Electronics (F.5 & C.3)

Mr. JeanApril 16th, 2014

The plan:

• Analog to Digital• Storage Devices and systems• Amplifiers• Input / Output• Gain• Comparator• Schmitt Trigger

Analogue Signals

Analogue Use

• Sound transmission is an example of an analogue signal– When you speak into a microphone the change in

pressure causes the inside of the microphone to vibrate and change the potential difference

– This signal can be fed through an amplifier which will increase the strength of the signal reproducing the signal but louder

Analogue Storage• Vinyl Records– A record is made of plastic that has a thin groove

cut into it by a needle that moves at the same frequency as the sound it is recording

– Playback involves a needle connected to a circuit that follows the grooves

Analogue Storage

• Audio Tape– A tape also uses an analogue signal to store data.

Instead of varying grooves however, the tape, which is made out of magnetic material, has varying magnetic fields.

– To record, the tape is run through an electromagnet which varies the field at the same rate as the sound signal

Digital Signals

• A digital signal does not vary over time but rather changes from one discrete value to another.– In a circuit with a switch and a light bulb, the bulb

is on when the switch is closed and off when the switch is open

Digital Signals

Binary Number Systems

• “There are 10 kinds of people in the world, those who understand binary and those who don’t”

• Digital Signals are encoded/stored using the binary number system– This is a system of 1’s and 0’s– Our normal numbering system uses a base-

10 system while the binary system uses a base-2 system

Binary Number System

Base 10 3 2 1 0

1000 100 10 1

Base 2 3 2 1 0

8 4 2 1

Decimal Binary

1 00000001

2 00000010

3 00000011

4 00000100

5 00000101

ASCII CodeA 01000001B 01000010C 01000011D 01000101

Binary Number System

• In the binary number system, each 1 or 0 is called a bit– There are 8 bits in a byte • An 8 bit system has 8 places 00000000• A 128-bit encryption has 128 places• With the 8-bit system all western characters can be

coded• Each symbol (letter, number, etc.) takes up 1 byte of

memory

LSB and MSB

• Least significant bit – bit that is farthest to the right– Determines whether the number will be even or odd.– Changes with any small number change

• Most significant bit – bits farthest to the left– Don’t change unless there is a large number change– Often 000

• 0000101 LSB is 1 and MSB is 0

Converting to Binary

• Find the largest power of 2 that is less that the decimal

• Subtract that number from the initial• Repeat until you reach 20

• Convert 67 to binary

– 01000011

7 6 5 4 3 2 1 00 2 1 2 0 2 0 2 0 2 0 2 1 2 1 2x x x x x x x x

Analogue to Digital Conversion• Analogue signals can be converted to digital

by breaking the analogue signal into discrete values (generally pd)– The more values that are used, the more accurate

the digital signal will be, but more storage space will be required

Analogue to Digital Conversion

• The quantized values (pd) can then be converted into binary– If the quantized values range from -6V to +6V this

can be represented most easily by the numbers 0 – 12

– A 4-bit system can be used to represent these numbers (0000 – 1100)

– As long as the bit rate is known, the signal can then be converted back to a pd.

Sampling Rate

• The sampling rate is how often the pd is measured and recorded– The higher the sampling rate, the more accurate

the digital conversion will be– Nyquist theory states that to record a certain

frequency the sample rate needs to be at least 2x the frequency• This is so at least 1 peak value and 1 trough value can

be recorded

Sample Rate

• Here there are 22 samples taken for every cycle. What if there were only 2? 4? Etc.?

Storage on a CD

• Basic structure of a CD

– Information is stored on the CD as a series of bumps and flats pressed into the aluminum

Storage on a CD

• The data is ‘read’ by a laser that shines along the tracks– The light reflected off of the flat sections will be

read as a ‘1’, – If the pit/bump is just the right depth the light

reflected off will destructively interfere with itself and the lack of light will be read as a ‘0’

Storage on a CD

• Destructive Interference Review:

– The reflected wave must be a ½ λ (π) out of phase

Storage on a CD

• How deep do the pits need to be?– If light with a wavelength of 780nm is used to read

a CD, what is the minimum depth the pits need to be?• The light that hits the pit travels 2d farther than the

light reflected from the flat portions.

22780 195

4 4

d

nmd nm

Reading a CD

• So ‘0’s are actually read every time depth changes – Both the start of a pit and the end

CD vs. DVD

• CDs can hold about 650MB of info while DVDs can hold about 4.7 GB– DVDs use light with a wavelength of about 640 nm

which means that smaller (thinner) pits can be read

– This is because of the resolution of the light, shorter wavelengths can be resolved (separated) more clearly

Analogue vs. Digital Storage

• Benefits of Digital– Quality and Corruption

• Digital data is far less likely to be corrupted– On a tape the magnetic fields can fade, on an LP the tracks will wear– Even if a CD wears, the distinction between a 1 and a 0 is still

apparent

– Accurate Reproducibility• Data can be stored and retrieved with much more accuracy in

digital form

– Greater Portability and Capacity– Easier to Manipulate

Analogue vs. Digital Storage

• Benefits of Analogue Storage– With analogue there is the potential for infinite

signal variation• Digital is constrained by the number of bits

– Processing and retrieving equipment is simpler (not necessarily easier to use)

Implications of digital data storage

• What possible negative could all this cool technology have?

Operational Amplifier

• An amplifier is a device that takes a signal and makes its bigger.– An mp3 player gives out a very small pd that you

can hear with your headphones– If you connect it to a pair of speakers the sound

can be amplified with a power source• An operation amplifier (op-amp) can be made

to do more than just amplify signals, based on how it is wired

Op-Amp

• An actual op amp is a small black rectangle called a chip– The chip has 8 ‘legs’ or connections but only 5 are

used for our purposes– Inside the chip is a complicated circuit composed of

transistors and resistors that we don’t need to be concerned with

Op Amp• In the top diagram (how an op

amp is represented in a circuit diagram);– The inputs are where the signal is

fed into the amp– The output is where the amplified

signal comes out– The +/- V is where the supply

(power is connected)• This is the energy that is used to

amplify the signal

– In a circuit diagram the V+ and V- are often omitted

The Ideal Op Amp

• An ideal operational amplifier has three primary characteristics– Infinite input impedance– Zero output impedance– Infinite gain

Input impedance

• This is essentially the resistance that would be measured across the input terminals– This means that the input current to the amplifier

is negligible– The amplifier measures the difference between

the two inputs

Output Impedance

• The output of an op amp is like a power source– It can be used to power loudspeakers, lightbulbs,

etc.– The output impedance is equal to the internal

resistance of the power source• In an ideal op amp this is zero

– To get a current to flow through a load resistor there must be a pd across it• This is done by connecting the resistor to a wire at 0V.

This is called an earth or ground

Open Loop Gain

• If a very small pd is applied between the inputs, a large potential is created on the output– The ratio: is called the open loop gain of the

amplifier• This value is typically in the range of 106

• This means that if the pd between the input terminals were 0.01V, then the output potential would be 10000 V• In an ideal op amp this is infinite but it is controlled by

the supply voltage

0

( )V

V V

Gain

• A lone op amp is not particularly useful for amplifying music– If the open loop gain is 106, once the signal goes

above 0.000009 V, the output will be a constant 9V with a 9V supply

– The amplifier must be able to produce a signal that is the same as the input but with a larger amplitude

Inverting Op Amp• An op amp is said to be inverting if the + (non-

inverting) input is grounded and the – (inverting) input is connected to a resistor and an input signal– Rin is the input resistor

– Rf is the feedback resistor since it is feeding the output voltage back to the input

Inverting Op Amp

• When a voltage is applied to the inverting input (-) a voltage of the opposite polarity develops on the output– if Vin is +, then Vout is -; if Vin is -, then Vout is +

Inverting Op Amp

• Finding the Gain– The difference between V+ and V- must be small

so we can say they are equal• Since + is connected to Earth, • The potential at a point (P) between R1 and R2 is

therefore also 0V• Applying Ohm’s Law to R1 and R2

0V V

input

in

VI

Routput

f

VI

R

output f

input in

V RV R

Non-Inverting Op Amp

• An op amp is said to be non- inverting if the – (inverting) input is grounded and the + (non-inverting) input is connected to an input signal– The polarity of the voltage at the output is the same as

that of the input (if Vin is +, then Vout is +; if Vin is -, then Vout is - )

Non-Inverting Op Amp

• The input signal is applied to the non-inverting (+) lead• The amount the signal is amplified is determined by

the value of resistors Rout and Rf

– If the difference between + and – is more than 9μV, the output will be a constant 9V so we can say the two inputs are about the same

– This means that the potential at point P is also Vinput

inputV V V

Non-Inverting Op Amp

• If the current through the resistors is I then we get

• To Rout alone;

• The 2 currents are equal so

output

out f

VI

R R

input

out

VI

R

output input

out f out

V VR R R

1output f fout

input out out out

V R RRV R R R

Comparator

• A comparator compares two potentials– If the potential on the + input is higher, then the

output is V+ and if the – input is higher, then the output is V-

Comparator• Fire Alarm– At normal room temp all resistances are equal so both

inputs equal V and the output is 0– If the temp increases then the resistance of the thermistor

drops and the pd across it drops. This results in an increase in the potential at the – input which results in an output of 9 V and the bell will ring

Schmitt Trigger

• A type of comparator that switches to a high output when the input is above a given value (upper threshold)– Only switches to a low output when the input gets

lower than another low value (lower threshold)– Schmitt triggers are often used for reshaping

digital signals to remove noise

Schmitt Trigger