Transcript Ohm`s Law

Lecture 2
• Most basic facts from Electricity needed for
understanding telecommunications
• Local transmission lines in the telephone
system
• Decibels
• Signals and Noise
• Mathematical facts
• Resistors are components that oppose the flow of current
• Resistors transform electrical energy into heat and
dissipate it to the environment
• Resistance is measured in units called Ohm, e.g. R =1 
• Ohm’s Law says that:
•The voltage across an ideal resistor is proportional to the
current through it., V = I R, where V is Voltage in Volts
and I is the current in Amps
• The larger the resistance, the weaker the current that
flows through the resistor (assuming same voltage).
• A capacitor is essentially a sandwich of two layers of
metal separated by an insulating material, or dielectric.
• Its primary function is to store electrical energy.
• Its capacitance depends on the size, geometry and on
materials.
• Capacitors of various capacitances are used in circuits to
create dynamic effects
• Capacitance is measured in units called “farads”. 1F
• 1 Farad is very large, practically we use microfarads or
even smaller capacitances
• Inductors are elements that transform the electric energy of
the current into a magnetic energy of the field in the
environment
• Inductors are “obstacles” for high frequency electric
currents, but an ideal inductor has zero resistance and is
not an obstacle to constant (DC) current
• inductance L is measured in units of henrys H.
On-line resources for basic concepts of Electricity
Electric circuits
http://www.fclabs.com.au/onlinesamples/ec/elect01/els01dx.htm
Animation of Ohm's law
http://www.phy.ntnu.edu.tw/java/rc/rc.html
Animation of an RLC circuit with AC currents
http://www.phy.ntnu.edu.tw/java/rlc/rlc.html
Animation of a clipping circuit
http://www.phy.ntnu.edu.tw/java/electronics/clip_e.html
Animation of Fourier synthesis of oscillatory signals
http://www.phy.ntnu.edu.tw/java/sound/sound.html
Propagation of Electromagnetic Wave
http://www.phy.ntnu.edu.tw/java/emWave/emWave.html
Transmission lines
• Copper wire is still the most widely used transmission
medium
• Impairments: losses due to resistance R, attenuation at
higher frequencies due to inductance L and capacitance C,
electromagnetic coupling between parallel lines, echoes,
and noise.
• Telephone lines are often called “twisted pair” – these are
insulated copper wires twisted together; neighboring pairs
are twisted with different twist lengths; the pairs are
stranded into units of up to 100 pairs and cables into
plastic-sheathed cores.
• The primary constants R, L, C depend on the gauge of the
wire, temperature, materials, and operating frequency.
Z0 
L
C = characteristic impedance of the line - must be
matched by source impedance and load impedance
Transmission lines, part 2
• American Wire Gauge, AWG standard
Gauge
19
22
24
26
28
Diameter, mm
0.91
0.644
0.511
0.405
0.302
Diameter, in
0.036
0.025
0.020
0.016
0.012
Transmission lines, pt 3
• To ensure sufficient current level in the loop (20 mA) the
resistance of the wire should not exceed certain limit. This
limits the length of the twisted pair line from central office
to the subscriber. 1700 Ohms is a typical value.
AWG
28
26
24
22
Ohms/1000 ft
132
83.5
51.9
32.4
Thus for the 26-gauge loop the maximum length limit is
1700/83.5 = 20,359 feet. A different limit, called loss limit
is 15, 680 ft (to ensure no more than 8 dB loss of voice)
Decibels
• Decibel, dB, is a measure of a relative amplitude (or power) of a
signal, be it acoustic or electric
• The term “relative” means that we are measuring the ratio of the given
amplitude to another amplitude, for example the ratio of the amplitude
(Volts) at the end of the phone line to the amplitude (Volts) at the
beginning of the phone line
• In acoustics, the decibel is a measure of the relative level of sound or
noise compared to some standardized level of sound or noise. One
decibel (0.1 bel) equals 10 times the logarithm of the power ratio of the
given sound to the power of the sound barely perceptible by human
ear.
• The minimum audible pressure amplitude, at the threshold of hearing,
is about 10-5 pascal, or about 10-10 standard atmosphere,
corresponding to a minimum intensity of about10-12 watt per square
meter.
• Doubling the intensity of a sound means an increase of a little more
than three dB.
Decibels, part 2
Network element
Signal Input
Signal Output
dB value = 10 log (Output power/Input Power)
dB value = 20 log (Output voltage/ Input Voltage)
e.g. power gain = 2 implies dB value = 10 log 2 = +3.01 dB
e.g. voltage gain = 100 implies dB value 20 log 100 = 40 dB
e.g. voltage loss 50% implies 20 log (0.5) = - 6.6 dB
e.g. AWG 24 produces loss of 2.127 dB/km or 2.16 dB/mile
Transmission Impairments
• Signal transmitted gets distorted
• Causes:
–
–
–
•
Attenuation and attenuation distortion
Delay distortion
Noise
Effects: either the analog signal distortion or
the binary signal errors
Attenuation
• Signal strength weakens with distance
• Received signal strength:
– must be enough to be detected (e.g. 20 mA)
– must be sufficiently higher than noise to be
received without error (8 dB power loss)
• Attenuation is a function of frequency
Noise sources
• Thermal
– Due to thermal agitation of electrons
– Uniformly distributed, white noise
• From other signals
– Signals that are combinations of original
frequencies sharing a medium
Noise sources continued
• Cross-talk
– A signal from one line is picked up by another
• Impulse disturbance
– Irregular pulses or spikes of short duration and
high amplitude
– electromagnetic interference
Characterizations of Channel
Capacity
• Data rate
– Bps, In bits per second
– Sps - In bauds: symbols per second
• Bandwidth
– In cycles per second or Hertz
– Bandwidth is limited by electronics and
medium