Department of Electronic and Information Engineering, Hong Kong Polytechnic University

EIE403: High Frequency Circuit Design

Subject Lecturer: Prof. Michael Tse



HIS HOMEPAGE contains information about the final-year elective High Frequency Circuit Design offered in the first semester of 2005/2006 It tells you everything about this course including its aims, contents, teaching schedule, assessment methods, etc.



Designing electronic circuits in the tens and hundreds of MHz range can be a challenge because the presence of parasitics presents a lot of problems in the physical circuits. This makes designing high-frequency circuits a rather specialised subject, although much can still be resolved under the lumped circuit assumption. But as the frequency moves up to GHz range, we have serious trouble using lumped circuit models because voltage and current change within the physical boundary of the circuit as a result of the wavelength being comparable to the dimension of the physical circuits. We therefore have to use a different approach to look at the problem. In this course we will look mainly at circuit design in the tens-hundreds MHz range and will touch upon some basics for the GHz range design.


WHAT YOU WILL LEARN (Some philosophical notes about this course):
  1. Essential overview of analog electronics (3 weeks):

    My experience of doing this course is that students came from various backgrounds due to the many possible combinations of study tracks that students took in previous years. Sometimes, students claimed they hadn't learnt this and that. So, I will assume that everyone knows just a little basics about circuits, but not anything advanced. I will spend two to three weeks to go over the essential concepts of analog circuits including devices, amplifier configurations, feedback, etc. This will be like a compressed course of all electronics fundamentals up to EC2 and ADIC. Then, you will have no excuse of not knowing what feedback is, how driving impedance can be deduced, or why Miller can reduce gain, etc. Moreover, in doing this revision, I will put emphasis on high-frequency effects so that you will appreciate more easily the problems to be studied in the later part of the course.

  2. Radio frequency circuit techniques (2 weeks):

    This part of the course introduces you to the basic elements of desiging circuits at high-frequency range. I will emphasize conceptual understanding of the problems of high-frequency roll-off that limits the operation of amplifiers at high frequencies. An important skill to acquire here is to identify the vulnerable parts of a given circuit that can lead to roll-off. With this knowledge, we can devise methods to combat it, and we will systematically study a few popular amplifier configurations for high-frequency applications.

  3. High-frequency filter design (2 weeks):

    This is a difficult part, because you have never done anything seriously about filter synthesis and design. Obviously this would have been due to a flaw in our curriculum design. But as I have to take care of it anyway, I have to make sure you will get the salient design concepts necessary for high-frequency filter design. So, I will try to summarize the whole filter technology background in a compact manner, up to a point where we can start looking at high-frequency filter design. Essentially, our de facto starting point is the inadequacy of operational amplifiers in handling high-frequency signals. This leads to the introduction of a "new" element (in the sense of usage rather than history of existence) known as operational transconductance amplifier or the OTA. Sometimes, we just call it transconductance or even simply Gm. Using Gm as the basic amplifier block, we can design filters in the hundreds of MHz range. We will study design examples using signal flow graphs as tools and examine a few BJT and MOS OTAs.

  4. Impedance matching (2 weeks):

    In high-frequency circuit design, an important procedure that must be incorporated in every design is matching. The purpose of matching is to prevent signals from being reflected as they move along the various parts of a circuit or system. This in turn ensures maximum power transfer from the signal source to the load. Matching also has an important role to play in the stability of circuits. In this part of the course, we focus ourselves on a few popular matching methods. Essentially, we will derive, from very basic circuit theory, some simple matching circuits that can achieve impedance matching for a narrow bandwidth. In particular we will take a look at L-circuits, T-circuits, pi-circuits, tapped capacitor circuits, etc., using a simple design approach employing the concept of Q-factor. I will also briefly talk about the double-tuned circuit for wider band matching.

  5. Transmission line matching (2 weeks):

    At high frequencies (up to microwave range), transmission lines are not just "nothing" as in lumped circuit analysis. They can affect power transfer and even stability because they can reflect signals back and create standing wave patterns. I will explain the concepts of travelling waves in transmission lines and interpret the famous Telegrapher's equations. What is important here is to understand the various effects a transmission line has on the signal transmission. I will use the Smith chart as a tool to make things appear very intuitive so that you can easily visualize the many effects of a transmission line. Then, the matching method can be easily derived, of course with the help of the Smith chart. I will try to cover some simple matching examples using the transmission line itself as a matching element! This is called stub matching.

  6. Power amplifier design (2 weeks):

    Designing power amplifiers at high frequencies has a rather different set of criteria, which are developed to combat the easily unstable devices. Engineers usually call it oscillation. Then, why is the amplifier so easily become unstable or oscillatory? The problem is the internal parasitics that form internal feedback paths. We know from EC1 that whenever there is a roundtrip gain of just higher than 1, the circuit oscillates. To study this problem, we begin with an appropriate characteristion---the scattering parameters. I will explain what scattering parameters are. Their physical meanings are important to understanding the many aspects of high-frequency design. With scattering parameters, I will explain some concepts of power gains in amplifiers and once again the matching problem in order to maximize power gain. We will see later that what is important really is the so-called transducer power gain because it measures how much power that can be used relative to how much power that is available. Our final task is to examine in detail the problem of stability. I will explain, from the basic stability requirements, how stability conditions can be visualized on the Smith chart and be checked mathematically. To finish off, I will examine one way (out of the many possibilities) of making an unstable amplifier stable by neutralizing (cancelling) the internal feedback.



This year, the weekly lecture and tutorial are scheduled on every Friday evening. This is an unfortunate arrangment, I would say, because three hours of continuous concentration is not practical. To make the best use of the time, I will spend the first 2 hours every Friday evening to present the lecture material, and will use the last hour as tutorial where I will answer specific questions and discuss homework problems. As indicated above, the teaching schedule is roughly as follows:

Dates TopicsNotes
9 September - 30 September Overview of analog electronics
printed notes to be handed out
7 October & 14 October Radio frequency circuit techniques printed notes to be handed out
21 OctoberLecture and tutorial cancelled.
28 October & 4 November High-frequency filter design (660KB)
printed notes to be handed out
4 November & 11 November Impedance matching (1MB)
printed notes to be handed out
11 November & 18 November Transmission line matching (773KB)
printed notes to be handed out
25 November Power amplifier design (1.6MB)
printed notes to be handed out
2 DecemberRevision



From time to time, I will hand out problem sets. You must try to work out solutions all on your own. During the tutorials, I will explain some of the problems related to the assignments. Remember assignments do count towards your continual assessments.

Assignment 1:
Please submit solution to Question 2 of Problem Set 1 by 7 October 2005.
Click this link to see the solution for this assignment.

Assignment 2:
Please submit solution to Question 6 of Problem Set 2 by 28 October 2005.
Click this link to see the solution for this assignment.

Mid-Semester Test:
The mid-term test will be composed of only ONE problem: Question 3 of Problem Set 3. This forms a "take-home test" to be handed in on 11 November 2005. That means each of you will have to reproduce the answer all on your own. Your submission will be counted as mid-semester test.

HINT: The following formula gives the drain current of MOSFET Q1 and Q2:

iD = [ μn Cox /2 ] [ W/L ] Veff2

where Veff = vgs - VTH. This formula is true for MOSFET Q1 and Q2. But for Q3 and Q4, they are in triode region. Then, the total current that flows through Q3 and Q4 is given by
2 iD3 = 2 μn Cox (W/L)3 [ Veff2vds3 - vds32 / 2 ]

where we note that Veff3 = Veff2.

Also, you should know that this total current through Q3 and Q4 plus the current in Q2 must be equal to I1. So, you should be able to get a total of three equations containing the unknowns Veff1, Veff2 and vds3.

In part (b), you may need to solve this set of equations, requiring numerical solution procedures. To save your time, you may assume that you already know vds3 = 0.0015648 V for the case v1 = 2.5 mV, and you may also assume that you know vds3 = 0.18297 V for the case v1 = 250 mV.

In part (c), you may take vds3 = 0.0015648 V for the case v1 = 2.5 mV, and you may also take vds3 = 0.15625 V for the case v1 = 250 mV.

Click this link to see the solution for this test.

Assignment 4:
Please submit solution to Question 5 of Problem Set 4 by 25 November 2005.
See lecture notes for matching procedure.

Mini-project topics and requirements ---IMPORTANT!--- :
Mini-projects will be done in lieu of laboratory works. There are a few reasons for this. First, many design approaches can be computerised and it is an extremely good exercise for you to develop computer software to aid design. Second, our laboratory is not (at the moment) well geared towards high-frequency experiments. Third, because our course emphasizes conceptual understanding, mini-projects are good tools to stretch your thinking.

The stipulated practical work for this subject is 9 hours of work related to topics taught in the course. I believe it is reasonable to ask you to develop a complete and fully working software to aid the design of high frequency circuits. The 9 hour schedule is the main constraint, which means that I can only specify relatively simple projects. As more topics will be covered as we go along, I suggest that you do a quick preview of the lecture materials to find out if you would like to pursue your mini-project on a topic which will be taught at the later part of the semester. The following topics are arranged in the sequence they are taught. You may choose any ONE of these topics.

  • Topic 1: High frequency roll-off of transistor amplifiers
    You are required to develop a complete computer software which can generate all poles and zeros, and complete frequency response of the common-emitter amplifier. Your software should input sufficient number of parameters and produce complete list of results. Graphical results would be desirable in the case of frequency responses. A clearly written and complete user manual and a CD-ROM (or floppy diskette) containing the software will be required in the final submission.

  • Topic 2: Design of matching circuits
    You are required to develop a complete software which can generate all the circuit component values for the following types of matching circuits: L-circuit, pi-circuit, T-circuit and tapped capacitor circuit. Your software should input sufficient number of parameters (e.g., type of matching circuits, Q factor, resistances to be matched, etc.) and produce complete list of results. A clearly written and complete user manual and a CD-ROM (or floppy diskette) containing the software will be required in the final submission.

  • Topic 3: Transmission line matching
    You are required to develop a complete software which can generate the information (e.g., position of inserting stub, length of stub, type of stub, etc.) required to match a given load to a transmission of any characteristic impedance. Incorporating the Smith chart geometry is preferred over the use of first-principle equations. A clearly written and complete user manual and a CD-ROM (or floppy diskette) containing the software will be required in the final submission.

Note that this is NOT a group project. Each one of you is required to submit a report outlining the objective and your approach (together with a CD-ROM (or floppy diskette) of the software and a complete user manual). The deadline of submission is the day of my last lecture, 2 December 2005. I will test your software and verify its functionality, and I will also do a simple "independency check". If two or more of you are found to have submitted essentially the same software, you will get zero mark for this component.



There will be a mid-semester test for the purpose of assessment. But it may be more appropriate to do a take-home test which consists of a difficult design problem. This will save a week of lecture time.

The written examination will consist of a 2.5 hour paper. I will set questions in a way that you will not be able to avoid knowing the basic principles. I will put the basic things in one or two compulsory questions, but will still allow choices so that students with different interests and abilities will be able to pass the examination.

Altogether, the mid-semester test, mini-projects and assignments will account for 35% of the final marks, and the written examination will account for 65% of the final marks.

Let me stress that I never scale marks! What you get is what you get! But you can be assured that my exam paper is always set to test what you know rather than to test what you don't know. So, you should find the paper very answerable if you have followed my course; in other words, I accept no excuse of failure.



I am usually available for consultation any time I don't have a class or meeting. My time-table is posted outside my office. But since our class is on every Friday, it seems to be convenient if you can see me (if you have a question about your study) in the afternoon before the lecture starts. This will allow me to replicate interesting problems to the whole class, if it is appropriate to do so. Also, Friday afternoons will be more convenient for part-timers as they may just drop in a bit earlier in the same evening.

Preferred consultation time: Friday 3pm to 6 pm


  • Smith chart
  • Semi-log graph paper



Learn with only your heart!


  1. Kenneth R. Laker and Willy M.C. Sansen, Design of Analog Integrated Circuits and Systems, New York: McGraw Hill, 1994.
  2. Paul R. Gray, Paul J. Hurst, Stephen H. Lewis and Robert G. Meyer, Analysis and Design of Analog Integrated Circuits, New York: Wiley, 2001.
  3. W. Alan Davis and Krishna K. Agarwal, Radio Frequency Circuit Design, New York: Wiley, 2001.
  4. Herbert L. Krauss, Charles W. Bostian and Frederick H. Raab, Solid State Radio Engineering, New York: Wiley, 1980.


Michael Tse, 1 September 2005