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

2. 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: http://scholar.cu.edu.eg/anader/ Email: anader@ieee.org TA: Eng. Mazen Soliman Office hours: Sunday 4:00 – 5:00 pm Monday 4:00 – 5:00 pm 6/8/2016

3. 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 13 - 3Faculty of Engineering Cairo University 6/8/2016

4. 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

5. Lecture 1 Small-Signal Modeling and Linear Amplification (Chapter 13) Dr. Ahmed Nader Adapted from presentation by Richard C. Jaeger Travis N. Blalock Chap 13 - 5Faculty of Engineering Cairo University 6/8/2016

6. 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 13 - 6Faculty of Engineering Cairo University 6/8/2016

7. Faculty of Engineering Cairo University Review: Operation Regions of Bipolar Transistors Chap 13 - 7 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

8. 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 13 - 8 6/8/2016

9. 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 13 - 9 Collector current expression has the same form as that of the diode equation

10. 6/8/2016Faculty of Engineering Cairo University Chap 13 - 10 Common-Emitter Voltage Transfer Characteristic

11. 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 13 - 11

12. 6/8/2016Faculty of Engineering Cairo University NMOS Transistor: Saturation Region (contd.) for is also called saturation or pinch-off voltage Chap 13 - 12

13. 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 13 - 13Faculty of Engineering Cairo University 6/8/2016

14. 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 13 - 14Faculty of Engineering Cairo University 6/8/2016

15. 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 180 0 phase shift between input and output signals. Chap 13 - 15Faculty of Engineering Cairo University 6/8/2016

16. 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 13 - 16Faculty of Engineering Cairo University 6/8/2016

17. 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 13 - 17Faculty of Engineering Cairo University 6/8/2016

18. 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 13 - 18Faculty of Engineering Cairo University 6/8/2016

19. 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 13 - 19Faculty of Engineering Cairo University 6/8/2016

20. ac Equivalent for BJT Amplifier Chap 13 - 20Faculty of Engineering Cairo University 6/8/2016

21. DC and AC Equivalents for MOSFET Amplifier dc equivalent ac equivalent Simplified ac equivalent Chap 13 - 21 Full circuit Faculty of Engineering Cairo University 6/8/2016

22. 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 13 - 22

23. 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 13 - 23

24. 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 = 10 -15 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 13 - 24

25. 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 13 - 25Faculty of Engineering Cairo University 6/8/2016

26. 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 13 - 26Faculty of Engineering Cairo University 6/8/2016

27. 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 13 - 27Faculty of Engineering Cairo University 6/8/2016

28. BJT Small Signal Parameters Chap 13 - 28Faculty of Engineering Cairo University 6/8/2016

29. 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 13 - 29Faculty of Engineering Cairo University 6/8/2016

30. 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 13 - 30Faculty of Engineering Cairo University 6/8/2016

31. 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 13 - 31Faculty of Engineering Cairo University 6/8/2016

32. 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. Chap13 - 32Faculty of Engineering Cairo University 6/8/2016

33. 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 13 - 33Faculty of Engineering Cairo University 6/8/2016

34. 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 14 - 34Faculty of Engineering Cairo University 6/8/2016 What is the current gain?

35. 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 14 - 35Faculty of Engineering Cairo University 6/8/2016

36. 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 13 - 36Faculty of Engineering Cairo University 6/8/2016

37. 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 13 - 37Faculty of Engineering Cairo University 6/8/2016

38. © Ahmed Nader, 2013 38 Amplifier 6/8/2016 General Concept

39. 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 13 - 39Faculty of Engineering Cairo University 6/8/2016

40. 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 13 - 40Faculty of Engineering Cairo University 6/8/2016

41. Sample Analysis of C-E Amplifier (cont.) Next we construct the ac equivalent and simplify it. Chap 13 - 41Faculty of Engineering Cairo University 6/8/2016

42. 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 13 - 42Faculty of Engineering Cairo University 6/8/2016

43. 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 13 - 43Faculty of Engineering Cairo University 6/8/2016

44. 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 13 - 44Faculty of Engineering Cairo University 6/8/2016

45. 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 13 - 45Faculty of Engineering Cairo University 6/8/2016

46. 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 13 - 46Faculty of Engineering Cairo University 6/8/2016

47. Summary of FET and BJT Small-Signal Models Chap 13 - 47Faculty of Engineering Cairo University 6/8/2016

48. 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 13 - 48Faculty of Engineering Cairo University 6/8/2016

49. 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 13 - 49Faculty of Engineering Cairo University 6/8/2016

50. C-S Amplifier Voltage Gain: Example Problem: Calculate voltage gain Given data:  n = 0.5 mA/V 2, V TN = 1V, = 0.0133 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 13 - 50Faculty of Engineering Cairo University 6/8/2016

51. 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. Chap13 - 51Faculty of Engineering Cairo University 6/8/2016

52. C-S Amplifier Input Resistance Input resistance of C-S amplifier is much larger than that of corresponding C-E amplifier. Chap 13 - 52Faculty of Engineering Cairo University 6/8/2016

53. C-S Amplifier Output Resistance Output resistance is calculated in a manner similar to that of CE amplifier with r  infinite. Chap 13 - 53Faculty of Engineering Cairo University 6/8/2016

54. Sample Analysis of C-S Amplifier Problem: Find voltage gain, input and output resistances. Given data:  n = 500  A/V 2, V TN = 1V,  = 0.0167 V -1 Analysis: dc equivalent circuit is constructed and analyzed Chap 13 - 54Faculty of Engineering Cairo University 6/8/2016

55. Sample Analysis of C-S Amplifier (cont.) Next we construct the ac equivalent and simplify it. Chap 13 - 55Faculty of Engineering Cairo University 6/8/2016

56. Summary CE and CS Characteristics Chap 13 - 56Faculty of Engineering Cairo University 6/8/2016

57. Signal Range Constraints Chap 13 - 57 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