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 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


Antenna gain in dBd vs dBi:

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

Effective radiated power:

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

Length of transmission line:

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

Forward and reflected power:

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

Third-order intermodulation products:

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


Operational amplifiers:

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

$$ A_V = \frac{R_F}{R1} $$
 

Image response frequencies:

$$ f_{img1} = f_{RF} - 2 \times f_{IF} $$

$$ f_{img2} = f_{RF} + 2 \times f_{IF} $$
 

Noise floor:

$$ BNF = NF + 10 \times \text{log}(BW) $$

where:

$$ BNF $$ is the bandwidth noise floor (the noise for the entire received bandwidth) (in dBm)

$$ NF $$ is the 1-Hz noise floor (in dBm/Hz)

$$ BW $$ is the receive filter bandwidth (in Hz)
 

Time constant (all components in parallel):

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

$$ C_t = C_1 + C_2 $$

$$ T = R \times C $$
 

Parts per million:

$$ maximum \text{-} error = measurement \times accuracy $$
 

Resonant frequency:

$$ f_R = \frac{1000}{2\pi \sqrt{LC}} $$

where:

$$ L $$ in $$ \mu\text{H} $$

$$ C $$ in $$ \text{pF} $$

$$ f_R $$ in $$ \text{MHz} $$
 

Half-power bandwidth:

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

Transformer turns #1:

$$ N = 100 \times \sqrt{\frac{L}{A_L}} $$

where:

L in $$ \mu\text{H} $$

AL in $$ \mu\text{H} / 100 \text{ turns} $$


Transformer turns #2:

$$ N = 1000 \times \sqrt{\frac{L}{A_L}} $$

where:

L in $$ \text{mH} $$

AL in $$ \text{mH} / 1000 \text{ turns} $$
 

Frequency modulation:

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

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

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:

$$ power \text{-}\!factor = \text{cos} \left(\theta \right) $$

$$ apparent \text{-}power = V_{RMS} \times I $$

$$ true \text{-}power = apparent \text{-}power \times power \text{-}\!factor $$

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