
S
S
12 21
22
111
s
out
s
S S
S
S
• The stability of an amplifier, or its resistance to oscillate, is a very
important consideration in a design and can be determined from the
S parameters, the matching networks, and the terminations.
• Oscillations are possible when either the input or output port presents
a negative resistance, i.e., or ( or for a
unilateral device).
1in 1out 22 1S11 1S
Transistor
[S]
sE
sZ
out
LZ
in
s L
• The two-port network is said to be unconditionally stable at a given
frequency if the real parts of Zin and Zout are greater then zero for a
passive load and source impedances. For potentially unstable, that is,
some passive load and source terminations can produce input and
output impedances having a negative real part.
5/45
6. Department of Electronic Engineering, NTUT
Stability Considerations
1s
12 21
22
11
1
1
s
out
s
S S
S
S
1L
12 21
11
22
1
1
L
in
L
S S
S
S
22 11 12 21
2 2 2 2
22 22
L
S S S S
S S
11 22 12 21
2 2 2 2
11 11
s
S S S S
S S
11 22 12 21S S S S
• In terms of reflection coefficients, the conditions for unconditionally
stability at a given frequency are
• The region where produces is determined.L 1in
• Stability Circles include
and
Transistor
[S]
sE
sZ
out
LZ
in
s L
• The region where produces is determined.s 1out
and
where
6/45
7. Department of Electronic Engineering, NTUT
The Stability Circles
12 21
2 2
22
L
S S
r
S
22 11
2 2
22
L
S S
C
S
12 21
2 2
11
s
S S
r
S
11 22
2 2
11
s
S S
C
S
• Output Stability Circle ( values for )L 1in
Center
Radius
• Input Stability Circle ( values for )
Center
Radius
s 1out
1in
1out
LC
Lr
LC
sC
sr
sC
-planeL
-planes
7/45
8. Department of Electronic Engineering, NTUT
Determine the Stable Region
LC
LC
Lr 1in
sr
sC
sC
1out
• How do we determine the stable region? Inside or outside the
stability circle? The and can help! (see next two slides)11S
-planeL -planes
Output Stability Circle Input Stability Circle
22S
8/45
9. Department of Electronic Engineering, NTUT
Determine the Stable Region of Plane
LC
LC
Lr
1in
11 1S
12 21
11
221
L
in
L
S S
S
S
0L
LC
LC
0L
Lr
1in
• Criteria: virtually make , then and0L 11in S L oZ Z
-planeL -planeL
L
Case (1): 11 1S Case (2):
stable region stable region
9/45
10. Department of Electronic Engineering, NTUT
Determine the Stable Region of Plane
12 21
22
111
s
out
s
S S
S
S
22 1S 22 1S
s
Case (1): Case (2):
• Criteria: virtually make , then and0s 22out S s oZ Z
stable region stable region
-planes -planes
0s 0s
sC sC
sC
srsr
sC
1out 1out
10/45
11. Department of Electronic Engineering, NTUT
Unconditionally Stable (I)
-planeL -planes
0s 0L
LC
sC
sC
sr
Lr
LC
1in
1out
• For the cases of and11 1S 22 1S
Make the stability circles completely outside the Smith Chart!
11/45
12. Department of Electronic Engineering, NTUT
Unconditionally Stable (II)
• For the cases of and11 1S 22 1S
Make the stability circles completely enclose the Smith Chart!
-planeL -planes
0s
0L
LC sCsC
sr
Lr
LC
1in
1out
12/45
13. Department of Electronic Engineering, NTUT
Stability Tests
2 2 2
11 22
12 21
1
1
2
S S
K
S S
• Rollet’s Condition (K-∆ test):
For unconditional stability
11 22 12 21 1S S S Sand
The K-∆ test is a mathematically rigorous condition for unconditional stability.
However, it cannot be used to compare the relative stability of two or more
devices (or bias conditions) since it involves constraints on two parameters.
K>1 and |∆|<1 must
simultaneously hold for
unconditionally stable
• In 1992, Edwards, et. al. derived a new criterion that involves only a
single parameter μ for unconditional stability. Thus, if μ > 1, the device
is unconditionally stable. In addition, it can be said that larger values of
μ imply greater stability.
2
11
22 11 12 21
1
1
S
S S S S
13/45
14. Department of Electronic Engineering, NTUT
Example (I)
Determined the stability. If the transistor is potentially unstable at a
given frequency, draw the input and output stability circles.
2 2 2
11 22
12 21
1
1
2
S S
K
S S
11 22 12 21 1S S S S
K
0.482 0.221 123
0.857 0.173 162.9
1.31 0.174 160
1.535 0.226 121
(GHz)f
0.5
1
2
4
• The S-parameter of a BJT at VCE = 15 V and IC = 15 mA at f=500 MHz,
1 GHz, and 4 GHz are as follows:
2
11
22 11 12 21
1
1
S
S S S S
0.49
14/45
15. Department of Electronic Engineering, NTUT
Example (II)
22 11
2 2
22
L
S S
C
S
12 21
2 2
22
L
S S
r
S
11 22
2 2
11
s
S S
C
S
12 21
2 2
11
s
S S
r
S
sC sr
1.36 157.6 0.558 2.8 57.86 2.18
1.28 169 0.315 2.62 51.3
(GHz)f
0.5
1
LC Lr
1.71
15/45
16. Department of Electronic Engineering, NTUT
Stabilization Methods
• Stabilization methods described below are used to stabilize the
transistor unconditionally.
1R
2R
6R
5R
3R
4R
Stabilization of input port through series or shunt resistance, eg., R1, R2.
Stabilization of output port through series or shunt resistance, eg., R3, R4.
Stabilization using series or shunt negative feedback, eg., R5, R6. Inductances
and capacitances are also commonly used as feedback elements.
Stabilization results in a loss of gain and an increase in noise figure.
16/45
17. Department of Electronic Engineering, NTUT
Example (I)
• The S-parameter of a transistor at f=800 MHz are :
11 0.65 95S 12 0.035 40S 21 5 115S 22 0.8 35S
Determine the stability circle and show how resistive loading can stabilize the
transistor.
2 2 2
11 22
12 21
1
0.547
2
S S
K
S S
11 22 12 21 0.504 249.6S S S S
Since K<1, the transistor is potentially unstable at f=800MHz.
1.79 122sC 1.04sr
1.3 48LC 0.45Lr
Input Stability Circle:
Output Stability Circle:
17/45
18. Department of Electronic Engineering, NTUT
Input and Output Stability Circle
1.79 122sC
1.3 48LC
18/45
19. Department of Electronic Engineering, NTUT
Stabilization – Input Series Resistance
1.79 122sC
1.3 48LC
9
s
9s sZ Z
s
sZ
19/45
23. Department of Electronic Engineering, NTUT
Stability Considerations (I)
• For a unilateral transistor, S12=0 (or it is so small that can be set to
zero). In unilateral case, and (the transistor
output signal would not go through back to the input). If , the
transistor presents a negative resistance at the input, and if the
transistor presents a negative resistance at the output.
11in S 22out S
11 0S
22 0S
• For unconditionally stability any passive load and or source in the
network must produce a stable condition. For and ,
we want the stability circles to fall completely outside the Smith Chart.
(Or completely enclosed for and )
11 0S 22 0S
11 0S 22 0S
• It is convenient to use the μ parameter to check the stability, the
transistor will be more stable for a larger μ.
• For the unilateral case, we have unconditionally stability if
and for all passive source and load terminations.11 0S 22 0S
23/45
24. Department of Electronic Engineering, NTUT
Stability Considerations (II)
• A potentially unstable transistor can be made unconditionally stable
by either resistively loading the transistor or by adding negative
feedback. These techniques are nor recommended in narrowband
amplifiers because of the resulting degradation in power gain, noise
figure, and VSWRs.
• Usually, stabilizing one port of a transistor results in an
unconditionally stable device.
• All four choices of resistive loading affects the gain performance of
the amplifier. In practice, resistive loading at the input is not used
because it produces a significant deterioration in the noise
performance of the amplifier.
• Negative feedback can be used to stabilize a transistor by neutralizing
S12 (making S12=0). However, this is not commonly done. In a
broadband design, a common procedure is to use resistive loading to
stabilize the transistor and negative feedback to provide the proper ac
performance (constant gain and low input and output VSWR).
24/45
25. Department of Electronic Engineering, NTUT
Unilateral Transducer Power Gain
11S
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s L22S
2 2
2
212 2
11 22
1 1
1 1
s L
TU s o L
s L
G S G G G
S S
2
2
11
1
1
s
s
s
G
S
2
21oG S
2
2
22
1
1
L
L
L
G
S
(dB) (dB) (dB) (dB)TU s o LG G G G
• Unilateral Transducer Power Gain GTU
• The term Gs and GL represent the gain or loss produced by the
matching or mismatching of the input or output circuits.
12 0S
25/45
26. Department of Electronic Engineering, NTUT
Maximum Unilateral Transducer Power Gain
11S
1E
oZ
oZ
Transistor
oG
Output
matching
,maxLG
Input
matching
,maxsG
11s S
22L S
22S
11s S
22L S
,max 2
11
1
1
sG
S
,max 2
22
1
1
LG
S
2
,max ,max ,max 212 2
11 22
1 1
1 1
TU s o LG G G G S
S S
• Maximum Unilateral Transducer Power Gain GTU,max
Optimize and to provide maximum gain in Gs and GL.s L
and
2
2
11
1
1
s
s
s
G
S
2
2
22
1
1
L
L
L
G
S
and
and
26/45
27. Department of Electronic Engineering, NTUT
General Form of the Matching Gain
2
2
1
1
i
i
ii i
G
S
• General form of the matching gains Gs and GL :
with 11, and with 22i s ii i L ii
(1) Unconditionally stable case: 1iiS
,max 2
1
1
i
ii
G
S
,max0 i iG G
i iiS
For optimum terminations:
Other values of (mismatched) produce Gi between zero and Gi,max:i
• The values of that produce a constant gain Gi will be shown to lie in a
circle in the Smith Chart. These circles are called constant Gi circles.
i
Constant Gs circles: i = s
Constant GL circles: i = L
27/45
28. Department of Electronic Engineering, NTUT
Constant Gi Circle – Unconditionally Stable
• Normalized Gain Factor:
2
2 2
,max
1
1 1
1
ii
i i ii ii
i ii i
G
g G S S
G S
such that 0 1ig
• Constant Gi circle in the Smith Chart
The values of that produce a constant values
of gi lie in a circle.
i
i ii g gC r
2
1 1i
i ii
g
ii i
g S
C
S g
2
2
1 1
1 1i
i ii
g
ii i
g S
r
S g
Each gi generates a constant Gi circle.
When gi =1 gives
0igr ig iiC S
and
Maximum gain is
represented by a
point located at iiS
giC
gir
iiS
i iiS
iU
iV
-planei
Maximum gain Gi,max occurs
Locate iiS
Determine Gi and gi
Use gi to find igr,igC
Center:
Radius:
28/45
29. Department of Electronic Engineering, NTUT
Example (I)
• The S parameters of a BJT measured at VCE = 10 V, IC = 30 mA, and
the operating frequency f = 1 GHz, in a 50-Ohm system, are:
11 0.73 175 ,S 12 0,S 21 4.45 65 , andS 22 0.21 80S
(a) Calculate the optimum terminations.
(b) Calculate Gs,max, GL,max, and GTU,max in dB.
(c) Draw several Gs constant-gain circles.
(d) Design the input network for Gs = 2 dB.
(a)
11 0.73 175s S
12 0S unilateral
Optimum terminations: 22 0.21 80L S
and
7.6 2.35sZ j and 48.5 21.5LZ j
29/45
30. Department of Electronic Engineering, NTUT
Example (II)
(b)
,max 2
11
1
2.141 3.31 dB
1
sG
S
,max 2
22
1
1.046 0.195 dB
1
LG
S
2
21 19.8 12.97 dBoG S
The transistor inherently provides 12.97 dB gain
,max dB 3.31 12.97 0.195 16.47 dBTUG
Input and output matching networks provide
excess gain for transducer power
(c) ,max 3.31 dBsG
30/45
32. Department of Electronic Engineering, NTUT
Constant Gi Circle – Potentially Unstable
(2) Potentially unstable case: 1iiS
2
2
1
1
i
i
ii i
G
S
Critical value of
,
1
, andi c i
ii
G
S
i
2
2 21
1 1
1
i
i i ii ii
ii i
g G S S
S
Since , thus 0ig 1iiS
2
1 1i
i ii
g
ii i
g S
C
S g
2
2
1 1
1 1i
i ii
g
ii i
g S
r
S g
Maximum gain Gi,max (infinite) occurs
Center
Radius
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33. Department of Electronic Engineering, NTUT
When and , has a maximum value, and the ratio is bounded
by
Unilateral Figure of Merit (I)
• When S12 can be set to zero, the design procedure is much simpler. In
order to determine the error involved in assuming S12 = 0, we form
the magnitude ratio of GT and GTU, namely,
2
1
1
T
TU
G
G X
2 2
2
212 2
11
1 1
1 1
s L
T
s out L
G S
S
2 2
2
212 2
11 22
1 1
1 1
s L
TU
s L
G S
S S
12 21
11 221 1
s L
s L
S S
X
S S
2 2
1 1
1 1
T
TU
G
GX X
11s S
22L S
TUG
2 2
1 1
1 1
T
TU
G
GU U
is known as the
Unilateral Figure of Merit
and
where
12 21 11 22
2 2
11 221 1
S S S S
U
S S
where
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34. Department of Electronic Engineering, NTUT
Unilateral Figure of Merit (II)
f
dBU
5
10
15
• The value of U varies with frequency because of its dependence on
the S parameter.
100 MHz 1 GHz
@100 MHz, and 1 GHz 15 dB 0.03U
2 2
1 1
1 0.03 1 0.03
T
TU
G
G
0.9426 1.031T
TU
G
G
0.26 dB 0.26 dBT
TU
G
G
• The maximum error is ±0.26 dB at 100 MHz and 1 GHz. In some
designs this error is small enough to justify the unilateral assumption.
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35. Department of Electronic Engineering, NTUT
Simultaneous Conjugate Match: Bilateral Case
in
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s Lout
s in
L out
• Maximum Simultaneous Conjugate Matched Transducer Power Gain GT,max
and
22
1 1 1
1
4
2
Ms
B B C
C
and
12 21
11
221
L
in s
L
S S
S
S
12 21
22
111
s
out L
s
S S
S
S
and
22
2 2 2
2
4
2
ML
B B C
C
2 2 2
1 11 221B S S
2 2 2
2 22 111B S S
1 11 22C S S
2 22 11C S S
where
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36. Department of Electronic Engineering, NTUT
Stability and Simultaneous Conjugate Match
22
1 1 1
1
4
2
Ms
B B C
C
22
2 2 2
2
4
2
ML
B B C
C
1K 1K
1K 1K
Simultaneous conjugate
match can be achieved
Simultaneous conjugate
match doesn’t exist
Potentially unstable or
Unstable
1 1
Unconditionally
stable
Potentially
unstable
Any reference to a simultaneous conjugate match assumes
that the two port network is unconditionally stable.
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37. Department of Electronic Engineering, NTUT
Maximum Stable and Available Gain
2 2
2
212 2
22
1 1
1 1
s L
T
in s L
G S
S
in
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s Lout
s in Ms
L out ML
2
2 21 2
,max 212 2
1222
11
1
1 1
ML
T
Ms ML
S
G S K K
SS
• Maximum Simultaneous Conjugate Matched Transducer Power Gain GT,max
and
• Maximum Stable Gain (MSG) is defined when K =1:
21
12
MSG
S
G
S
(potentially unstable)
(unconditionally stable)
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38. Department of Electronic Engineering, NTUT
Operating Power-Gain Circle
2 2
21 2
212
211
22
22
1
1 1
1
L
p p
L
L
L
S
G S g
S
S
S
• Unconditionally stable bilateral case:
2 2
2 2 2 2 2 2
22 11 11 22 2
1 1
1 1 2Re
L L
p
L L L L
g
S S S S C
2 22 11C S S
Gp and gp are the functions of the device
S parameters and ΓL. The values of ΓL
that produce a constant gp are shown to
lie on a circle, known as an operating
power-gain circle.
L p pC r
2
2 2
221
p
p
p
g C
C
g S
2 2
12 21 12 21
2 2
22
1 2
1
p p
p
p
K S S g S S g
r
g S
Center Radius
where
• Operating Power-Gain Circle:
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39. Department of Electronic Engineering, NTUT
Maximum Operating Power-Gain
2 2
12 21 12 21
2 2
22
1 2
1
p p
p
p
K S S g S S g
r
g S
• The maximum operating power gain occurs when rp = 0.
2 2
12 21 ,max 12 21 ,max1 2 0p pK S S g S S g
2
,max
12 21
1
1pg K K
S S
21 2
,max ,max
12
1p T
S
G K K G
S
• The value of ΓL that produces Gp,max follows by substituting gp =
gp,max for Cp. This value of ΓL = Cp,max must be equal to ΓML.
,max 2
,max 2 2
,max 221
p
ML p
p
g C
C
g S
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40. Department of Electronic Engineering, NTUT
Maximum Operating Power Gain
• For a given Gp,ΓL is selected from the constant operating power-gain
circles. Gp,max, results when ΓL is selected at the distance where
gp,max = Gp,max /|S21|2 . The maximum output power results when a
conjugate match is selected at the input (i.e., ), and it follows
that the input power is equal to the maximum available input power.
Therefore, in this circumstances GT,max = Gp,max . The values of Γs and
ΓL that result in Gp,max are identical to ΓMs and ΓML , respectively.
s in
in
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s L
• Design Procedure:
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41. Department of Electronic Engineering, NTUT
Example (I)
• Design a microwave amplifier using a GaAs FET to operate f = 6 GHz
with maximum transducer power gain. The transistor S parameters
at the linear bias point, VDS = 4 V and IDS = 0.5 IDDS, are
11 0.641 171.3S 12 0.057 16.3S 21 2.058 28.5S 22 0.572 95.7S
Use (1) Transducer power gain method (2) Operating power gain
method to find the matching networks (3) Gp=9 dB amplifier design
(1) Transducer power gain method
1.504K 0.3014 109.88 Unconditionally stable
0.1085UCheck unilateral: 0.89 dB 1 dBT
TU
G
G
S12 cannot be neglected
(bilateral case)
1 2 1 20.9928, 0.8255, 0.4786 177.3 , 0.3911 103.9B B C C
0.762 177.3Ms
0.718 103.9ML
2
,max
2.058
1.504 1.504 1 13.74 or 11.38 dB
0.057
TG
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42. Department of Electronic Engineering, NTUT
Example (II)
(2) Operating power gain method:
,max 2
,max 2 2
,max 22
0.718 103.9
1
p
ML p
p
g C
C
g S
,max
,max 2 2
21
13.74
3.24
2.058
p
p
G
g
S
,max 0pr
12 21
11
22
0.762 177.3
1
ML
Ms in
ML
S S
S
S
(3) Operating power gain method: Gp = 9 dB
,max ,max 13.74T pG G
2 2
21 2.058 4.235 or 6.27 dBS
2
21
7.94
1.875
4.235
p
p
G
g
S
1.504K 0.3014 109.88 2 0.3911 103.9C 0.431pr 0.508 103.9pC
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43. Department of Electronic Engineering, NTUT
Example (III)
Select point A for matching: 0.36 47.5L
12 21
11
22
0.629 175.51
1
L
s in
L
S S
S
S
Since , it follows that
GT = Gp = 9 dB
s in
1 0.622
4.3
1 0.622out
VSWR
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44. Department of Electronic Engineering, NTUT
Available Power-Gain Circle
2 2
21 2
212
222
11
11
1
1 1
1
s
A a
s
s
s
S
G S g
S
S
S
• Unconditionally stable bilateral case:
2
2 2 2 2 2
21 22 11 1
1
1 2Re
sA
a
s s
G
g
S S S C
1 11 22C S S
Ga and ga are the functions of the device
S parameters and Γs. The values of Γs
that produce a constant ga are shown to
lie on a circle, known as an available
power-gain circle.
s a aC r
1
2 2
111
a
a
a
g C
C
g S
2 2
12 21 12 21
2 2
11
1 2
1
a a
a
a
K S S g S S g
r
g S
Center Radius
• Available Power-Gain Circle:
where
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45. Department of Electronic Engineering, NTUT
Design Procedures
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s Lout
• Design using operating power gain:
• Design using available power gain:
in
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
s L
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