Theory Of Operation - Greenlee CMGRT-100A Instruction Manual

Theory of Operation

The CMGRT-100A performs two measurements: resistance and current. It measures resistance by applying
a voltage at 2.403 kHz and indirectly measuring the resulting current. It measures current indirectly by
measuring the electromagnetic field around a conductor, which is proportional to the current flowing through
the conductor.
The following illustration and schematic diagram represent a typical multiple ground rod system.
The ground electrodes are represented by R (R1, R2, R3 ... Rn), and the CMGRT-100A is represented
by ~V.
The CMGRT-100A induces a voltage (V) into the system and measures the resulting current (I). The CMGRT-
100A then divides the voltage by the current to derive the resistance (V/I = R). The equation for the resistance
of Rx is shown below.
Rx R1
V
= Rx +
I
The equation shown above is the standard equation for finding the resistance of one leg of a parallel circuit.
V
However, the CMGRT-100A uses a simplified equation (V/I = Rx) since the rightmost section of
I
1
1
the formula ( ) is a very small amount of resistance if "n" is sufficiently large. This is shown
n
Σ
Ri
i=1
mathematically in the example below.
Example: A grid with 101 ground electrodes, each with a resistance of 25 Ω.
The measured resistance, Rx, would equal the resistance of Rx in series with the parallel resistance of
the other 100 ground rods:
1
1
n
Σ
Rx = 25 Ω +
Ri
i=1
Note, however, that most grounded systems have more than 100 ground electrodes. Therefore, the parallel
resistance is negligible. It is practical to simplify the equation and the calculation to V/I = Rx.
Rn-1 Rn
1
where, usually
1
n
Σ
Ri
i=1
1
= Rx +
1
n
Σ
Ri
i=1
V 1
= Rx +
1
I
n
Σ
Ri
i=1
Rx = 25 Ω + 0.25 Ω
V 1
= Rx +
1
I
n
Σ
Ri
i=1
1
V
Rx »
= Rx +
1
I
n
Σ
Σ
Ri
i=1
1
V
Rx »
= Rx +
1
n I
Σ
Ri
i=1
1
Rx » V
1
n
Σ I
Ri
i=1
Rx = 25.25 Ω
1
Rx » V
1
100
Σ I
Ri
i=1
CMGRT-100A
1
Rx »
1
n
Ri
i=1
1
Rx »
1
n
Σ
Ri
i=1
1
= Rx + Rx »
1
n
Σ Σ
Ri
i=1
1
= Rx + Rx »
1
n 100
Σ Σ
Ri
i=1
1
1
n
Σ
Ri
i=1
1
1
n
Σ
Ri
i=1
1
1
n
Ri
i=1
1
1
23
Ri
i=1