CHAPTER 3: FORMULAS AND NUMBERS



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Port to Port Isolation  Temperature Induced Attenuation  DC Loop Resistance  Calculating Attenuation  Units Of Voltage  Metric Notation  OHMs LAW  DB  DBmV  AC Waveforms 

TV and Radio signals occupy RF spectrum from 5 MHz to 1002 MHz
Analog channels are 6 MHz wide and made up of a video carrier and audio carrier
Audio carriers are always 4.5 MHZ above video carriers
40 mph or less, tapering formula is L=(W x S²) / 60
      L = Tapering distance in feet
      W= width of closed lane in feet
      S = Posted speed limit
45 MPH or greater the formula is L = W x S
Input signal level greater than or equal to amp rated noise figure
Ohm's Law: I =E/R or R=E/I or E=IR
Power: P=energy/time; I=P/E or E=P/I or P=IE
Bel is a 10:1 power ratio
1 Bel = 10 db
1 dB power ratio is 1.2589 to 1
Voltage formula: E = the square root of P x R
Voltage ratio 3.162:1
1 mV = 0 dBmV is need for good picture
Port to port isolation
      Higher amount of isolation between splitter output ports less chance of passing interference from 1 TV to another

To determine P2P isolation
      Terminate input port
      Connect input to 1 output
      Measure signal from outer output
      P2P is difference between the 2
      The > the number the > the isolation
      35 dB is the norm for 2-way at 5-400 MHz
      27 dB @ 400-500 MHZ
Inadequate RFI shielding (less than 60 dB)
Splitter insertion loss can be checked by measuring the input levels and minus the port loss (i.e. 3.5 dB for a 2 way). If the       loss is greater than what is on the splitter the device is probably defective.
Digital signals 6 dB to 10 dB below the analog signals can result in low distortion and good error performance
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Temperature induced attenuation
       A (@T) = A (@68°F)[1 + .001 (T-68°F)]
            A = Cable attenuation in dB/100'
            T = Cable temperature
       Subtract 68° from new temperature
       Multiply change in temperature by .001 to obtain attenuation percentage change
      Add 1 to attenuation percentage change to obtain attenuation percentage multiplier
      Multiply the cable attenuation rate of cable at "?" Mhz/100' x attenuation percentage multiplier to obtain corrected cable loss
      Multiply corrected cable loss times cable length (100' units)
Signal loss of cable at 750 Mhz
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      RG-59 = 6.71 dB per 100'
      RG-6 = 5.45 dB per 100'
      RG-11 = 3.60 dB per 100'
DC loop resistance (inner conductor resistance + outer conductor resistance)
C = Q/V (C= capacitance in farads, Q=Quantity of charge stored, V= voltage applied to capacitor plates)
XL = Inductive reactance
Inductive reactance (Ohm's law) I = E/XL XL replaces R
Lowercase letter omega ω is symbol for angular velocity of I or E in an AC circuit
ω =2πf or angular velocity =2x3.14xFrequency in hertz
1 radian = 57.3° in a circle 0f 360°
XL = ωL or XL = 2πfL
1 mh = 1x10-3h
I μf = 1x10-6f
1 cycle of a sine wave also equals 2π radians
DC Loop Resistance
      For RG-6 at 100' is 4.026 Ω
DC Loop Resistance 40.26 Ω
÷ 1,000 ÷ 1,000
= Ω Per foot = .04026 Ω per foot
VOM measurement 2.013 Ω
÷ DC loop resist per foot ÷ .04026 Ω per foot
= Footage to short = 50 feet to short

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Calculating attenuation of cable
      Cable length x cable attenuation at particular frequency = total attenuation at freq
      After that minus this total from tap output at particular frequency
      This should give the necessary input signal at ground block for particular frequency
      Using this, you should be able to determine expected RF
The amount of 1 coulomb (6.28 x 1018 electrons) passing a given point during 1 second is equivalent to 1 ampere
Volt is the amount of EMF required to produce a current or 1 ampere through a resistance of 1 Ω

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UNITS OF VOLTAGE

1 microvolt µV 1/1,000,000 volt .000001 volt
1 millivolt mV 1/1,000 volt .001 volt
1 kilovolt kV 1,000 volt -
1 Megavolt MV 1,000,000 volt -


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UNITS OF CURRENT

1 Ampere A 1 coulomb per sec -
1 microampere µA 1,000,000A .000001 A
1 milliampere mA 1/1,000 A 001 A
1 kiloampere kA 1,000 A -


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METRIC NOTATION

109 One Billion giga G
106 One Million Mega M
103 One Thousand Kilo k
10-3 One Thousandth milli m
10-6 One Millionth micro µ
10-9 One Billionth nano η
10-12 One Trillionth Pico p


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OHMS LAW

      Basic Electrical characteristics
      Voltage
            Is a measurement of the force or pressure that causes electrons to move
      Current
            Is the transfer of energy from electron to electron resulting from the directed movement or flow of electrons through a conductor
      Resistance
            The opposition a material offers to the flow of current
      Power
            The rate at which work is done

VOLTAGE E VOLT V
CURRENT I AMPERE A
RESISTANCE R OHM Ω
POWER P WATT W


Current = Voltage/resistance           I=E/R or R =E/I or E=IR
When the voltage doubles, the current also doubled because current is inversely proportional to voltage
When the resistance doubles, the current is halved because current is inversely proportional to resistance
Power = energy/ime
Joule: The unit of energy
One joule of electric energy is developed when one volt forces one coulomb of electrons through a circuit
Power = Time/Energy = EQ/T = EI
P=IE or I=P/E or E=P/I
P=I2R:: The amount of power wasted s a result of conversion to heat, heat loss, is directly proportional to the amount of resistance present and to the square of the amount of current flowing through the resistance.
      P == power wasted (heat loss)
      I = Amount of current flowing through the conductor
      R = Total resistance of conductor
Power lost is any electrical energy that is not being used productively
Series circuits must have a power source, a load, connecting conductors and only 1 path of current flow
Characteristics of a series circuit
Individual resistance adds up the total circuit resistance
The same amount of current flows at all points within a series circuit
The voltage across the individual resistance in a series circuit add up to the total voltage applied to the circuit
Total series resistance (RT = R1+R2+R3…)
The value of the current is the same at all points in a series circuit
Total current (ET = ER1+ER2+ER3…)
Total power (PT = PR1+PR2+PR3…)

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Db

A bel: a 10 to 1 input to output power ratio
A decibel: 1/10 of a bel
1 bel = 10 dB
Almost half of the signal power is lost in the first 3 dB of cable and almost half of the remaining signal power is lost in the next 3 db of cable
Voltage does not reduce by the same ratio as power
Voltage ratios are always the square root of the power ratios

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DBmV

0 dBmV equals 1mV across 75 Ω and has a power of 13.33 Nanowatts
A 1 dB increase can be significant because it represents slightly more than a ¼ increase in power
Data carrier levels are typically 10-17dB below analog video carriers
4 x 7 is the only self-terminating tap
Any small amount of impedance occurs, a small amount of energy is sent back, resulting In return loss

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AC WAVEFORMS

CPS =Cycles per second
1 hertz is the same as 1 CPS
The speed of light is about 186,000 miles per second
186,000 = 3000,000,000 meters per second
1 cycle occurs in 1/60 of a second so 1 cycle of 60 Hz current only travels 1/60 of distance or 3100 miles per second
Wavelength = speed of light/frequency of the current (λ=c/f)
Period = 1 cycle ÷ frequency in cps
T = 1 ÷f (Period is equal to 1/frequency))
One hertz is the same as one cps
AC Ohm's law is represented as i (t) =e (t)/R with t = a time element

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