Download Math for the 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?
2
C
2
=A
+
2
B
Math Vocabulary
What 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
• A number divided by the same number is 1,
X
= 1
X
• 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
What does solving an equation mean?
Example #1
2
C
2
=A
2
B
+
2
2
2
C =  A + B
2
2
2
C =  A + B
2
2
C = A + B
Assume A and B are known
Want to solve for C.
Apply same operation to
both sides
Opposite operations cancel
each other
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*R
R=E/I
Let’s do some math!
R1  R2  R3  RN  RT
• Simple addition
Let’s do some math!
R1 R2
 RT
R1  R2
• Multiply R1 times R2
– Write the number down
• Add R1 and R2
• R1 = 50
– Write the number down
• R2 = 200
• RT = Total Resistance = ? • Divide the first number
by the second to find the
answer.
Let’s do some math!
R1 R2
 RT
R1  R2
• R1 = 50
• R2 = 200
• RT = ?
• R1 * R2 = ?
 50 * 200 = 10,000
• R1 + R2 = ?
 50 + 200 = 250
• RT = 10,000/250 = 40
Let’s do some math!
1
1
1
1
1



R1 R2 R3 R N
• Do each fraction in the
denominator in turn 1/Rn
 RT
– 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!
1
1
1
1
1



R1 R2 R3 R N
 RT
• 1/R1 = ?
 1/50 = 0.02
• 1/R2 = ?
 1/100 = 0.01
• R1 = 50
• R2 = 100
• R3 = 200
• 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!
2
E
P
R
• E = 300
• R = 450
• Square the numerator E
– Same as E * E
– Write the number down
• Divide the squared
number by R.
Let’s do some math!
2
E
P
R
• E = 300
• R = 450
• E2 = ? (square E)
 3002 = 90,000
• 90,000/R = ?
 P = 90000/450 = 200
Let’s do some math!
VPeak  1.414VRMS
• VPeak = 100
• VRMS = ?
• Solve for VRMS
 VRMS = VPeak / 1.414
• Plug in value for VPeak
 VRMS = 100/1.414
 100/1.414 = 70.7
Let’s do some math!
VPeak  1.414VRMS
PEP 
VRMS 2
R
• VPeak = 300
• R = 50
• PEP = ?
• 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.
Let’s do some math!
VPeak  1.414VRMS
PEP 
VRMS 2
R
• VPeak = 300
• R = 50
• PEP = ?
• 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
Let’s do some math!
ES N S

EP N P
•
•
•
•
NS = 300
NP = 2100
EP = 115
ES = ?
• Solve for ES
– Multiply both sides by EP
– The EP values on the left
cancel
ES N S
EP 

 EP
EP N P
• Solution is
N S  EP
ES 
NP
Let’s do some math!
N S  EP
ES 
NP
•
•
•
•
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!
ZP NP

ZS
NS
• 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!
ZP NP

ZS
NS
• ZP / ZS = ?
 1600/8 = 200
 Write the number down
• 2001/2 = ?
• ZP = 1600
• ZS = 8
• Ratio of NP to NS = ?
 2001/2 = 14.1
• Ratio of NP to NS =
14.1 / 1
 Ratio is 14.1 to 1
Let’s do some math!
L  log 10 N
N  10
L
←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
Ratio of the Power Out to the Power In
 P2 
dB  10 * log 10 

 P1 
Examples of Power Ratios
commonly expressed in dB:
• Gain of an amplifier stage
• Pattern of an antenna
• Loss of a transmission line
Common Decibel Tables
1dB
3dB
6dB
7dB
9dB
10dB
13dB
17dB
20dB
=
=
=
=
=
=
=
=
=
10 x log101.26
10 x log102
10 x log104
10 x log105
10 x log108
10 x log1010
10 x log1020
10 x log1050
10 x log10100
-1dB
-3dB
-6dB
-7dB
-9dB
-10dB
-13dB
-17dB
-20dB
=
=
=
=
=
=
=
=
=
10 x log101/1.26
10 x log101/2
10 x log101/4
10 x log101/5
10 x log101/8
10 x log101/10
10 x log101/20
10 x log101/50
10 x log101/100
Let’s do some math!
 P2 
dB  10 log 10 

 P1 
• P2 = 200
• P1 = 50
• dB = ?
• 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 
dB  10 log 10 

 P1 
• P2/P1 = ?
 200/50 = 4
 Write the number down.
• Log 4 = ?
• P2 = 200
• P1 = 50
• dB = ?
 Log (4) = 0.602
 Write the number down.
• 0.602 * 10 = ?
 0.602 * 10 = 6.02
Thank goodness it’s over!