MICROELECTRONICS ELCT 703 (W19) LECTURE 1: ANALOG MULTIPLIERS Dr. Eman Azab Assistant Professor Office: C3.315 E-mail: [email protected] DR. EMAN AZAB ELECTRONICS DEPT., FACULTY OF IET THE GERMAN UNIVERSITY IN CAIRO 1
MICROELECTRONICS ELCT 703 (W19) LECTURE 1: ANALOG MULTIPLIERS
Dr. Eman Azab
Assistant Professor
Office: C3.315
E-mail:
[email protected]. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
1
COURSE OVERVIEWCourse Team
Lecturer
Dr. Eman AzabE-mail: [email protected]
Office: C3.315
Office hours: Via E-mail
Teaching
Assistant
Eng.: Radwa KhairyE-mail: [email protected]
Office: C3.307
Office hours: Via E-mail
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
2
Teaching Method Location
One Lecture per Week
(Thursday 2nd Slot)H6
One Tutorial per Week
(Tuesday 1st/3rd)
Check Your
Schedule
Evaluation Method Percentage %
Assignments 10
Quizzes 15
Project 10
Mid-Term 25
Final 40
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
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
3
TENTATIVE COURSE SCHEDULELecture # Lecture Description
1Revision: Differential Amplifiers & Analog
MultipliersAnalog Multipliers Transistor level design
2 &3 Feedback and Power Amplifiers Feedback Theory in Electronic Circuits and Power amplifiers
4 & 5 Op-amp Circuit design & non-idealities Op-amp Circuit design on the transistor level & Non-ideal
characteristics of Op-amp Circuit realization
6 Compensation TheoryCompensation theory: How to design Stable closed loop systems
using Op-amp?
7 & 8 Op-amp Circuit Applications Linear and Non-linear Closed-loop Applications using Op-amps
9 Active-RC Filters Op-amp based Filters
10 & 11 Switched Capacitors Circuits SC Circuits Design Concept and Applications
12Operational Trans-conductance Amplifiers
Circuit design & ApplicationsOTA CMOS Transistor Level Circuit Design
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
4
TENTATIVE COURSE EVALUATION SCHEDULE
Assignment Quiz Project
Milestone 1: CMOS Op-
amp Modeling (Verilog A)
Quiz 1: Feedback and
Compensation Theory
Milestone 2: CMOS Op-
amp Circuit Design
(Simulation)
Milestone 3: Op-amp
Application (Simulation)
Assignment 1: Feedback and
Compensation Theory
Mid-Term
Milestone 4: PCB for Op-
amp Application
(Hardware)
Assignment 2: Research Paper
Part 1
Quiz 2: Op-amp
nonlinear Applications
Assignment 3: Research Paper
Part 2
Quiz 3: OTA-C/Switched
cap Filters
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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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 e-mail for urgent questions
Attend the lectures and take notes!
All the Course material will be available on the website
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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REFERENCES1. “Analysis and Design of Analog Integrated Circuits”, Gray,
Hurst, Lewis & Meyer
2. “ Fundamentals of Microelectronics”, Razavi
3. “ Design of Analog CMOS Integrated Circuits”, Razavi
4. “Analog Integrated Circuit Design”, Johns & Martin
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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ANALOG MULTIPLIERS Transistor level Circuit
Design
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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ANALOG MULTIPLIERS: INTRODUCTIONAnalog Multiplier is a circuit that takes two analog inputs (I/V) andgenerate an output proportional to their Product
K is the multiplication gain factor
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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𝑋𝑜𝑢𝑡 = 𝐾 𝑋𝑖1 × 𝑋𝑖2
Multiplier
(K)
Xi1
Xi2
Xout
ANALOG MULTIPLIER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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Amplitude Modulation Illustration
The circuit is used in communication systems for modulation/demodulation
ANALOG MULTIPLIER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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Analog Multipliers can be one, two or four quadrant multipliers
This classification depends on the polarity of the input signals
Multiplier
(K)
Xi1
Xi2
Xout
Multiplier Xi1 Xi2
Single (one) Quadrant Unipolar Unipolar
Two Quadrant Unipolar Bipolar
Four Quadrant Bipolar Bipolar
ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT
Emitter Coupled Circuit can beused as a two Quadrant analogmultiplier
It is formed with two matchedBJT with their emitters connectedtogether
Assume Q1 and Q2 are Active and βF
is large
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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𝐼𝐸1 + 𝐼𝐸2 = 𝐼
𝐼𝐶1 = 𝐼𝑠𝑒𝑉𝐵𝐸1𝑉𝑇 𝐼𝐶2 = 𝐼𝑠𝑒
𝑉𝐵𝐸2𝑉𝑇
𝐼𝐶1 ≅ 𝐼𝐸1 & 𝐼𝐶2 ≅ 𝐼𝐸2
Where Is is the reverse saturation current and VT is the thermal voltage
(25mV @ room temperature)
ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT
The input voltage Vi1 changesthe collector currents
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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𝑉𝑖1 = 𝑉𝐵𝐸1 − 𝑉𝐵𝐸2𝐼𝐶2𝐼𝐶1
= 𝑒−𝑉𝑖1𝑉𝑇
𝐼𝐶1 + 𝐼𝐶2 = 𝐼𝐶1 + 𝐼𝐶1𝑒−𝑉𝑖1𝑉𝑇 ≅ 𝐼
𝐼𝐶1 =𝐼
1 + 𝑒−𝑉𝑖1𝑉𝑇
𝐼𝐶2 =𝐼
1 + 𝑒𝑉𝑖1𝑉𝑇
ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT
The ECC differential output current orvoltage is related to the input voltage“Vi1” and biasing current “I” as follows:(Prove that:)
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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∆𝐼𝐶 = 𝐼𝐶1 − 𝐼𝐶2
∆𝐼𝐶 = 𝐼 tanh𝑉𝑖12𝑉𝑇
∆𝑉𝐶 = −𝐼𝑅𝐶 tanh𝑉𝑖12𝑉𝑇
∆𝑉𝐶 = 𝑉𝐶1 − 𝑉𝐶2
Note: tanh(x) ≈ x for x<<1
ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT
To use ECC as a multiplier, the followingcondition must be satisfied:
The input voltage Vi1 value must be lessthan 50mV (2VT)
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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Note: tanh(x) ≈ x for x<<1
for Vi1<<2VT
∆𝑉𝐶 ≅ −𝑅𝐶2𝑉𝑇
𝐼 𝑉𝑖1
∆𝐼𝐶 ≅1
2𝑉𝑇𝐼 𝑉𝑖1∆𝐼𝐶 = 𝐼 tanh
𝑉𝑖12𝑉𝑇
∆𝑉𝐶 = −𝐼𝑅𝐶 tanh𝑉𝑖12𝑉𝑇
ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT
The ECC output is proportional to themultiplication of the differential inputvoltage “Vi1” and the biasing current “I”
ECC is a two quadrant multiplier as thecurrent “I” is unipolar
If the current “I” becomes negative, Q1 and Q2will not operate in the active mode, then theexponential equation is not valid anymore
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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for Vi1<<2VT
∆𝑉𝐶 ≅ −𝑅𝐶2𝑉𝑇
𝐼 𝑉𝑖1∆𝐼𝐶 ≅1
2𝑉𝑇𝐼 𝑉𝑖1
𝐾𝑉 = −𝑅𝐶2𝑉𝑇
𝐾𝐼 =1
2𝑉𝑇 Note: tanh(x) ≈ x for x<<1
ANALOG MULTIPLIER: EMITTER COUPLED CIRCUIT
The ECC can be modified to be a twoquadrant voltage multiplier by replacingthe biasing current source “I” with thecircuit shown
The circuit has another condition on “Vi2”to work as a multiplier
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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for Vi1<<2VT
𝐼 =𝑉𝑖2 − 𝑉𝐵𝐸,𝑜𝑛
𝑅
∆𝑉𝐶 ≅ −𝑅𝐶2𝑉𝑇
𝑉𝑖2 − 𝑉𝐵𝐸,𝑜𝑛𝑅
𝑉𝑖1
for Vi1<<2VT & Vi2>>VBE,on
∆𝑉𝐶 ≅ −𝑅𝐶2𝑉𝑇𝑅
𝑉𝑖2𝑉𝑖1 𝐾𝑉 = −𝑅𝐶2𝑅𝑉𝑇
Figure from Gray & Mayer, “Analysis and Design of Analog Integrated Circuits”
John Wiley & Sons, inc.
ANALOG MULTIPLIER: GILBERT CELL
The ECC is used as a basicbuilding unit for a four quadrantmultiplier: Gilbert Cell
The circuit is formed with threecross coupled ECCs as shown inFigure
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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∆𝐼𝐶 = 𝐼𝐶3−5 − 𝐼𝐶4−6
∆𝐼𝐶 = 𝐼𝐶3 + 𝐼𝐶5 − 𝐼𝐶4 + 𝐼𝐶6
∆𝐼𝐶 = 𝐼𝐶3 − 𝐼𝐶4 + 𝐼𝐶5 − 𝐼𝐶6
𝐼𝐶3 − 𝐼𝐶4 = 𝐼𝐶1 tanh𝑉𝑖12𝑉𝑇
𝐼𝐶5 − 𝐼𝐶6 = 𝐼𝐶2 tanh −𝑉𝑖12𝑉𝑇
= −𝐼𝐶2 tanh𝑉𝑖12𝑉𝑇
Figure from Gray & Mayer, “Analysis and Design of Analog Integrated Circuits”
John Wiley & Sons, inc.
ANALOG MULTIPLIER: GILBERT CELL
Gilbert Cell analysis (Cont.)
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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∆𝐼𝐶 = 𝐼𝐶3 − 𝐼𝐶4 + 𝐼𝐶5 − 𝐼𝐶6
𝐼𝐶1 − 𝐼𝐶2 = 𝐼 tanh𝑉𝑖22𝑉𝑇
∆𝐼𝐶 = 𝐼𝐶1 − 𝐼𝐶2 tanh𝑉𝑖12𝑉𝑇
∆𝐼𝐶 = 𝐼 tanh𝑉𝑖12𝑉𝑇
tanh𝑉𝑖22𝑉𝑇
for Vi1 & Vi2 <<2VT
∆𝐼𝐶 ≅𝐼
2𝑉𝑇2𝑉𝑖1𝑉𝑖2 𝐾𝐼 =
𝐼
2𝑉𝑇2
ANALOG MULTIPLIER: GILBERT CELL
Gilbert Cell is a four quadrantmultiplier
The differential output current isproportional to the multiplication ofthe voltages “Vi1” and “Vi2”
the voltages “Vi1” and “Vi2” mustbe less than 50mV (2VT)
The output current can beconverted to a voltage signal
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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∆𝑉𝐶 ≅ −𝐼𝑅𝐶2𝑉𝑇
2𝑉𝑖1𝑉𝑖2 𝐾𝑉 = −
𝐼𝑅𝐶2𝑉𝑇
2
ANALOG MULTIPLIER: GILBERT CELL
To remove the constraint of the input voltage to be less than 50mV, thefollowing Circuit can be used
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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𝑉𝑖1′ ∝ tanh−1 𝑉𝑖1
𝑉𝑖2′ ∝ tanh−1 𝑉𝑖2
∆𝐼𝐶 = 𝐼 tanh𝑉𝑖1′
2𝑉𝑇tanh
𝑉𝑖2′
2𝑉𝑇
ANALOG MULTIPLIER: GILBERT CELL
To remove the constraint of the inputvoltage to be less than 50mV, thefollowing Circuit can be used
Assume Q7 and Q8 Active and matched withlarge β
The Differential voltage-to-current Converterhas the output current given as:
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
22Figure from Gray & Mayer, “Analysis and Design of Analog Integrated Circuits”
John Wiley & Sons, inc.
𝑉𝑖1′ = 𝑉𝐵𝐸8 − 𝑉𝐵𝐸7
𝑉𝑖1′ = 𝑉𝑇𝑙 𝑛
𝐼𝑐8𝐼𝑐7
= 𝑉𝑇𝑙𝑛𝐼2𝐼1
𝐼2 = 𝐼𝑜1 +1
𝑅1𝑉𝑖1 𝐼1 = 𝐼𝑜1 −
1
𝑅1𝑉𝑖1
ANALOG MULTIPLIER: GILBERT CELL
The Differential voltage-to-current Converterhas the output current given as:
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
23
𝑉𝑖1′ = 𝑉𝑇𝑙 𝑛
𝐼𝑐8𝐼𝑐7
= 𝑉𝑇𝑙𝑛𝐼2𝐼1
𝐼2 = 𝐼𝑜1 +1
𝑅1𝑉𝑖1 𝐼1 = 𝐼𝑜1 −
1
𝑅1𝑉𝑖1
𝑉𝑖1′ = 𝑉𝑇𝑙 𝑛
𝐼𝑜1 +1𝑅1
𝑉𝑖1
𝐼𝑜1 −1𝑅1
𝑉𝑖1
= 𝑉𝑇𝑙𝑛1 +
𝑉𝑖1𝑅1𝐼𝑜1
1 −𝑉𝑖1𝑅1𝐼𝑜1
𝑙 𝑛1 + 𝑥
1 − 𝑥= 2 tanh−1 𝑥
𝑉𝑖1′ = 𝑉𝑇𝑙 𝑛
1 +𝑉𝑖1𝑅1𝐼𝑜1
1 −𝑉𝑖1𝑅1𝐼𝑜1
= 2𝑉𝑇 tanh−1
𝑉𝑖1𝑅1𝐼𝑜1
Note that:
ANALOG MULTIPLIER: GILBERT CELL
Now the Output differential Current of Gilbert Cell is:
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
24
∆𝐼𝐶 = 𝐼 tanh𝑉𝑖1′
2𝑉𝑇tanh
𝑉𝑖2′
2𝑉𝑇
𝑉𝑖1′ = 2𝑉𝑇 tanh
−1𝑉𝑖1𝑅1𝐼𝑜1
𝑉𝑖2′ = 2𝑉𝑇 tanh
−1𝑉𝑖2𝑅2𝐼𝑜2
∆𝐼𝐶 = 𝐼 tanh2𝑉𝑇 tanh
−1 𝑉𝑖1𝑅1𝐼𝑜1
2𝑉𝑇tanh
2𝑉𝑇 tanh−1 𝑉𝑖2
𝑅2𝐼𝑜22𝑉𝑇
∆𝐼𝐶 =𝐼
𝑅1𝑅2𝐼𝑜1𝐼𝑜2𝑉𝑖1𝑉𝑖2 𝐾𝐼 =
𝐼
𝑅1𝑅2𝐼𝑜1𝐼𝑜2
ANALOG MULTIPLIER: GILBERT CELL
Circuit Implementation of Differential voltage to differential CurrentConverter:
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
25
𝐼𝑜1 =𝑉𝐶𝐶 − 𝑉𝐵𝐸13,𝑜𝑛
𝑅
𝐼1 = 𝐼𝑜1 +𝑉𝑖1𝑅1
𝐼1 = 𝐼𝑜1 −𝑉𝑖1𝑅1
ANALOG MULTIPLIER: GILBERT CELL
Assignment: Draw the complete Gilbert CellMultiplier (Transistor Level)
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
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