Transcript Analog-to-Digital Converter and Multivibrators

Analog-to-Digital Converter
and Multi-vibrators
PHY 202 (Blum)
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Simple Digital to Analog Converter
V1
5V
.111
corresponds to
7/8
J1
Key = A
J2
Key = B
7/8 of 5 is 4.375
J3
Key = C
R1
1.0k
R2
2.0k
R4
4.02k
R3
4.02k
+
-
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4.377
V
U1
DC 10M
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Simple Digital to Analog Converter
V1
5V
.100
corresponds to
1/2
J1
Key = A
J2
Key = B
1/2 of 5 is 2.5
J3
Key = C
R1
1.0k
R2
2.0k
R4
4.02k
R3
4.02k
+
-
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2.503
V
U1
DC 10M
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Analog-to-Digital
• We have seen a simple digital-to-analog converter,
now we consider the reverse process
• For this purpose we introduce a new circuit
element — the comparator
• We have seen last semester a digital comparator, a
logic circuit that determined whether the input
word A is larger than the input word B
• Now we look at an analog comparator, it
determines whether voltage A is larger than
voltage B
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Comparator (analog)
U1
V1
3.1 V
COMPARATOR_VIRTUAL
V2
3V
R1
1.0k
+
-
4.651
V
U2
DC 10M
+ Input higher than – input, output is high
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Comparator (analog)
U1
V1
2.9 V
COMPARATOR_VIRTUAL
V2
3V
R1
1.0k
+
-
0.000
V
U2
DC 10M
+ Input lower than – input, output is low
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1-bit analog-digital converter
R1
1.0k
V2
2.4 V
V1
5V
U1
COMPARATOR_VIRTUAL
R2
1.0k
Reference Voltage
PHY 202 (Blum)
Input voltage
X1
2.5 V
Input voltage is
less than half of
reference
voltage, result is
low.
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1-bit analog-digital converter
R1
1.0k
V2
2.6 V
V1
5V
U1
COMPARATOR_VIRTUAL
R2
1.0k
Reference Voltage
PHY 202 (Blum)
Input voltage
X1
2.5 V
Input voltage is
more than half
of reference
voltage, result is
high.
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Toward a 2-bit analog-digital converter
R1
1.0k
V2
4V
V1
5V
R2
1.0k
U1
X1
2.5 V
Greater than 3/4
COMPARATOR_VIRTUAL
U2
X2
2.5 V
Greater than 1/2
R4
1.0k
COMPARATOR_VIRTUAL
U3
X3
2.5 V
Greater than 1/4
R5
1.0k
PHY 202 (Blum)
COMPARATOR_VIRTUAL
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Toward a 2-bit analog-digital converter
R1
1.0k
V2
2.6 V
V1
5V
R2
1.0k
U1
X1
2.5 V
Greater than 3/4
COMPARATOR_VIRTUAL
U2
X2
2.5 V
Greater than 1/2
R4
1.0k
COMPARATOR_VIRTUAL
U3
X3
2.5 V
Greater than 1/4
R5
1.0k
PHY 202 (Blum)
COMPARATOR_VIRTUAL
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Toward a 2-bit analog-digital converter
R1
1.0k
V2
2.2 V
V1
5V
R2
1.0k
U1
X1
2.5 V
Greater than 3/4
COMPARATOR_VIRTUAL
U2
X2
2.5 V
Greater than 1/2
R4
1.0k
COMPARATOR_VIRTUAL
U3
X3
2.5 V
Greater than 1/4
R5
1.0k
PHY 202 (Blum)
COMPARATOR_VIRTUAL
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Toward a 2-bit analog-digital converter
R1
1.0k
V2
1.1 V
V1
5V
R2
1.0k
U1
X1
2.5 V
Greater than 3/4
COMPARATOR_VIRTUAL
U2
X2
2.5 V
Greater than 1/2
R4
1.0k
COMPARATOR_VIRTUAL
U3
X3
2.5 V
Greater than 1/4
R5
1.0k
PHY 202 (Blum)
COMPARATOR_VIRTUAL
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Finish this truth table
>3/4
Comparator
>1/2
Comparator
>1/4
Comparator
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
½’s place
¼’s place
Doesn’t occur
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Integrated circuit version
PHY 202 (Blum)
Warning: may need to
flip switch back and
forth.
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3.7 / 5 (in Scientific Mode)
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*
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2
x^y
8
=
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Binary Mode
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Compare
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Scientific Mode
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Multi-vibrators
http://www.ee.ed.ac.uk/~kap/Hard/555/node1.html
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Multi-vibrator
• A multi-vibrator is an electronic circuit that
can exist in a number of “states” (voltage
and/or current outputs).
• A flip-flop is a bi-stable multi-vibrator,
bi-stable means it has two stable states.
• A state is stable if it is robust against the
fluctuations (noise) that are always
occurring.
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Mono-stable multi-vibrator
• A mono-stable multi-vibrator has one stable
output (usually zero).
• It also has an unstable state. Certain input will
put the circuit into its unstable state, which lasts
for a set length of time before returning to the
stable state.
– Unstable states are still robust to noise but do not last
indefinitely long.
• In wave terminology, this provides one with a
single pulse.
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Pulse
STABLE
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UNSTABLE
STABLE
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One shots
• One purpose of a mono-stable multi-vibrator is to
output a signal of a specified duration.
• The input (trigger) may be short (or unknown) in
duration, but the output pulse has a predictable
duration (can be controlled by the time constant
of an RC circuit).
–  = RC
– The time constant and duration are not equal but
are proportional.
• Such a circuit is called a “one shot.”
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Shapers
• Another purpose of mono-stable multivibrators is to “shape” input signals.
• Recall in digital circuits we want signals to
be clearly high or low; a mono-stable multivibrator can take signals which are not of
this form and create signals which are.
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Schmitt trigger
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Schmitt trigger
• If the voltage is above a certain value (the
upper trip point) and rising, the output is
high.
• If the voltage is below another value (the
lower trip point) and falling, the output is
low.
• Otherwise, it remains whatever it was.
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Schmitt trigger
The upper trip point
Above the upper
trip and going up
The lower trip point
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Below the lower trip
and going down
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A-stable multi-vibrator
• In an a-stable multi-vibrator, there are
typically two states, neither of which is
stable.
• The circuit repeatedly flips back and forth
between the states.
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A-stable multi-vibrator
J1
Key = Space
R3
1.0k
R2
10.0k
XSC1
R1
1.0k
R4
10.0k
G
T
C1
A
B
C2
V1
5V
2.0uF
Q2
BJT_NPN_VIRTUAL
PHY 202 (Blum)
2.0uF
Q1
BJT_NPN_VIRTUAL
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A-stable Multi-vibrator
• Assume a state where the transistor on left
is ON and transistor on right is OFF and
the capacitor on the left has no charge.
• Since the left transistor is on (hard) it is not
dropping much voltage, therefore “all” the
voltage is being dropped by the resistors
• The capacitor on the left begins to charge
through the 10K resistor on the right
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A-stable Multi-vibrator
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A-stable Multi-vibrator
Oscilloscope
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A-stable
high
low
ON
OFF
Charge building up
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A-stable
• Charge builds up on the left capacitor, “pullingup” the voltage presented to the base of the
transistor on the right.
• When the base reaches about 0.7v the transistor
on the right turns on.
• Current now starts to flow through the 1K resistor
on the far right, thus dropping the voltage level at
the collector.
• That low voltage makes its way to the base of the
transistor on the left turning it off.
• The cycle repeats itself.
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A-stable
low
Turns
off
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ON
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Duty cycle
• In a square wave (e.g. a computer’s clock),
the wave is characterized by its frequency,
its amplitude and its duty cycle.
• The duty cycle is the percent of time that
the signal is high.
• Duty cycle = thigh/(thigh+tlow)*100%
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Duty cycle example: thigh = 1.407 ms
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Duty cycle example: thigh + tlow = 2.111 ms
Duty cycle = (1.407/2.111) = 66.65%
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555 Timer
• A similar circuit uses the 555 chip
(Integrated circuit)
• The resistors and capacitors are external to
the chip so that the period and duty cycle of
the circuit can be controlled.
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555
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555 as Monostable multivibrator
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555 as Astable Multivibrator
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555 Timer (WorkBench version)
XSC1
R1
1.0k
G
T
A
8
U1
VCC
V1
5V
C2
10nF
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RST
7
DIS
6
THR
2
TRI
5
CON
OUT
3
B
R2
1.0k
C1
1.0uF
GND
1
LM555CM
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Crystals
• The very high frequency square wave used
for the CPU clocks are not generated in the
manner described on the previous slides.
• The high frequency signal is supplied by
crystals subjected to an electric field.
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References
• http://www.ee.ed.ac.uk/~kap/Hard/555/node
2.html#modes
• http://en.wikipedia.org/wiki/555_timer_IC
• http://www.kpsec.freeuk.com/555timer.htm
PHY 202 (Blum)
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