Loop resistance help

hello, I am a qualified electrician and currently studying Instrumentation and control, im currently working through a self paced work book and there is one question that for the life of me i cannot understand:

Why is loop resistance limited to about 1500 ohms where the supply voltage is 42 volts?

I have read through my resources numerous times but cant seem to reference this anywhere

Here’s an explanation from Rosemount’s Temperature Engineering Guide.

https://s15.postimg.org/7e40fynpn/Loop_Loading_Rosemount_pg_91_Eng_Temp_Guide_201.jpg

The cited maximum 42.4V limit is a safety issue.

The lift-off voltage is the the minimum voltage needed to power the transmitter when the loop load is zero ohms, nothing but the power supply across the (+) and (-) terminals (negligible copper wire resistance). The example uses a lift-off voltage of 12V for the transmitter.

The loop resistance versus power supply voltage is a trend curve on a “load line” graph, which is what the example is. Where the graph intersects the X axis on the left is the lift-off voltage. The web example is 12.0V lift-off. The lift-off voltage varies from device to device. I’ve seen lift-offs as high as 18Vdc.

The example also uses a maximum loop current of 24mA. Every commercial transmitter has a fail-safe mode which when the transmitter detects a major fault, it invokes a fail-safe mode. When the fail-safe mode is upscale, the transmitter will go to an upscale/offscale current value well above the 20.0mA signal maximum as a fault indication. The NAMUR value is 21.0mA, but different vendors have used different failsafe values over the years. In any event, the example uses 24mA.

In summary, the power supply voltage has to drive the functions internal to the transmitter (the required lift-off voltage) and the total loop resistance.

If you use 24mA as the max loop current value for a 42V power supply (unusual, the vast majority are 24Vdc), then

24mA = 0.024A E = I*R 1500 ohm * 0.024 A = 36V 42V - 36V = 6V, which allows only 6V for lift-off, which is too low a voltage.

At 21mA max loop current 1500 ohms * 0.021A = 31.5V 42V - 31.5V = 10.5V, a marginal lift-off for a lot of transmitters.

But how often does a transmitter drive 1500 ohms? Not very often.

Two, split ranged positioners or I/P’s are a serious load in a 4-20mA circuit, but rarely do a 2-wire loop powered transmitter power two split ranged positioners or two I/P’s, rather, a controller with an active 4 wire analog output powers two split ranged positioners or two I/P’s.

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