Spectral Analysis: Modulation and Multiplexing II: Wire Technologies I

February 25, 2004

More on Modulation and Multiplexing

Recapitulation of Lecture 3                - Multiple Access Methods (Multiplexing) Revisited

All About Modulation (local pdf) part of the valuable Complex2Real.com tutorial seriesA review of signal encoding

Frequency Multiplexing - Frequency Division Multiple Access (FDMA)

Temporal Multiplexing - Time Division Multiple Access (TDMA)

Signal Sampling and Quantization

The Sampling Theorem: When sampling an analog signal the sampling frequency must be greater than twice the highest frequency component of the analog signal to be able to reconstruct the original signal from the sampled version.

Sampling Paradigm.

The Shannon-Whittaker-Nyquest theorem may be simply phrased to say that if you want to convey the content of a repetitive signal by sampling the signal, then you have to sample the signal at a frequency at least twice the maximum frequency content of the signal itself. For example, to measure the rotational frequencies of the three hands of a watch, a collection of snapshots taken with a frequency of at least twice per minute would be needed.
A short, but fairly complete definition of the sampling theorem from Wikipedia

An insightful sampling theorem applet from Friedrich-Alexander-Universität, Erlangen-Nürnberg

Analog to digital conversion:

Pulse Code Modulation (PCM)

A PCM Tutorial  from the Aydin Telemetry 

PCM configuration

Comparison of a few pulse formats

PCM A-to-D conversion: simple example

Quantization

Linear Signal Quantization: Illustration

Linear Quantization of a Sine Wave: Illustration

Nonlinear Signal Quantization: Illustration

Logarithmic Signal Quantization: Illustration

Wire Technologies - Background physics:

Goal 1: To establish a viable model for characterizing information flow along a wire.

Goal 2: To establish some important electrical concepts.

As a starting point let us look at the propagation characteristic of a kind of toy hydraulic telegraph:

• Description of system: Hydraulic Telegraph I

• What limits the transmitted data rate in the system? Hydraulic Telegraph II

Most of us follow Ben Franklin and derive our intuitive picture of electrical conduction in terms of the simple flow of a fluid in a pipe. Sketch of a continuous fluid flow system. (Note)
 
For most folks, the most important and difficult issue is to distinquish between the flow variable (gallons/sec or electric charge units/sec) and the forcing variable (pressure or voltage). Sketch of a section of a fluid flow system showing a resistive element.
 

In this context, confronted with a trickle of water even when the valve is fully open, you complain to the landlord "there's virtually no pressure". That's usually wrong. The problem is, there's virtually no flow. The pipe is clogged.  There is resistance to flow.

We can deduce a reasonable physical law (Ohm's law) relating the flow through and force across a porous plug.  
 
Now let us consider the role of energy storage in fluid flow I:  Suppose that a rubber membrane stretched across the inside of the pipe (Sketch of energy storage element).  If there is a flow (to the right, as shown by the arrow), the rubber membrane gets increasingly distended.  It's interesting to note that no molecule of fluid ever goes in on the left and comes out on the right.  Nevertheless there is a flow in the pipe (indicated by the red arrow) and the flow is the same at every point along in the pipe.

Hydraulic model of a wired channel -- an RC transmission line.

Real wire channels:

• Two-wire or untwisted pair: reference
  
• Twisted pair: reference and picture
  
• Coaxial line: reference and picture
  
• Undersea cables: sketches and photographs of undersea cables

Response of an RC circuit

See two wonderful applets from Molecular Expressions - i.e.

Factors Affecting Capacitance
Charging And Discharging A Capacitor
Variable CapacitorRC Time Constant

Response of an RC transmission line.

Character of pulse propagation on a RC transmission line.

Simulink files for RC response curves

Output for one element of an RC transmission line

Output for four elements of an RC transmission line

 
 

 

Note 1:  Several of the illustration used here are taken from an excellent introductory tutorial from Northwestern University (see an  adapted local copy the electrical sections of that tutorial).