Formulas on the Extra Exam

This page contains all the formulas needed for the Extra class ham radio license exam.  You might want to print out these formulas and review them just before entering the exam room, but leave this sheet in the car!  Do not bring it into the exam room with you!

International System of Units (SI)
Prefix
name
Prefix
symbol
Value
giga- G 109 1,000,000,000 one billion
mega- M 106 1,000,000 one million
kilo- k 103 1,000 one thousand
(none) (none) 100 1 one
centi- c 10−2 .01 one one-hundredth
milli- m 10−3 .001 one one-thousandth
micro- µ 10−6 .000001 one one-millionth
nano- n 10−9 .000000001 one one-billionth
pico- p 10−12 .000000000001 one one-trillionth

Determine the maximum carrier frequency for operating USB close to band-edge:

$$ maximum\text{-}carrier\text{-}frequency = top\text{-}of\text{-}USB\text{-}segment - width\text{-}of\text{-}USB\text{-}signal $$
 

Antenna gain in dBd vs dBi:

$$ gain\text-of\text-antenna\text-in\text-dBd = gain\text-of\text-antenna\text-in\text-dBi - 2.15~ \text{dB} $$
 

Forward and reflected power:

$$ power\text-to\text-load = forward\text-power - reflected\text-power $$
 

Convert dBm to watts:

$$ x\text{ dBm} = 10^\left(\large \frac{x}{10}\right) \text{ mW}$$
 

Time constant (all components in parallel):

$$ R_t = \frac{R_i}{n} $$

$$ C_t = C_1 + C_2 $$

$$ T = R \times C $$
 

Length of transmission line:

$$ \lambda = \frac{c~ \times~ velocity \text{-}\!factor}{f} $$
 

Effective radiated power:

$$ ERP = transmitter \text{-}power \times 10^\left(\frac{gain~in~dBd}{10}\right) $$

$$ EIRP = transmitter \text{-}power \times 10^\left(\frac{gain~in~dBi}{10}\right) $$
 

Resonant frequency:

$$ f_R = \frac{1000}{2\pi \sqrt{LC}} $$    (where $$ L $$ in $$ \mu\text{H} $$, $$ C $$ in $$ \text{pF} $$, returns $$ f_R $$ in $$ \text{MHz} $$)
 

Half-power bandwidth:

$$ hal\!f \text{-} power \text{-} bandwidth = \frac {f_R}{Q} $$
 

Operational amplifiers:

$$ V_{OUT} = -V_{IN} × \frac{R_F}{R1} $$

$$ A_V = \frac{R_F}{R1} $$
 

Image response frequencies:

$$ f_{possible1} = f_{RF} - 2 \times f_{IF} $$

$$ f_{possible2} = f_{RF} + 2 \times f_{IF} $$
 

Frequency modulation:

$$ deviation \text{-}ratio = \frac{D_{MAX}}{M_{MAX}} $$

$$ modulation \text{-}index = \frac{frequency\text-deviation}{modulating\text-frequency} $$
 

Intermodulation:

 Formula  Solve for ƒ2
$$f_i = 2f_1 - f_2 $$ $$ f_2 = 2f_1 - f_i $$
$$f_i = 2f_2 - f_1 $$ $$ f_2 = \frac{f_i + f_1}{2} $$

Inductive and capacitive reactances:

$$ X_L = 2\pi fL $$

$$ X_C = \frac{1}{2\pi fC} $$

$$ X = X_L - X_C $$
 

Phase angle:

$$ \theta = \text {arctan} \left(\frac {X}{R}\right) $$
 

Power factor:

$$ P = I^2 \times R $$