LF: Measuring earth resistance

["Dick Rollema" <d.w.rollema@freeler.nl>]

To All from PA0SE

In my previous message I made a mistake in the formula for the reactance
of a capacitor.  In this repeat the correct formula is
used.

There were some requests for info on the way I
measured the earth resistance of my aerial system.

In 1988 I made an impedance bridge with a noise source.  In the
first version of this e-mail the circuit diagram was included but it did
not pass the reflector.  
Most bridges of this type have a transformer between the noise amplifier
and the bridge circuit. But I found it impossible to make the bridge
frequency independent up to 30MHz. By putting the transformer between the
bridge circuit and the detector I managed to make the readings reliable
up to 30MHz.

For measuring earth resistance I connect the bridge between the bottom
end of the loading coil and the earth connection, after disconnecting the
transmitter from the coil.  The X-control is left at the zero
position 
The detector (receiver = "ontvanger " in Dutch) is tuned to
136.5kHz and the vacuum capacitor in parallel with the tuning coil and
the R-control of the bridge tuned for minimum noise.  The minimum is
so frequency-dependent that it becomes deeper as the bandwidth of the
receiver is reduced! 
The total resistance of the aerial system can then be read from the
R-control. But for better accuracy I measure its value  with a
digital multimeter.
 From the value so found I subtract the loss resistance of the loading
coil. What remains I call the earth resistance. Of course in that value
are also included the radiation resistance and the resistance of the
aerial and earth wire, But these quantities are negligible as compared to
the earth resistance.

In the earth resistance will also be included losses in the aerial
insulation and in the capacitance of the aerial to surrounding objects
like trees (no trees in my case). But these losses are impossible to
separate from the real earth resistance.

Measuring earth resistance at 50Hz has no meaning  for the loss at
136kHz because the earth resistance (impedance is more correct) is
frequency dependent. At  low frequencies earth acts like a resistor,
at high frequencies like a capacitor in parallel with a
resistor.

I find the loss resistance of the loading coil with its tuning capacitor
in parallel as follows.

I use my W & G signal generator and tracking selective voltmeter type
PSM-5. The generator is connected to a one-turn loop that is positioned
at some 35cm from the bottom end of the coil. An oscilloscope probe is
connected to the level meter and hung near the top end of the coil. The
aerial is replaced by a variable capacitor (broadcast receiver type). The
PSM-5 is adjusted to 136500Hz and the variable capacitor tuned for
maximum voltage over the coil and its value noted. The PSM-5 is then
tuned higher and lower to the frequencies where the voltage over the coil
has dropped to 0.707 (-3dB) of the maximum. The frequency difference
between these two frequencies is B (I use a frequency counter to improve
accuracy; B is rather small). This yields Q =
136.5/B (Q = 350 in my case).
The value C of the variable capacitor is then measured. This yields the
reactance of the capacitor 
X = 1/6.28 * f * C
ohms.  Because there was resonance this is also
the reactance of the loading coil in parallel with its tuning capacitor.
We now find for the loss resistance of the loading coil:
R = X/Q.

My measurements support the findings by Alan Melia. The earth resistance
is higher in winter than in summer and is maximum when the earth is
soaked with water. When the water freezes the resistance goes
down.

I hope this info is of some use.

73, Dick, PA0SE