Noise and two-wire to four-wire converter

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).