# Symbol rate, Bandwidth and Bit rate definition and conversion of each other’s.

Symbol rate:
In Digital Communication, the symbol rate means that the changes of symbol per second (signaling events or waveform changes) through a digital modulated signal transmission path. Symbol rate is indicate by symbols/second or baud (Bd) units.

Bandwidth:

Bandwidth is often used as a synonym of data transfer rate. Moving data from one point to another, in a given time period (usually a second), is called bandwidth. Bandwidth is indicate by bits (of data) per second (bps).

Bit rate:
In telecommunications and computing, bit rate (sometimes written bit rate, data rate) is the number of bits that are conveyed or processed per unit of time. The bit rate is quantified using the bits per second (bit/s or bps) unit.

Symbol Rate = Bandwidth / 1+Roll of Factor

= Bandwidth / 1.35       (When, Roll off factor is 35%)

Or,

= Bandwidth / 1.25        (When Roll off factor is 25%)

Bit Rate = Symbol Rate * Modulation * Framing * FEC

Where, Modulation:

BPSK      : 2^1 = 1 bit/sec/Hz
QPSK     : 2^2 = 2 bit/sec/Hz
8PSK      : 2^3 = 3 bit/sec/Hz
16QAM   : 2^4 = 4 bit/sec/Hz
32QAM   : 2^5 = 5 bit/sec/Hz
64QAM   : 2^6 = 6 bit/sec/Hz
256QAM : 2^8 = 8 bit/sec/Hz

Framing = 188/204 or 204/188 (depends on user selected options)
FEC = 1/2, 2/3, 3/4, 5/6, 7/8

Example:

If the bandwidth is 5MHz and others options are DVB, PAL, FEC=3/4, QPSK Modulation. What is the symbol rate and bit rate?

Solution:

Symbol Rate = Bandwidth / 1.35

= 5 (MHz) / 1.3

= 5* 1000 / 1.35

= 3703.7

≈ 3704

Maximum Symbol Rate is 3704 Hz. Now, we can set 3600Hz apart for some side band or safety guard.

Bit Rate = Symbol Rate * Modulation * Framing * FEC

= 3600*2*(188/204)*(3/4)

= 4976.47 bit/sec

=4.97647 Mbit/sec

Updated: June 20, 2019 — 7:14 PM

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