body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 800px;
margin: 0 auto;
padding: 20px;
}
.calculator-wrapper {
background: #f8f9fa;
border: 1px solid #e9ecef;
border-radius: 8px;
padding: 30px;
margin-bottom: 40px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-header {
text-align: center;
margin-bottom: 25px;
}
.calc-header h2 {
margin: 0;
color: #2c3e50;
}
.input-group {
margin-bottom: 20px;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: #495057;
}
.input-row {
display: flex;
gap: 10px;
}
.input-field {
width: 100%;
padding: 12px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 16px;
}
select.input-field {
background-color: white;
}
button.calc-btn {
width: 100%;
padding: 14px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.2s;
margin-top: 10px;
}
button.calc-btn:hover {
background-color: #0056b3;
}
.results-area {
margin-top: 30px;
padding-top: 20px;
border-top: 2px solid #dee2e6;
display: none;
}
.result-box {
background: white;
padding: 20px;
border-radius: 6px;
border-left: 5px solid #28a745;
margin-bottom: 15px;
box-shadow: 0 2px 4px rgba(0,0,0,0.05);
}
.result-label {
font-size: 14px;
color: #6c757d;
text-transform: uppercase;
letter-spacing: 0.5px;
}
.result-value {
font-size: 28px;
font-weight: 700;
color: #212529;
margin-top: 5px;
}
.result-sub {
font-size: 13px;
color: #868e96;
margin-top: 5px;
}
.article-content h2 {
color: #2c3e50;
margin-top: 30px;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
}
.article-content h3 {
color: #495057;
margin-top: 20px;
}
.formula-box {
background: #eef2f5;
padding: 15px;
border-radius: 4px;
font-family: monospace;
margin: 15px 0;
border-left: 4px solid #17a2b8;
}
.error-msg {
color: #dc3545;
font-weight: bold;
display: none;
margin-top: 10px;
}
function calculateBaud() {
// Get DOM elements
var bwInput = document.getElementById('bandwidth');
var unitInput = document.getElementById('freqUnit');
var modInput = document.getElementById('modulation');
var resultContainer = document.getElementById('results');
var errorDiv = document.getElementById('errorMsg');
var baudDisplay = document.getElementById('baudResult');
var bitRateDisplay = document.getElementById('bitRateResult');
var subDisplay = document.getElementById('bitsPerSymbolDisplay');
// Parse values
var bandwidth = parseFloat(bwInput.value);
var multiplier = parseFloat(unitInput.value);
var levels = parseInt(modInput.value);
// Validation
if (isNaN(bandwidth) || bandwidth = 1000000000) {
return (num / 1000000000).toFixed(2) + " G";
}
if (num >= 1000000) {
return (num / 1000000).toFixed(2) + " M";
}
if (num >= 1000) {
return (num / 1000).toFixed(2) + " k";
}
return num.toLocaleString();
}
function formatBits(num) {
if (num >= 1000000000) {
return (num / 1000000000).toFixed(2) + " Gbps";
}
if (num >= 1000000) {
return (num / 1000000).toFixed(2) + " Mbps";
}
if (num >= 1000) {
return (num / 1000).toFixed(2) + " kbps";
}
return num.toLocaleString() + " bps";
}
Understanding Baud Rate vs. Frequency
When designing digital communication systems, understanding the relationship between the available frequency bandwidth and the transmission speed is crucial. While the terms "Baud" and "Bit Rate" are often used interchangeably in casual conversation, they represent distinct concepts in telecommunications physics.
What is Baud Rate?
Baud Rate (measured in symbols per second or Bd) refers to the number of signal unit changes per second. It essentially measures the speed at which the carrier signal changes states. If a signal changes its phase, frequency, or amplitude 1,000 times per second, the Baud rate is 1,000 Bd.
The Nyquist Theorem: Calculating Baud from Frequency
The fundamental limit of a telegraph line or any communication channel is governed by the Nyquist Theorem. This theorem states that for a noise-free channel with a bandwidth of B (measured in Hertz), the maximum theoretical symbol rate (Baud Rate) is twice the bandwidth.
Max Baud Rate = 2 × Bandwidth (Hz)
For example, a standard telephone line with a bandwidth of roughly 3000 Hz (3 kHz) has a maximum theoretical baud rate of 6000 Bd.
Baud Rate vs. Bit Rate
This is where modulation comes into play. If your system uses a simple binary signal (High/Low), each symbol carries exactly 1 bit of data. In this case, Baud Rate equals Bit Rate.
However, modern modulation techniques like QAM (Quadrature Amplitude Modulation) pack more data into each symbol. By using multiple signal levels (M), we can transmit multiple bits per symbol. The relationship is defined as:
Bit Rate (bps) = Baud Rate × log₂(M)
Example Calculation:
If you have a 1 MHz channel bandwidth using 16-QAM modulation (which has 16 signal levels):
- Bandwidth: 1,000,000 Hz
- Max Baud Rate: 2 × 1,000,000 = 2,000,000 symbols/sec (2 MBd)
- Bits per Symbol: log₂(16) = 4 bits
- Total Bit Rate: 2,000,000 × 4 = 8,000,000 bps (8 Mbps)
Real-World Constraints
While the calculator above uses the ideal Nyquist limit, real-world systems are affected by noise (Shannon-Hartley Law) and practical filter roll-off factors. In practice, the achievable baud rate is often slightly less than 2x Bandwidth depending on the quality of the filters used in the transmitter and receiver.