# Design of CMOS Fixed-Gain Differential Amplifiers

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## Small Signal Parameters

In many cases, we are interested to determine the dynamic parameters of CMOS circuits as the voltage gain of amplifier, input or output impedances etc. Usually, this family of parameters makes use of linearized static parameters, what refers to the 1st derivative of the I-V characteristics. The linearized parameters are called “small signal” parameters and analysis dealing these parameters is called small signal analysis.
Basically, two kinds of parameters are used in the analysis: static small signal transconductance (or conductance) g and small signal capacitance c. The interest this use can be realized during the analysis, where even a complex circuit can be modelled by a simple linear model. However, the results are only valid for signals that are relatively small as compared to eventual nonlinearities of the circuit characteristics.
The transistor MOS is described by the basic parameters:
• Gate transconductance gm.
• Channel conductance gDS.
• Body transconductance gmB.

### Parasitic Elements in the MOS Device

The aim of the mathematical description of the MOS transistor is to approximate the behaviour of a real device. However, a real MOS transistor is affected by many “secondary” parameters. A complex mathematical description of such parameters is available in the appropriate CAD models. In this section, we will focus to the most important “parasitic” elements: capacitances in the MOS device and effects arising from the low dimensions of the transistor.

#### Capacities in the MOS transistor

If the small signal model is used for the dynamic analysis (AC or transient), it has to be completed by the parasitic capacitances present in the structure. In the previous section, we have noticed, that the capacitance is considered as a small signal parameter. Generally, two types of capacitances are present in the CMOS circuits:
􀂾 Capacitances caused by device geometry.
􀂾 Variables capacitances depending on the operating point.
Since the sum of theses capacitances on the device terminals is present, the total capacitance has to be evaluated for a given operating point. The basic model, including all terminal capacitances is shown in Fig. 2.10 a) and the physical meaning of these capacitances is presented in the device model Fig. 2.10 b).
The gate-drain and gate-source overlap capacitances CGDO, CGSO, respectively, originate from the device shape. The gate electrode covers the drain and source areas and are characterized by the overlap length LD (Fig. 2.10). Since the dielectric is characterized by the thickness tox and εr, the CGDO and CGSO capacitances can be expressed as the product: 0 r GSO GDO D OX D ox C C WL C WL t ε ε = = ⋅ = ⋅ ⋅ .

Figure of Merit of the MOS Transistor

Reaching the optimal performances of electrical circuits is naturally conditioned by the optimal choice of the CMOS process. It is common, for instance, to choose a process with lower VTH, to provide a larger switching speed in digital circuits. On the contrary, from low VTH can result an unwanted higher leakage in the switch-off state which is an important drawback for a low power design.
Each process (e.g. CMOS, BiCMOs) is characterised through key parameters, as the geometrical resolution, SiO2 oxide thickness or doping concentration. In electronic design, we are interested to use rather “electrical” parameters such as KP, VTH, or some specific parameters as further introduced gm/ID or parameters describing the maximal frequency range.
One of the frequently considered parameters of the MOS transistor is the transconductance efficiency. Generally, the performances of CMOS circuits (gain, transition speed) are improved by higher transconductance. Therefore, the transconductance related to the static drain current (i.e. power consumption), expressed as gm/ID is one of the fundamental figures of merit of the transistor. The curve gm/ID=f(ID) is almost the same for all transistors fabricated on the identical technological process. This feature would allow a simple comparison between different transistors with respect to goal application. Moreover it provides an interesting tool allowing the designer to get an optimal choice of transistor operating conditions.
An example of the gm/ID=f(ID) characteristic is plotted for N-MOS and P-MOS transistors (W/L=10 μm/1 μm) operating in all important areas (e.g. velocity saturation, saturation, and subthreshold), as shown in Fig. 2.16.

I Theoretical introduction
Bolometric Detectors
1.1 Terahertz Imaging
1.2 Principal Detectors for the THz Area
1.2.1 Bolometric Detectors
1.2.2 Hot Electron Bolometric Effect
1.2.3 Variety of Bolometric Sensors
1.3 Heterodyne Detection
1.4 Noise in Bolometric Detectors
The Transistor MOS
2.1 CMOS Device Overview
2.2 Physics of the MOS Transistor
2.2.1 Semiconductors
2.2.2 Physical Overview of the MOS Transistor
2.3 Electrical Characteristics of the MOS Transistor
2.3.1 Static I-V Characteristic
2.3.2 Small Signal Parameters
2.4 Parasitic Elements in the MOS Device
2.4.1 Capacities in the MOS transistor
2.4.2 Small Scale Transistor Devices
2.4.3 Figure of Merit of the MOS Transistor
2.5 Basic process parameters
2.6 Trends in CMOS development
2.6.1 Very Low Dimension Transistors
2.6.2 Single Electron Transistor
Noise in Electronic Circuits
3.1 Noise in Electronic Circuits
3.1.1 The Random Nature of Noise
3.2 Noise Sources in Electronic Systems
3.2.1 Thermal Noise
3.2.2 The 1/fα Low Frequency Noise
3.2.3 Shot Noise
3.2.4 Non-Electrical Noise Sources
3.3 Noise Analysis, Basic Noise Characteristics
3.3.1 Signal to Noise Ratio SNR
3.3.2 Noise Figure NF
3.3.3 Noise Temperature
3.3.4 Equivalent Input Noise Voltage
3.3.5 Correlation
3.4 Noise in the MOS Transistors
3.5 Low Noise Design
3.5.1 Feedback in Electrical Circuits
3.5.2 Chopper Amplifier
3.5.3 Superconducting Quantum Interference Device
4.1 Electrical Specification of Sensors
4.2 Basic Concepts of Readout Electronics
4.2.1 Current and Voltage Bias
4.4 Differential Voltage Amplifiers
4.4.1 Dynamic Model of Operational Amplifier
4.5 Applications of Operational Amplifiers
4.5.1 Inverting Amplifier
4.5.2 Differential Amplifiers
4.5.3 Cryogenic Aspects
4.6 Specification of Amplifiers to be Designed
4.6.1 Choice of CMOS/Bipolar Process
4.6.2 Choice of Amplifier Topology
4.6.3 Specifications of Electrical Performances
4.7 Conclusion
III Design of CMOS amplifiers
Design of CMOS Fixed-Gain Differential Amplifiers
5.1 Constant Gain Amplifiers, Design Approaches
5.1.1 Structures of Feedback-Free Voltage Amplifiers
5.2 Temperature Modelling of the MOS Transistor
5.2.1 Thermal Behaviour of the MOS Transistor
5.2.2 Extraction of the Parameters
5.2.3 LS Model Parameters Fitting
5.2.4 Verification of the Model
5.3 Structures of CMOS Fixed Gain Amplifiers
5.3.1 Common Source Amplifier
5.3.2 Increasing of the Voltage Gain
5.3.4 Low gm Composite Transistor
5.3.5 Analysis of the Low gm Composite Transistor
5.3.7 Common Source Amplifier with Low gm Load
5.4 Differential Pair and Cascode Effect
5.4.1 Cascode and Folded Cascode
5.4.2 MOS Input Differential Pair
5.5 Amplifier with Low gm Composite Transistor
5.5.4 Summary of 1st Amplifier Basic Parameters
5.6 Linear Temperature Compensated Amplifier
5.6.1 Low Transconductance Linear Composite Load
5.6.2 Differential Folded Cascode with Linear Load
5.6.3 Basic Characteristics of the Linear Amplifier
5.6.4 Analysis of the Temperature Behaviour
5.6.5 Design of the Type II Amplifier
5.6.6 Performances of the 2nd (Linear) Amplifier: Summary
5.7 Output Voltage Buffer
5.7.1 Common Drain Voltage Follower
5.7.2 Linear Low Offset Voltage Buffer
Appendix: Simulated operating points
AC and Noise Analysis
6.1 AC Analysis of the Amplifier
6.1.1 AC Response of Folded Cascode Transconductor
6.1.2 Analysis of the Low gm Composite Transistor
6.1.3 CMRRatio and the Gain Symmetry
6.2 Noise of the Amplifier
6.2.1 Noise of the MOS Input Differential Pair
6.2.2 Noise of the Low Composite Transistor
6.3.3 Noise Characteristic of the Amplifiers
Integration in CMOS AMS 0.35 μm: Results
7.1 Layout of the Differential Amplifiers
7.1.1 Matching of the MOS Transistors
7.1.2 Symmetric Layout, Common Centroid Structure
7.1.3 Layout of the Amplifiers
7.2 Testing the Amplifiers
7.2.1 Test Facility
7.3 Type I Geometry-Fixed Gain Amplifier
7.3.1 DC characteristics
7.3.2 AC Performances of the 1st Amplifier
7.3.3 Wide Temperature Range Measurements
7.4 Type II Temperature-Compensated Linear Amplifier
7.4.2 AC Performances of 2nd Amplifier
7.4.3 Cryogenic measurements of Type II amplifier
7.5 Summary of Achieved Results
7.5.1 Comparison with the State-of-the-Art
Conclusion of part III
IV High performance active frequency filters
Design of active frequency filters
8.1 Frequency Filters in the Amplification Chain
8.2 Scope of the Work
8.3 Design Approaches to Active Frequency Filters
8.3.1 Approximation of Transfer Function
8.3.1 Design of Passive RLC Ladder Filters
8.3.2 Active Simulation of Passive RLC Filters
8.3.3 Cascade Synthesis of Frequency Filters
8.4 Imperfections of Frequency Filters
8.5 Digitally Controlled Analog Filtering Systems
8.5.1 Structure of the Universal Analog Frequency Filter
8.5.2 Electrical Design of Filter Blocks
8.5.3 Control Software of Frequency Filter
8.5.4 Realisation of the Instrument and Conclusion
9.2.2 Multiple Active Element Biquad: Antonius GIC
9.3 Degradation in the Stopband of LP Filters
9.3.1 Causes of the Parasitic Effect
9.3.2 attenuation of the Sallen-Key LP Section
9.3.3 The lossy RCD 2nd Order Section
9.3.4 Causes of LP Stopband Degradation
9.4 Type II Sallen-Key filter
9.5 Current Mode CCII cascade Section
Design of CMOSSecond Generation Current Conveyor CCII
10.1 Current Conveyor
10.1.1 Second Generation Current Conveyor
10.1.2 Basic Structure of the Current Conveyor
10.1.3 Real Properties of CCII
10.2 CMOS Realisation of the CCII-
10.2.1 Low Impedance Voltage Buffer
10.2.2 CCII- CMOS Current Conveyor
10.3 CMOS Integration of CCII-
10.3.1 AC & DC Characteristic of integrated Circuit
10.3.2 1.5MHz 5th order LP filter
10.4 Conclusion
Conclusion of Part III
Appendix
Summary in French
Présentation
I Electronique de lecture
I.1 Capteur bolométrique
I.2 Configuration de l’électronique de lecture
I.3 « Architecture sans contre-réaction »
II Conception des amplificateurs CMOS
II.1 Comportement thermique d’un transistor MOS
II.2 Méthode de Conception
II.3 Amplificateur de Type I
II.3 Amplificateur de type II
L’analyse thermique
II.4 Conclusion A
III Filtres de fréquences actifs
III.1 L’atténuation des filtres passe-bas
III.2 Sallen-Key de type II
III.4 Convoyeur de courant CCII
III.3 Conclusion B
References

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