Math for the General Class Ham Radio Operator

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Math for the General Class Ham Radio Operator

• A Prerequisite Math RefresherFor The Math-Phobic
  Ham

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Why is This Lesson for You?
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Math Vocabulary

• What are equations and formulas?
• What do variables mean?
• What is an operator?

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C2 A2 B2
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Math VocabularyWhat is an operator?

• Math operations
• Add
• Subtract -
• Multiply X or ?
• Divide / or
• Exponents YX
• Roots or

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Math Vocabulary

• What does solving an equation mean?
• Getting the final answer!

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Getting the Final AnswerTricks of the Trade

• Opposite math operations
• Addition ? Subtraction
• Multiplication ? Division
• Roots ? Exponents

• A number divided by the same number is 1,
  1
• A number multiplied by 1 is that number, Y 1 Y

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
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What does solving an equation mean?Example 1
C2 A2 B2
Assume A and B are known Want to solve for C.
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What does solving an equation mean?Example 2

• The equation for Ohms Law is
• E I R
• The variables mean
• E represents voltage
• I represents current
• R represents resistance
• The math operator is multiplication.

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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 1050
• E 500 (in this case volts)

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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

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Lets do some math!

• Simple addition

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Lets 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.

• R1 50
• R2 200
• RT Total Resistance ?

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Lets do some math!

• R1 R2 ?
• 50 200 10,000
• R1 R2 ?
• 50 200 250
• RT 10,000/250 40

• R1 50
• R2 200
• RT ?

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Lets 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.

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Lets do some math!

• 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

• R1 50
• R2 100
• R3 200

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Lets 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

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Lets do some math!

• E2 ? (square E)
• 3002 90,000
• 90,000/R ?
• P 90000/450 200

• E 300
• R 450

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Lets do some math!

• Solve for VRMS
• VRMS VPeak / 1.414
• Plug in value for VPeak
• VRMS 100/1.414
• 100/1.414 70.7

• VPeak 100
• VRMS ?

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Lets do some math!

• Sometimes two formulas need to be used to come to
  a final answer.

• Solve equation 1 for VRMS
• Plug the value of VRMS into equation 2.

• VPeak 300
• R 50
• PEP ?

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Lets 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

• VPeak 300
• R 50
• PEP ?

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Lets do some math!

• NS 300
• NP 2100
• EP 115
• ES ?

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Lets do some math!

• NS EP ?
• 300 115 34,500
• Write the number down
• Result / NP ?
• ES 34500/2100 16.4

• NS 300
• NP 2100
• EP 115
• ES ?

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Lets 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.

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Lets do some math!

• 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

• ZP 1600
• ZS 8
• Ratio of NP to NS ?

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Lets 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.

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Making Sense of Decibels
Ratio of the Power Out to the Power In

• Examples of Power Ratios commonly expressed in
  dB
• Gain of an amplifier stage
• Pattern of an antenna
• Loss of a transmission line

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Common Decibel Tables

• 1dB 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

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Lets 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 ?

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Lets do some math!

• 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

• P2 200
• P1 50
• dB ?

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Thank goodness its over!