Analog Computer
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