Dear LF,

 

in the recent discussion we have basically considered two different methods to estimate VLF noise background. One (called "A" here) was directly measuring the noise voltage at an electric antenna of known effective height. The other ("method B") involved transmitting with a known current, calculating radiated power, and comparing the received signal at a distant location to background noise. Both require a priori knowledge of the effective height (h), which is somewhat uncertain.

 

But it is interesting to note that height uncertainty has an inverse effect on the result of A and B. When h is lower than expected, with A we measure a smaller noise voltage, and will underestimate the noise floor. However with B, we overestimate radiated power and received signal, and thus come up with a higher noise floor result. So in principle a combination of both methods should enable us to measure h and cancel its effect.

 

This concept can be generalized. It will allow us to formulate another method to measure effective height and efficiency, which does not require any kind of calibrated reference antenna, but is only based on reciprocity.

 

Let's consider a set of three antennas in three different known locations:

 

- Antenna A1 will be used only for transmitting. It could be a distant source like DCF39 or Alpha, absolute EMRP1 does not have to be known. It could also be homogeneous background noise,
- A2 is the device under test, whose height h2 we are interested in. It will both have to transmit a known current i2, and receive a measurable voltage,
- A3 is an uncalibrated receive only antenna, like an active probe, connected to a receiver which can measure relative voltages.

 

Then we will do three measurements:

 

- u12 is the received open-circuit voltage at the output of A2, coming across a distance r12 from A1,
- u13 is the receive level caused by A1 at A3,
- u23 is the receive level at A3 when transmitting with current i2 into A2.

 

Assuming 1/r propagation for simplicity, we arrive at

 

 u12 = sqrt (90 ohm * EMRP1) * h2 / r12,
 u13 = sqrt (90 ohm * EMRP1) * h3 / r13,
 u23 = sqrt (90 ohm * 1589 ohm) * i2 * h2 / lambda * h3 / r23.

 

We can eliminate EMRP1 and h3 by taking

 

 u12 * u23 / u13 = h2 * h2 * r13 / r12 / r23 * Zo / lambda * i2

 

with Zo = 377 ohms, and finally extract h2

 

 h2 = sqrt ((u12 * r12) / (u13 * r13) * (u23 * r23) / i2 * lambda / Zo) .

 

Well I have probably reinvented another wheel here... but anyway I think this method can be quite useful for determining our antenna efficiencies.

 

Kind regards,
MArkus (DF6NM)