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)
https://gyazo.com/99e7adc309abe509e33ac56097826ae6
Capacitors (C)
https://gyazo.com/3e0f2d2d39e4030070cd235255dcd75a
Active circuits
Vacume tubes
https://gyazo.com/0b71d0bafb06783a38ebe48d1371ed60
Transistors
https://gyazo.com/421f3a00d8453d4ae0d7c12fdbdec4e3
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
http://gyazo.com/9613e3a5c6802479768ee80c452297e4.png
http://www.youtube.com/watch?v=4eUibFQKJqI
http://gyazo.com/294bda8926da9d8c4aaf73883e79766e.png
http://gyazo.com/1098f554a9d8190760dfe0fdd527d1ce.png
Eternal clock
http://gyazo.com/05ef29b013f05be940a6496b72801d5b.png
http://gyazo.com/ddac413408d10b7404f6e4fa2151518b.png
https://www.youtube.com/watch?v=N35jJKJKRl8
Analog computers in a narrow sense
Use electronic circuits
Especially op-amps
Calculate analog values
Solve differencial equations
Analog addition
http://gyazo.com/e828d9011808fd4599ce18a15f746d73.png
Analog multiplication
http://gyazo.com/ee618c323f74ac653805b84e8ed3804d.png
Hitachi analog computer
http://gyazo.com/0daf68e885430abacba83c76b5cd2125.png
Solving van der Pol equasion
$ {d^2 y \over {dt}^2} - \mu (1 - 10 y^2){dy \over dt} + y = 0
http://gyazo.com/c20bfc824dad6c7cb3271e8cd1a4434a.png
Solution of van der Pol equasion
https://gyazo.com/88c020279cc3c1129441d11a01271f78
Symbol for an op-amp
http://gyazo.com/b3c0a8411cef921cc06710841ab6adae.png
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
https://gyazo.com/06d3d7e97be61453e1ec3955a08a3c8b
Example: Measuring weight
Amplify small signals from a sensing device
http://gyazo.com/58ec8f6e4568698e22b947765a1bd708.png
Using a strain gauge
http://gyazo.com/dabf55e3400b07e962c2060785c2637d.png
"load cell" module
http://gyazo.com/e97d25b8d64ddbf16db4070999cec7b4.png
Found in Wii Fit and kitchen scale
Very subtle signal output
Wii Fit
4 load cells
https://gyazo.com/697b8047d0ae3b14522ba4e189ca04f8
Kitchen scale
https://gyazo.com/043cb221ace19844c758d6ffa5584ff5
Wheatstone bridge
http://gyazo.com/0d91468096a4c3ca191d7914be7668d2.png
Ohm's law
http://gyazo.com/fcdeddfdb1fb6ef75cfd6f33885d02e2.png
Circuit equation
Kirchhoff's circuit laws
http://gyazo.com/b632c2c20b93d5897977747e71fea59f.png
Wheatstone bridge
http://gyazo.com/a879483c2cd6f33e2f70e145eb5b0d8c.png
Circuit equation of Wheatstone bridge
http://gyazo.com/c2eec45feb582339bf49599b44a967a4.png
Generating signals
Oscillator
Function generator
https://gyazo.com/464cbb58d20ff39c8b68ffbee00e24a2
Signal filtering
LPF (Low-pass filter)
HPF (High-pass filter)
BPF (Band-pass filter)
Low-pass filter
https://gyazo.com/17240d6305e75d9d59f1fbdb422b6c32
Music synthesizer
http://gyazo.com/f7edb08ee0577f9f6dc02e8f53450258.png
Sine wave, saw wave, etc.
Signal filters
Ideal op-amp
http://gyazo.com/b3c0a8411cef921cc06710841ab6adae.png
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
http://gyazo.com/07c210c3a2249eabbbabcd03dd36cfc5.png
μA741
http://gyazo.com/e3784544d45742b19a40aa64e0b8ab07.png
Inside of μA741
http://gyazo.com/4f0cedd54caf96be90e332c6d21f8d1a.png
Inverting amplifier
http://gyazo.com/1f8fe56e7b9381c2369450c39d70956f.png
Inverting amplifier
http://gyazo.com/8f36053af76bf689824367624b49d1af.png
Inverting amplifier
http://gyazo.com/bb484c46fb253b0563341e797fef11aa.png
Non-inverting amplifier
http://gyazo.com/d228365f8efc169d9f86414f0dfefefb.png
Voltage follower
http://gyazo.com/67250acb95d1044852f27733c8d2d4ff.png
Differential amplifier
http://gyazo.com/7cca4d29bcff79081e0210cf92f2a3af.png
Summation circuit
http://gyazo.com/1ab50a7c3d8434b9094e27cf1c67441c.png
Using negative feedbacks
Using inverse function
http://gyazo.com/688fb1653f1bbecb59fbc11515a9e0ff.png
Calculating square root
http://gyazo.com/6d8703f6c4746ffa79a50c3b5dba32ab.png
Logarithm circuit
http://gyazo.com/66535a90b0e75fd76b54e19b45fd870f.png
http://gyazo.com/4364e32f26d0f3f2bcc259e6afe2f7f4.png
Logarithm circuit
http://gyazo.com/17711505f0375183bb5aafa58133f3cb.png
Exponential circuit
http://gyazo.com/25ec4dee248a463a396ae4386e54572b.png
Multiplier circuit
http://gyazo.com/3a5c38829f1d1aae4e7396d2076633e6.png
Transistor-based multiplier circuit
http://gyazo.com/ecc6d2edf5db16458d7af3f5b4c90361.png
Differential calculus
Calculate$ dV_{in} \over dt
http://gyazo.com/cc431022b678a6c2db57858bc9358f88.png
Integration
Calculate $ \int V_{in} dt
http://gyazo.com/07fdd9593a936008429f1f2ec94d768b.png
Integration
http://gyazo.com/e5cd7ee0b9def4c9169575591d569e4d.png
Comparator
http://gyazo.com/65b1f7d61fbf1c57635e712c064e76ad.png
Hysteresis comparator
http://gyazo.com/f2a83371306dee5d0a378e9b9ba2cda5.png
http://gyazo.com/42a4b93babc216ebdf92ab0ed8379e27.png
Oscillator
Hysteresis comparator + Integrator
http://gyazo.com/d150975c96844086e6a370098a380ba6.png
Signal filters
Manage frequency characteristic
Filters
http://gyazo.com/32442e6e5628a48d8e3031f8ce7324b4.png
Low-pass filter
http://gyazo.com/f69dc97fa3f6b1dac0bb7f813faa82ed.png
High-pass filter
http://gyazo.com/1e498e0335db99715a554badee4d71e0.png
Analog computer
Simple calculation
Summation, log/exp, etc.
Solving differential equation
Analog computer museum
http://web.archive.org/web/20100721013502im_/http://dcoward.best.vwh.net/analog/atitle.gif http://www.analogcomputermuseum.org/index.html
Analog Computer Museum
Elements used in an analog computer
http://gyazo.com/0af2074bf7dabe00eb587b237046188a.png
Differential equation for a spring
http://gyazo.com/b74471b31471218aac8902e0a22dbc98.png
http://gyazo.com/837922696977db030a42cb6c0d7b4a71.png
$ m {d^2x \over {dt}^2} + c { dx \over dt} + kx = F
m: Mass
c: Friction
k: Strength of the spring
F: External force
Changing the formula
http://gyazo.com/7436304056c397c10e834828f31c0bfa.png
Constructing an analog computer with integrators
http://gyazo.com/49b0b3528ade2fbbccf2e8ebc9b83e63.png
Reducing components
http://gyazo.com/06eb3cabfe37602d9f8d34b4b45b1a1d.png
http://gyazo.com/d25cae770c251e4fe7e207de5103d8b9.png
Drawing a chaotic signal using a XY plotter
http://gyazo.com/44563859953ad97f528607888798b3c6.png
Plotted drawing
http://gyazo.com/dead13aa9e1803908f3703196bed8aa4.png
Schematics
http://gyazo.com/7e6c8f159a8c60529f2714696eab7052.png
LTSpice
SPICE
https://gyazo.com/8796257d2e82cfef275e90e1fc36f9f2
Linear Technology
Acquired by Analog Devices in March, 2017
https://gyazo.com/bff559074ed3ad1fadf91de845fa8c9b
Simulation by LTSpice
http://ntoshio.la.coocan.jp/rakuen/spice/anacom/index.htm https://gyazo.com/29533207ff4d81dc991a56ef517ba0c9
http://gyazo.com/2a708a2ab1ba3492c6f5f64322aba32e.png
http://gyazo.com/c20bfc824dad6c7cb3271e8cd1a4434a.png
Conclusions
Analog computers are actually out of date
But the concept is still interesting
Op-amps are useful everywhere
Everyone should know the basics