Waves

Digitising analogue data

Analogue

• What we see in the real world around us

• Continuously varying– Temperature– Land contours– Speed– Time

Tem

p

Time

But how do we make measurements

• We cannot record measurements continuously (too much storage)

• Once every second? Minute? Millisecond?

Tem

p

Time

And we record with a certain granularity too

• 15oC• 15.4oC• 15.358oC• 15.358374864826535243oC• So we have compromised on both axes – we can’t

be sure of the temperature at all between the measuring points, and we don’t know the exact temperature at any moment anyway

This is what we have to do to digitise data

• We lose information – inevitably

• Analogue data is continuous– Digital data has a discrete set of values

• But there are big advantages– Computers can handle the data when digitised– It allows us to store, process and transmit the

data more easily

Just 1s and 0s

• Analog to Digital Convertor (ADC)– Converts wave form to binary – Samples at known rate– Known resolution

• Say waveform 0 ≤ V ≤ 10 at 8 bits

• Step = 10 /256 = .039v per step

Logic levels

• Problem: A voltage on a wire is actually an analogue signal! It is continuously varying.

• HIGH may be interpreted as (e.g.) any time the voltage is between 2V and 5V

• LOW may be any time it is between 0V and 0.8V

VH(max)

VH(min)

VL(max)

VL(min)

HIGH (Binary 1)

Uncertain

LOW (Binary 0)

Digital waveforms

• A pulse is generated when a signal goes from LOW to HIGH, and back again (+ve pulse)

• A pulse has a rising edge, and a falling edge

Rising (leading) edge

Falling (trailing) edge

Rising (trailing) edge

Falling (leading) edge

Negative-going pulsePositive-going pulse

Not so simple

• The figures on the last slide are ideal – instantaneous change between HIGH and LOW

• But reality is not like that– The waves take time to transition from HIGH

to LOW

A digital wave

90%

10%

tr tf

50%tw

Pulse width

Voltage (pulse)

amplitude

Overshoot and ringing

These effects are caused by capacitance and inductance in the circuit

Waveform Characteristics

• Most waveforms encountered are composed of a series of pulses, sometimes called pulse trains, and can be classified as either periodic or nonperiodic.

• A periodic pulse train pulses at a fixed interval, called a period (T). The frequency (f) is the rate at which it beats (pulses) itself and is measured in hertz (Hz).

• The frequency (f) of a pulse waveform is the reciprocal of the period, f = 1/T

Periodic

Nonperiodic

Duty Cycle

• An important characteristic of a periodic waveform is its duty cycle. This is defined as the ratio of the pulse width (tw) to the period (T) expressed as a percentage, – Duty cycle = (tw/T) × 100% tw

T

Exercise: for the diagram, work out the:

a) periodb) frequencyc) duty cycle 0 1 3 t (ms)

Many digital systems are synchronised with a waveform called the clock

The Clock

This is a periodic waveform in which each interval between pulses (the period) equals one bit time

Timing diagrams

You’ll often see diagrams like this, showing the time relationship between waveforms

The Integrated Circuit• Used almost exclusively

• Low power consumption

• Small

• Reliable

• Cheap

ICs• One single piece of silicon

• All the components – transistors, diodes, resistors and capacitors – are an integral part of that chip

• Various types of package exist

Pin numbering

All IC packages have a standard format for numbering the pins (leads).

Pin 1 is always identified by either a small dot or a notch or a bevelled edge. Starting with pin 1, the numbering is always anti-clockwise as viewed looking down upon the package