"The highway addressable remote transducer (HART®) protocol
uses 1200 baud frequency shift keying (FSK) based on the Bell 202
standard to superimpose digital signals on conventional 4-20 mA analog
signals. This enables two-way communication and facilitates the
transmission of information beyond normal process variables to and from
smart field instruments. The HART protocol communicates without
interrupting the analog signal and allows a host application (master)
to receive two or more digital updates per second from a field device
(slave). Because they are phase-continuous, the digital FSK signals do
not interfere with the analog 4-20 mA signals. HART is a registered
trademark of the HART Communication Foundation."
Basically speaking HART is just one form of SMART transmitter. SMART implies the use of electronics within the transmitter to offer additional functionality to what you would get with a standard transmitter, ie just the basic process variable converted to 4/20mA. This additional functionality might be additional process variables in digital form or the ability to remotely re-configure the device.
HART was probably the first protocol to become widely used by different manufacturers, before that each had his own (Foxboro FoxCom, Honeywell DE etc) .
These days we have Foundation Fieldbus and things have moved on.
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