RS-485 / Modbus RTU Calculator

Method, formulas and references

RS-485 bias and termination

For TI's loaded-bus model with matched end termination, RB(max) = Vmin / [Vidle(1/375 + 4/Z0)]. Divide by 1 + resistor tolerance to obtain the nominal upper bound; the suggested E96 value rounds downward. This is a conservative design check for conventional receiver biasing, not a prediction of actual idle voltage.

Match each end resistor to the cable impedance. TI's stub guideline requires one-way stub delay below one tenth of driver rise time: length = tr × velocity / 10. Use the driver's fastest applicable rise time. This calculation does not establish trunk reach or device count.

Modbus RTU timing

Each RTU character occupies eleven bits. At up to 19200 baud, t1.5 and t3.5 are 1.5 and 3.5 character times. Above that rate, the specification recommends fixed timers of 750 µs and 1.75 ms. Frame sizes include address, function and CRC.

The original polling model uses the larger of device processing time and the required request-to-response silence, then adds the response and silence before the next request. It is a timing estimate, not measured throughput. Bias at one location and termination at both trunk ends concern the physical RS-485 network; Modbus is the protocol using it.

Data sources

1. Texas Instruments SLLA272D — The RS-485 Design Guide (May 2021)
   §6 equation 1: stub electrical delay below one tenth of driver rise time. §7 equation 2: conservative external fail-safe bias resistor bound for a fully loaded, matched bus.
2. Modbus over Serial Line Specification and Implementation Guide V1.02 (20 December 2006)
   §2.5.1: 11-bit RTU characters, maximum 256-byte frame, t1.5/t3.5 and recommended fixed timers above 19200 baud. §3.4: two bus-end terminations and one bias location.