ELCN 201 Analog & Digital Electronics Dr. Ahmed Nader Dr. Ahmed Hussein Fall 2013 Faculty of Engineering Cairo University 6/8/2016

Faculty of Engineering Cairo University Grading Final Exam40 Term work60 Quizzes20 Project(s)20 Mid-Term Exam20 Text book: Microelectronic Circuit Design by Richard C. Jaeger & Travis N. Blalock Website: TA: Eng. Mazen Soliman Office hours: Sunday 4:00 – 5:00 pm Monday 4:00 – 5:00 pm 6/8/2016

Introduction Electronic Circuits can be divided into 2 main categories 1- Analog  Operational Amplifiers  Applications (Linear and Non-linear)  Waveform generation (Oscillators), analog multiplier (Mixer), phase detection (PLL) 2- Digital  Logic gates (TTL, ECL, CMOS)  Applications (Flip Flops, Counters, Memory, ) Chap Faculty of Engineering Cairo University 6/8/2016

Faculty of Engineering Cairo University Syllabus WeekLecture/Studio Topic Assignment 1Small signal model (BJT + MOS) 1 2Linear amplification 1 3Single stage amplifiers (CE/CS,CB/CG,CC/CD) 2 4Differential amplifiers 3 5Multistage amplifiers 4 6Frequency Response: transfer function 5 7Short circuit time constant method Miller effect and HF analysis 5 8 Current Sources 9Advanced Current Sources 10Digital logic 11Digital logic 12Digital logic 13Digital logic 14 6/8/2016

Lecture 1 Small-Signal Modeling and Linear Amplification (Chapter 13) Dr. Ahmed Nader Adapted from presentation by Richard C. Jaeger Travis N. Blalock Chap Faculty of Engineering Cairo University 6/8/2016

Chapter Goals Understanding of concepts related to: Transistors as linear amplifiers dc and ac equivalent circuits Use of coupling and bypass capacitors and inductors to modify dc and ac equivalent circuits Small-signal voltages and currents Small-signal models transistors (BJT and MOS) Amplifier characteristics such as voltage gain, input and output resistances and linear signal range Identification of common-source and common-emitter amplifiers Rule-of-thumb estimates for voltage gain of common-emitter and common-source amplifiers. Chap Faculty of Engineering Cairo University 6/8/2016

Faculty of Engineering Cairo University Review: Operation Regions of Bipolar Transistors Chap Base-Emitter Junction Base-Collector Junction Reverse BiasForward Bias Forward-Active Region (Good Amplifier) Saturation Region (Closed Switch) Reverse Bias Cutoff Region (Open Switch) Reverse-Active Region (Poor Amplifier) Binary Logic States 6/8/2016

Faculty of Engineering Cairo University i-v Characteristics of Bipolar Transistor: Common-Emitter Output Characteristics For i B = 0, transistor is cutoff. If i B > 0, i C also increases. For v CE > v BE, npn transistor is in forward-active region, i C =  F i B is independent of v CE. For v CE < v BE, transistor is in saturation. For v CE < 0, roles of collector and emitter reverse. Chap /8/2016

Faculty of Engineering Cairo University i-v Characteristics of Bipolar Transistor: Common-Emitter Transfer Characteristic Defines relation between collector current and base-emitter voltage of transistor. Almost identical to transfer characteristic of pn junction diode Setting v BC = 0 in the collector-current expression yields Chap Collector current expression has the same form as that of the diode equation

6/8/2016Faculty of Engineering Cairo University Chap Common-Emitter Voltage Transfer Characteristic

6/8/2016Faculty of Engineering Cairo University NMOS Transistor: Saturation Region If v DS increases above triode region limit, channel region disappears, also said to be pinched-off. Current saturates at constant value, independent of v DS. Saturation region operation mostly used for analog amplification. Chap

6/8/2016Faculty of Engineering Cairo University NMOS Transistor: Saturation Region (contd.) for is also called saturation or pinch-off voltage Chap

Introduction to Amplifiers BJT is used as an amplifier when biased in the forward-active (active) region FET can be used as amplifier if operated in the saturation (pinch-off) region In these regions, transistors can provide high voltage, current and power gains Bias is provided to stabilize the operating point in a desired operation region Q-point also determines –Small-signal parameters of transistor –Voltage gain, input resistance, output resistance –Maximum input and output signal amplitudes –Power consumption Chap Faculty of Engineering Cairo University 6/8/2016

BJT Amplifier BJT is biased in active region by dc voltage source V BE. Q-point is set at (I C, V CE ) = (1.5 mA, 5 V) with I B = 15  A. Total base-emitter voltage is: Collector-emitter voltage is: This is the load line equation. Chap Faculty of Engineering Cairo University 6/8/2016

BJT Amplifier (cont.) 8 mV peak change in v BE gives 5  A change in i B and 0.5 mA change in i C. 0.5 mA change in i C produces a 1.65 V change in v CE. If changes in operating currents and voltages are small enough, then i C and v CE waveforms are undistorted replicas of input signal. Small voltage change at base causes large voltage change at collector. Voltage gain is given by: Minus sign indicates phase shift between input and output signals. Chap Faculty of Engineering Cairo University 6/8/2016

MOSFET Amplifier MOSFET is biased in active region by dc voltage source V GS. Q-point is set at (I D, V DS ) = (1.56 mA, 4.8 V) with V GS = 3.5 V. Total gate-source voltage is: 1 V p-p change in v GS gives 1.25 mA p-p change in i D and 4 V p-p change in v DS. Chap Faculty of Engineering Cairo University 6/8/2016

Coupling and Bypass Capacitors AC coupling through capacitors is used to inject ac input signal and extract output signal without disturbing Q-point Capacitors provide negligible impedance at frequencies of interest and provide open circuits at dc. C 1 and C 3 are large-valued coupling capacitors or dc blocking capacitors whose reactance at the signal frequency is designed to be negligible. C 2 is a bypass capacitor that provides a low impedance path for ac current from emitter to ground, thereby removing R E (required for good Q-point stability) from the circuit when ac signals are considered. Chap Faculty of Engineering Cairo University 6/8/2016

dc and ac Analysis DC analysis: –Find dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits. –Find Q-point from dc equivalent circuit by using appropriate large- signal transistor model. AC analysis: –Find ac equivalent circuit by replacing all capacitors by short circuits, inductors by open circuits, dc voltage sources by ground connections and dc current sources by open circuits. –Replace transistor by small-signal model –Use small-signal ac equivalent to analyze ac characteristics of amplifier. –Combine end results of dc and ac analysis to yield total voltages and currents in the network. Chap Faculty of Engineering Cairo University 6/8/2016

dc Equivalent for BJT Amplifier All capacitors in original amplifier circuits are replaced by open circuits, disconnecting v I, R I, and R 3 from circuit. Chap Faculty of Engineering Cairo University 6/8/2016

ac Equivalent for BJT Amplifier Chap Faculty of Engineering Cairo University 6/8/2016

DC and AC Equivalents for MOSFET Amplifier dc equivalent ac equivalent Simplified ac equivalent Chap Full circuit Faculty of Engineering Cairo University 6/8/2016

Faculty of Engineering Cairo University Small-Signal Operation of Diode The slope of the diode characteristic at the Q-point is called the diode conductance and is given by: g d is small but non-zero for I D = 0 because slope of diode equation is nonzero at the origin. Diode resistance is given by: Chap

6/8/2016Faculty of Engineering Cairo University Small-Signal Operation of Diode (cont.) Subtracting I D from both sides of the equation, For i d to be a linear function of signal voltage v d, This represents the requirement for small-signal operation of the diode. Chap

6/8/2016Faculty of Engineering Cairo University Current-Controlled Attenuator Magnitude of ac voltage v o developed across diode can be controlled by value of dc bias current applied to diode. From dc equivalent circuit I D = I, From ac equivalent circuit, For R I = 1 k , I S = A, If I = 0, v o = v i, magnitude of v i is limited to only 5 mV. If I = 100  A, input signal is attenuated by a factor of 5, and v i can have a magnitude of 25 mV. Chap

Small-Signal Model of BJT Using 2-port y-parameter network, The port variables can represent either time-varying part of total voltages and currents or small changes in them away from Q-point values.  o is the small-signal common- emitter current gain of the BJT. Chap Faculty of Engineering Cairo University 6/8/2016

Hybrid-Pi Model of BJT The hybrid-pi small-signal model is the intrinsic representation of the BJT. Small-signal parameters are controlled by the Q-point and are independent of geometry of the BJT Transconductance: Input resistance: Output resistance: Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Current Gain and Amplification Factor of BJT  o >  F for i C I M, however,  F and  o are assumed to be equal. Amplification factor is given by: For V CE << V A,  F represents maximum voltage gain individual BJT can provide and doesn’t change with operating point. Chap Faculty of Engineering Cairo University 6/8/2016

BJT Small Signal Parameters Chap Faculty of Engineering Cairo University 6/8/2016

Equivalent Forms of Small-Signal Model for BJT Voltage -controlled current source g m v be can be transformed into current-controlled current source, Basic relationship i c =  i b is useful in both dc and ac analysis when BJT is in forward-active region. Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Operation of BJT For linearity, i c should be proportional to v be with Change in i c that corresponds to small-signal operation is: Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Model for pnp BJT For pnp transistor Signal current injected into base causes decrease in total collector current which is equivalent to increase in signal current entering collector. Identical to that of npn transistor Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Analysis of Complete C-E Amplifier: ac Equivalent Ac equivalent circuit is constructed by assuming that all capacitances have zero impedance at signal frequency and dc voltage sources are ac ground. Assume that Q-point is already known. Chap Faculty of Engineering Cairo University 6/8/2016

Input applied to Base Output appears at Collector Emitter is common (through R E ) to both input and output signal - Common-Emitter (CE) Amplifier. is the terminal voltage gain of the CE amplifier. Small-Signal Analysis of Complete C-E Amplifier: Small-Signal Equivalent Chap Faculty of Engineering Cairo University 6/8/2016

Common-Emitter (CE): Terminal Voltage Gain Using alternate small-signal model form and test source v b to drive the base terminal of the transistor, neglecting r o, For and Solving for i b and substituting, Chap Faculty of Engineering Cairo University 6/8/2016 What is the current gain?

Common-Emitter (CE): Input Resistance and Signal Source Voltage Gain Rewriting the previous equation, we can find the impedance looking into the base terminal: is the impedance in the emitter side of the transistor reflected to the base side. Combining equations, the overall voltage gain can be written as: Chap Faculty of Engineering Cairo University 6/8/2016

C-E Amplifier Voltage Gain Example with R E = 0 Problem: Calculate voltage gain Given data:  F = 100, V A = 75 V, Q-point is (1.45 mA, 3.41 V), R 1 = 10 k , R 2 = 30 k  R 3 = 100 k , R C = 4.3 k  R I = 1k . Assumptions: Transistor is in active region,  O =  F. Signals are low enough to be considered small signals. Analysis: Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Model Simplification For max gain For maximum gain we set R 3 >> R C and load resistor R C << r o. If we assume I C R C =  V CC with 0 <  < 1 Typically,  = 1/3, since common design allocates one-third power supply across R C. To further account for other approximations leading to this result, we use: Also, if the load resistor approaches r o (R C and R 3 infinite), voltage gain is limited by amplification factor,  f of BJT itself. For large R E, voltage gain can be aproximated as: Chap Faculty of Engineering Cairo University 6/8/2016

© Ahmed Nader, Amplifier 6/8/2016 General Concept

C-E Amplifier Output Resistance Output resistance is the total equivalent resistance looking into the output of the amplifier at coupling capacitor C 3. Input source is set to 0 and a test source v x is applied at output. Chap Faculty of Engineering Cairo University 6/8/2016

Sample Analysis of C-E Amplifier Problem: Find voltage gain, input and output resistances. Given data:  F = 65, V A = 50 V Assumptions: Active-region operation, V BE = 0.7 V, small signal operating conditions. Analysis: To find the Q-point, dc equivalent circuit is constructed. Chap Faculty of Engineering Cairo University 6/8/2016

Sample Analysis of C-E Amplifier (cont.) Next we construct the ac equivalent and simplify it. Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Model for the MOSFET Using 2-port y-parameter network, The port variables can represent either time-varying part of total voltages and currents or small changes in them away from Q-point values. Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Parameters of MOSFET Since gate is insulated from channel by gate-oxide input resistance of transistor is infinite. Small-signal parameters are controlled by the Q-point. For same operating point, MOSFET has lower transconductance and lower output resistance that BJT. Transconductance: Output resistance: Amplification factor for V DS <<1: Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Operation of MOSFET For linearity, i d should be proportional to v gs: Since the MOSFET can be biased with (V GS - V TN ) equal to several volts, it can handle much larger values of v gs than corresponding the values of v be for the BJT. Change in drain current that corresponds to small-signal operation is: Chap Faculty of Engineering Cairo University 6/8/2016

Body Effect in Four-terminal MOSFET Drain current depends on threshold voltage which in turn depends on v SB. Back-gate transconductance is: 0 <  < 1 is called back-gate tranconductance parameter. Bulk terminal is a reverse-biased diode. Hence, no conductance from bulk terminal to other terminals. Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Model for PMOS Transistor For PMOS transistor Positive signal voltage v gg reduces source- gate voltage of the PMOS transistor causing decrease in total current exiting drain, equivalent to an increase in the signal current entering the drain. Chap Faculty of Engineering Cairo University 6/8/2016

Summary of FET and BJT Small-Signal Models Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Analysis of Complete C-S Amplifier: ac Equivalent ac equivalent circuit is constructed by assuming that all capacitances have zero impedance at signal frequency and dc voltage sources represent ac grounds. Assume that Q-point is already known. Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Analysis of Complete CS Amplifier: Small-Signal Equivalent Noting similarity to CE case, Terminal voltage gain between gate and drain is found as: With r  infinite, R iG is also infinite, therefore overall voltage gain from source v i to output voltage across R L is: Chap Faculty of Engineering Cairo University 6/8/2016

C-S Amplifier Voltage Gain: Example Problem: Calculate voltage gain Given data:  n = 0.5 mA/V 2, V TN = 1V, = V -1, Q-point is (1.45 mA, 3.86 V), R 1 = 430 k , R 2 = 560 k  R 3 = 100 k , R D = 4.3 k  R I = 1 k . Assumptions: Transistor is in active region. Signals are low enough to be considered small signals. Analysis: Chap Faculty of Engineering Cairo University 6/8/2016

Small-Signal Model Simplification If we assume R I << R G Generally R 3 >> R D and load resistor << r o. Hence, total load resistance on drain is R D. For this case, common design allocates half the power supply for voltage drop across R D and (V GS - V TN ) = 1V Also, if load resistor approaches r o, (R D and R 3 infinite), voltage gain is limited by amplification factor,  f of the MOSFET itself. This implies that total signal voltage at input appears across gate-source terminals. Chap Faculty of Engineering Cairo University 6/8/2016

C-S Amplifier Input Resistance Input resistance of C-S amplifier is much larger than that of corresponding C-E amplifier. Chap Faculty of Engineering Cairo University 6/8/2016

C-S Amplifier Output Resistance Output resistance is calculated in a manner similar to that of CE amplifier with r  infinite. Chap Faculty of Engineering Cairo University 6/8/2016

Sample Analysis of C-S Amplifier Problem: Find voltage gain, input and output resistances. Given data:  n = 500  A/V 2, V TN = 1V,  = V -1 Analysis: dc equivalent circuit is constructed and analyzed Chap Faculty of Engineering Cairo University 6/8/2016

Sample Analysis of C-S Amplifier (cont.) Next we construct the ac equivalent and simplify it. Chap Faculty of Engineering Cairo University 6/8/2016

Summary CE and CS Characteristics Chap Faculty of Engineering Cairo University 6/8/2016

Signal Range Constraints Chap Minimum output voltage set by active region constraints of Q, maximum set by drop across R C. For a sine wave with peak V M, we can express the limits as: Faculty of Engineering Cairo University 6/8/2016