Sources of attenuation and distortion

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--/\/\/--mmmm--+----+--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 the 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 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.