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 |
| $$f_i = 2f_1 - f_2 $$ |
$$ f_2 = 2f_1 - f_i $$ |
| $$f_i = 2f_2 - f_1 $$ |
$$ f_2 = \frac{f_i + f_1}{2} $$ |
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)
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:
$$ power \text{-}\!factor = \text{cos} \left(\theta \right) $$
$$ apparent \text{-}power = V_{RMS} \times I $$
$$ true \text{-}power = apparent \text{-}power \times power \text{-}\!factor $$
$$ P = I^2 \times R $$
