General Formula for Bandwidth Calculation
The general formula for digital modulation bandwidth is:
BW = Bit Rate / Bits per Symbol
or equivalently:
BW = Rb / log2(M)
Where:
- BW = Minimum Nyquist Bandwidth
- Rb = Bit Rate (bps)
- M = Number of signal states (modulation levels)
Baud Rate (Symbol Rate)
Rs = Rb / log2(M)
For ideal Nyquist signaling:
BWmin = Rs
Examples
1. BPSK
M = 2
log2(2) = 1
BW = Rb
2. QPSK
M = 4
log2(4) = 2
BW = Rb / 2
3. 16-QAM
M = 16
log2(16) = 4
BW = Rb / 4
Summary
| Modulation | Bits/Symbol | Bandwidth |
|---|---|---|
| BPSK | 1 | Rb |
| QPSK | 2 | Rb / 2 |
| 8-PSK | 3 | Rb / 3 |
| 16-QAM | 4 | Rb / 4 |
Practical Bandwidth Requirements
Bandwidth ($B$) is the physical "width" of the frequency spectrum used. It is primarily determined by the symbol rate and the filter shape.
B = Rs × (1 + α)
Where α (Alpha) is the roll-off factor (typically 0.2 to 0.5). For an ideal theoretical system, $B \approx R_s$.
The General Case: Shannon-Hartley Theorem
The absolute maximum data rate (Capacity) of any channel (Wireless, Fiber, Copper) is limited by Bandwidth and Noise.
C = B × log₂(1 + SNR)
- C: Channel Capacity (max bps)
- B: Bandwidth (Hz)
- SNR: Signal-to-Noise Ratio (Linear)