ING-INF/01 - 9 CFU - 1° Semester

Teaching Staff


Learning Objectives

The objective of this course is the analysis, the simulation and the design of feedback circuits with particular emphasis on single and multi-stage amplifiers.

Knowledge and understanding

The course will highlight the design of circuits in CMOS technology thus leading the student through the comprehension of the main single-transistor circuit configurations (common source, common drain and common gate) and of the multiple-transistor ones (current mirrors, cascode amplifiers and differential amplifiers). The student will also know the static and dynamic properties of the feedback circuits as well as the techniques for circuit analysis and design. The course will be completed by some common-used topologies of amplifiers for integrated technology.

Applying knowledge and understanding

At the end of the course the students will be able to analyze the behavior of a feedback circuit by means of a "pencil-and-paper" analysis and to simulate its main characteristics. Students, with the aid of the computer, will also be able to design the compensation network of a feedback circuit with one or two gain stages and to design the most common topologies of integrated amplifiers. Students will also be trained to the design through the use of the SPICE simulator.


Students should have prior knowledge about Laplace transform, Bode plots and methods for the analysis of linear circuits. They are also required to have prior knowledge about the modeling of common electronic devices (diodes, BJTs and MOSFETs), as well as the ability in the analysis of simple circuits with active elements.

Course Structure

The course includes 42 hours of lectures, 30 of numerical exercises and 25 hours of laboratory lessons with the use of the SPICE simulator and the development of a design project that will be described in a final report. The laboratory experience will be aimed at putting into practice, developing and consolidating the theoretical contents and the design techniques learned. Finally, seminars will be organized by researchers and designers from industries operating in the microelectronics sector.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Learning assessment procedures

Learning assessment is verified through the final exam. This consists of an oral exam preceded by the evaluation of a design project. For students who have not attended the laboratory lessons for at least 18 hours, the project is replaced by a written test lasting 2 hours.

The design project is a brief report regarding the analysis and design of a feedback circuit that students, in groups of two, will have faced in the laboratory lessons. In the report it will be necessary to describe:

  1. How the circuit is dimensioned so to obtain a given bias point (“pencil and paper” evaluation of the bias point as well as comparison with the simulation);
  2. The evaluation of the loop-gain transfer function and the design of the compensation network (“pencil and paper” evaluation, simulation with the initial design values and subsequent fine tuning using the simulator);
  3. The asymptotic gain and the input (or output) resistance by applying the methods of Rosenstark and Blackman (“pencil and paper” evaluation and comparison with the results obtained in simulation);
  4. Simulation of the DC input-output transfer characteristic and evaluation of the signal swing;
  5. Simulation of the of the closed-loop bandwidth of the circuit;
  6. Simulation of the step response and evaluation of the settling time;
  7. Simulation of the large-signal step response and evaluation of the slew-rate;
  8. Simulation of the time response to a sinusoidal signal and evaluation of the total harmonic distortion.

The teacher will interact with the different groups during the laboratory lessons. Students, in turn, can interact with the teacher, bearing in mind that they are carrying out a part of the final exam. At the end of the course, the groups can interact only once with the teacher to verify the correctness of what they are doing (note that in this period the student is carrying out his own exam, therefore he cannot be admitted to the office hours for explanations concerning doubts or questions). The report must be delivered in pdf version to the teacher's email address at least one week before the beginning of the first session of exams. The evaluation of the report is expressed as PASS/FAIL. In the case of negative evaluation, the student must take the written test to be admitted to the oral exam. The list of the students admitted to the oral exam will be published on the Studium platform ( in time to take the oral exam.

The written test must demonstrate the student's ability to correctly analyze a feedback circuit. Specifically, the evaluation will take into account the ability to correctly identify and analyze the elementary circuits studied during the course lessons, the ability to identify and design the adequate compensation network and the ability to correctly apply the analysis techniques for feedback circuits. For each point, the evaluation will also take into account the correctness and consistency of the procedure, the clarity of presentation, the correctness of the numerical calculations (where required) and how much the student was able to complete. The result of the written test, published on the Studium platform (, is expressed through a scale of judgments (FAIL, POOR, PASS, FAIR, GOOD). Anyone admitted with POOR will have a limitation on the final mark (max 25/30).

The oral exam is the last part of the exam and consists of two questions on two course topics. In the answers, the student must demonstrate adequate understanding, mastery of the topics discussed and clarity of presentation. Students who completed the design project, can be asked a further question on the project itself. The average duration of the oral exam is 40 minutes. The final mark will take into account the work done in the laboratory lessons, the quality of the design project (or the outcome of the written test) and, most of all, the result of the oral exam.

Learning assessment may also be carried out on-line, should the conditions require it.

Detailed Course Content

Bipolar transistor models
The pn junction. BJT forward active region. Large-signal dc models. Operating modes. Small-signal models. Parasitic elements.

MOS transtor models
MOS structure and operating regions. MOSFET operating regions. MOSFET I-V characteristic. Large-signal dc models. Small-signal models.

Basic MOSFET circuits
MOSFETs’ external resistances. Single-transistor circuits(CS, CD and CG). Current mirrors. Differential amplifiers. High-gain stages. BiCMOS stages.

Frequency response
General amplifiers' structure. Seeking poles and zeros. Single transistor stages: CS, CD and CG. Current mirrors. Differential pair. High-gain stages.

Amplifiers dc analysis
General amplifiers' structure. Feedback. Two-port theory. Return ratio. Rosenstark method. Blackman method

Amplifiers ac analysis
Feedback amplifiers' general characteristics. Stability analysis. Stability criteria. Compensation techniques.

Voltage and current reference circuits
Voltage/Current reference parameters. Current reference circuits. VBE vs T modeling. Bandgap voltage reference circuits: Widlar, Brokaw, Kuijk and Banba.

Operational Transconductance Amplifiers (OTAs)
Two-stage class-A OTA. Stacked mirrors OTA. Folded cascode OTA

The SPICE simulator
Design of electronic circuits by means of SPICE

Textbook Information

  1. Gray, Hurst, Lewis, Meyer, Analysis and design of Analog Integrated Circuits, 5th Ed., John Wiley & Sons, Inc.
  2. P. R. Gray, R. G. Meyer, Circuiti Integrati Analogici, II Edizione, McGraw-Hill
  3. J. Millman & A. Grabel, Microelectronics, McGraw-Hill.
  4. Alan B. Grebene, Bipolar and MOS Analog Integrated Circuit Design, John Wiley & Sons, Inc.
  5. A. Vladimirescu, Guida a SPICE, McGraw-Hill Libri Italia.

Open in PDF format Versione in italiano