Bandwidth Of Signals And Transmission Medium

Bandwidth is the range of frequencies a signal contains or a channel can carry. If a voice signal uses frequencies from 300 Hz to 3400 Hz, its bandwidth is 3100 Hz. A transmission medium like a wire, optical fibre or free space also has a limited bandwidth, just like a road has a limited width for vehicles.

Bandwidth matters because it decides how much information can be sent per second and how clearly it arrives. A narrow channel can carry a telephone voice but not a high quality video. Understanding bandwidth helps us choose the right medium for radio, TV, internet and mobile phones.

Key Concepts

Signal: Information converted into electrical form, such as voltage varying with time. Bandwidth of signal: Difference between highest and lowest frequency present, measured in hertz (Hz). Channel bandwidth: Frequency range a medium allows to pass with acceptable loss. Bit rate: Bits sent per second, measured in bits per second, roughly proportional to bandwidth. Attenuation: Weakening of signal with distance, measured in decibels (dB).

• Audio signal: about 20 Hz to 20 kHz
• Telephone speech channel: 300 Hz to 3400 Hz
• TV video signal: about 4.2 MHz bandwidth
• Optical fibre: bandwidth in terahertz range

Formulas

Bandwidth: B equals highest frequency minus lowest frequency. Frequencies are in hertz, so B is also in hertz. It applies to any signal whose spectrum is known.

Maximum data rate by Shannon: C equals B times log base 2 of (1 plus S divided by N). C is capacity in bits per second, B in Hz, S/N is signal to noise power ratio with no unit. It assumes random noise and gives an upper limit, real systems stay below it.

Worked Example

A music signal contains frequencies from 100 Hz to 15100 Hz. Find its bandwidth. Step 1: Highest frequency is 15100 Hz and lowest is 100 Hz. Step 2: B equals 15100 minus 100 equals 15000 Hz. Step 3: Convert to kHz: 15000 Hz equals 15 kHz. So the channel must pass at least 15 kHz to carry this music without cutting notes.

If the same channel has signal to noise ratio 1023, capacity equals 15000 times log base 2 of 1024. That log value is 10, so capacity is 150000 bits per second or 150 kbps. This shows more bandwidth or cleaner signal raises data speed.

Common Misconceptions

• Bandwidth means speed only: Wrong. Bandwidth is frequency width, speed in bits per second depends also on noise and coding.
• All media have same bandwidth: Wrong. A twisted copper pair supports megahertz range, coaxial cable supports higher, optical fibre supports far higher frequencies.
• Wider bandwidth always wastes spectrum: Wrong. Wider bandwidth can give better quality and faster data, but spectrum must be shared fairly by regulation.

Real-World Applications

Broadband internet uses wide bandwidth for fast downloads. FM radio stations are spaced with enough channel width for stereo music. Mobile networks divide total spectrum into channels for many users. Optical fibres carry many calls together because their huge bandwidth allows many light colours to carry separate data streams.

In short, bandwidth tells us how much frequency space a signal needs and how much a medium can offer. Matching the two is the first rule of any communication system, from a simple phone call to high speed internet.