Transmission Media

Wired vs wireless communication media

Four-wire transmission system

In a four-wire circuit, each direction of transmission uses a separate pair (or separate channel), so amplifiers, multiplexers and digital equipment, which are one-way devices, can be used. The subscriber loop, however, is two-wire (both directions on one pair). A hybrid converts between the two at each end.

  West                                       East
 2-wire  ┌──────┐   Tx pair  ──>  (amp)  ┌──────┐ 2-wire
 ────────┤Hybrid├──────────────────────> ┤Hybrid├────────
 sub A   │  H1  │ <──────────────────────┤  H2  │ sub B
         └──┬───┘   Rx pair  <──  (amp)  └──┬───┘
           Z_B                             Z_B

• Speech from A enters hybrid H1 and goes only to the transmit (go) pair, is amplified and reaches hybrid H2, which sends it to subscriber B.
• Speech from B goes through H2 to the return pair and then through H1 to A.
• Long-distance and carrier/PCM systems are four-wire; the conversion happens at the exchange or line card.

Operation of the hybrid

                    4-wire receive (from far end)
                         │  (amplifier)
                         v
              ┌──────────────────────┐
  2-wire  ────┤ T1             T2    │
  line   ─────┤  (hybrid transformer)│
  (Z_L)       │   centre-tapped      │
              │   windings           │
  Balance ────┤                      ├───> 4-wire transmit
  network Z_B └──────────────────────┘     (to far end)

Operation of the hybrid (bridge principle):

1. Receive → 2-wire: a signal arriving on the 4-wire receive pair is fed to the centre-tapped winding. It divides equally between the 2-wire line ($Z_L$) and the balance network ($Z_B$). Half the power reaches the line (3 dB loss).
2. No leakage to transmit pair: the two halves flow in opposite senses through the windings coupled to the transmit pair, so their magnetic effects cancel when $Z_B = Z_L$. Ideally no receive signal appears on the transmit side.
3. 2-wire → transmit: speech from the 2-wire line divides between the transmit and receive ports; the transmit port gets half (3 dB loss), and the part going to the receive port is absorbed by the amplifier output and does no harm.
4. Balance: in practice $Z_B$ only approximates $Z_L$ over the band, so a small signal leaks across. This is measured by the balance return loss

$$B = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Poor balance causes echo, and if the loop gain round the four-wire circuit exceeds unity, singing (oscillation).

Guided vs unguided media

Need for a two-wire to four-wire hybrid converter

• The local loop uses two wires for both directions to save copper.
• Long-distance transmission needs four-wire operation because amplifiers, repeaters, multiplexers and PCM codecs are one-directional.
• Hence at the junction a hybrid separates the two directions of the 2-wire line into separate "go" and "return" paths, without letting the received signal leak back into the transmit path (which would cause echo and singing).

Operating mechanism

                    4-wire receive (from far end)
                         │  (amplifier)
                         v
              ┌──────────────────────┐
  2-wire  ────┤ T1             T2    │
  line   ─────┤  (hybrid transformer)│
  (Z_L)       │   centre-tapped      │
              │   windings           │
  Balance ────┤                      ├───> 4-wire transmit
  network Z_B └──────────────────────┘     (to far end)

Operation of the hybrid (bridge principle):

1. Receive → 2-wire: a signal arriving on the 4-wire receive pair is fed to the centre-tapped winding. It divides equally between the 2-wire line ($Z_L$) and the balance network ($Z_B$). Half the power reaches the line (3 dB loss).
2. No leakage to transmit pair: the two halves flow in opposite senses through the windings coupled to the transmit pair, so their magnetic effects cancel when $Z_B = Z_L$. Ideally no receive signal appears on the transmit side.
3. 2-wire → transmit: speech from the 2-wire line divides between the transmit and receive ports; the transmit port gets half (3 dB loss), and the part going to the receive port is absorbed by the amplifier output and does no harm.
4. Balance: in practice $Z_B$ only approximates $Z_L$ over the band, so a small signal leaks across. This is measured by the balance return loss

$$B = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Poor balance causes echo, and if the loop gain round the four-wire circuit exceeds unity, singing (oscillation).

Typical loss through the hybrid is about 3.5 dB in each direction, and good balance gives a transhybrid loss of 20 dB or more.

Transmission media are the physical paths that carry signals between transmitter and receiver. They are classed as guided (wired) and unguided (wireless).

Guided media

1. Twisted pair cable

  ~~~/\/\/\/\/\/\/\~~~   two insulated copper
  ~~~\/\/\/\/\/\/\/~~~   wires twisted together

• Two insulated copper wires twisted to reduce crosstalk and noise pickup; UTP and STP types.
• Used for telephone subscriber loops, DSL and LAN (Cat-5/6).
• Cheap, easy to install; attenuation high at high frequency, limited distance/bandwidth.

2. Coaxial cable

  | outer jacket | braid (shield) | insulator | core |
       ( ( ( ( ●  center conductor ) ) ) )

• Central copper conductor, dielectric insulator, outer braided conductor and jacket.
• Wider bandwidth and better shielding than twisted pair; used in cable TV, old long-distance FDM trunks, antenna feeders.

3. Optical fibre

  cladding  ───────────────────────
  core      ═══> light by total ═══>
            internal reflection
  cladding  ───────────────────────

• Glass core with higher refractive index than the cladding; light is guided by total internal reflection.
• Single-mode and multimode types; very low loss (~0.2 dB/km at 1550 nm), huge bandwidth, immune to EMI, light and secure.
• Used in backbone, undersea cables, FTTH.

Unguided media

1. Radio waves (HF/VHF/UHF): omnidirectional antennas; ground wave, sky wave (HF via ionosphere), line-of-sight; used in broadcasting, mobile, walkie-talkies.

2. Terrestrial microwave (1–40 GHz):

  [Dish]))) ─ line of sight ─ (((([Dish]
   tower    repeater every 40-60 km  tower

Highly directional parabolic dishes on towers; used for long-distance trunks and mobile backhaul; affected by rain and obstacles.

3. Satellite:

              [Satellite]
             ^          \
   uplink   /            v  downlink
 [Earth stn A]         [Earth stn B]

Geostationary satellite (36,000 km) acts as a repeater in the sky; wide coverage; delay about 250 ms one way.

4. Infrared and light-wave: short range, line of sight (remote controls, IrDA, free-space optics).

Transmission media: classes and characteristics

General characteristics to compare: bandwidth/data rate, attenuation per km, repeater spacing, noise immunity, security, cost and installation, mobility support.

Working principle of a hybrid transformer

A hybrid transformer converts a two-wire circuit (both directions on one pair) into a four-wire circuit (separate transmit and receive pairs) and back, while preventing the received signal from passing into the transmit path.

                    4-wire receive (from far end)
                         │  (amplifier)
                         v
              ┌──────────────────────┐
  2-wire  ────┤ T1             T2    │
  line   ─────┤  (hybrid transformer)│
  (Z_L)       │   centre-tapped      │
              │   windings           │
  Balance ────┤                      ├───> 4-wire transmit
  network Z_B └──────────────────────┘     (to far end)

Operation of the hybrid (bridge principle):

1. Receive → 2-wire: a signal arriving on the 4-wire receive pair is fed to the centre-tapped winding. It divides equally between the 2-wire line ($Z_L$) and the balance network ($Z_B$). Half the power reaches the line (3 dB loss).
2. No leakage to transmit pair: the two halves flow in opposite senses through the windings coupled to the transmit pair, so their magnetic effects cancel when $Z_B = Z_L$. Ideally no receive signal appears on the transmit side.
3. 2-wire → transmit: speech from the 2-wire line divides between the transmit and receive ports; the transmit port gets half (3 dB loss), and the part going to the receive port is absorbed by the amplifier output and does no harm.
4. Balance: in practice $Z_B$ only approximates $Z_L$ over the band, so a small signal leaks across. This is measured by the balance return loss

$$B = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Poor balance causes echo, and if the loop gain round the four-wire circuit exceeds unity, singing (oscillation).

Comparison of guided transmission media

Operation of hybrid transformer

                    4-wire receive (from far end)
                         │  (amplifier)
                         v
              ┌──────────────────────┐
  2-wire  ────┤ T1             T2    │
  line   ─────┤  (hybrid transformer)│
  (Z_L)       │   centre-tapped      │
              │   windings           │
  Balance ────┤                      ├───> 4-wire transmit
  network Z_B └──────────────────────┘     (to far end)

Operation of the hybrid (bridge principle):

1. Receive → 2-wire: a signal arriving on the 4-wire receive pair is fed to the centre-tapped winding. It divides equally between the 2-wire line ($Z_L$) and the balance network ($Z_B$). Half the power reaches the line (3 dB loss).
2. No leakage to transmit pair: the two halves flow in opposite senses through the windings coupled to the transmit pair, so their magnetic effects cancel when $Z_B = Z_L$. Ideally no receive signal appears on the transmit side.
3. 2-wire → transmit: speech from the 2-wire line divides between the transmit and receive ports; the transmit port gets half (3 dB loss), and the part going to the receive port is absorbed by the amplifier output and does no harm.
4. Balance: in practice $Z_B$ only approximates $Z_L$ over the band, so a small signal leaks across. This is measured by the balance return loss

$$B = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Poor balance causes echo, and if the loop gain round the four-wire circuit exceeds unity, singing (oscillation).

Noise

Noise is any unwanted electrical signal that adds to the wanted signal in a communication system and reduces its quality (measured by signal-to-noise ratio).

Types of noise

• Thermal (Johnson) noise: due to random motion of electrons in conductors; present in all equipment; power $N = kTB$.
• Intermodulation noise: produced when signals of different frequencies pass through non-linear devices, creating sum and difference frequencies.
• Crosstalk: coupling of signals from one pair/channel into another (near-end and far-end crosstalk).
• Impulse noise: short, high-amplitude spikes from lightning, switching contacts, power lines; harmful to data.
• Shot noise in semiconductor devices; also quantisation noise in PCM.

Need for a two-wire to four-wire converter

The subscriber loop is two-wire (both directions on one pair), but amplifiers, repeaters, multiplexers and digital transmission equipment work in one direction only, so long-distance circuits are four-wire. A hybrid (2W/4W converter) at each end separates the two directions and keeps the received signal out of the transmit path, preventing echo and singing.

  West                                       East
 2-wire  ┌──────┐   Tx pair  ──>  (amp)  ┌──────┐ 2-wire
 ────────┤Hybrid├──────────────────────> ┤Hybrid├────────
 sub A   │  H1  │ <──────────────────────┤  H2  │ sub B
         └──┬───┘   Rx pair  <──  (amp)  └──┬───┘
           Z_B                             Z_B

Operating mechanism

                    4-wire receive (from far end)
                         │  (amplifier)
                         v
              ┌──────────────────────┐
  2-wire  ────┤ T1             T2    │
  line   ─────┤  (hybrid transformer)│
  (Z_L)       │   centre-tapped      │
              │   windings           │
  Balance ────┤                      ├───> 4-wire transmit
  network Z_B └──────────────────────┘     (to far end)

Operation of the hybrid (bridge principle):

1. Receive → 2-wire: a signal arriving on the 4-wire receive pair is fed to the centre-tapped winding. It divides equally between the 2-wire line ($Z_L$) and the balance network ($Z_B$). Half the power reaches the line (3 dB loss).
2. No leakage to transmit pair: the two halves flow in opposite senses through the windings coupled to the transmit pair, so their magnetic effects cancel when $Z_B = Z_L$. Ideally no receive signal appears on the transmit side.
3. 2-wire → transmit: speech from the 2-wire line divides between the transmit and receive ports; the transmit port gets half (3 dB loss), and the part going to the receive port is absorbed by the amplifier output and does no harm.
4. Balance: in practice $Z_B$ only approximates $Z_L$ over the band, so a small signal leaks across. This is measured by the balance return loss

$$B = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Poor balance causes echo, and if the loop gain round the four-wire circuit exceeds unity, singing (oscillation).

High-frequency (HF) radio (3–30 MHz)

            ionosphere (F, E layers)
           /\            /\
          /  \  refract /  \
  [Tx] __/    \________/    \__ [Rx]
       sky wave hops (1000s of km)

• Long-distance communication by sky-wave propagation: the wave is refracted back to earth by the ionosphere, possibly in several hops, covering thousands of km without repeaters; ground wave for shorter ranges.
• Simple equipment (transmitter, antenna such as dipole/rhombic, receiver); used for maritime, military, aviation, amateur and emergency links, and earlier for international telephony and remote districts in Nepal.
• Limitations: ionosphere changes with day/night, season and sunspot cycle, so frequency must be changed (MUF); fading due to multipath, noise and interference; narrow bandwidth (few kHz) and low data rates.

Microwave transmission (1–40 GHz)

 [Dish]))))  ──── line of sight ────  ((((([Dish]
  Tower A        40-60 km hop           Tower B/repeater

• Terrestrial line-of-sight links using highly directional parabolic antennas on towers; repeaters every 40–60 km (depending on tower height, earth curvature and Fresnel zone clearance).
• Large bandwidth – carries hundreds to thousands of voice channels or high-rate digital streams (PDH/SDH); used for trunk networks and mobile backhaul.
• Satellite microwave uses the satellite as a repeater in the sky (uplink/downlink, e.g. C, Ku bands).
• Impairments: rain attenuation above ~10 GHz, multipath fading, obstruction; reduced by diversity (space/frequency) and fade margins.

Typical error rates

Error rate is given as bit error rate (BER) = erroneous bits / total bits. Typical values (without heavy error correction):

HF needs ARQ and forward error correction for reliable data, while microwave links are designed for BER around $10^{-6}$ or better for most of the time.

A small length $\Delta x$ of a uniform line is modelled with series resistance $R\Delta x$ and inductance $L\Delta x$, and shunt conductance $G\Delta x$ and capacitance $C\Delta x$ ($R, L, G, C$ per unit length).

   i(x)   R.dx      L.dx         i(x+dx)
 o──>──[/\/\/]──[ coil ]──┬───────┬────o
 +                        │       │    +
                        [G.dx]  [C.dx]
 v(x)                     │       │   v(x+dx)
 -                        │       │    -
 o────────────────────────┴───────┴────o
 |<──────────────── dx ─────────────>|

Series impedance per unit length $Z = R + j\omega L$; shunt admittance $Y = G + j\omega C$; characteristic impedance $Z_0 = \sqrt{Z/Y}$.

Given: signal power 10 mW = 10 dBm; line 100 km at 2 dB/km; amplifier gain 50 dB, noise factor $F$ = 7 dB; line noise $-138$ dBm; received signal must also be 10 mW.

Step 1 – Number of amplifiers

$$\begin{aligned} \text{Total line loss} &= 100 \times 2 = 200\ \text{dB} \\ \text{Amplifiers needed} &= \frac{200}{50} = 4 \end{aligned}$$

So the line is divided into 4 sections of 25 km (50 dB loss each), each followed by a 50 dB amplifier. Output = 10 dBm, as required.

Step 2 – Signal at each amplifier input

$$S_{in} = 10\ \text{dBm} - 50\ \text{dB} = -40\ \text{dBm}$$

Step 3 – Effective noise at each amplifier input (line noise raised by the noise factor)

$$N_{in,eff} = -138 + 7 = -131\ \text{dBm}$$

Step 4 – SNR due to one section

$$\left(\frac{S}{N}\right)_1 = -40 - (-131) = 91\ \text{dB}$$

Step 5 – Four identical sections: every section adds the same noise power, so total noise is 4 times, i.e. SNR falls by $10\log_{10}4 = 6.02$ dB.

$$\left(\frac{S}{N}\right)_{out} = 91 - 6.02 = 84.98\ \text{dB}$$

Answer: output SNR ≈ 85 dB.

Assumptions (standard four-wire model): $L$ = overall loss of the four-wire circuit between its two-wire terminals (hybrid to hybrid), $B$ = balance return loss of each hybrid, stability margin $S = L + B$ (half the loss round the four-wire loop). Each subscriber is joined to a hybrid by a two-wire circuit of 6 dB loss and 1 ms delay.

Four-wire loss

$$L = S - B = 3 - 3 = 0\ \text{dB}$$

 Talker─[2W: 6dB,1ms]─H1══ 4-wire (L) ══H2─[2W]─Listener
           ^                               │ reflects (B)
           └──────── talker echo <─────────┘

Talker echo (talker's speech reflected at the far hybrid and heard by the talker):

$$\begin{aligned} A_{TE} &= 6 + L + B + L + 6 \\ &= 6 + 0 + 3 + 0 + 6 = 15\ \text{dB} \end{aligned}$$ $$\begin{aligned} \text{Delay}_{TE} &= 20\ \text{ms (4-wire round trip)} + 2 \times 1\ \text{ms (own 2-wire both ways)} \\ &= 22\ \text{ms} \end{aligned}$$

Listener echo (signal reflected at the far hybrid, then again at the near hybrid, reaching the listener late). Compared with the direct signal it travels once more round the four-wire loop:

$$A_{LE} = 2L + 2B = 2S = 2 \times 3 = 6\ \text{dB below the direct signal}$$

(absolute: $6 + 3L + 2B + 6 = 18$ dB from talker to listener, against 12 dB for the direct signal), delayed by 20 ms relative to it.

Answer: talker echo attenuation = 15 dB, talker echo delay = 22 ms, listener echo attenuation = 6 dB (relative to the received speech, i.e. 18 dB overall).

Impairments to voice channel transmission

Impairments are the changes that a voice-frequency channel (nominally 300–3400 Hz) makes to a signal so that the received signal is not an exact copy of the transmitted one. They reduce speech quality and data accuracy. Main impairments: attenuation and attenuation distortion, phase (delay) distortion, noise, echo, crosstalk, frequency offset and jitter.

Attenuation distortion

• The loss of a channel is not the same at all frequencies in the band; different frequency components of the signal are attenuated by different amounts.
• Caused by cable capacitance (more loss at high frequency), transformers and filters (more loss near band edges).
• Specified as loss at each frequency relative to the loss at 1004 Hz (reference), e.g. −1 to +3 dB from 500–2500 Hz.

 Relative
 loss(dB)
   +  ┐                          ┌
      │ \                      / │
   0  │   ─────────────────────  │
      └───┴────────┴──────────┴──┴── f
         300      1004      3400 Hz

• Effect: speech sounds muffled; data pulses distorted. Corrected by equalisers and loading coils.

Phase (delay) distortion

• Different frequencies travel with different delays because the phase shift is not linear with frequency. Measured as envelope delay distortion – group delay $\tau = d\phi/d\omega$ relative to the minimum delay (usually near 1700–1800 Hz).
• Delay rises sharply near band edges due to filters.
• Little effect on speech (ear is insensitive to phase), but serious for data: causes intersymbol interference. Corrected by delay equalisers.

Noise

Unwanted signals added to the channel:

• Thermal noise ($kTB$, white) – sets the noise floor.
• Intermodulation noise – from non-linear devices (sum/difference frequencies).
• Crosstalk – coupling from adjacent pairs (NEXT, FEXT).
• Impulse noise – spikes from switching, lightning; causes burst errors in data.
• Quantisation noise in PCM systems.

Noise is measured with weighting (dBrnC, psophometric dBmp) and limits the signal-to-noise ratio of the channel (a voice channel needs SNR of about 30 dB or more).

Full duplex on a single twisted pair

In the local loop both directions of speech travel on the same two wires at the same time. This is possible because the signals are added on the pair and separated by hybrid circuits at each end: an anti-sidetone/hybrid network in the telephone set and a hybrid (2W/4W converter) in the exchange line card. Each hybrid passes the outgoing signal to the line and the incoming signal to the receiver while largely blocking the outgoing signal from its own receive path (balanced bridge). Since the two directions are kept apart by balance, not by frequency or time, the loop works as full duplex.

Need for the two-wire to four-wire converter

• Amplifiers, repeaters, multiplexers and PCM codecs carry signals in one direction only, so trunk transmission is four-wire (separate go and return paths).
• The converter (hybrid) joins the two-wire loop to the four-wire trunk, separating the two directions, and avoids echo and singing caused by signal returning round the four-wire loop.

Operating mechanism

                    4-wire receive (from far end)
                         │  (amplifier)
                         v
              ┌──────────────────────┐
  2-wire  ────┤ T1             T2    │
  line   ─────┤  (hybrid transformer)│
  (Z_L)       │   centre-tapped      │
              │   windings           │
  Balance ────┤                      ├───> 4-wire transmit
  network Z_B └──────────────────────┘     (to far end)

Operation of the hybrid (bridge principle):

1. Receive → 2-wire: a signal arriving on the 4-wire receive pair is fed to the centre-tapped winding. It divides equally between the 2-wire line ($Z_L$) and the balance network ($Z_B$). Half the power reaches the line (3 dB loss).
2. No leakage to transmit pair: the two halves flow in opposite senses through the windings coupled to the transmit pair, so their magnetic effects cancel when $Z_B = Z_L$. Ideally no receive signal appears on the transmit side.
3. 2-wire → transmit: speech from the 2-wire line divides between the transmit and receive ports; the transmit port gets half (3 dB loss), and the part going to the receive port is absorbed by the amplifier output and does no harm.
4. Balance: in practice $Z_B$ only approximates $Z_L$ over the band, so a small signal leaks across. This is measured by the balance return loss

$$B = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Poor balance causes echo, and if the loop gain round the four-wire circuit exceeds unity, singing (oscillation).

Advantages of optical fibre over twisted pair and coaxial cable

• Very large bandwidth (THz range) – Gbps to Tbps with WDM.
• Very low attenuation (~0.2 dB/km at 1550 nm), so repeater spacing of 50–100 km or more.
• Immune to electromagnetic interference and lightning; no crosstalk between fibres.
• High security – very hard to tap without detection.
• Small size and light weight; easy to lay in ducts.
• Electrical isolation – no ground loops, no sparks (safe in hazardous areas).
• Made from silica (sand), long life, no corrosion.

Wireless transmission media

1. Radio waves (3 kHz–1 GHz, mainly HF, VHF, UHF): omnidirectional; ground wave and sky wave (HF reflected by ionosphere gives long range); used for AM/FM broadcasting, mobile radio, cellular phones. Prone to fading and interference.
2. Terrestrial microwave (1–40 GHz): directional parabolic dishes on towers, line of sight, repeater every 40–60 km; high capacity trunks and mobile backhaul; affected by rain and obstruction.
3. Satellite microwave: a geostationary satellite (about 36,000 km) receives the uplink and retransmits the downlink; very wide coverage, ideal for remote and international links (VSAT); one-way delay about 250 ms.
4. Infrared: short-range (few metres), line of sight, cannot pass walls; TV remotes, IrDA.
5. Free-space optics / light wave: laser links between buildings; high rate but affected by fog.

Causes of crosstalk

Crosstalk is the unwanted coupling of a signal from one circuit (disturbing) into another (disturbed), so that a conversation on one line is heard on another.

• Capacitive (electric) coupling between adjacent conductors in the same cable.
• Inductive (magnetic) coupling between pairs due to mutual inductance.
• Unbalance of pairs – unequal resistance, capacitance to earth, or poor twisting, so coupled currents do not cancel.
• Long parallel runs of pairs and close spacing; higher frequencies increase coupling.
• Non-linearity and poor filtering in FDM/carrier systems (inter-channel crosstalk).
• Faulty joints, moisture in cables and poor shielding.

Types: near-end crosstalk (NEXT) – measured at the same end as the disturbing transmitter; far-end crosstalk (FEXT) – at the far end. Reduced by twisting, shielding, balanced lines and separation of go/return pairs.

Operation of the two-wire to four-wire hybrid transformer

                    4-wire receive (from far end)
                         │  (amplifier)
                         v
              ┌──────────────────────┐
  2-wire  ────┤ T1             T2    │
  line   ─────┤  (hybrid transformer)│
  (Z_L)       │   centre-tapped      │
              │   windings           │
  Balance ────┤                      ├───> 4-wire transmit
  network Z_B └──────────────────────┘     (to far end)

Operation of the hybrid (bridge principle):

1. Receive → 2-wire: a signal arriving on the 4-wire receive pair is fed to the centre-tapped winding. It divides equally between the 2-wire line ($Z_L$) and the balance network ($Z_B$). Half the power reaches the line (3 dB loss).
2. No leakage to transmit pair: the two halves flow in opposite senses through the windings coupled to the transmit pair, so their magnetic effects cancel when $Z_B = Z_L$. Ideally no receive signal appears on the transmit side.
3. 2-wire → transmit: speech from the 2-wire line divides between the transmit and receive ports; the transmit port gets half (3 dB loss), and the part going to the receive port is absorbed by the amplifier output and does no harm.
4. Balance: in practice $Z_B$ only approximates $Z_L$ over the band, so a small signal leaks across. This is measured by the balance return loss

$$B = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Poor balance causes echo, and if the loop gain round the four-wire circuit exceeds unity, singing (oscillation).

Use: at the junction of the two-wire subscriber loop and the four-wire trunk at both ends of a long-distance call, so that one-way amplifiers and digital equipment can be used.

Need for pulse stuffing

When several digital tributaries (e.g. four 2.048 Mbps E1 streams) are combined into a higher-order stream (8.448 Mbps) in the plesiochronous digital hierarchy (PDH), each tributary has its own clock, which is nominally the same but can differ slightly (e.g. ±50 ppm). The multiplexer reads them at one common, slightly higher rate. If nothing is done, a slower tributary would run out of bits (or a faster one would overflow the buffer), causing slips and lost data.

Pulse stuffing (justification) solves this:

• The multiplexer output frame has a few stuffing (justification) bit positions for each tributary.
• When a tributary's buffer is about to empty, a dummy (stuff) bit is inserted instead of a data bit; otherwise the position carries data.
• Justification control bits (sent several times and decided by majority vote) tell the demultiplexer whether the position holds data or a stuff bit, so it can remove the stuff bits and recover the original clock with a phase-locked loop.
• Thus tributaries with slightly different rates are brought to exactly the same rate without slips.

LED vs LASER as optical sources

LEDs suit short, low-cost multimode links; lasers are used for high-speed, long-distance single-mode systems.

Attenuation is the loss of signal power as it travels along a transmission medium; distortion is the change in the shape of the signal because different frequency components are treated differently by the medium. Both limit how far a signal can go before it must be amplified or regenerated.

Sources of attenuation

A telephone line or cable is a distributed network of series resistance $R$, series inductance $L$, shunt capacitance $C$ and shunt conductance $G$ per unit length.

   R dx     L dx
 o--/\/\/--@@@@--+------o
                 |    |
              C dx  G dx
                 |    |
 o---------------+----+-o
   one small section dx of a line

1. Conductor (copper) loss – $I^2R$ heating in the wire resistance. Resistance rises with frequency due to skin effect, so loss rises with frequency.
2. Dielectric (leakage) loss – current leaking through the insulation (conductance $G$), which also rises with frequency.
3. Radiation loss – part of the energy is radiated away, mainly from open-wire lines and unshielded cables at high frequency.
4. Spreading / free-space loss – in radio links power spreads over a larger area ($\propto d^2$); rain, fog and atmospheric gases add absorption.
5. Coupling and joint losses – poor joints, connectors, splices and impedance mismatch (reflection) waste power.

Attenuation is expressed in dB: $\alpha = 10\log_{10}(P_{in}/P_{out})$ dB, and per km of cable. On a matched line the attenuation constant is the real part of $\gamma = \sqrt{(R+j\omega L)(G+j\omega C)}$.

Sources of distortion

1. Attenuation (amplitude) distortion – $\alpha$ varies with frequency, so high voice frequencies are lost more than low ones and the received waveform changes shape.
2. Delay (phase) distortion – the phase velocity varies with frequency, so components arrive at different times. It is serious for data and pulses (causes inter-symbol interference).
3. Non-linear distortion – amplifiers and saturating devices create harmonics and intermodulation products.
4. Noise and crosstalk – thermal noise, impulse noise and coupling from neighbouring pairs add unwanted signals.
5. Echo – reflections at hybrids or mismatched points return delayed copies of the signal.

 sent pulse        received pulse
   +---+               __
   |   |             _/  \__
 --+   +--   ==>  __/       \____
                 (attenuated, spread out)

Remedies

• Loading coils (Heaviside condition $R/L = G/C$) reduce attenuation distortion on voice cables.
• Equalisers flatten amplitude and delay response.
• Repeaters/regenerators restore level (analogue) or reshape pulses (digital).
• Impedance matching removes reflections and echo.

A hybrid (four-wire/two-wire termination set) is a bridge transformer that joins the two-wire subscriber line to the four-wire transmission path (separate GO and RETURN pairs). Together with a balancing network it passes signals from the 2-wire line to the 4-wire GO path and from the 4-wire RETURN path to the 2-wire line, while keeping the RETURN path isolated from the GO path.

Construction and operation

   4-wire RECEIVE (in)          2-wire line
   ---------+                  +---------- Z_L
            |   +----------+   |
            +---|  hybrid  |---+
                | (bridge  |
   4-wire SEND  |  transf.)|---+
   <--------+---|          |   |
            |   +----------+   +---------- Z_B
                              balancing network

The hybrid has a centre-tapped (differential) winding. One half connects to the two-wire line (impedance $Z_L$), the other half to the balancing network $Z_B$, which is designed to copy the impedance of the line over the voice band.

1. 2-wire to 4-wire (transmit): speech from the subscriber enters the line winding, induces voltage in the send winding and goes out on the 4-wire GO pair. Half the power is wasted in $Z_B$ (about 3 dB loss).
2. 4-wire to 2-wire (receive): the incoming signal enters the centre tap and splits into two equal currents, one into $Z_L$ and one into $Z_B$. Since the currents flow in opposite senses through the two halves of the winding, their fluxes cancel in the send winding when $Z_B = Z_L$. So no receive signal leaks into the GO path; the subscriber still gets half of it (3 dB loss).
3. The loss from receive port to send port is called transhybrid loss. With perfect balance it is very large (ideally infinite); in practice it is set by the balance return loss

$$BRL = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Singing and how it is eliminated

A four-wire circuit with a hybrid at each end forms a closed loop: GO amplifier – far hybrid – RETURN amplifier – near hybrid – GO amplifier.

        G1 (amplifier) -->
 hyb A ===================== hyb B
        <-- G2 (amplifier)
 leak through A (L_A)   leak through B (L_B)

If the hybrids leak, part of the signal goes round the loop. When the total loop gain is $\geq 0$ dB, i.e.

$$G_1 + G_2 - (L_A + L_B) \geq 0\ \text{dB}$$

the circuit oscillates (sings), producing a howl. Smaller leakage that does not oscillate still produces echo and a hollow sound ("near-singing").

The balancing network prevents singing by making $Z_B \approx Z_L$, which keeps transhybrid losses $L_A, L_B$ high. Then the loop has a net loss (a singing margin, typically a few dB) and cannot oscillate. Further aids are compromise networks for varying line lengths, adding fixed loss (via net loss) in the loop, and echo suppressors/cancellers on long circuits.

Types of transmission media

1. Guided (wired) media
   • Open-wire lines
   • Twisted pair cable (UTP/STP)
   • Coaxial cable
   • Optical fibre cable (single-mode, multimode)
2. Unguided (wireless) media
   • Radio waves (ground wave, sky wave, broadcast)
   • Terrestrial microwave (line of sight)
   • Satellite links
   • Infrared and light-wave (free-space optics)

Four-wire transmission system

In a four-wire system each direction of transmission has its own pair: one pair (GO) carries speech from A to B and the other pair (RETURN) carries speech from B to A. Subscriber lines are two-wire (both directions on one pair), but long trunk circuits need one-way amplifiers and multiplexing equipment, which work in one direction only, so trunks are four-wire.

 Sub A                                         Sub B
 2-wire  +-----+   GO pair  ->[amp]->  +-----+ 2-wire
 o-------| HYB |=======================| HYB |-------o
         |  A  |=======================|  B  |
         +-----+  <-[amp]<-  RET pair  +-----+
              4-wire trunk / carrier

Features:

• Gain can be inserted separately in each direction, so long distances are possible.
• Required for FDM/TDM carrier and radio links, which are inherently one-way.
• Needs a hybrid (2W/4W termination) at each end to connect the two-wire subscriber loops.
• Risk of echo and singing if the hybrids are not balanced.

Operation of hybrid

A hybrid is a three-winding bridge transformer with a balancing network $Z_B$ that matches the two-wire line impedance $Z_L$.

1. Transmit: speech from the 2-wire line is coupled to the 4-wire GO (send) pair.
2. Receive: speech from the 4-wire RETURN pair is fed to the centre tap and splits equally between $Z_L$ and $Z_B$; the subscriber hears it.
3. Isolation: the two receive currents produce opposite fluxes in the send winding, so when $Z_B = Z_L$ they cancel and nothing from the RETURN pair reaches the GO pair. This high transhybrid loss prevents echo and singing.
4. Each through path loses about 3 dB, since half the power goes into the balancing network.

A transmission medium is the physical path between transmitter and receiver. For a radio-frequency (RF) signal it can be guided, where the wave is confined and directed by a physical structure (wire, cable, fibre or waveguide), or unguided, where the electromagnetic wave travels through free space (air, vacuum, sea water) radiated by an antenna.

Guided media

The wave travels along a conductor or dielectric that sets its path.

• Twisted pair – two insulated copper wires twisted together to cancel interference; used for telephone loops and LAN (up to about 100 MHz for Cat-5e/Cat-6).
• Coaxial cable – centre conductor, dielectric, braided shield; 50 Ω or 75 Ω; carries RF up to a few GHz (cable TV, antenna feeders, old trunk carrier).
• Optical fibre – light guided by total internal reflection in a glass core; very large bandwidth and low loss (≈0.2 dB/km at 1550 nm).
• Waveguide – hollow metal tube carrying microwaves between radar/microwave equipment and the antenna.

Unguided media

The antenna launches an electromagnetic wave which propagates as:

• Ground wave (LF/MF, follows the earth's surface, AM broadcast)
• Sky wave (HF, reflected by the ionosphere, long-distance radio)
• Space / line-of-sight wave (VHF and above: FM, TV, terrestrial microwave, mobile)
• Satellite links (uplink/downlink via a geostationary or LEO satellite)
• Infrared / free-space optics (short range, line of sight)

 Guided:   Tx ===== cable / fibre ===== Rx

 Unguided:  Tx                      Rx
            |  ~ ~ ~ free space ~ ~ ~ |
           /_\  (antenna)           /_\

Comparison

Choice in practice

Guided media are preferred for high-capacity, stable backbone links in cities (fibre between exchanges). Unguided media suit mobile users, rural and mountainous areas (very common in Nepal, e.g. microwave and VSAT links to remote districts), quick deployment and broadcasting. Modern networks combine both: fibre backbone plus radio access.

Two-wire communication carries both directions of speech on a single pair of wires; four-wire communication uses two separate pairs (or two separate channels), one for each direction.

Difference between two-wire and four-wire communication

Four-wire communication

In long-distance circuits the signal must be amplified many times. Amplifiers are one-way devices, so the two directions are separated: a GO path from A to B and a RETURN path from B to A. Subscriber lines remain two-wire, so a hybrid (four-wire termination set) at each end converts 2-wire to 4-wire.

 Sub A                                         Sub B
         +-----+  GO  ->[A1]->[A2]->  +-----+
 o-------| HYB |=======================| HYB |-------o
 2-wire  |  A  |=======================|  B  | 2-wire
     Z_B-+-----+  <-[A3]<-[A4]<- RET  +-----+-Z_B

Working:

1. Speech from subscriber A enters hybrid A and is sent on the GO pair. Amplifiers along the route make up for line loss.
2. At B the hybrid passes the GO signal to subscriber B's two-wire line.
3. B's reply travels on the RETURN pair the same way to A.
4. In each hybrid the balancing network $Z_B$ copies the 2-wire line impedance, so the incoming RETURN signal is not passed back into the GO pair (high transhybrid loss).

Equivalent four-wire: on carrier and radio systems there are no physical pairs; the two directions use different frequency bands (FDM) or time slots/channels (TDM) — still treated as four-wire.

Advantages:

• Gain can be set separately for each direction and the circuit can be made very long with low net loss.
• Directly suits multiplexing, digital transmission and radio/satellite links.
• Four-wire switching in trunk exchanges avoids repeated 2W/4W conversions and the loss and echo they cause.

Problems and remedies:

• Echo: imperfect hybrid balance reflects some received speech back to the talker. Long-delay circuits use echo suppressors or cancellers.
• Singing: if total loop gain $G_1 + G_2 - (L_A + L_B) \geq 0$ dB the loop oscillates. Good balancing and a net-loss margin prevent it.
• Cost: twice the conductors and the hybrids add cost, justified only on long routes.

Optical fibre carries information as light pulses through a glass core by total internal reflection, while copper cable (twisted pair, coaxial) carries electrical signals. Fibre is now the main medium for backbone networks.

Advantages of fibre over copper

1. Huge bandwidth – tens of GHz·km per fibre and terabit capacity with WDM, compared with a few hundred MHz on copper.
2. Low attenuation – about 0.2 dB/km at 1550 nm, so repeater spacing of 80–100 km or more; copper needs repeaters every 1–2 km at high bit rates.
3. Immunity to EMI/RFI – glass is non-conducting, so no electrical interference, lightning surge or ground-loop problems; can run beside power lines (e.g. OPGW on HV towers).
4. No crosstalk – light does not leak into neighbouring fibres.
5. Security – very hard to tap without detection; no radiation.
6. Small size and weight – a thin cable holds many fibres; easier to install in ducts.
7. Electrical isolation and safety – no sparks; usable in hazardous areas.
8. Raw material – silica is abundant; no copper theft value.
9. Long life – no corrosion.

Limitations: higher cost of terminal equipment (lasers, photodetectors), difficult splicing, fragile, and cannot carry power to remote equipment.

Suitable applications

In short, fibre is used where distance, capacity or interference is the main issue, and copper where the distance is short, the data rate modest, power feeding is needed, or low cost of terminal equipment matters.

Radio/electrical signals travel along guided copper media as an electromagnetic wave between two conductors.

• Twisted pair: two insulated wires are twisted together. The signal travels as a voltage difference between the wires (balanced line). Twisting makes noise picked up by both wires nearly equal, so it cancels at the receiver, and it reduces crosstalk. Loss and radiation rise quickly with frequency, so it suits voice, DSL and LAN signals up to about 100 MHz over short distances.
• Coaxial cable: a centre conductor surrounded by a dielectric and an outer braided shield. The field is confined between the conductors (unbalanced line), so there is very little radiation or pick-up. It has a fixed characteristic impedance (50 Ω or 75 Ω) and carries RF up to several GHz, used for antenna feeders, cable TV and old carrier trunks.

Characteristic impedance $Z_0$ is the ratio of voltage to current of a wave travelling along an infinitely long line:

$$Z_0 = \sqrt{\frac{R + j\omega L}{G + j\omega C}}$$

(≈ 50 Ω or 75 Ω for coax, ≈ 100 Ω for twisted pair, ≈ 600 Ω for telephone lines).

Its role in carrying a signal from one equipment to another:

• If the source, line and load are all matched ($Z_S = Z_0 = Z_L$), all the power is delivered to the load and nothing is reflected.
• A mismatch causes reflection (reflection coefficient $\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$), standing waves (high VSWR), power loss, echo and ghost images, and in transmitters even damage.
• So cables, connectors and equipment ports are all designed for the same $Z_0$.

A hybrid transformer (or hybrid circuit) is the interface between the two-wire subscriber line and the four-wire transmission/switching path.

Its roles:

• 2W→4W: passes the subscriber's speech from the two-wire line to the four-wire transmit (GO) path.
• 4W→2W: passes the received speech from the four-wire RETURN path to the two-wire line.
• Isolation: with a balancing network equal to the line impedance, it prevents the received signal from leaking into the transmit path (high transhybrid loss). This stops echo and singing on long four-wire circuits.
• Each through path has about 3 dB loss.

It is used in telephone sets (sidetone control), line cards of digital exchanges and the ends of trunk/carrier circuits.

A transmission plan fixes how losses, levels, delays and the number of circuits are shared among the links of a connection so that any two subscribers, national or international, get acceptable speech quality. CCITT Recommendation Q.40 ("The transmission plan", in the Q-series together with G.101) gives these guidelines for international connections (the common textbook version is given below):

1. Structure of a connection: an international connection is made of a national system at each end plus an international chain between the two international (CT) exchanges.
2. Number of circuits: the international chain should have as few circuits as possible; at most 12 circuits in tandem in a whole connection, normally not more than 4 in each national extension and 4 in the international chain (6 only in exceptional cases).
3. Four-wire working: international circuits and international switching centres are four-wire; the 2W/4W conversion is done inside the national system.
4. Nominal losses: each international circuit has a fixed nominal transmission loss (about 0.5 dB between virtual switching points, at the relative level −3.5 dBr), so the chain loss does not depend on the route.
5. Loudness (reference equivalent) limits: the national sending and receiving systems up to the international centre must not exceed set limits (classically sending RE about 21 dB and receiving RE about 12 dB), keeping the overall connection loudness within an acceptable figure.
6. Stability: each circuit must have a margin against singing; loss at 2W/4W points is controlled.
7. Echo and delay: echo suppressors (now cancellers) are required when the one-way propagation time exceeds about 25 ms; mean one-way delay should preferably be below 150 ms and never above 400 ms.
8. Noise and levels: circuit noise and transmitted power levels at the reference points are limited, so many circuits in tandem still give adequate signal-to-noise ratio.

Nations then build their own national transmission plans to fit within these limits.