Transcript Board Game Counter

Understanding Analog Design
The Random Number Generator
Digital Electronics
© 2014 Project Lead The Way, Inc.
Random Number Generator
Analog Design - Demo
This presentation will
• Review the Random Number Generator block
diagram.
• Review the circuit design of the analog section of
the Random Number Generator.
2
Random Number Generator
Block Diagram
A
Analog
Section
CLOCK
Sequential
Logic
Section
0 0 0 1 1 1
B 0 1 1 0 0 1
C 1 0 1 0 1 0
Combinational
Logic
Section
L1
L2
L3
L4
L5
L6
L7
1 2 3 4 5 6
The Analog Section
produces a dampened
square wave that “rolls”
the count and slowly
stops.
On every pulse of the
clock, the Sequential
Logic Section
increments a binary count
from 1 to 6, then repeats.
The Combinational
Logic Section
encodes the binary
count into the die’s
seven dots.
3
Random Number Generator
Block Diagram
A
Analog
Section
CLOCK
The Analog Section
produces a dampened
square wave that “rolls”
the count and slowly
stops.
Sequential
Logic
Section
B
C
On every pulse of the
clock, the Sequential
Logic Section
increments a binary count
from 1 to 6, then repeats.
Combinational
Logic
Section
L1
L2
L3
L4
L5
L6
L7
The Combinational
Logic Section
encodes the binary
count into the die’s
seven dots.
4
Random Number Generator
Analog Section
Schematic Diagram
CLOCK
5
A Simplified Version
• When the push button switch is pressed, the 100uf capacitor (C1) will
quickly charge to 5 volts through the 1.2 k resistor (R8).
• As long as the push button switch remains pressed, top end of the 10
k resistor (R9) will be held at 5volts. This results in a simplified
version that is equivalent to a standard 555 time oscillator.
Actual Version
Simplified Version
6
Analysis of Simplified Version
R A  10 k  RB  18 k 
C  470 nF
Period:
T  0.693 R A  2RB  C
RA
A
T  0.693 10 k  2  18 k   470 nF
T  14.982 mSec
RB
Frequency:
1
1

T 14.982 mSec
ƒ  66.74 Hz
ƒ
C
7
Simulation of Simplified Version
VOUT
VC
8
Simplified Version – Timing Analysis
VOUT
VC
Period:
T  15 mSec
Frequency:
1
ƒ
T
1
ƒ
15 mSec
ƒ  66.66 Hz
9
The Actual Version
• When the push button switch is pressed and held, the actual analog
section of the Board Game Counter performs like a standard 555 time
oscillator. However, for the Board Game Counter to operate correctly,
the oscillation must slow and eventually stop.
• This is where the 100uF capacitor (C1) and the 1.2 k resistor (R8)
play a role.
Actual Version
10
Simplified Version
Simulation of Actual Version
Push
Button
Pressed
Push
Button
Released
VOUT
VC
VLimit
11
Actual Version – Timing Analysis
• When the push button is
pressed, the 555 Timer
produces a 66 Hz
square wave.
• Once the push button is
released, the frequency
gradually decreases
(period increases).
Push
Button
Pressed
Push
Button
Released
VOUT
VC
VLimit
A
B
C
• Eventually the oscillation
will stop.
12
Timing Analysis at Time A
Period:
T  15.536 mSec
Frequency:
A
1
T
ƒ  64.36 Hz
ƒ
13
Timing Analysis at Time B
Period:
T  27.50 mSec
Frequency:
B
1
T
ƒ  36.36 Hz
ƒ
14
Timing Analysis at Time C
Period:
T  51.429 mSec
Frequency:
C
1
T
ƒ  19.44 Hz
ƒ
15
Random Number Generator
Analog Section
Analog
Section
Sequential
Logic
Section
Combinational
Logic
Section
16
Discussed in a future lesson