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Math for the General Class Ham Radio Operator

Math for the General Class Ham Radio Operator. A Prerequisite Math Refresher For 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?. C 2 = A 2 + B 2. Math Vocabulary What is an operator?.

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Math for the General Class Ham Radio Operator

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  1. Math for the General Class Ham Radio Operator A Prerequisite Math RefresherFor The Math-Phobic Ham

  2. Why is This Lesson for You?

  3. Math Vocabulary • What are equations and formulas? • What do variables mean? • What is an operator?

  4. C2 =A2 + B2

  5. Math VocabularyWhat is an operator? • Math operations: • Add: + • Subtract: − • Multiply: X or ⃰ • Divide: ∕ or • Exponents: YX • Roots: or

  6. Math Vocabulary What does solving an equation mean? Getting the final answer!

  7. Getting the Final Answer:Tricks of the Trade: Opposite math operations: Addition  Subtraction Multiplication  Division Roots  Exponents X X • 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

  8. Apply same operation to both sides C2 =A2 + B2 C2 =A2 + B2 Opposite operations cancel each other C =A2 + B2 Voila!!! What does solving an equation mean?Example #1 C2 =A2 + B2 Assume A and B are known Want to solve for C.

  9. 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.

  10. 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)

  11. 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

  12. Simple addition Let’s do some math!

  13. 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. Let’s do some math! • R1 = 50 • R2 = 200 • RT = Total Resistance = ?

  14. R1 * R2 = ? 50 * 200 = 10,000 R1 + R2 = ? 50 + 200 = 250 RT = 10,000/250 = 40 R1 = 50 R2 = 200 RT = ? Let’s do some math!

  15. 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. Let’s do some math!

  16. 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 Let’s do some math!

  17. Square the numerator E Same as E * E Write the number down Divide the squared number by R. Let’s do some math! • E = 300 • R = 450

  18. E = 300 R = 450 E2 = ? (square E) 3002 = 90,000 90,000/R = ? P = 90000/450 = 200 Let’s do some math!

  19. 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

  20. Let’s 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 = ?

  21. 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 • VPeak = 300 • R = 50 • PEP = ?

  22. Solve for ES • Multiply both sides by EP • The EP values on the left cancel • Solution is Let’s do some math! • NS = 300 • NP = 2100 • EP = 115 • ES = ?

  23. NS = 300 NP = 2100 EP = 115 ES = ? NS * EP = ? 300 * 115 = 34,500 Write the number down Result / NP = ? ES = 34500/2100 = 16.4 Let’s do some math!

  24. 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. Let’s do some math!

  25. 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 Let’s do some math!

  26. Logarithms “the log of N is L.” Or “What power of 10 will give you N?” Anti-log: Reverse or opposite of the log. Let’s do some math!

  27. Examples of Power Ratios commonly expressed in dB: Gain of an amplifier stage Pattern of an antenna Loss of a transmission line Making Sense of Decibels Ratio of the Power Out to the Power In

  28. 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 Common Decibel Tables

  29. 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. Let’s do some math! • P2 = 200 • P1 = 50 • dB = ?

  30. 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 Let’s do some math!

  31. Thank goodness it’s over!

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