FNIRSI FNB48 USB meter – cable resistance measurement

The FNIRSI FNB48 USB meter is a flexible USB power meter that incorporates a facility to measure the resistance of a USB cable. The tested unit uses firmware v2.50.

The operation also needs a constant current load of 0.5 – 1A (for most cables).

The method is:

• attach the FNB48 with load to the power source, and adjust the current to say 0.5A;
• select the cable measure display and press the jog button to store the voltage and current setting of the loaded power source;
• insert a test cable between source and meter (same load setting), and the display now shows the new loaded voltage and current, and calculates and displays the cable resistance.

Above is a measurement result that is internally inconsistent.

A quick calculation shows that if the voltage difference at 0.5A is 0.78V, $$R=\frac{V}{I}=\frac{0.78V}{0.5}=1.6 \Omega$$, more than twice the displayed 0.7Ω. Yes, it displays 4 digits of precision, but it is grossly wrong at the first digit!

It turns out that this is not a trivial problem to solve, an interesting computational problem.

Essentially we have three unknowns, source voltage Vs, source resistance Rs, and cable resistance Rc. With the information presented, we can write two equations in three unknowns, so it cannot be solved by solving simultaneous equations.

It can be ‘solved’ by a GRG non-linear solver, so there is at least one solution, the data is not flawed, and that solution is:

• Vs=4.928;
• Rs=0.04216; and
• Rc=1.536.

But, that solution is not unique, it is just one of many, so it is of no use.

So, even with appropriate constraints applied, there is not a unique solution to the measurements shown on the FNB48 screen. There is not enough information captured to find a unique solution to the problem, ie the actual cable resistance.

Back to the FNB48, it would seem that the developer has misunderstood the problem and not provided a working solution.

My observation is that under some circumstances, the displayed value reconcile, but sometimes not, it is unreliable, Chinese Quality… bit of an oxymoron really.

If a third measurement was made of the unloaded source voltage, and assuming that the power supply has a linear V/I response (ie it can be represented by a Thevenin equivalent circuit), calculation is trivial. But they do not do that.

It can be solved by measuring unloaded source voltage, and that unique / correct solution is:

• Vs=4.988;
• Rs=0.1600; and
• Rc=1.5355.

I have written to the developer.

Their web site is encouraging… but can they be trusted? No response as yet.