Math for the General Class Ham Radio Operator A Prerequisite Math Refresher For The Math-Phobic Ham.
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Transcript of Math for the General Class Ham Radio Operator A Prerequisite Math Refresher For The Math-Phobic Ham.
Math for the General Class Ham Radio Operator
A Prerequisite Math RefresherFor The Math-Phobic Ham
Why is This Lesson for You?
Math Vocabulary
• What are equations and formulas?
• What do variables mean?
• What is an operator?
C2 = A2 + B2
Math VocabularyWhat is an operator?
• Math operations:– Add: +– Subtract: −
– Multiply: X or ⃰– Divide: ∕ or
– Exponents: YX
– Roots: or n
Math Vocabulary
• What does solving an equation mean?
• Getting the final answer!
Getting the Final Answer:Tricks of the Trade:
• Opposite math operations:
Addition Subtraction
Multiplication Division
Roots Exponents
If you do something to one side of the equation, do exactly the same thing to the other side of the equation to keep everything equal
XX
• A number divided by the same number is 1, = 1
• A number multiplied by 1 is that number, Y * 1 = Y
What does solving an equation mean?Example #1
C2 = A2 + B2 Assume A and B are knownWant to solve for C.
C2 = A2 + B2 Apply same operation to both sides
C2 = A2 + B2 Opposite operations cancel each other
C = A2 + B2 Voila!!!
What does solving an equation mean?Example #2
• The equation for Ohm’s Law is:
E = I * R
• The variables mean:
– E represents voltage
– I represents current
– R represents resistance
• The math operator is multiplication.
What does solving an equation mean?Example #2
• E = I * R – Current is 10 (we will disregard units for now)
– Resistance is 50
• Therefore: E = 10*50• E = 500 (in this case volts)
Math VocabularyWhat does solving an equation mean?
• What if we know the voltage and the current and want to find the resistance?
E = I * R R = E / I
Let’s do some math!
• Simple additionTN RRRRR 321
Let’s do some math!
• Multiply R1 times R2
– Write the number down
• Add R1 and R2
– Write the number down
• Divide the first number by the second to find the answer.
TRRR
RR
21
21
• R1 = 50
• R2 = 200
• RT = Total Resistance = ?
Let’s do some math!
• R1 * R2 = ? 50 * 200 = 10,000
• R1 + R2 = ? 50 + 200 = 250
• RT = 10,000/250 = 40
TRRR
RR
21
21
• R1 = 50
• R2 = 200
• RT = ?
Let’s do some math!
• Do each fraction in the denominator in turn 1/Rn
– Write the number down
• Add all fraction results together.– Write the number down
• Divide 1 by the sum of the fractions.
T
N
R
RRRR
11111
321
Let’s do some math!
• R1 = 50
• R2 = 100
• R3 = 200
• 1/R1 = ? 1/50 = 0.02
• 1/R2 = ? 1/100 = 0.01
• 1/R3 = ? 1/200 = 0.005
• Sum of fractions = ? 0.02 + 0.01 +0 .005 =0.035
• 1/Sum of fractions = ? RT = 1/0.035 = 28.6
T
N
R
RRRR
11111
321
Let’s do some math!
• Square the numerator E– Same as E * E
– Write the number down
• Divide the squared number by R.
• E = 300• R = 450
R
EP
2
Let’s do some math!
• E = 300• R = 450
• E2 = ? (square E) 3002 = 90,000
• 90,000/R = ? P = 90000/450 = 200
R
EP
2
Let’s do some math!
• VPeak = 100
• VRMS = ?
• Solve for VRMS
VRMS = VPeak / 1.414
• Plug in value for VPeak
VRMS = 100/1.414
100/1.414 = 70.7
RMSPeak VV 414.1
Let’s do some math!
• Sometimes two formulas need to be used to come to a final answer.
RMSPeak VV 414.1
R
VPEP RMS
2
• VPeak = 300
• R = 50
• PEP = ?
• Solve equation 1 for VRMS
• Plug the value of VRMS into equation 2.
Let’s do some math!• Solve for VRMS
VRMS = 300 / 1.414
300/1.414 = 212.2 Write the number down
• Plug the value into VRMS. VRMS2 = 45,013.6 Write the number down
• Divide the square by 50 45,013.6 /50 = 900.3
RMSPeak VV 414.1
R
VPEP RMS
2
• VPeak = 300
• R = 50
• PEP = ?
Let’s do some math!
P
S
P
S
N
N
E
E
• NS = 300
• NP = 2100
• EP = 115
• ES = ?
• Solve for ES
– Multiply both sides by EP
– The EP values on the left cancel
• Solution is
P
PSS N
ENE
PP
S
P
SP E
N
N
E
EE
Let’s do some math!
• NS = 300
• NP = 2100
• EP = 115
• ES = ?
• NS * EP = ? 300 * 115 = 34,500 Write the number down
• Result / NP = ? ES = 34500/2100 = 16.4
P
PSS N
ENE
Let’s do some math!
• The right side of this equation is a ratio.
• Ratios are numbers representing relative size
• A ratio compares two numbers.– Just a fraction with the two
numbers being compared making up the fraction.
S
P
S
P
N
N
Z
Z
Let’s do some math!
• ZP = 1600
• ZS = 8
• Ratio of NP to NS = ?
• ZP / ZS = ? 1600/8 = 200 Write the number down
• 2001/2 = ? 2001/2 = 14.1
• Ratio of NP to NS = 14.1 / 1 Ratio is 14.1 to 1
S
P
S
P
N
N
Z
Z
Let’s do some math!
←Logarithms– “the log of N is L.”
– Or “What power of 10 will give you N?”
←Anti-log: Reverse or opposite of the log.
NL 10log
LN 10
Making Sense of Decibels
Examples of Power Ratios commonly expressed in dB:
•Gain of an amplifier stage
•Pattern of an antenna
•Loss of a transmission line
1
2log*10 10 P
PdB
Ratio of the Power Out to the Power In
Common Decibel Tables1dB = 10 x log101.26
3dB = 10 x log102
6dB = 10 x log104
7dB = 10 x log105
9dB = 10 x log108
10dB = 10 x log1010
13dB = 10 x log1020
17dB = 10 x log1050
20dB = 10 x log10100
-1dB = 10 x log101/1.26
-3dB = 10 x log101/2
-6dB = 10 x log101/4
-7dB = 10 x log101/5
-9dB = 10 x log101/8
-10dB = 10 x log101/10
-13dB = 10 x log101/20
-17dB = 10 x log101/50
-20dB = 10 x log101/100
Let’s do some math!
• Divide P2 by P1.– Write the number down.
• Press the log key on your calculator and enter the value of P2/P1.– Write the number down.
• Multiply the result by 10.
• P2 = 200
• P1 = 50
• dB = ?
1
2log10 10 P
PdB
Let’s do some math!
• P2 = 200
• P1 = 50
• dB = ?
• P2/P1 = ? 200/50 = 4 Write the number down.
• Log 4 = ? Log (4) = 0.602 Write the number down.
• 0.602 * 10 = ? 0.602 * 10 = 6.02
1
2log10 10 P
PdB
Thank goodness it’s over!