_講義資料: アナログコンピュータ

講義資料: アナログコンピュータ

(expanded from Analog Computer このページは編集しないでください)

Toshiyuki Masui
2018/7/18

Why analog circuit and analog computer?
Simply interesting!
Useful for understanding ubicomp devices
Old technologies helpful sometimes

Analog circuits
Passive circuits
Active circuits

Passive circuits
Registers (R)
Capacitors (C)

Active circuits
Vacume tubes
Transistors

Analog computers
In a broad sense
Electronic/mechanic systems for solving problems
In a narrow sense
Op-amp-based circuits for solving mathematical problems

Various analog computers
Slide rules
Antikythera mechanism
"Eternal clock"
Sundial
Mechanical clock

Slide rule


Eternal clock

Analog computers in a narrow sense
Use electronic circuits
Especially op-amps
Calculate analog values
Solve differencial equations

Analog addition

Analog multiplication

Hitachi analog computer

Solving van der Pol equasion

Solution of van der Pol equasion


Symbol for an op-amp

Op-amp characteristics
Simple analog signal processing
Arbitrary function with feedback circuits
With passive components (R, C)
With active components

Op-amp usage
Signal amplification
Mathemetical operations
Signal comparison
Signal filtering
Signal generation

Signal amplification

Example: Measuring weight
Amplify small signals from a sensing device

Using a strain gauge
"load cell" module
Found in Wii Fit and kitchen scale
Very subtle signal output

Wii Fit
4 load cells

Kitchen scale

Wheatstone bridge

Ohm's law

Circuit equation
Kirchhoff's circuit laws

Wheatstone bridge

Circuit equation of Wheatstone bridge

Generating signals
Oscillator
Function generator

Signal filtering
LPF (Low-pass filter)
HPF (High-pass filter)
BPF (Band-pass filter)

Low-pass filter

Music synthesizer
Sine wave, saw wave, etc.
Signal filters

Ideal op-amp
Voltage difference between + and - will be multiplied by ∞
Using a feedback circuit
⇒ Eventually, the voltage at + and - will become the same
"Virtual Short"

Ideal op-amp
Infinite open-loop gain
Zero output impedance
Infinite current from output terninal
Infinite input impedance
No current to input terminal
No delay

Available op-amps
μA741
LM301A
RC4558
TL07x

μA741

μA741

Inside of μA741

Inverting amplifier

Inverting amplifier

Inverting amplifier

Non-inverting amplifier

Voltage follower

Differential amplifier

Summation circuit

Using negative feedbacks
Using inverse function

Calculating square root

Logarithm circuit

Logarithm circuit

Exponential circuit

Multiplier circuit

Transistor-based multiplier circuit

Differential calculus
Calculate

Integration
Calculate

Integration

Comparator

Hysteresis comparator

Oscillator
Hysteresis comparator + Integrator

Signal filters
Manage frequency characteristic

Filters

Low-pass filter

High-pass filter

Analog computer
Simple calculation
Summation, log/exp, etc.
Solving differential equation

Analog computer museum

Analog Computer Museum

Elements used in an analog computer

Differential equation for a spring

m: Mass
c: Friction
k: Strength of the spring
F: External force

Changing the formula

Constructing an analog computer with integrators

Reducing components


Drawing a chaotic signal using a XY plotter

Plotted drawing

Schematics

LTSpice

SPICE

Linear Technology
Acquired by Analog Devices in March, 2017


Simulation by LTSpice




Conclusions
Analog computers are actually out of date
But the concept is still interesting
Op-amps are useful everywhere
Everyone should know the basics

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