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Gain in cascade amplifiers

Attenuation, noise and gain in signal transmission

Attenuation

Signal Attenuation or degradation is the loss of signal strength as the signal travels through a medium. Attenuation is occurs in every medium of transmission. It is proportional to the square of the distance between the transmitter and the receiver.

Causes of signal attenuation:

  • Noise – electrical noise from other sources surrounding medium can leak into the medium, thereby degrading the signal.
  • Travel distance – the further the signal has to travel, the greater the degradation of the signal.
  • Frequency – some media are frequency-selective, which means that a given medium will degraded certain frequency of the transmitted signal.

Attenuation is calculated as follows:

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A_T = \frac{output}{input} = \frac{V_{out}}{V_{in}} whereby Vout is the output voltage and Vin is the input voltage.

A voltage divider can be used to introduce a calculated amount of attenuation into a circuit.

voltage divider attenuation

For a voltage divider, V_{out} = V_{in}(\frac{R_1}{R_1+R_2})

  • V_{out} = 20V(\frac{200 \Omega}{200 \Omega+400 \Omega})
  • V_{out} = 20V(\frac{200 \Omega}{600 \Omega})
  • V_{out} = 6.67V

And the attenuation is calculated as follows:

A_T = \frac{V_{out}}{V_{in}} \ or \ \frac{R_1}{R_1+R_2}

  • A_T = \frac{200 \Omega}{600 \Omega}
  • A_T = 0.333

Total attenuation in cascaded circuits

If two or more stages of signal processors are cascaded, the total attenuation of the whole setup is equal to the product of the attenuations of the individual component.

Attenuation in cascaded circuits

For example, the diagram above shows three signal processors connected in cascading form. The first component has an attenuation of 0.23, the second an attenuation of 0.3 and the third an attenuation of 0.87.

The total attenuation of the whole system now becomes:

A = 0.23 \times 0.3 \times 0.87 = 0.06003

Noise

Noise is the unwanted and irregular fluctuation that accompanies a transmitted signal. Noise is not the same as interference from other surrounding signals. High noise level coupled with the weak signal can cause the noise to completely obliterate the original transmitted signal. In digital data transmission noise can cause bit errors which can result in signal being garbled and the information lost.

The noise level in an electronic communication system is proportional to the following factors:

  • temperature
  • bandwidth
  • the amount of current flowing through an electronic component
  • the gain of the system
  • the impedance or resistance of a circuit.

An increasing in any of the above mentioned factors increases noise level of the system.

To reduce the noise of a system we generally use:

  • low-gain circuits
  • low direct current
  • low circuit resistance values
  • narrow bandwidth
  • low temperatures

Types of noise

External Noise

This type of noise comes from independent external sources which we usually have little or no control over. In this category we have:

  • Industrial noise – noise which is produced by industrial equipment, such as the electromagnetic noise produced by the sparking of a car ignition systems and electric motors. In actual fact, any industrial equipment that causes rapid switch of high voltages or currents produces electrical noise.
  • Atmospheric Noise – noise which is caused by natural electrical disturbances in the earth’s atmosphere. Such noise is also referred to as static. Static is usually caused by lightning and has the greatest impact on signal frequencies below 30 MHz.
  • Extraterrestrial Noise – noise which is causes by solar and cosmic events such as solar flares and cosmic generated by stars outside our solar system.

Internal noise

A receiver contains components such as resistors, diodes and transistors. These components are a major source of internal noise such as thermal noise, semiconductor noise, and intermodulation distortion. Although internal noise is low level, it is often enough to interfere with weak signals.

The biggest problem with internal noise the receiver usually receive weak signals and when the signal is amplified the noise is also amplifier. However this can be solved by proper circuit design since internal noise is a known effect.

Signal-to-Noise Ratio

The signal-to-noise (S/N) ratio, also known as SNR, is the relative signal strength to noise level in a communication system. A stronger signal and weaker the noise leads to a higher value of the S/N ratio and if the signal is weak and the noise is strong,
the S/N ratio becomes low.

When designing communication systems we always strive to produce the highest S/N ratio practically possible to reduce signal degradation. S/N ratio is calculated as follows:

S/N\ ratio = \frac{V_s}{V_n}

whereby V_s is the signal voltage and V_n is the noise voltage.

Or

S/N\ ratio = \frac{P_s}{P_n}

whereby P_s is the signal power and P_n is the noise power.

For example if the signal voltage is 2 µV and the noise is 0.5 µV.

  • S/N\ ratio = \frac{V_s}{V_n}
  • S/N\ ratio = \frac{2 \mu V}{0.5 \mu V}
  • S/N\ ratio = 4

And if the signal power is 2 µW and the power is 25 nW

  • S/N\ ratio = \frac{P_s}{P_n}
  • S/N\ ratio = \frac{2 \mu W}{25 n W}
  • S/N\ ratio = \frac{2 \times 10^{-6}}{25 \times 10^{-9}}
  • S/N\ ratio = 80

The preceding S/N value can be also be expressed decibels (dB) as follows:

S/N\ ratio\ in\ dB = 20\ log \frac{S}{N} if the S/N is calculated using voltages.

S/N\ ratio\ in\ dB = 10\ log \frac{S}{N} if the S/N is calculated using power.

If the S/N ratio is less than 1, the resultant dB value will be negative indicating that the noise is stronger than the signal.

Gain

In electronic systems, gain refers to amplification. Amplification results in the output signal of a system having a greater amplitude than the input signal.

Gain in cascade amplifiers

Gain is mathematically the ratio of the output to the input and is calculated as follows:

A_v = \frac{output}{input} = \frac{V_{out}}{V_{in}} whereby Vout is the output voltage and Vin is the input voltage.

For example, if an amplifier produces an output of 0.1 V for an input of 1 mV, the voltage gain is calculated as follows:

A_v = \frac{V_{out}}{V_{in}} = \frac{0.1V}{1mV}

  • A_v = \frac{0.1V}{1 \times 10^{-3}V}
  • A_v = 100

We can also calculate power gain using the ratio of the output power to input power. For example, if an amplifier that produces an output of 100 W for an input of 0.1 W, the power gain is calculated as follows:

A_p = \frac{P_{out}}{P_{in}} = \frac{100W}{0.1W}

  • A_p = 1000

Total gain of cascaded amplifiers

Gain in cascaded amplifiers

If two or more stages of amplifiers or other signal processors are
cascaded, the total gain of the whole setup is equal to the product of the gains of the individual component.

For example, the diagram above shows three amplifiers connected in cascading form. The first amplifier has a gain of 23, the second a gain of 3 and the third a gain of 87.

The total gain of the whole system now becomes:

A = 23 \times 3 \times 87 = 6003

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