In embedded systems development, configuring the UART (Universal Asynchronous Receiver-Transmitter) correctly is crucial for reliable serial communication. The baud rate determines the speed at which data is transmitted over the serial line. To set this speed, microcontrollers (like AVR, PIC, or STM32) use a clock divisor or register value derived from the system clock.
The Mathematical Formula
The calculation to determine the value for the baud rate register (often labeled UBRR in AVR or BRR in other architectures) depends on the system clock frequency and the oversampling mode. The standard formula for asynchronous normal mode is:
UBRR = ( F_osc / (16 × Desired Baud) ) – 1
Where:
UBRR: The value to write to the Baud Rate Register (0-65535).
F_osc: The system clock frequency in Hertz (Hz).
Desired Baud: The target communication speed (e.g., 9600 bps).
16: The oversampling multiplier (Normal Mode). Use 8 for Double Speed Mode.
Double Speed Mode (U2X)
If the error rate is too high in standard mode, many microcontrollers offer a "Double Speed" mode (or 8x oversampling). This reduces the divisor, effectively doubling the resolution for higher baud rates or lower clock frequencies.
UBRR = ( F_osc / (8 × Desired Baud) ) – 1
Why Error Calculation Matters
Since the register value must be an integer, the division often results in a remainder that is discarded. This creates a discrepancy between the Desired Baud Rate and the Actual Baud Rate.
UART communication relies on precise timing. If the cumulative timing error exceeds a certain threshold, bits will be sampled incorrectly.
Total Error %
Reliability Status
< 0.5%
Excellent. Highly reliable communication.
0.5% – 2.0%
Acceptable. Usually fine for short frames (8N1).
> 2.0%
Risky. Data corruption likely. Consider changing crystal or baud rate.
Common standard baud rates include 9600, 19200, 38400, 57600, and 115200. Always ensure both the transmitter and receiver are configured to the exact same speed.
function calculateBaud() {
// 1. Get Input Values
var clockVal = parseFloat(document.getElementById('sysClock').value);
var clockUnit = parseFloat(document.getElementById('clockUnit').value);
var targetBaud = parseFloat(document.getElementById('targetBaud').value);
var oversampling = parseFloat(document.getElementById('oversampling').value);
// 2. Validate Inputs
if (isNaN(clockVal) || clockVal <= 0) {
alert("Please enter a valid System Clock Frequency.");
return;
}
if (isNaN(targetBaud) || targetBaud <= 0) {
alert("Please enter a valid Desired Baud Rate.");
return;
}
// 3. Normalize Clock to Hz
var frequencyHz = clockVal * clockUnit;
// 4. Calculate Raw Divisor (Standard Formula: (F_osc / (Multiplier * Baud)) – 1)
// Note: Some architectures differ slightly, but this is the standard UBRR/Divisor logic
var rawDivisor = (frequencyHz / (oversampling * targetBaud)) – 1;
// 5. Round to nearest integer for the Register Value
var registerValue = Math.round(rawDivisor);
// Handle negative result (if baud is impossible for clock)
if (registerValue < 0) {
registerValue = 0;
}
// 6. Calculate Actual Baud Rate achieved with this integer
var actualBaud = frequencyHz / (oversampling * (registerValue + 1));
// 7. Calculate Error Percentage
var errorPercent = ((actualBaud – targetBaud) / targetBaud) * 100;
// 8. Display Results
document.getElementById('result-area').style.display = 'block';
// Display Decimal Divisor
document.getElementById('divisorResult').innerHTML = registerValue;
// Display Hex Value
document.getElementById('hexResult').innerHTML = "0x" + registerValue.toString(16).toUpperCase();
// Display Actual Baud (rounded to 2 decimals)
document.getElementById('actualResult').innerHTML = actualBaud.toFixed(1) + " bps";
// Display Error and Color Code
var errorEl = document.getElementById('errorResult');
var absError = Math.abs(errorPercent);
var errorStr = errorPercent.toFixed(2) + "%";
errorEl.innerHTML = errorStr;
// Styling based on tolerance
if (absError < 2.0) {
errorEl.className = "result-value error-indicator error-good";
} else {
errorEl.className = "result-value error-indicator error-bad";
}
}