Thermal Noise Definition - Telecommunications - Lecture Slides, Slides of Telecommunication electronics

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Thermal Noise Definition

• All dissipative (resistive) elements generate

thermal, or Johnson, noise.

• This noise power is expressed in Watts as

PN

= kTB (note: P

N

is not a function of resistance)

where

k — (Boltzman constant) 1.38 × 10

joule/K

T — the temperature in Kelvin

B — the bandwidth used to measure the noise power,

expressed in Hz

• In an ideal noiseless system, the thermal noise

controls the lowest detectable signal.

• In a true physical system, the noise of the system is

added to the thermal noise to establish the “Noise

Floor.”

• Generally the minimum useful signal level is well above

the Noise Floor.

Noise Floor Definition

• The dB difference between the KTB thermal

noise power and the actual noise power is called

Noise Figure (NF).

• When it is referenced to the input port of a circuit or

system, the Noise Figure:

P KTB

KTB

P

NF Nactual

Nactual

dB 10 log = 10 log − 10 log 















=

• In an actual physical system, in the absence of IM

distortion, the Noise Figure at the input

determines the lowest detectable signal.

• However, for error-free detection, a certain minimum

“signal-to-noise ratio” is required.

• Harmonic distortion in amplifiers is caused by

nonlinear effects on the sinusoidal waveform.

• Distortion components are created at integer multiples

of the signal frequency shown below:

• A memoryless nonlinearity may be described by a

Power Series where the real coefficients of some

of the terms may have negative signs.

• If the input signal is a sinusoidal wave,
• the higher order terms at the output show up in

forms of higher frequencies, harmonically related

to VIN.

v A cos( f t )

IN c

= 2 π

[ ] [ ] [ ]

[ ] [ ] [ ]

DC term Fundamental Harmonic Harmonic

f t

a A f t

a A f t

a A a A

a A a

a a A f t a A f t a A f t

a a A f t a A f t a A f t

v a a v a v a v a v

nd rd

c c c

c c c

c c c

n OUT IN IN IN n IN

3 3

2 2

2 3 2

2 2 0

3 3

2 0 1 2

3 3

2 0 1 2

3 3

2 0 1 2

cos( ) cos( ) cos( )

cos( ) cos( ) cos( )

cos( ) cos( ) cos( )

Gain Compression

• If the magnitude of the input signal (A) is raised

to a sufficient level, the gain term of the

fundamental output will compress, due to the fact

that the sign of a

is negative.

_ cos( f t^ )

a A

v (^) OUT Fund a A 2 π c

3 3

The power level where the actual

fundamental output power is 1 dB less

than expected, is called the 1dB Gain

Compression, or P 1dB of the amplifier.

• In hard compression, beyond P 1dB

, the higher

order terms become more dominant and the

output waveform begins to look like a square-

wave.

• Referred to the input this level is IIP3.
  • The 1dB compression level is ABOUT 10dB below

OIP3.

• In exceptional devices, 20dB.