# ELEMENTARY,MY DEAR WATSON

AKA: SDRI fifth meetup!

JULY 2016

Software Defined Radio Israel

## MAIN PRINCIPLE OF DECIBELS

{ Ratio }_{ [dB-reference] }=10\cdot \log _{ 10 }{ \left( \frac { { Value }_{ [base] } }{ Reference_{ [base] } } \right) }
${ Ratio }_{ [dB-reference] }=10\cdot \log _{ 10 }{ \left( \frac { { Value }_{ [base] } }{ Reference_{ [base] } } \right) }$

dBi

dBm

dBc

{ Ratio }_{ [dBm] }=10\cdot \log _{ 10 }{ \left( \frac { { Value }_{ [mW] } }{ 1_{ [mW] } } \right) }
${ Ratio }_{ [dBm] }=10\cdot \log _{ 10 }{ \left( \frac { { Value }_{ [mW] } }{ 1_{ [mW] } } \right) }$
{ Ratio }_{ [dBc] }=10\cdot \log _{ 10 }{ \left( \frac { frequency\_ component\_ power }{ Carrier\_ power } \right) }
${ Ratio }_{ [dBc] }=10\cdot \log _{ 10 }{ \left( \frac { frequency\_ component\_ power }{ Carrier\_ power } \right) }$
{ Ratio }_{ [dBi] }=10\cdot \log _{ 10 }{ \left( \frac { Gain }{ Gain-isotropic\_ antenna } \right) }
${ Ratio }_{ [dBi] }=10\cdot \log _{ 10 }{ \left( \frac { Gain }{ Gain-isotropic\_ antenna } \right) }$

## CHEAT-SHEET

DECIMAL DB
1 0
2 3
10 10
A\cdot B\Longleftrightarrow \log _{ x }{ \left( A \right) + } \log _{ x }{ \left( B \right) }
$A\cdot B\Longleftrightarrow \log _{ x }{ \left( A \right) + } \log _{ x }{ \left( B \right) }$
\frac { A }{ B } \Longleftrightarrow \log _{ x }{ \left( A \right) - } \log _{ x }{ \left( B \right) }
$\frac { A }{ B } \Longleftrightarrow \log _{ x }{ \left( A \right) - } \log _{ x }{ \left( B \right) }$
\log _{ x }{ \left( { A }^{ B } \right) =B\cdot } \log _{ x }{ \left( A \right) }
$\log _{ x }{ \left( { A }^{ B } \right) =B\cdot } \log _{ x }{ \left( A \right) }$

MULTIPLIERS

# WHAT IS NOISE?

## EVERYTHING THAT IS NOT YOUR SIGNAL

NOISE AND INTERFERENCES CAN:

​- MAKE THE TASK OF DECODING A SIGNAL (MUCH) MORE

DIFFICULT

- REDUCE THE QUALITY OF A RECEIVED SIGNAL

- (IN EXTREME CASES) DAMAGE YOUR EQUIPMENT

## POTENTIAL SOURCES

NATURE - THERMAL NOISE, MATHEMATICAL LIMITATIONS

DIFFERENT SIGNALS

UNCHARTED \ WRONG USAGE OF COMPONENTS (SPEC, MATCHING)

COMBINATION OF ALL THE ABOVE :-)

spur