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

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PHY 202 (Blum)2 Simple Digital to Analog Converter.111 corresponds to 7/8 7/8 of 5 is 4.375

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PHY 202 (Blum)3 Simple Digital to Analog Converter.100 corresponds to 1/2 1/2 of 5 is 2.5

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PHY 202 (Blum)4 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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PHY 202 (Blum)5

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6 Comparator (analog) + Input higher than – input, output is high

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PHY 202 (Blum)7 Comparator (analog) + Input lower than – input, output is low

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PHY 202 (Blum)8 1-bit analog-digital converter Reference Voltage Input voltage Input voltage is less than half of reference voltage, result is low.

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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.

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PHY 202 (Blum)10 Toward a 2-bit analog-digital converter

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PHY 202 (Blum)11 Toward a 2-bit analog-digital converter

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PHY 202 (Blum)12 Toward a 2-bit analog-digital converter

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PHY 202 (Blum)13 Toward a 2-bit analog-digital converter

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Finish this truth table >3/4 Comparator >1/2 Comparator >1/4 Comparator ½’s place¼’s place 000 001 010 011 100 101 110 111 PHY 202 (Blum)14 Doesn’t occur

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PHY 202 (Blum)15 Integrated circuit version Warning: may need to flip switch back and forth.

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PHY 202 (Blum)16 3.7 / 5 (in Scientific Mode)

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PHY 202 (Blum)17 *2x^y8=

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PHY 202 (Blum)18 Binary Mode

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PHY 202 (Blum)19 Compare

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PHY 202 (Blum)20 Scientific Mode

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PHY 202 (Blum)21 Multi-vibrators http://www.ee.ed.ac.uk/~kap/Hard/555/node1.html

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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.

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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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PHY 202 (Blum)24 Pulse STABLE UNSTABLE STABLE

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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.”

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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.

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PHY 202 (Blum)27 Schmitt trigger

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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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PHY 202 (Blum)29 Schmitt trigger The upper trip point The lower trip point Above the upper trip and going up Below the lower trip and going down

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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.

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PHY 202 (Blum)31 A-stable multi-vibrator

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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

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A-stable Multi-vibrator PHY 202 (Blum)33

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A-stable Multi-vibrator Oscilloscope PHY 202 (Blum)34

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PHY 202 (Blum)35 A-stable ON OFF low high Charge building up

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PHY 202 (Blum)36 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.

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PHY 202 (Blum)37 A-stable ON low Turns off

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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 = t high /(t high +t low )*100%

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PHY 202 (Blum)39 Duty cycle example: t high = 1.407 ms

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PHY 202 (Blum)40 Duty cycle example: t high + t low = 2.111 ms Duty cycle = (1.407/2.111) = 66.65%

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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.

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PHY 202 (Blum)42 555

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PHY 202 (Blum)43 555 as Monostable multivibrator

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PHY 202 (Blum)44 555 as Astable Multivibrator

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PHY 202 (Blum)45 555 Timer (WorkBench version)

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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.

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PHY 202 (Blum)47 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

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