📋 Formula Quick Reference

All the key formulas you need for the Advanced exam, in one place.

Impedance\( Z = R + jX \)

Impedance magnitude\( |Z| = \sqrt{R^2 + X^2} \)

Inductive reactance\( X_L = 2\pi fL \)

Capacitive reactance\( X_C = \frac{1}{2\pi fC} \)

Series impedance\( Z_T = Z_1 + Z_2 + \cdots \)

Parallel impedance (2)\( Z_T = \frac{Z_1 Z_2}{Z_1 + Z_2} \)

Resonant frequency\( f_r = \frac{1}{2\pi\sqrt{LC}} \)

Q factor\( Q = \frac{f_r}{BW} \)

Q (series RLC)\( Q = \frac{X_L}{R} \)

Bandwidth\( BW = \frac{f_r}{Q} \)

Rolloff per pole\( -20 \text{ dB/decade} \)

Power gain (dB)\( G = 10\log_{10}(P_{out}/P_{in}) \)

Voltage gain (dB)\( G = 20\log_{10}(V_{out}/V_{in}) \)

+3 dB\( \times 2 \text{ power} \)

+6 dB\( \times 4 \text{ power, } \times 2 \text{ voltage} \)

+10 dB\( \times 10 \text{ power} \)

dBm\( P_{dBm} = 10\log_{10}(P/1\text{mW}) \)

Half-wave dipole length\( L = 143/f_{MHz} \text{ metres} \)

dBi to dBd\( \text{dBi} = \text{dBd} + 2.15 \)

SWR from reflection coeff\( SWR = \frac{1+|\Gamma|}{1-|\Gamma|} \)

Quarter-wave match\( Z_m = \sqrt{Z_1 Z_2} \)

ERP\( ERP = P_{tx} + G_{dBd} - L_{dB} \)

FOT\( FOT = 0.85 \times MUF \)

Image frequency\( f_{image} = f_{sig} \pm 2f_{IF} \)

FM bandwidth (Carson)\( BW = 2(\Delta f + f_m) \)

PLL output\( f_{out} = N \times f_{ref} \)

Power density (far field)\( S = \frac{PG}{4\pi d^2} \)

Safe distance\( d = \sqrt{\frac{PG}{4\pi S_{limit}}} \)

Nyquist rate\( f_s \geq 2 f_{max} \)

ADC dynamic range\( \approx 6n \text{ dB} \)

Shannon capacity\( C = B\log_2(1 + SNR) \)

Friis noise figure\( NF_T \approx NF_1 + \frac{NF_2-1}{G_1} \)