Degree in Computer Engineering

Study Computer Engineering at La Salle and become a professional with the abilities to work with the latest technologies and new products, designing, implementing and maintaining computer systems for any sector of economic activity

Microwave Circuits

The subject is an introduction to the propagation of voltage and current waves in transmission lines, and the analysis and design of microwave circuits based on transmission lines. The topics addressed in the subject are: - First, the propagation of electromagnetic waves (characterized by voltage and current waves) in transmission lines is studied. - Then, a classic tool used in the analysis of microwave circuits, the Smith chart, is used to design matching networks with transmission lines, as first examples of high frequency and microwave circuits. - Next, the theory of characterization of microwave circuits using S parameters is developed. - Finally, a series of basic passive microwave circuits are presented, their structure and functionality analyzed, and used to build increasingly complex applications.
Type Subject
Previous Knowledge

Elementary circuit theory, and basic notions of propagation of electromagnetic waves.


The objectives of the subject of Microwave Circuits are that students acquire the knowledge and develop the skills indicated below:

1. Basic knowledge about methods of analysis and design of microwave circuits.

2. Ability to apply the knowledge acquired not only to its usual area of application (microwave circuits), but also to other areas of knowledge where the concepts studied are useful, such as electromagnetic compatibility, antennas, communications systems, or the electronic design.

3. Ability to reduce complex systems to simple analytical models that preserve their basic characteristics and allow their analysis and interpretation.


1. Transmission lines
1.1. Steady State
1.2. TL, definition and simbology
1.3. Modelling of transmission lines
1.4. Impedance, reflection coefficient and standing wave ratio
1.5. Excitation of transmission lines
1.6. Lossy transmission lines
1.7. Parameters of physical transmission lines
1.8. The Smith chart
1.9. Impedance matching networks

2. Analysis of microwave circuits
2.1. Microwave networks
2.2. Networks of one port. Normalized waves and generalized reflection coefficients
2.3. Normalized waves between generator and load
2.4. Networks of more than one port. S parameters of a circuit
2.5. Computation of the S parameters
2.6. Connections between ports

3. Passive microwave circuits
3.1. Power dividers and combiners
3.2. Hybrid rings
3.3. Directional couplers
3.4. Filters
3.5. Circulators and insulators
3.6. Attenuators
3.7. Switchable circuits.


The subject is taught in the format of master classes. The theoretical classes are complemented with problem classes that aim to settle the theoretical concepts and present a wide range of applications. It is expected that the student works on his / her own the theoretical concepts learned and applies them to different situations through problems suggested in the problem collections. For the analysis of complex circuits or situations, microwave simulators are used.


The subject is evaluated through continuous-evaluation assignments and a final exam (in May/June or, if needed, a supplemental final exam in July).

The continuous-evaluation assessments may heavily rely on computer-aided analysis or design and presentations in class, and are evaluated by means of an individual interview. At the lecturer’s discretion, some of the assessments may be evaluated by means of problems done in class. A late submission of a continuous-evaluation assessment (after the deadline given by your lecturer) will be penalized by -20% points of the maximum mark which can be achieved with the submission.

If the mark of each of the continuous-evaluation assessments is greater than or equal to 7, the student passes the subject without having to take the exam with an unrounded grade equal to the average of the marks of the continuous-evaluation assessments. Otherwise, the final grade for the course is computed as follows:

1. A continuous-evaluation grade is computed as the mean of the marks of the three continuous-evaluation assignments.
2. If the May/June exam grade (or, if the student does not pass the subject then, the July exam grade) is greater than or equal to 4.0, then the unrounded grade for the course is the maximum of:
the exam grade
0.6 times the exam grade plus 0.4 times the continuous-evaluation grade.
If the exam grade is less than 4.0, the unrounded grade for the course is the exam grade.

The final grade for the course is 4 if the unrounded grade for the course falls between 4 and 5. Otherwise, it is obtained by rounding the unrounded grade to the nearest whole number with one decimal.

Cheating of any valuable activity (even some parts of) will be penalized as established in the academic regulations of university. Both the source and the cheating students will be penalized.

Evaluation Criteria

The results will be evaluated according to the following criteria:

1. Mastery of the basic analysis tools of microwave circuits, both theoretical and software

2. Ability to apply the knowledge learned to complex situations or in other fields than microwave circuits

3. Critical capacity.

Basic Bibliography

[1] D.M. Pozar, Microwave Engineering, 3rd edition, John Wiley &Sons
[2] J. Bará, Circuitos de microondas con lineas de transmission, Edicions UPC.

Additional Material

[1] R.E. Collin, `Foundations for microwave Engineering´, 2nd editon, IEEE Press - John Wiley &Sons
[2] R. Sorrentino et al., `Microwave and RF Engineering´, John Wiley & Sons, 2010.