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? Math operations: –Add: + –Subtract: − –Multiply: X or –Divide: ∕ or –Exponents: Y X –Roots: or

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 XXXX 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 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!!!

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 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

Let’s do some math! Simple addition

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 = ?

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

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.

Let’s do some math! R 1 = 50 R 2 = 100 R 3 = 200 1/R 1 = ?  1/50 = /R 2 = ?  1/100 = /R 3 = ?  1/200 = Sum of fractions = ?  = /Sum of fractions = ?  R T = 1/0.035 = 28.6

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

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

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

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.

Let’s do some math! Solve for V RMS  V RMS = 300 /  300/1.414 =  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 = V Peak = 300 R = 50 PEP = ?

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

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

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.

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

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.

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

Common Decibel Tables 1dB=10 x log dB=10 x log dB=10 x log dB=10 x log dB=10 x log dB=10 x log dB=10 x log dB=10 x log dB=10 x log dB=10 x log 10 1/ dB=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

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 = ?

Let’s do some math! P2 = 200 P1 = 50 dB = ? P2/P1 = ?  200/50 = 4  Write the number down. Log 4 = ?  Log (4) =  Write the number down * 10 = ?  * 10 = 6.02

Thank goodness it’s over!