Transmission Fundamentals

Evolution of Telecommunication Systems

Digitisation enabled regeneration, multiplexing, and software-controlled switching. Packet networks then allowed voice, data, and video to share transport capacity instead of requiring separate service networks.

Stage	Main technology	Key feature
Telegraph era	Wired telegraph	Text signalling via electrical pulses
Manual telephony	Magneto exchange	Operator-assisted circuit connection
Automatic telephony	Strowger, crossbar	Dial-based automatic connection
Analog transmission	FDM, coax, microwave	Voice carried as analog channels
Digital transmission	PCM, TDM, PDH, SDH	Voice digitised and multiplexed
Data networks	X.25, Frame Relay, IP	Efficient bursty data transfer
Mobile networks	1G – 5G	Cellular mobility and broadband access
NGN	IP/MPLS, softswitch, IMS	Converged voice, data and video over IP

Evolution of telecommunication systems

Basic Telecommunication Network

A telecommunication network is a collection of terminals, transmission links, switching nodes and signalling systems used to transfer information from one point to another.

Architecture of a telecommunication network.

Element	Function	Example
Terminal	Converts user info to electrical/optical/radio signal	Phone, router
Transmission medium	Carries the signal between nodes	Fiber, microwave
Switching node	Selects path and connects users	Exchange, router
Signalling system	Controls setup, routing, charging, release	SS7, SIP
Network management	Fault, config, accounting, performance, security	NMS/OSS

Main elements of a telecommunication network

• Network hierarchy:

  • Access links connect subscribers to the provider through copper loops, FTTH, or cellular radio.

  • Aggregation combines access traffic on regional links, such as metro Ethernet or SDH rings.

  • The core carries aggregate traffic between regions using high-capacity optical and IP/MPLS transport.

• Topology: Star and tree structures concentrate traffic economically but depend on central nodes. Rings and meshes offer alternate paths when protection or routing mechanisms are provided, at the cost of additional links and control complexity.

Transmission Media

• Guided: Twisted pair, coaxial cable, and optical fibre constrain signal propagation to a conductor arrangement or dielectric waveguide.

• Unguided: Radio and optical wireless systems transmit electromagnetic energy through free space between antennas or optical terminals.

Guided medium	Use	Trade-off
Twisted pair	Telephone loop, DSL, Ethernet	Cheap; noise, crosstalk, attenuation
Coaxial cable	CATV, RF feeders, legacy trunk	Good shielding; bulkier, costlier
Optical fiber	Backbone, FTTH, submarine	Low loss, huge BW, EMI-immune; splicing cost

Guided transmission media

• Radio propagation: Diffraction, reflection, ground-wave, or ionospheric propagation can support non-line-of-sight reception in suitable bands. Fixed microwave links usually require line of sight and Fresnel-zone clearance.

• Satellite: Provides wide-area coverage; GEO links incur substantial propagation delay because of their long Earth–satellite paths.

• Infrared: Supports short-range optical wireless links but generally cannot pass through opaque walls.

• Selection: Required rate, distance, attenuation, interference, availability, installation cost, and spectrum regulation determine which medium is suitable.

Transmission Lines

• Propagation delay: Distributed-line analysis is needed when delay is appreciable relative to the signal period or rise time. A sinusoidal line length near $\lambda/10$ is a common guideline.

• Per-unit-length constants: $R$ and $L$ model series conductor resistance and inductance; $C$ and $G$ model shunt capacitance and dielectric leakage.

Equivalent circuit of a transmission-line section.

Note

Elemental section

• Series: A length $\Delta x$ has resistance $R\Delta x$ and inductance $L\Delta x$.

• Shunt: The same length has capacitance $C\Delta x$ and conductance $G\Delta x$. Its leakage resistance is $1/(G\Delta x)$; when $G=0$, only the resistive leakage branch is open.

[!NOTE]

Propagation constant and characteristic impedance

$$\gamma=\alpha+\mathrm{j}\beta=\sqrt{(R+\mathrm{j}\omega L)(G+\mathrm{j}\omega C)},\qquad Z_0=\sqrt{\frac{R+\mathrm{j}\omega L}{G+\mathrm{j}\omega C}}.$$

For a lossless line ($R=G=0$):

$$Z_0=\sqrt{\frac{L}{C}},\qquad v=\frac{1}{\sqrt{LC}},\qquad \lambda=\frac{v}{f},\qquad \beta=\frac{2\pi}{\lambda}.$$

Here $\alpha$ is attenuation in Np/m, $\beta$ is phase change in rad/m, and $\omega=2\pi f$ is angular frequency in rad/s.

Characteristic Impedance and Matching

Characteristic impedance $Z_0$ is the voltage-to-current ratio of a forward travelling wave. It is also the input impedance of an infinitely long uniform line, or a finite line terminated in $Z_0$. A load $Z_L=Z_0$ produces no reflection.

Note

Reflection and standing wave

The load reflection coefficient is $\Gamma$. The VSWR expression assumes a lossless line with a passive load.

$$\Gamma=\frac{Z_L-Z_0}{Z_L+Z_0},\qquad \text{VSWR}=\frac{1+\left\lvert \Gamma\right\rvert}{1-\left\lvert \Gamma\right\rvert}.$$

Condition	$\Gamma$	Result
$Z_L=Z_0$ (match)	$0$	No reflection, VSWR $=1$
Open circuit	$+1$	Full reflection, same polarity
Short circuit	$-1$	Full reflection, opposite polarity

Load matching suppresses reflections, standing waves, and reflection-related echo, reducing power returned toward the transmitter. Maximum available power from a source additionally depends on matching at the source port.

Return Loss

Note

Return loss

For incident and reflected powers measured at the same plane with a real reference impedance,

$$\text{RL}=-20\log_{10}\left\lvert \Gamma\right\rvert=10\log_{10}\!\frac{P_i}{P_r}\ dB, \qquad \left\lvert \Gamma\right\rvert=\frac{\text{VSWR}-1}{\text{VSWR}+1}.$$

[!NOTE]

Return-loss interpretation

• High return loss $\Rightarrow$ low reflected power $\Rightarrow$ good matching.

• $20\,dB$ return loss $\Rightarrow 1\%$ reflected power.

• $30\,dB$ return loss $\Rightarrow 0.1\%$ reflected power.

• Open or short circuit gives $\text{RL}=0\,dB$ and total reflection.

Transformers and the Hybrid Circuit

• Coupling and isolation: A transformer transfers AC energy magnetically while isolating the DC paths. Winding configuration can provide impedance transformation and balanced-to-unbalanced conversion.

• Turns ratio: Let $a=N_p/N_s$. For an ideal transformer, voltage and current magnitudes and the secondary load referred to the primary satisfy:

Note

Impedance transformation

$$\frac{V_p}{V_s}=a,\qquad \frac{I_p}{I_s}=\frac{1}{a},\qquad Z_p=a^2 Z_s.$$

A $150\,\Omega$ secondary load appears as $600\,\Omega$ at the primary when $a=\sqrt{600/150}=2$, so the required primary-to-secondary turns ratio is $2{:}1$.

Two-wire to four-wire hybrid circuit.

• Two-wire/four-wire conversion: A subscriber pair carries both directions on the same two conductors. A hybrid couples it to separate transmit and receive paths, allowing independent amplification and digital processing in the two directions.

• Balance: A balancing impedance $Z_B$ approximates the two-wire line impedance over the speech band. The hybrid cancels the component that would otherwise leak from the incoming four-wire path into the outgoing path.

• Trans-hybrid loss: High loss between these two four-wire ports means good isolation. An impedance mismatch weakens cancellation, returning part of the incoming signal as electrical echo.

Signal Level and Noise Measurements

Note

Decibel scales and thermal noise

$$G_{\text{dB}}=10\log_{10}\!\frac{P_2}{P_1},\qquad P_{\text{dBm}}=10\log_{10}\!\frac{P}{1\,\mathrm{mW}}=P_{\text{dBW}}+30.$$

For RMS voltages across equal real impedances, $G_{\text{dB}}=20\log_{10}|V_2/V_1|$. With unequal resistances, use $P=V_{\mathrm{rms}}^2/R$ first.

$$N=kTB,\qquad k=1.380649\times10^{-23}\,\mathrm{J/K}.$$

$N$ is available thermal noise power in watts, $T$ is absolute temperature, and $B$ is equivalent noise bandwidth in Hz. At $T_0=290\,\mathrm{K}$, the receiver’s equivalent input noise, including noise figure, is

$$N_{\mathrm{eq,in}}\,[\mathrm{dBm}]=-174+10\log_{10}\!\left(\frac{B}{1\,\mathrm{Hz}}\right)+\mathrm{NF}.$$

Output noise also includes the receiver’s power gain in dB.

[!NOTE]

Noise factor and noise figure

• Noise factor $F=(S/N)_{\text{in}}/(S/N)_{\text{out}}$ measures SNR degradation using linear ratios, conventionally with a $290\,\mathrm{K}$ source.

• Noise figure is $\mathrm{NF}=10\log_{10}F$ in dB. An ideal device that adds no noise has $F=1$ and $\mathrm{NF}=0\,\mathrm{dB}$.

Echo and Singing

• Echo: A delayed copy of speech returns through an electrical reflection or acoustic coupling path.

  • Talker echo returns to the original speaker. Listener echo reaches the listener as a delayed duplicate after additional reflections.

  • Poor hybrid balance causes electrical echo; loudspeaker-to-microphone coupling causes acoustic echo.

  • Audibility depends on both echo delay and attenuation. Longer delays generally require greater echo attenuation; there is no universal acceptable-delay threshold independent of echo level.

  • Matching and balancing reduce the echo path. An echo suppressor attenuates a direction when appropriate; an adaptive echo canceller estimates the echo from a reference signal and subtracts it, allowing simultaneous speech.

• Singing: Excess gain and leakage through hybrids can close a positive-feedback loop around the four-wire path. A small disturbance grows into an audible oscillation when the loop gain exceeds unity at a frequency with reinforcing phase. Reducing gain and improving hybrid isolation restore a stability margin.

Note

Singing onset

For forward gain $A$ and feedback factor $\beta$, a frequency at which

$$\left\lvert A\beta\right\rvert>1,\qquad \angle A\beta = 0^\circ\pmod{360^\circ}$$

can support growing oscillations. At sustained amplitude, gain compression or limiting reduces the effective loop-gain magnitude to unity.

Feature	Echo	Singing
Nature	Delayed reflected speech	Continuous oscillation/howl
Main cause	Reflection (mismatch)	Positive feedback, high loop gain
Delay-sensitive	Yes	Not mainly
Control	Cancellation, matching	Reduce gain, improve balance

Solved Examples

Note

Example: Reflection, VSWR and return loss

A lossless $50\,\Omega$ line is terminated in $75\,\Omega$. Its load reflection coefficient, VSWR, and return loss are

$$\Gamma=\frac{75-50}{75+50}=0.2,\quad \text{VSWR}=\frac{1.2}{0.8}=1.5,\quad \text{RL}=-20\log_{10}0.2=13.98\,dB.$$

[!NOTE]

Example: Thermal noise power

A receiver has noise bandwidth $B=200\,\mathrm{kHz}$ and noise figure $\mathrm{NF}=5\,\mathrm{dB}$. With a $290\,\mathrm{K}$ source, its equivalent input noise is

$$N_{\mathrm{eq,in}}\,[\mathrm{dBm}]=-174+10\log_{10}(200\times10^3)+5 =-174+53.01+5\approx-116\,dBm.$$

The source thermal noise alone is approximately $-121\,\mathrm{dBm}$; the receiver’s noise figure raises the input-referred total by $5\,\mathrm{dB}$.