MICROELECTRONICS ELCT 703 (W17) LECTURE 1: ANALOG MULTIPLIERS

Transcription

1 MICROELECTRONICS ELCT 703 (W17) LECTURE 1: ANALOG MULTIPLIERS Dr. Eman Azab Assistant Professor Office: C

2 COURSE OVERVIEW Lecturer Teaching Assistant Course Team Dr. Eman Azab Office: C3.315 Office hours: Via Eng.: Yehia Hamdy Office:C3.222 Office hours: Via Teaching Method One Lecture per Week (Thursday 2 nd Slot) One Tutorial per Week (Tuesday 1 st /3 rd ) Location H6 Check Your Schedule Evaluation Method Percentage % Assignments 10 Quizzes 15 Project 10 Mid-Term 25 Final 40 2

3 COURSE GUIDELINES Please follow GUC regulations for attendance Course Prerequisites: Semiconductors Electronic Circuits Radio Frequency Course Objectives: Analog Signal Processing Circuits Design Analog Multipliers: Differential Amplifier Op-amp Circuit design, non-idealities, Linear and Non-linear applications Active RC Filters Switched capacitor circuits and applications Operational Trans-conductance Amplifiers Circuit design and Applications 3

4 TENTATIVE COURSE SCHEDULE Lecture # Lecture Description 1 Introduction & Analog Multipliers Analog Multipliers Transistor level design 2 Op-amp Circuit design Two-stage Op-amp Circuit design 3 Op-amp Circuit Frequency Response 4 Op-amp Circuit non-idealities 5 Op-amp Circuit Applications Compensation theory: How to design Stable closed loop systems using Op-amp? Non-ideal characteristics of Op-amp CMOS Circuit realization Linear and Non-linear Closed-loop Applications using Op-amps 6 & 7 Active-RC Filters Op-amp based Filters 8 & 9 Switched Capacitors Circuits SC Circuits Design Concept and Applications 10 Operational Trans-conductance Amplifiers Circuit design OTA CMOS Transistor Level Circuit Design 11 &12 OTA Applications Filters, Amplifiers using OTA 4

5 TENTATIVE COURSE EVALUATION SCHEDULE Assignment Quiz Project Assignment 1: Op-amp Circuit Design Assignment 2: Switched Capacitor based Filter Design Quiz 1: Analog Multipliers Quiz 2: Op-amp based Analog Signal Processing Applications Practical Project (Filter Design) Quiz 3: OTA Circuit Design 5

6 COURSE GRADING RULES Grading scheme is based on GUC Regulations Copies will be graded as ZERO This is applicable for Assignments, quizzes and Projects Stick to the office hours for questions Send an for urgent questions Attend the lectures and take notes! All the Course material will be available on the website 6

7 REFERENCES 1. Analysis and Design of Analog Integrated Circuits, Gray, Hurst, Lewis & Meyer 2. Fundamentals of Microelectronics, Razavi 3. Analog Integrated Circuit Design, Johns & Martin 7

8 ANALOG MULTIPLIERS Transistor level Circuit Design 8

9 ANALOG MULTIPLIERS: INTRODUCTION Analog Multiplier is a circuit that takes two analog inputs (I/V) and generate an output proportional to their Product X i1 X i2 Multiplier (K) X out X out = K X i1 X i2 K is the multiplication gain factor 9

10 ANALOG MULTIPLIER The circuit is used in communication systems for modulation/demodulation Amplitude Modulation Illustration 10

11 ANALOG MULTIPLIER Analog Multipliers can be one, two or four quadrant multipliers This classification depends on the polarity of the input signals X i1 X i2 Multiplier (K) X out Multiplier X i1 X i2 Single (one) Quadrant Unipolar Unipolar Two Quadrant Unipolar Bipolar Four Quadrant Bipolar Bipolar 11

12 ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT Emitter Coupled Circuit can be used as a two Quadrant analog multiplier It is formed with two matched BJT with their emitters connected together Assume Q1 and Q2 are Active and β F is large I E1 + I E2 = I I C1 I E1 & I C2 I E2 I C1 = I s e V BE1 V T I C2 = I s e V BE2 V T Where I s is the reverse saturation current and V T is the thermal voltage room temperature) 12

13 ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT The input voltage changes the collector currents = V BE1 V BE2 I C2 I C1 = e V T I C1 + I C2 = I C1 + I C1 e V T I I C1 = I 1 + e V T I C2 = I 1 + e V T 13

14 ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT The ECC differential output current or voltage is related to the input voltage and biasing current I as follows: (Prove that:) I C = I C1 I C2 I C = I tanh V C = V C1 V C2 V C = IR C tanh Note: tanh(x) x for x<<1 14

15 ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT To use ECC as a multiplier, the following condition must be satisfied: for << I C = I tanh I C 1 I V C = IR C tanh V C R C I The input voltage value must be less than 50mV ( ) Note: tanh(x) x for x<<1 15

16 ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT The ECC output is proportional to the multiplication of the differential input voltage and the biasing current I ECC is a two quadrant multiplier as the current I is unipolar If the current I becomes negative, Q1 and Q2 will not operate in the active mode, then the exponential equation is not valid anymore for << I C 1 I K I = 1 V C R C I K V = R C Note: tanh(x) x for x<<1 16

17 ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT The ECC can be modified to be a two quadrant voltage multiplier by replacing the biasing current source I with the circuit shown for << I = V i2 V BE,on R V C R C V i2 V BE,on V R i1 The circuit has another condition on V i2 to work as a multiplier for << & V i2 >>V BE,on V C R C R V i2 K V = R C 2RV T Figure from Gray & Mayer, Analysis and Design of Analog Integrated Circuits John Wiley & Sons, inc. 17

18 ANALOG MULTIPLIER: GILBERT CELL The ECC is used as a basic building unit for a four quadrant multiplier: Gilbert Cell The circuit is formed with three cross coupled ECCs as shown in Figure I C = I C3 5 I C4 6 I C = I C3 + I C5 I C = I C3 I C4 I C4 + I C6 + I C5 I C6 I C3 I C4 = I C1 tanh I C5 I C6 = I C2 tanh = I C2 tanh Figure from Gray & Mayer, Analysis and Design of Analog Integrated Circuits John Wiley & Sons, inc. 18

19 ANALOG MULTIPLIER: GILBERT CELL Gilbert Cell analysis (Cont.) I C = I C3 I C4 + I C5 I C6 I C = I C1 I C2 tanh I C1 I C2 = I tanh V i2 I C = I tanh tanh V i2 for & V i2 << I C I 2 V i2 K I = I 2 19

20 ANALOG MULTIPLIER: GILBERT CELL Gilbert Cell is a four quadrant multiplier The differential output current is proportional to the multiplication of the voltages and V i2 the voltages and V i2 must be less than 50mV ( ) The output current can be converted to a voltage signal V C IR C 2 V i2 K V = IR C 2 20

21 ANALOG MULTIPLIER: GILBERT CELL To remove the constraint of the input voltage to be less than 50mV, the following Circuit can be used tanh 1 V i2 tanh 1 V i2 I C = I tanh tanh V i2 21

22 ANALOG MULTIPLIER: GILBERT CELL To remove the constraint of the input voltage to be less than 50mV, the following Circuit can be used Assume Q7 and Q8 Active and matched with large β = V BE8 V BE7 = V T l n I c8 I c7 = V T ln I 2 I 1 The Differential voltage-to-current Converter has the output current given as: I 2 = I o1 + 1 R 1 I 1 = I o1 1 R 1 Figure from Gray & Mayer, Analysis and Design of Analog Integrated Circuits John Wiley & Sons, inc. 22

23 ANALOG MULTIPLIER: GILBERT CELL The Differential voltage-to-current Converter has the output current given as: = V T l n I c8 I c7 = V T ln I 2 I 1 I 2 = I o1 + 1 R 1 I 1 = I o1 1 R 1 = V T l n I o1 + 1 R 1 I o1 1 R 1 = V T ln 1 + R 1 I o1 1 R 1 I o1 Note that: l n 1 + x 1 x = 2 tanh 1 x = V T l n 1 + R 1 I o1 Vi1 1 V = tanh 1 i1 R 1 I o1 R 1 I o1 23

24 ANALOG MULTIPLIER: GILBERT CELL Now the Output differential Current of Gilbert Cell is: I C = I tanh tanh V i2 = tanh 1 R 1 I o1 V i2 = tanh 1 V i2 R 2 I o2 I C = I tanh tanh 1 R 1 I o1 tanh tanh 1 V i2 R 2 I o2 I C = I R 1 R 2 I o1 I o2 V i2 K I = I R 1 R 2 I o1 I o2 24

25 ANALOG MULTIPLIER: GILBERT CELL Circuit Implementation of Differential voltage to differential Current Converter: I o1 = V CC V BE13,on R I 1 = I o1 + R 1 I 1 = I o1 R 1 25

26 ANALOG MULTIPLIER: GILBERT CELL Assignment: Draw the complete Gilbert Cell Multiplier (Transistor Level) 26