Lecture 4 - Dependent Sources and Amplifiers

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.

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1. Signal amplification

• Amplifier increases the magnitude of a signal:

• Amplifiers: essential components in communications, signal processing, memory, logic, etc.

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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…

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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/

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3 https://www.forbes.com/sites/bobodonnell/2019/11/22/real-world-5g-speeds/#46d1c3924f96

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• 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?

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4 2. Dependent sources

• Recall “independent” current and voltage sources:

v=V

i=I

• These are (two-terminal) one-port devices.

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• 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 – –

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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 – –

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• i-v characteristics of dependent sources: – Dependent voltage source:

0 v 0 O

V=f(vI ,iI )

– Dependent current source:

I=f(vI ,iI )

0 0 v O Demo

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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 – –

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• 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

• In order to have amplification, need:

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7 Amplifier transfer characteristics

• Graph vO-vI equation:

RLG 0

0 vI VS

RLG

Demo

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Dependent sources are used in many places, and also model transducers…

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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)

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• Superposition: only apply superposition to independent sources. Same example:

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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:

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10 • Sometimes, dependent sources are other components in disguise! Example: what are the i-v characteristics of this circuit?

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• Sometimes, dependent sources are other components in disguise! Example: what are the i-v characteristics of this circuit?

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11 How to build dependent sources?

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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

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12 • i-v characteristics of 2N7000

Saturation-controlled

(i.e. currentVoltage source!!)

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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.

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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?