CIRCUITS AND 6.002 ELECTRONICS Lecture 4 - Dependent Sources and Amplifiers February 13th, 2020 Contents: 1. Signal amplification 2. Dependent sources 3. Circuits with dependent sources 4. Transistors and MOSFETs (to be continued) Reading Assignment: Agarwal and Lang, Ch. 2 (§2.6), Ch. 3 (§§3.3.3, 3.5.1), Ch. 7 (§§7.1, 7.2) Handouts: Lecture 4 notes Announcement: Please do prelab 2 and lab 2 analysis in advance. 6.002 Spring 2020 Lecture 4 1 1 1. Signal amplification • Amplifier increases the magnitude of a signal: • Amplifiers: essential components in communications, signal processing, memory, logic, etc. 6.002 Spring 2020 Lecture 4 2 2 1 • Signal amplification brings signal to reQuired level and enhances noise tolerance: – Without amplification: 10 mV 1 mV noise useful signal huh? – With amplification: noise AMP not bad! 6.002 Spring 2020 Lecture 4 3 3 Amplifiers… 6.002 Spring 2020 Lecture 4 4 4 2 Amplifier research today… https://www.researchgate.net/figure/a- Block-diagram-of-the-transmitter-unit-in- the-wireless-implantable-neural- recording_fig1_224500155 6.002 Spring 2020 Lecture 4 5 5 Amplifier research today… https://www.mpdigest.com/2018/10/24/gan-power-amplifiers-serving-satellite- industry-on-multiple-levels/ 6.002 Spring 2020 Lecture 4 6 6 3 https://www.forbes.com/sites/bobodonnell/2019/11/22/real-world-5g-speeds/#46d1c3924f96 6.002 Spring 2020 Lecture 4 7 7 • Amplifier is a 3-port system: Power port iI iO Output Input + + v port – vI Amplifier – O port …but often power port not explicitly shown. • All ports are referenced to a common “ground” node: POWER IN OUT • How do we build an amplifier? 6.002 Spring 2020 Lecture 4 8 8 4 2. Dependent sources • Recall “independent” current and voltage sources: v=V i=I • These are (two-terminal) one-port devices. 6.002 Spring 2020 Lecture 4 9 9 • Dependent sources are two-port devices: – Control port: sets the value of the source – Output port: source terminals • Types of dependent current sources: – Voltage-controlled current source: iI iO + + v f (v ) output control I I vO port port – – – Current-controlled current source: iI iO + + v f (i ) output control I I vO port port – – 6.002 Spring 2020 Lecture 4 10 10 5 • Dependent voltage sources: – Voltage-controlled voltage source: iI iO + + v f (v ) + output control I I - vO port port – – – Current-controlled voltage source: iI iO + + v f (i ) + output control I I - vO port port – – 6.002 Spring 2020 Lecture 4 11 11 • i-v characteristics of dependent sources: – Dependent voltage source: iO 0 v 0 O V=f(vI ,iI ) – Dependent current source: iO I=f(vI ,iI ) 0 0 v O Demo 6.002 Spring 2020 Lecture 4 12 12 6 • How does one make an amplifier with a dependent source? • Consider the following circuit: + R VS – i L I iO + + + Gv vO vI – vI I – – 6.002 Spring 2020 Lecture 4 13 13 • Analyzing the circuit: V + RL S – i I iO + + + v GvI vO vI – I – – • vO linearly proportional to vI à no distortion • Notice minus sign: output is out of phase from input à not generally a problem vI vO • In order to have amplification, need: 6.002 Spring 2020 Lecture 4 14 14 7 Amplifier transfer characteristics • Graph vO-vI equation: vO VS RLG 0 0 vI VS RLG Demo 6.002 Spring 2020 Lecture 4 15 15 Dependent sources are used in many places, and also model transducers… 6.002 Spring 2020 Lecture 4 16 16 8 3. Circuits with dependent sources • Solving circuits with dependent sources reQuires special care. • Node method: Express dependent source in terms of node voltages. G(e1-e2) 6.002 Spring 2020 Lecture 4 17 17 • Superposition: only apply superposition to independent sources. Same example: 6.002 Spring 2020 Lecture 4 19 19 9 • Thévenin and Norton. When computing Thévenin or Norton resistance, the dependent source should not be turned off. Example: Open circuit calculation: Note: R2 branch open, u=0, then Gu=0, then voc=V. 6.002 Spring 2020 Lecture 4 20 20 Thévenin resistance: Turn off V but not Gu! Equation for node e: Solve for e: Then: And: 6.002 Spring 2020 Lecture 4 21 21 10 • Sometimes, dependent sources are other components in disguise! Example: what are the i-v characteristics of this circuit? 6.002 Spring 2020 Lecture 4 22 22 • Sometimes, dependent sources are other components in disguise! Example: what are the i-v characteristics of this circuit? 6.002 Spring 2020 Lecture 4 23 23 11 How to Build dependent sources? 6.002 Spring 2020 Lecture 4 25 25 4. Transistors… The MOSFET • MOSFET=Metal-Oxide-Semiconductor Field-Effect Transistor • MOSFET=three terminal semiconductor device • In the MOSFET: Current through two terminals (source and drain) controlled by voltage in third terminal (gate). • A modern microprocessor contains ~108-3x109 MOSFETs Intel 22 nm MOSFET 6.002 Spring 2020 Lecture 4 26 26 12 • i-v characteristics of 2N7000 Saturation-controlled (i.e. currentVoltage source!!) 6.002 Spring 2020 Lecture 4 27 27 Summary • Amplifiers: enhance the magnitude of a signal, essential to cope with noise. • In a dependent source, magnitude of source depends on a voltage or current at a control port. • Can build amplifier with one dependent source and one resistor. • Solving circuits with dependent sources reQuire special care: – In node method, express dependent source magnitude in terms of node voltages – Only apply superposition over independent sources – Never turn off dependent source when computing Thévenin resistance • MOSFET transistors behave like voltage-controlled current sources when they are biased in saturation. 6.002 Spring 2020 Lecture 4 28 28 13 Amplification DAC from Lab 2 3.3 V GPIO pins + DAC Teensy VO speaker VO<3.3 - V GND Resistive networks can only attenuate signals How can we amplify signals? 29 14.