# 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!

 Prefix Prefix Value name symbol International System of Units (SI) 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:

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

Length of transmission line:

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

Forward and reflected power:

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

Image response frequencies:

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

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

Time constant (all components in parallel):

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

$$C_t = C_1 + C_2$$

$$T = R \times C$$

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

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

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:

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

$$A_V = \frac{R_F}{R1}$$

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:

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

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

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

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