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Annulment: A+ 1 = 1
A.0 = 0
Association: (A+ B)+ C = A+(B+ C)
(A.B).C = A.(B.C)
Commutation: A+ B = B+ A
A.B = B.A
Complements: A+ ¯A = 1
A.¯A = 0
(
A
+
B
)
= ¯
¯
A.B
(A.B) = ¯A+ ¯B
Distributive: A.(B+ C) =(A.B)+(A.C) A+(B.C) =(A+ B).(A+ C)
¯
Double negation: A = A
Identity: A+ O = A
A.1 = A
Tautology: A.A = A
A+ A = A
C is in picofarads,K is the dielectric constant(air = 1).A is the area of the plate in square cm andd the thickness of the dielectric. Calculation of overall capacitance with:
Parallel capacitors −C = C1 + C2+···
Series capacitors − 1 =1 +1 +···C C1 C2
open wire
)Z
=
276 log 2
D
ohmsd
where
D= wire spacing in same units.d = wire diameter
( coaxial)Z =138 logdo ohms√(K) di whereK = dielectric constant,do = outside diameter of inner conductor,di = inside diameter of outer conductor.
Rd = L =QωL = Q ohmsCr ωC
where L = inductance (henries), C = capacitance (farads), r = effective series resistance (ohms).Q =Q-value of coil, andω = 2π × frequency (hertz).
The velocity of propagation of a wave is
v =fλ metres per second
wheref = frequency (hertz) andλ = wavelength (metres).
For electromagnetic waves in free space the velocity of propagationv is approximately 3× 108 m/sec, and iff is expressed in kilohertz andλ in metres
f 300 000 kilohertz f = 300 megahertz =λ λor
λ 300 000 metres λ = 300 metres =f f
f in kilohertz f in megahertz
Z
=
R
2 + ωL−1 2 ωC
where R = resistance (ohms), ω = 2π × frequency (hertz). L = inductance (henries), andC = capacitance (farads).
L(
in microhenries
)
=
a2N29a + 10l approximately
If the desired inductance is known, the number of turns required may be determined by the formula
î ù
N
=
5Lð1+ 1+ 0.36n2a3
na2 Lû
where N = number of turns,a = radius of coil in inches,n = number of turns per inch.L = inductance in microhenries (µH) andl = length of coil in inches.
Calculation of overall inductance with:Series inductors −L = L1 + L2+···
Parallel inductors −1 =1 +1 +···L L1 L2
Increasing range of ammeters or milliammeters
Current range of meter can be increased by connecting a shunt resistance across meter terminals. IfRm is the resistance of the meter;Rs the value of the shunt resistance andn the number of times it is wished to multiply the scale reading, then
s
=
Rm (n− 1)
Increasing range of voltmeters
Voltage range of meter can be increased by connecting resistance in series with it. If this series resistance isRs andRm andn as before, thenRs =Rm ×(n− 1).
Gain with feedback
=
A 1+Ab whereA is the original gain of the amplifier section over which feedback is applied (including the output transformer if included) andb is the fraction of the output voltage fed back.
Distortion with feedback d approximately =1+Abwhered is the original distortion of the amplifier.
whereI = current (amperes),V = voltage (volts), andR = resistance (ohms).
2
W2R watts =VI =V =IR
whereV = voltage (volts),I = current (amperes), andR = resistance (ohms).
=
10 log
P1 P2 whereP = ratio in decibels,P1 andP2 are the two power levels.
ωLQ = R
The radio horizon at VHF/UHF and up is approximately 15% further than the optical horizon. Several equations are used in calculating the distance. IfD is the distance to the radio horizon, andH is the antenna height, then:
D√H =k1. WhenD is in statute miles (5280 feet) andH in feet, thenK =
1 .42.
2. WhenD is in nautical miles (6000 feet) andH in feet, thenK =
1.23.
3. WhenD is in kilometres andH is in metres, thenK = 4.12.
XL =ωL ohms XC =1 ohmsωC
where ω = 2π × frequency (hertz), L = inductance (henries), and C = capacitance (farads).
The total resistance of an inductance and a capacitance in series isXL −XC.
1 f =2π√LC hertz
whereL = inductance (henries), andC = capacitance (farads). IfL is in microhenries (µH) andC is picofarads, this becomes
10
6
f =2π√LC kilohertz
The basic formula can be rearranged
1 1 L =4π2f 2C henries C =4π2fL farads Since 2πf is commonly represented byω, these expressions can be written
1 1 L =ω2C henries C =ω2L farads
For a combination of inductance and resistance in series the time constant (i.e. the time required for the current to reach 63% of its final value) is given by
τ =L secondsRwhereL = inductance (henries), andR = resistance (ohms).
For a combination of capacitance and resistance in series the time constant (i.e. the time required for the voltage across the capacitance to reach 63% of its final value) is given by
τ =CR seconds whereC = capacitance (farads), andR = resistance (ohms).The ratio of a transformer refers to the ratio of the number of turns in one winding to the number of turns in the other winding. To avoid confusion it is always desirable to state in which sense the ratio is being expressed: e.g. the ‘primary-to-secondary’ rationp/ns. The turns ratio is related to the impedance ratio thus
np Zp ns Zswhere np = number of primary turns,ns = number of secondary turns, Zp = impedance of primary (ohms), andZs = impedance of secondary (ohms).
W =I2R whenI is in amperes or milliamps2 W = 1 000 000 ×R If wattage rating and value of resistance are known, the safe current for the resistor can be calculated from
milliampers
=
1
.
000
×
watts
ohms
Formula for the wavelength in metres of a tuned oscillatory circuit is: 1885√LC,whereL = inductance in microhenries andC = capacitance in microfarads.