# Asynchronous Operational Range

The operational range of the receiver is dependent on the mismatch between the received bit rate and the internally generated baud rate. If the transmitter is sending frames at too fast or too slow bit rates or the internally generated baud rate of the receiver does not have a similar base frequency (see recommendations below), the receiver will not be able to synchronize the frames to the start bit.

The following equations can be used to calculate the ratio of the incoming data rate and internal receiver baud rate.

 Rslow=(D+1)SS−1+D⋅S+SF Rfast=D+2SD+1S+SM
• D: Sum of character size and parity size (D = 5 to 10 bit).
• S: Samples per bit. S = 16 for Normal Speed mode and S = 8 for Double Speed mode.
• SF: First sample number used for majority voting. SF = 8 for normal speed and SF = 4  for Double Speed mode.
• SM: Middle sample number used for majority voting. SM = 9 for normal speed and  SM = 5 for Double Speed mode.
• Rslow : is the ratio of the slowest incoming data rate that can be accepted in relation to the  receiver baud rate. Rfast is the ratio of the fastest incoming data rate that can be  accepted in relation to the receiver baud rate.

The following tables list the maximum receiver baud rate error that can be tolerated. Note that Normal Speed mode has higher toleration of baud rate variations.

Table 1. Recommended Maximum Receiver Baud Rate Error for Normal Speed Mode (U2Xn = 0)
D # (Data+Parity Bit) Rslow [%] Rfast [%] Max. Total Error [%] Recommended Max. Receiver Error [%]
5 93.20 106.67 +6.67/-6.8 ±3.0
6 94.12 105.79 +5.79/-5.88 ±2.5
7 94.81 105.11 +5.11/-5.19 ±2.0
8 95.36 104.58 +4.58/-4.54 ±2.0
9 95.81 104.14 +4.14/-4.19 ±1.5
10 96.17 103.78 +3.78/-3.83 ±1.5
Table 2. Recommended Maximum Receiver Baud Rate Error for Double Speed Mode (U2Xn = 1)
D # (Data+Parity Bit) Rslow [%] Rfast [%] Max Total Error [%] Recommended Max Receiver Error [%]
5 94.12 105.66 +5.66/-5.88 ±2.5
6 94.92 104.92 +4.92/-5.08 ±2.0
7 95.52 104,35 +4.35/-4.48 ±1.5
8 96.00 103.90 +3.90/-4.00 ±1.5
9 96.39 103.53 +3.53/-3.61 ±1.5
10 96.70 103.23 +3.23/-3.30 ±1.0

The recommendations of the maximum receiver baud rate error was made under the assumption that the receiver and transmitter equally divide the maximum total error.

There are two possible sources for the receivers baud rate error. The receiver’s System Clock (EXTCLK) will always have some minor instability over the supply voltage range and the temperature range. When using a crystal to generate the system clock, this is rarely a problem, but for a resonator, the system clock may differ more than 2% depending on the resonator's tolerance. The second source for the error is more controllable. The baud rate generator cannot always do an exact division of the system frequency to get the baud rate wanted. In this case, an UBRRn value that gives an acceptable low error can be used if possible.