Tutorial 13 - Time Division Multiplexing

Remote Controlling

In the earliest days of steam power, the engines had to be operated where the engine stood.  There were controls on the engine itself and the boiler to provide the steam was close by, if not in the same room.  Orders to increase (or decrease) the output of the engine had to be sent to the engine house by a runner.  This was not an efficient process.  This was particularly the case in steam ships.  One way of improving that was to have a speaking tube, in which the captain of the ship would speak into a tube to give his orders to the engine room crew.  It was simple but not foolproof.

 

Wikimedia Commons: Biblioteca de la Facultad de Derecho y Ciencias del Trabajo Universidad de Sevilla

 

Such devices are still in use today.

 

A development of this was the ship's telegraph as shown here:

Photo from Pinterest (Ruby Lane)

The captain would pull the lever to, say, Half Speed Ahead. A repeater in the engine room would relay that message to the operators of the engine.

 

On small branch railway lines a small engine would push and pull a couple of coaches up and down the branch line.  This would save the need for the engine to run around the train at the far end.  The driver would stand in a compartment at the far end of the train and would issue bell codes to the fireman to open up the regulator (throttle) and change the valve gear.

 

Question 1

What do you think the weakness is of such practices?

Answer

 

When electric multiple unit trains were first introduced, they offered the advantage that they could easily be controlled from either end.  However they often had a motorised carriage (power car) in the middle of the train that needed to be controlled remotely.  If a pair of wires was needed for each control, this could end up needing a lot of wiring, which is expensive and bulky.  The wires needed to be able to be split for maintenance purposes, which required multi-way plugs.  These could be a source of trouble.

 

A single cable can be used to control remotely a locomotive using the system of Time Division Multiplexing (TDM).

 

 

Basic Ideas

Multiplexing (sometimes abbreviated to muxing - horrible word) is about loading multiple signals onto a single connecting channel.  It is not a new technology.  It was introduced in 1910 by an American engineer, George Owen Squier (1865 - 1934).  Both analogue and digital signals can be multiplexed.  The multiple channels are combined by a multiplexer (MUX).  The signals are sent down a single channel (wire, optical fibre, or radio link).  They are then sorted out into the same number of channels by a demultiplexer (DMX).  This is shown by the diagram below:

 

 

In this example there are 9 low data rate input channels.  The high data rate channel must be able to carry data at a rate of 9 times each of the input channels. 

 

There are several ways that data can be multiplexed.  We will consider the ideas of time division multiplexing (TDM) which is the one on the syllabus.  The animated gif shows the idea of time division multiplexing:

Image from Wikimedia Commons Tony R. Kuphaldt - Socratic Electronics website

 

In this tutorial, we will consider how multiplexing principles can be used with a number of different applications.  We will use TDM to explain what is going on in these systems.  However in reality, other techniques can be used. We will mention these at the end of the tutorial.

 

 

Aircraft Systems

Most aeroplanes have control surfaces that are operated by the pilot through a system of rods and wires with levers.  With larger aircraft, simple cable and rod systems can be heavy to use, so power assistance is included. Such systems are widely employed, but are rather bulky.  In a machine like the huge aeroplane in the picture below, the controls would be operated by hydraulic systems.  In other older aeroplanes compressed air would be used.

 

 

Unnecessary weight wastes fuel, which is expensive.   So instead of using rods, cables, levers, and power assistance, we could use a system of motors and actuators connected to pilot's controls.  Let's look at how it could be done:

 

 

The flight yoke is the primary control.  It activates various control surfaces.  It can steer left and right.  If the pilot pulls it towards her, the aeroplane will go up.  If she pushes it away from her, the aeroplane will go down.  This is, of course, a simplistic summary, but this is a physics tutorial, not a flight school!  The pilot also has a trim-wheel that enables her to fly the aeroplane level without having to push or pull on the yoke to keep the aeroplane level.

 

With an electric (or hydraulic) control system, the control surfaces are moved by motors.

 

The systems are shown in a schematic form here:

You can see that it's starting to get complicated.  The more circuits there are, the more likely it is that there are going to be problems.  Murphy's Law (If it can go wrong, it will) was coined by an aircraft engineer.  If something goes wrong when you are up in the air, you can't land on a cloud, park up, and sort it out.

 

Multiplexing
In aeroplanes the saving of weight is critical. If we can have one wire feeding several sensors, that saves a lot of weight. We use a technique called multiplexing to splice the output of each sensor before it is sent down the wire to the computer.  In the picture below the control surface systems have been multiplexed.  The control inputs from the pilot are carried to a multiplexer and computer. 

Then the signals are sent to the ailerons and tail plane through multiplex buses.  (A bus is a common conductor.)  Then the command signals are de-multiplexed so that the relevant control surfaces are activated. 

In time division multiplexing (TDM) the data from each sensor are split up into equal sections of time. They are then sent down the wire to a demultiplexer, where they are reassembled, giving as many outputs as there were inputs. TDM is often used in trains where a single wire carries the control signals from the remote driving cab to the locomotive.  In earlier systems, the data were analogue, but modern systems are digital.

 

So for our aeroplane the inputs from the pilot are as follows:

 

So in the diagram, Y1 refers to Yaw command 1, while R1 refers to Roll command 1, etc.

 

 

So the multiplexer sends command Y1 in the first block of time, then  R1 in the next block of time, then P1, and then T1.  Each command is sent one by one in its own block of time.  Each system shares the time equally.  The demultiplexer then distributes the relevant commands to the different surfaces.  Each command will have an identifier, so that it is sent to the correct destination.  If this didn't happen, the aeroplane would do things it shouldn't do.  This could rapidly make it un-flyable.

 

Let us suppose that the system uses 8-bit words (i.e. from 00000000 to 11111111).  Let's say that the yoke is at 00000000 at fully nose-up and 11111111 at full nose-down.  Suppose the pitch of the yoke were neutral (neither up nor down).  It would give out a command 01000000.  If two successive commands were the same, the demultiplexer would interpret the situation as no change.  Therefore the elevator actuators would do nothing, and the aeroplane would maintain the same pitch.

 

Question 2

(a) How many possible positions would there be with 8-bit words?

(b) Why is the neutral position given by 01000000 rather than 00001111?

Answer

 

Suppose we allocated each system an identification number using an 8-bit word:

The commands have values between 00000000 (full up, full left) and 11111111 (full down, full right).

 

The system needs to know three things:

Let's think about the message in a block of time.  The multiplexer and demultiplexer are co-ordinated with a clock that sends out pulses.  This system of multiplexing is called synchronous multiplexing.  The message in each block of time consists of two bytes (two 8-bit words).  First is the system to be addressed.  Second is the value that the system should be at.  Consider this message:

 

00000001 01000000

Question 3

What is this message saying?

Answer

 

 So let's look at the sequence of commands that occurs through the multiplex wire:

 

Time Block

Command

First Byte

Second Byte

Change

Effect on the plane

1

Y1

00000011

01000000

 

Rudder neutral

2

R1

00000010

01000000

 

Ailerons neutral

3

P1

00000001

01000000

 

Pitch neutral

4

T1

00000100

01000010

 

Trim 2 places down from neutral, so nose slightly down

5

Y2

00000011

01000000

No change

Rudder neutral

6

R2

00000010

01000000

No change

Ailerons neutral

7

P2

00000001

01000000

No change

Pitch neutral

8

T2

00000100

01000110

Change

Trim 6 places down from neutral, so nose slightly further down.

 

This is a very simplified version of what really happens.  The real situation is more complex with other systems being addressed and controlled.  There are also sensors that feed the positions of control surfaces to the flight computer.

 

Question 4                       Later on in the flight, the multiplex wire carries these commands. 

 

Time Block

Command

First Byte

Second Byte

1001

Y1

00000011

01000011

1002

R1

00000010

01000011

1003

P1

00000001

01000000

1004

T1

00000100

01000010

1005

Y2

00000011

01000000

1006

R2

00000010

01000000

1007

P2

00000001

00111111

1008

T2

00000100

01000010

 

                                    How does the plane respond?                                                                                                                                                Answer

 

In real systems the clocks run at many thousands of times per second.  They also carry much more information than suggested by this model.

 

Aircraft that use this system are called fly-by-wire and are controlled with flight computers.  The aircraft manufactured by Airbus Industrie SA use this system.  The aeroplane below is one such example.

 

 

There are back up computers in case the main computer goes wrong.  The systems are very expensive and have back-up systems which take over should the main one go wrong.  The aircraft can fly, but will be grounded until it is repaired.  While the computers do much of the flying, they are supervised by pilots who can take over to fly the aeroplane if needed. However if all the computers fail completely, there is no way of controlling the plane and it becomes unflyable.  In one case, a pilot put his aeroplane into a stall during bad weather.  The other pilot panicked and pulled back on his control stick, while the first pilot pushed forward...  The aeroplane fell into the sea.

 

(A stall is where the aeroplane goes too slowly to fly.  You should push the yoke forward in a stall to make the aeroplane drop and gain speed.  It will then resume flight.  All novice pilots are taught how to recover from a stall.)

 

The Eurofighter aircraft uses the system to such effect that an aeroplane, which is very unstable and in theory impossible for a human to fly, is as easy to fly as a light sports aircraft.  The aircraft are very expensive, so only highly trained pilots are allowed anywhere near them.

 

 

Computer Networks

Time Division Multiplexing is used widely in computer networking, especially where a company has two sites that are many kilometres apart.  If each site had 100 computers, each of which needed to exchange data with the others, there would be thousands of kilometres of wire needed.  With multiplexing, one wire can carry all the data.  Consider this set of computers:

 

(Yes I know that they all have CRT monitors, but that was the clip-art I had.)

 

Each computer can send messages to any of the others.  So A can send messages to A' or B' and so on.  The demultiplexer in this case would have a router, and the data would have an address to which to send the data item.  This is different to the aeroplane multiplexing in which one control input would only affect one control system.  Notice that computers B and C are sending null or blank messages.  They may be off-line or even switched off.  That is no problem to the multiplexing system.

 

There are two drawbacks:

 

 

Asynchronous TDM

There is another method of multiplexing that addresses these two draw-backs.  This is asynchronous TDM.  The multiplexer reacts to the inputs according to the demands of the machines.  It uses a statistical algorithm (computer-speak for say how often each computer needs to send messages).

 

Consider the four computers (complete with their ancient CRT monitors) multiplexing using asynchronous TDM.

 

The data from each computer are put into blocks of three.  So the first block is A1, B1, and C1.  Then the second block is D1, A2, B2.  And so on.  The fifth block is B4 and A5.  The third space is empty.  The multiplex system can cope with that.

 

We can think of each block of three as a wagon onto which three containers are placed.

 

There are fourteen blocks of data that are being carried in fifteen spaces.

 

Question 5

(a) What is the transmission efficiency of the asynchronous multiplexing?

(b) Suppose the data are transmitted using synchronous multiplexing.  What is the transmission efficiency in this case?

Answer

 

The advantages of this system are:

The disadvantage is that the synchronisation is lost.  Therefore checking signals have to be sent to verify the data to ensure that they are not corrupted.

 

 

Multiplex Transmission

We have assumed that the multiplexed data are being transmitted using a wire.  Remember that wires have problems of their own (see Tutorial 12), especially with high frequency signals.  We can use optical fibres, in which the problems are much fewer.  Optical fibre land-lines are much more common nowadays.

 

Where it's difficult or expensive to lay land-lines, radio signals are used.

 

Multiplex radio signals are essential for mobile telephones.  Your mobile number does not have a dedicated frequency of its own.  Instead the frequency is determined by the service provider.  For example Virgin Media 4 G has frequencies of either 1800 MHz or 2600 MHz.  O2 4G is on 800 MHz.  (Other mobile phone providers are available.) 

 

The calls to your phone are multiplexed with many other calls in a similar manner to that described above.  You will be sharing your connection with several thousand other users.  Your phone will only pick up the blocks of data that are addressed to your number.  The blocks of data are transmitted so rapidly that you would not detect the gaps between each block.

 

 

Digital Audio Broadcasting

Radios using digital audio broadcasting have been around for about twenty years.  DAB for the BBC is transmitted at a frequency of about 226 MHz.  You do not have to retune the radio to a different frequency to change station.  Instead signals are multiplexed, and when you change stations, you are changing the demultiplexer to recognise a different identifier.  The picture below shows a stereo DAB radio tuner for a Hi-Fi system.

 

Consider four commercial stations that are multiplexed to a digital audio broadcast.   Junko Punko Radio has identifier JP.  Brain Dead FM has the identifier BD.  Drivel FM has the identifier DV.  Ear-Buster Radio has the identifier EB.   Each is transmitting data as shown in the picture below.

 

 

The multiplexer is transmitting one block of data at a time, JP1, BD1, etc.  The receiver is picking up all the blocks of data.  Since it is set to receive Ear-Buster Radio, the demultiplexer only responds to the code with the identifier EB.  The rest are ignored.  If the listener wants to listen to Brain Dead FM, then the multiplexer then is changed to detect BD.  Then only the data with the identifier BD are processed.

 

As well as the data that make the music, the receiver will display other information about the music being played:

Advantages

 

Disadvantages

 

 

Digital audio broadcasting uses statistical time division multiplexing.  The details are beyond the scope of this discussion.

 

 

Other ways of Multiplexing

We have considered time division multiplexing as it's the easiest way of  describing the concept.  However there are other ways that data can be transmitted down a channel.  You are not expected to know these for the exam, but it is useful to be aware of them.

It is also possible to have inverse multiplexing whereby a single data stream is broken up into several parallel data streams and is transmitted over several data transmission lines.  Then the data streams are reassembled into a single data stream.  This is useful for increasing the data transfer rate if the transmission lines have a low data transfer rate.