PHY 202 (Blum)1 Analog-to-Digital Converter and Multi-vibrators.

PHY 202 (Blum) 1

Analog-to-Digital Converter and Multi-vibrators

PHY 202 (Blum) 2

Simple Digital to Analog Converter

V15 V

J1

Key = AJ2

Key = B

J3

Key = CR11.0k

R22.0k

R34.02k

R44.02k

U1DC 10M4.377 V

+

-

.111 corresponds to 7/8

7/8 of 5 is 4.375

PHY 202 (Blum) 3

Simple Digital to Analog Converter

V15 V

J1

Key = AJ2

Key = B

J3

Key = CR11.0k

R22.0k

R34.02k

R44.02k

U1DC 10M2.503 V

+

-

.100 corresponds to 1/2

1/2 of 5 is 2.5

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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

PHY 202 (Blum) 5

PHY 202 (Blum) 6

Comparator (analog)

U1

COMPARATOR_VIRTUALV13.1 V V2

3 V

R11.0k

U2DC 10M4.651 V

+

-

+ Input higher than – input, output is high

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Comparator (analog)U1

COMPARATOR_VIRTUALV12.9 V V2

3 V

R11.0k

U2DC 10M0.000 V

+

-

+ Input lower than – input, output is low

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1-bit analog-digital converter

V15 V

R11.0k

R21.0k

V22.4 V

U1

COMPARATOR_VIRTUAL

X1

2.5 V

Reference Voltage

Input voltage

Input voltage is less than half of reference voltage, result is low.

PHY 202 (Blum) 9

1-bit analog-digital converter

Reference Voltage

Input voltage

Input voltage is more than half of reference voltage, result is high.

V15 V

R11.0k

R21.0k

V22.6 V

U1

COMPARATOR_VIRTUAL

X1

2.5 V

PHY 202 (Blum) 10

Toward a 2-bit analog-digital converter

V15 V

R11.0k

R21.0k

V24 V

U1

COMPARATOR_VIRTUAL

X1

2.5 VGreater than 3/4

R41.0k

R51.0k

U2

COMPARATOR_VIRTUALU3

COMPARATOR_VIRTUAL

X2


X3


PHY 202 (Blum) 11


V15 V

R11.0k

R21.0k

V22.6 V

U1

COMPARATOR_VIRTUAL

X1


R41.0k

R51.0k

U2


COMPARATOR_VIRTUAL

X2


X3


PHY 202 (Blum) 12


V15 V

R11.0k

R21.0k

V22.2 V

U1

COMPARATOR_VIRTUAL

X1


R41.0k

R51.0k

U2


COMPARATOR_VIRTUAL

X2


X3


PHY 202 (Blum) 13


V15 V

R11.0k

R21.0k

V21.1 V

U1

COMPARATOR_VIRTUAL

X1


R41.0k

R51.0k

U2


COMPARATOR_VIRTUAL

X2


X3


Finish this truth table

>3/4 Comparator

>1/2 Comparator

>1/4 Comparator

½’s place ¼’s place

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

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Doesn’t occur

PHY 202 (Blum) 15

Integrated circuit version

Warning: may need to flip switch back and forth.

PHY 202 (Blum) 16

3.7 / 5 (in Scientific Mode)

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* 2 x^y 8 =

PHY 202 (Blum) 18

Binary Mode

PHY 202 (Blum) 19

Compare

PHY 202 (Blum) 20

Scientific Mode

PHY 202 (Blum) 21

Multi-vibrators

http://www.ee.ed.ac.uk/~kap/Hard/555/node1.html

PHY 202 (Blum) 22

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.

PHY 202 (Blum) 23

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 UNSTABLESTABLE

PHY 202 (Blum) 25

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.”

PHY 202 (Blum) 26

Shapers

• Another purpose of mono-stable multi-vibrators is to “shape” input signals.

• Recall in digital circuits we want signals to be clearly high or low; a mono-stable multi-vibrator can take signals which are not of this form and create signals which are.

PHY 202 (Blum) 27

Schmitt trigger

PHY 202 (Blum) 28

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

The lower trip point

Above the upper trip and going up

Below the lower trip and going down

PHY 202 (Blum) 30

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.

PHY 202 (Blum) 31

A-stable multi-vibrator

R11.0kR2

10.0k

V15 V

C1

2.0uF

C2

2.0uF

J1

Key = Space

Q1

BJT_NPN_VIRTUAL

Q2

BJT_NPN_VIRTUAL

R31.0k R4

10.0k

XSC1

A B

G

T

PHY 202 (Blum) 32

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

A-stable Multi-vibrator

PHY 202 (Blum) 33

A-stable Multi-vibrator Oscilloscope

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A-stable

ON OFF

low

high

Charge building up

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A-stable

• Charge builds up on the left capacitor, “pulling-up” 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.

PHY 202 (Blum) 37

A-stable

ON

low

Turns off

PHY 202 (Blum) 38

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%

PHY 202 (Blum) 39

Duty cycle example: thigh = 1.407 ms

PHY 202 (Blum) 40

Duty cycle example: thigh + tlow = 2.111 msDuty cycle = (1.407/2.111) = 66.65%

PHY 202 (Blum) 41

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.

PHY 202 (Blum) 42

555

PHY 202 (Blum) 43

555 as Monostable multivibrator

PHY 202 (Blum) 44

555 as Astable Multivibrator

PHY 202 (Blum) 45

555 Timer (WorkBench version)

U1

LM555CM

GND

1

DI S7

OUT 3RST4

VCC

8

THR6

CON5

TRI2

V15 V

C11.0uF

C210nF

R11.0k

R21.0k

XSC1

A B

G

T

PHY 202 (Blum) 46

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.

PHY 202 (Blum) 47

References

• http://www.ee.ed.ac.uk/~kap/Hard/555/node2.html#modes

• http://en.wikipedia.org/wiki/555_timer_IC

• http://www.kpsec.freeuk.com/555timer.htm

PHY 202 (Blum)1 Analog-to-Digital Converter and Multi-vibrators.

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Transcript of PHY 202 (Blum)1 Analog-to-Digital Converter and Multi-vibrators.