Multiplexage pour les nuls

(1)

HAL Id: hal-03252697

https://cel.archives-ouvertes.fr/hal-03252697

Submitted on 23 Aug 2021

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Damien Prêle

To cite this version:

Damien Prêle. Multiplexage pour les nuls. École thématique. France. 2016. �hal-03252697�

(2)

Damien PRÊLE

p

[email protected]

August 23, 2021

(3)

1

Basic multiplexing considerations

2

Multiplexing/Demultiplexing of tones

3

Technological considerations

(4)

Multiplexing general

Transmission of N signals over 1 channel

N data/signals INFORMATION

Multiplexer One channel TRANSMISSION

Introduced for telegraphy at the end of the 19 ^{t h} century and widely applied in telecommunications during the 20 ^{t h} century :

several telephone calls may be carried using one wire

(5)

Multiplexing general

Transmission of N signals over 1 channel

N data/signals INFORMATION

Multiplexer One channel TRANSMISSION

That is not a real multiplexer, because this need to reduces - Data compression - the transmitted informations to use the same output

channel capacity

[email protected] 4 / 35 Damien PRÊLE - Multiplexing for dummies - Préparation WorkshopMultiplexageX-IFU 2016

(6)

Multiplexing general

Transmission of N signals over 1 channel with HIGHER "capacity"

N data/signals INFORMATION

Multiplexer One channel TRANSMISSION

B To transmit N signals via One channel, the "channel" must

provides better performances than for a single signal transmission .

(7)

Multiplexing notice

B To transmit N signals via one channel, the "channel" must provides better performances than for a single signal transmission .

⇒ The increasing of the required performances is directly linked to the number N of multiplexed signals.

⇒ The affected performances are both : Band Width

Dynamic / Signal to Noise Ratio

the multiplexing divides the capacity of the high-level communica- tion channel into several low-level sub-channels, one for each mes- sage, signal or data to be transmited.

(8)

Multiplexing as a modulation

There are intersections between modulation and multiplexing Multiplexing = modulation of input signals by orthogonal signals:

×

× Σ N input signals

Modulation by orthogonal signals

Multiplexed output

Mod ul at i on ⇒ Higher BW

Σ ⇒ Higher Dynamic/SNR

Orthogonal : boxcar functions or carriers at different frequencies.

Orthogonality ⇒ demultiplexer able to recover each input signal without

interference from the other.

(9)

Orthogonal functions

boxcar functions ≡ sampling

0 +1

t carriers ≡ modulation

FT

f linear codes ^* ≡ coding

-1 +1

t

*as used for error-detection/correction code. Especially, Hadamard/Walsh code could be used for multiplexing.

(10)

Multiplexing type vs standard modulations

Multiplexing

Time Domain Multiplexing (TDM) Frequency Domain Multiplexing (FDM)

Wave length Domain Multiplexing for optical fiber Coded Domain Multiplexing (CDM)

Coding

Amplitude Shift Keying (ASK) Frequency Shift Keying (FSK)

Coded Division Multiple Access (CDMA)

(11)

Code as a third dimension ?

t code

f

TDM t

code

f

FDM t

f code

CDM

Multiplexing ⇒ spread spectrum

Code is represented as a third dimension even if this is not necessarily a physical dimension.

CDM is usually used to spread the spectrum of the multiplexed signal. But the code dimension is often a repartition both in time, in frequency and some times in amplitude.

(12)

Time Domain Multiplexing (TDM)

Time slot of limited duration of each input signal (S x ) is summed

t

S1

t

S2

t

S3

bo xcar modul at ion t

S1×boxcar1

t

S2×boxcar2

t

S3×boxcar3

summat ion

t

MU X

Requires a specific boxcar (time shifted) modulation / signal Limited duration ≡ sampling

⇒increasing of the bandwidth

= risk of noise aliasing

(13)

Frequency Domain Multiplexing (FDM)

Frequency transposition of each input signal (S x ) is summed

f

S1

f

S2

f

S3

ca rr ier modul a tion f

S1×carrier1

f

S2×carrier2

f

S3×carrier3

summat ion

f

MU X

Requires a specific frequency carrier / signal

Summation ≡ increasing the bandwidth and the dynamic

(14)

Sine waves multiplexing

until now, signal has been represented as a time or freq. "tophat"

t

S

f

S

from now, signals will be represented as 4 sine waves

(15)

Time Domain/Division Multiplexing - TDM

Modulation - Sampling

(16)

Time Domain/Division Multiplexing - TDM

Summation - multiplexing

Σ

(17)

Time Domain/Division Multiplexing - TDM

Spectrum occupancy : BW T D M > N × fs > 2 × N × BW Si g

(18)

Time Domain/Division Multiplexing - TDM

Shannon-Nyquist Unsatisfied ⇒ Alias the unfiltered white noise spectresig1

0 200 400 600 800 1000 1200

Frequency [Hz]

0.001 0.010 0.100 1.000

Amplitude [V]

spectresig1nf

0 200 400 600 800 1000 1200

Frequency [Hz]

0.001 0.010 0.100 1.000

Amplitude [V]

(19)

Time Domain/Division Multiplexing - TDM

demultiplexing before sample & hold and filtering

×

(20)

Frequency Domain/Division Multiplexing - FDM

Modulation - Frequency transposition

(21)

Frequency Domain/Division Multiplexing - FDM

Summation - multiplexing

Σ

(22)

Frequency Domain/Division Multiplexing - FDM

Increasing of the amplitude of the multiplexed signal

(23)

Frequency Domain/Division Multiplexing - FDM

Spectrum occupancy : BW F D M > 2 × N × BW Si g

Multiplexing

(24)

Frequency Domain/Division Multiplexing - FDM

Aliasing of the unfiltered signal and white noise

As for TDM, there is a "Shannon-Nyquist" law (modulation vs

sampling) which need to limit the signal (and noise) to a bandwidth

below an half of the carriers frequency separation

(25)

Frequency Domain/Division Multiplexing - FDM

demultiplexing before filtering

×

(26)

Frequency Domain/Division Multiplexing - FDM

demultiplexing in the frequency domain

(27)

Coded Domain/Division Multiplexing - CDM

Modulation - Coding

(28)

Coded Domain/Division Multiplexing - CDM

Summation - multiplexing

Σ

(29)

Coded Domain/Division Multiplexing - CDM

Increasing of the amplitude of the multiplexed signal

(30)

Coded Domain/Division Multiplexing - CDM

Spectrum occupancy : BW F D M > 2 × N × BW Si g

Multiplexing

(31)

Coded Domain/Division Multiplexing - CDM

Spectrum occupancy : wide "spread" spectrum

Multiplexing

(32)

TDM vs FDM principle

Multiplexer 1D

V bi as

i out

4 control wires

Car1, Car2, Car3 and Car4 Biasin

g

Detec tor

array Multiplexer

Sum

v _{bi as}

i out

4 carriers in the same biasing

Car1 + Car2 + Car3 + Car4 L1 C1 L2 C2 L3 C3 L4 C4 Biasin

g

Detec tor

array Multiplexer

Sum

(33)

TDM vs FDM with SQUID 1D

Multiplexer 1D

shuntshunt

T E S1

T E S2

T E Sn IT E Sn

shunt DCBIAS RFB

i F

B

VT DM

ad d.

T E Sn Ln Cn T E S1 L1 C1

T E S2 L2 C2

shunt ACBIAS f1+f2...f n

RFB

i F

B

VF DM

bias

(34)

TDM for QUBIC (APC) 2D

(35)

TDM by NIST 2D

(36)

FDM by SRON 1D

(37)

Multiplexage pour les nuls

HAL Id: hal-03252697

https://cel.archives-ouvertes.fr/hal-03252697

Submitted on 23 Aug 2021

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Damien Prêle

To cite this version:

Damien Prêle. Multiplexage pour les nuls. École thématique. France. 2016. �hal-03252697�

p

August 23, 2021

Basic multiplexing considerations

Multiplexing/Demultiplexing of tones

Technological considerations

Multiplexing general

Transmission of N signals over 1 channel

N data/signals INFORMATION

Multiplexer One channel TRANSMISSION

Introduced for telegraphy at the end of the 19 t h century and widely applied in telecommunications during the 20 t h century :

several telephone calls may be carried using one wire

Multiplexing general

Transmission of N signals over 1 channel

N data/signals INFORMATION

Multiplexer One channel TRANSMISSION

That is not a real multiplexer, because this need to reduces - Data compression - the transmitted informations to use the same output

channel capacity

Multiplexing general

Transmission of N signals over 1 channel with HIGHER "capacity"

N data/signals INFORMATION

Multiplexer One channel TRANSMISSION

B To transmit N signals via One channel, the "channel" must

provides better performances than for a single signal transmission .

Multiplexing notice

B To transmit N signals via one channel, the "channel" must provides better performances than for a single signal transmission .

⇒ The increasing of the required performances is directly linked to the number N of multiplexed signals.

⇒ The affected performances are both : Band Width

Dynamic / Signal to Noise Ratio

the multiplexing divides the capacity of the high-level communica- tion channel into several low-level sub-channels, one for each mes- sage, signal or data to be transmited.

Multiplexing as a modulation

There are intersections between modulation and multiplexing Multiplexing = modulation of input signals by orthogonal signals:

×

×

× Σ N input signals

Modulation by orthogonal signals

Multiplexed output

Mod ul at i on ⇒ Higher BW

Σ ⇒ Higher Dynamic/SNR

Orthogonal : boxcar functions or carriers at different frequencies.

Orthogonality ⇒ demultiplexer able to recover each input signal without

interference from the other.

Orthogonal functions

boxcar functions ≡ sampling

t carriers ≡ modulation

FT

f linear codes * ≡ coding

t

Multiplexing type vs standard modulations

Multiplexing

Time Domain Multiplexing (TDM) Frequency Domain Multiplexing (FDM)

Wave length Domain Multiplexing for optical fiber Coded Domain Multiplexing (CDM)

Coding

Amplitude Shift Keying (ASK) Frequency Shift Keying (FSK)

Coded Division Multiple Access (CDMA)

Code as a third dimension ?

t code

f

TDM t

code

f

FDM t

f code

CDM

Multiplexing ⇒ spread spectrum

Code is represented as a third dimension even if this is not necessarily a physical dimension.

CDM is usually used to spread the spectrum of the multiplexed signal. But the code dimension is often a repartition both in time, in frequency and some times in amplitude.

Time Domain Multiplexing (TDM)

Time slot of limited duration of each input signal (S x ) is summed

t

t

t

Introduced for telegraphy at the end of the 19 ^{t h} century and widely applied in telecommunications during the 20 ^{t h} century :

f linear codes ^* ≡ coding