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Math for the General Class Ham Radio Operator A Prerequisite Math Refresher For 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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C 2 = A 2 + B 2

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Math Vocabulary What is an operator? Math operations: –Add: + –Subtract: − –Multiply: X or –Divide: ∕ or –Exponents: Y X –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 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 XXXX A number divided by the same number is 1, = 1 A number multiplied by 1 is that number, Y * 1 = Y

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What does solving an equation mean? Example #1 C 2 = A 2 + B 2 Assume A and B are known Want to solve for C. C 2 = A 2 + B 2 Apply same operation to both sides C 2 = A 2 + B 2 Opposite operations cancel each other C = A 2 + B 2 Voila!!!

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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.

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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 = 10*50 E = 500 (in this case volts)

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Math Vocabulary What does solving an equation mean? What if we know the voltage and the current and want to find the resistance? E = I * RR = E / I

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Let’s do some math! Simple addition

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Let’s do some math! Multiply R 1 times R 2 –Write the number down Add R 1 and R 2 –Write the number down Divide the first number by the second to find the answer. R 1 = 50 R 2 = 200 R T = Total Resistance = ?

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Let’s do some math! R 1 * R 2 = ? 50 * 200 = 10,000 R 1 + R 2 = ? 50 + 200 = 250 R T = 10,000/250 = 40 R 1 = 50 R 2 = 200 R T = ?

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Let’s do some math! Do each fraction in the denominator in turn 1/R n –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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Let’s do some math! R 1 = 50 R 2 = 100 R 3 = 200 1/R 1 = ? 1/50 = 0.02 1/R 2 = ? 1/100 = 0.01 1/R 3 = ? 1/200 = 0.005 Sum of fractions = ? 0.02 + 0.01 +0.005 =0.035 1/Sum of fractions = ? R T = 1/0.035 = 28.6

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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

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Let’s do some math! E = 300 R = 450 E 2 = ? (square E) 300 2 = 90,000 90,000/R = ? P = 90000/450 = 200

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Let’s do some math! V Peak = 100 V RMS = ? Solve for V RMS V RMS = V Peak / 1.414 Plug in value for V Peak V RMS = 100/1.414 100/1.414 = 70.7

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Let’s do some math! Sometimes two formulas need to be used to come to a final answer. V Peak = 300 R = 50 PEP = ? Solve equation 1 for V RMS Plug the value of V RMS into equation 2.

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Let’s do some math! Solve for V RMS V RMS = 300 / 1.414 300/1.414 = 212.2 Write the number down Plug the value into V RMS. V RMS 2 = 45,013.6 Write the number down Divide the square by 50 45,013.6 /50 = 900.3 V Peak = 300 R = 50 PEP = ?

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Let’s do some math! N S = 300 N P = 2100 E P = 115 E S = ? Solve for E S –Multiply both sides by E P –The E P values on the left cancel Solution is

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Let’s do some math! N S = 300 N P = 2100 E P = 115 E S = ? N S * E P = ? 300 * 115 = 34,500 Write the number down Result / N P = ? E S = 34500/2100 = 16.4

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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.

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Let’s do some math! Z P = 1600 Z S = 8 Ratio of N P to N S = ? Z P / Z S = ? 1600/8 = 200 Write the number down 200 1/2 = ? 200 1/2 = 14.1 Ratio of N P to N S = 14.1 / 1 Ratio is 14.1 to 1

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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.

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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 Ratio of the Power Out to the Power In

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Common Decibel Tables 1dB=10 x log 10 1.26 3dB=10 x log 10 2 6dB=10 x log 10 4 7dB=10 x log 10 5 9dB=10 x log 10 8 10dB=10 x log 10 10 13dB=10 x log 10 20 17dB=10 x log 10 50 20dB=10 x log 10 100 -1dB=10 x log 10 1/1.26 -3dB=10 x log 10 1/2 -6dB=10 x log 10 1/4 -7dB=10 x log 10 1/5 -9dB=10 x log 10 1/8 -10dB=10 x log 10 1/10 -13dB=10 x log 10 1/20 -17dB=10 x log 10 1/50 -20dB=10 x log 10 1/100

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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 = ?

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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

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Thank goodness it’s over!

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