noise performance of cw system
TRANSCRIPT
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 1
Noise performance of CW system
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 2
Narrow band noise
Narrow Band BPF Hn(f)
Pass band 2B
Channel
white noise w(t)Narrow band
Noise n(t)
Receiverdemodulator
LPF cut off W
fc-B fc fc+B-fc-B -fc -fc+B
Sn(f)
fc-B fc fc+B-fc-B -fc -fc+B
Hn(f) Sw(f)
• First stage at the receiver end is BPF of pass band 2B to limit the noise. • spectral density of white Noise Sw(f) at input of BPF is constant (/2)• spectral density of Noise Sn(f) at output of BPF is narrow band
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 3
Narrow band noiseFrom the narrow band spectral density function of noise , it is evident that narrow band noise n(t) is approximately a sinusoidal function of frequency fc with amplitude and phase varying randomly.
= Where In phase component of narrow band noise, And quadrature phase component of narrow band noise,
Thus narrow band noise can be viewed as sum of In-phase component of noise modulated on carrier signal and quadrature phase component of noise modulated with quadrature shifted version of carrier signal
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 4
Narrow band noiseProperties of narrow band noise• If and has zero mean• • Both and has same power spectral density which is related to spectral density of
narrow band noise, as ==+ Thus
f
𝑆𝑛𝐼 ( 𝑓 )𝑜𝑟 𝑆𝑛𝑄 ( 𝑓 )
B-Bfc-B fc+B
𝜂2
𝑆𝑛 ( 𝑓 )
f-fc-B -fc+B
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 5
Noise performance of DSB-SC system (coherent detection)
For DSB-SC, Input to demodulator, Signal power at input, Noise power at input,
Input of multiplier =Output of the multiplier=cos()
Narrow Band BPF Hn(f)
Pass band 2W
Channel
white noise w(t)
s(t)+n(t)
Receiver
LPF cut off W
s(t) +nw(t) demodulator
cos(2fct)
sd(t)+nd(t)Si
Ni
So
No
s(t)
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 6
Noise performance of DSB-SC system (coherent detection)
Output of the multiplier=Output of Low pass filter=• It can be observed that message component and in phase component of noise appear in the
output with half magnitude• Quadrature component of noise is fully rejected by coherent receiverat the output, Signal power , Noise power,
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 7
Noise performance of DSB-SC system (coherent detection)
noise figure of DSB-SC receiver, Figure of merit of DSB-SC receiver =1/ F 2• Noise figure of DSB-SC receiver implies that noise power is reduced by half. IT eliminates
quadrature component of noise power
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 8
Noise performance of SSB-SC system (coherent detection)
For SSB-SC, , +ve sign for LSB and –ve sign for USBInput to demodulator, Signal power at input, or, as [ is Hilbert transform of m(t)]Thus signal power is half of that in DSB-SCNoise power at input,
Narrow Band BPF Hn(f)
Pass band W
Channel
white noise w(t)
s(t)+n(t)
Receiver
LPF cut off W
s(t) +nw(t) demodulator
cos(2fct)
sd(t)+nd(t)Si
Ni
So
No
s(t)
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 9
Noise performance of SSB-SC system (coherent detection)
Input of multiplier =Output of the multiplier
Output of Low pass filter=at the output, Signal power , , Noise power,
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 10
Noise performance of SSB-SC system (coherent detection)
noise figure of SSB-SC receiver, Figure of merit of DSB-SC receiver =1/ F 1• It implies that noise performance of SSB-SC is inferior to DSB-SC. • But closer examination reveals that signal power and bandwidth at the input of SSB-
SC is half of that in DSB-SC (due to one sideband removed in filtering method).• coherent receiver rejects quadrature component of noise. Also message and in
phase component of noise appear in the output with half magnitude . • Thus for same average input power and same transmission bandwidth performance
of both DSB-SC and SSB-SC receivers will be same
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 11
Noise performance of AM system (Envelope detector)
For AM, Input to demodulator, Signal power at input, or, Noise power at input,
Narrow Band BPF Hn(f)
Pass band 2W
Channel
white noise w(t)
s(t)+n(t)
Receivers(t) +nw(t)
demodulator
Si
Ni
So
No
s(t) Envelope detector
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 12
Noise performance of AM system (Envelope detector)
Input of multiplier = can be represented in polar form as
where is envelope of AM wave
And is phase angle
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 13
Noise performance of AM system (Envelope detector)
𝐴𝑐+𝑘𝑎m( t) 𝑛𝐼(𝑡)𝑛𝑄 (𝑡)𝑅 (𝑡 )𝑒(𝑡)
𝜓 (𝑡) 𝜃(𝑡)
small noise
Small noise caseIn this case, Under this condition e(t) can be approximated as‘Ignoring higher order terms being very small
Or output of envelope detector. and
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 14
Noise performance of AM system (Envelope detector)
Signal power at the output Noise power at the output Noise figure As (modulation index is less than 100 %), noise figure of AM receiver is always greater than 1For single tone message , Noise figure where m is modulation indexFor maximum modulation (m=1), noise figure will be minimum i.e. Minimum • Noise figure of AM with envelope detector (small noise) is same as that of Noise
figure of AM with coherent detector
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 15
Noise performance of AM system (Envelope detector)
𝐴𝑐+𝑘𝑎m( t) 𝑛𝐼(𝑡)
𝑛𝑄 (𝑡 )𝑅 (𝑡)𝑒(𝑡)
𝜓 (𝑡) 𝜃(𝑡 )
Large noise
Large noise caseIn this case, Under this condition e(t) can be approximated as‘Ignoring higher order terms being very small and using
Or output of envelope detector. As the term containing message is multiplied by noise term, message signal can not be recovered.
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 16
Noise performance of FM system
For FM, , where Also narrow band noise, Where and Signal power at input, Noise power at input, Input to demodulator, Envelope ofis of no interest and any variation in envelope will be removed by hard limiter, while relative phasor is of the interest.
Narrow Band BPF Hn(f)
Pass band BT
Channel
white noise w(t)
s(t)+n(t)
Receivers(t) +nw(t)
demodulator
Si
Ni
So
No
s(t) Hard limiter
12𝜋
𝑑𝑑𝑡
LPFCutoff Wsd(t) +nd(t)
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 17
Noise performance of FM system Small noise case In this case, Choosing as reference for phasor diagram. Relative phase angle [for small . tan = ] The differentiator output The signal component will pass through LPF, so signal power in the output
𝐴𝑐
𝑅 (𝑡)𝑒(𝑡)
𝜓 (𝑡 )−𝜙 (𝑡) 𝜃 (𝑡 )−𝜙 (𝑡 )
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 18
Noise performance of FM system Noise component As is random and uniformly distributed, so it can be fairly assumed that is uniformly distributed over 2. So noise component will be independent of message signal.
So noise component Thus noise component at differentiator output. can be obtained passing through a system whose frequency response is given as
Power spectral density of noise component is given as Where =+
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 19
Noise performance of FM system
𝜂2
𝑆𝑛 ( 𝑓 )
f
f
𝑆𝑛𝑄 ( 𝑓 )
−𝐵𝑇
2𝐵𝑇
2
f
( 𝐵𝑇
2 𝐴𝑐)2
𝑆𝑛𝑑 ( 𝑓 )
−𝐵𝑇
2𝐵𝑇
2
f
(𝑊𝐴𝑐 )2
𝑆𝑛𝑜 ( 𝑓 )
−𝑊 𝑊
Again Output noise power, Or
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 20
Noise performance of FM systemNoise figure For single tone message . modulation index and and So, For NBFM, , For WBFM, , Thus FM improves noise performance with increase in modulation index
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 21
Noise performance of FM systemBest noise figure obtained in AM is 1.5 (for m=1), for better noise performance of FM than AM, NBFM noise figure must be less than AM noise figure i.e. <1.5 or Thus for noise performance of FM is similar to AM while for higher noise performance of FM is superior to AM and In FM SNR improves with increase in modulation index.FM Threshold Effect: Above results were based on assumptions that carrier component is much lather than noise component.If input signal is decreased input SNR will also decrease, resulting in decrease in SNR improvement. There will be a point below which if input SNR decreases, output SNR will decrease more rapidly. That value of input SNR is referred as FM threshold. FM threshold is 13 dB or 20i.e . Input SNR implies that carrier power at the input
02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 22
Threshold improvement in FM: Pre-emphasis de-emphasis
• In practical signals amplitude decreases with increase in frequency. This implies lower SNR (more effect of noise) for high frequency components of message.
• High frequency component may suffer from FM threshold effect.• High frequency components have lower amplitude but are most
important for quality of message.This difficulty can be solved by use of Pre-emphasis de-emphasis.Pre emphasis: High frequency components are boosted (amplified) before modulation.
De emphasis: After demodulation High frequency components are de-boosted to restore original signal.
dB
f
Pre-emphasis gaindB
fDe-emphasis gain