Rudementary Impedance measurements for VLF antenna system

Question

I am looking for ideas to improve my Impedance measurements I perform on my VLF antenna system.

Due to circumstances my VLF experiments are usually "on location / in a field" so I do not have the luxury of a fully stacked workbench.

The setup I have is: - a function generator - 4000 Hz output - an audio amplifier - feedline - Antenna

I consider the feedline part of the antenna system, and I use the following method of determining the Impedance of the antenna system:

• Measure the open output voltage of the Amplifier = Vopen
• Measure the output voltage with a known load (Rload=1000) = Vload
• Calculate the output impedance of the amplifier Rout = Rload * ((Vopen/Vload)-1)
• Measure the output voltage with the antenna system = Vant
• Calculate the antenna system impedance Rant = Rout / ((Vopen - Vant)-1)

I would repeat this process with multiple values of Rload to ensure measurements are accurat; usually I use the following values: 1000 Ohm and 2400 Ohm.

This way I can determine/tune the antenna system to come as close to 8 ohm impedance which the amplifier wants to see.

My questions are:

1) is this method correct ?

2) are there better methods given the limitation of being "on location" ?

Answer 1

At 4 kHz you could use your laptop as a rudimentary two-channel oscilloscope.

First find out if it has a useful two-channel input sound card, and find a way of recording a stereo 16-bit WAV and processing it. Octave or Python would work, or you could write your own.

Then build a circuit like this, adjusting parameters to suit:

^{simulate this circuit – Schematic created using CircuitLab}

I've chosen to float the laptop and measure current in the live wire, as the laptop is the most likely part of the circuit to be battery powered. Keep the laptop away from the ground and don't connect anything else to it.

Now you may see a graph of Voltage (R) and Current (L) like this:

Meaning your load is purely resistive, or like this:

Meaning your load is purely capacitive, or like this:
Which will give both the magnitude and phase relationship of the voltage and current, allowing you to measure your antenna impedance.

You should probably calibrate the whole thing - try it out with a 1k resistor instead of the antenna, and check voltage/current readings, then try a modest capacitor and check that you get the right impedance.

I've used this method with a high speed 'scope, to measure an unknown impedance at 500 MHz. Results were within 10% of the network analyser figures.

PS. For an 8-ohm source and antenna, you'll need a much smaller current sense resistor, perhaps 0.1 ohms. I was still thinking of higher impedances.

Answer 2

Your method only crudely measures the magnitude of the feedline impedance, without taking into account the fact that it is probably a complex value, with a phase shift between voltage and current.

Also, the output impedance of most modern audio power amplifiers is very low — usually way less than an ohm. I'm surprised that you get any useful answers by testing it with 1000Ω and 2400Ω load resistors. The goal here is not to match the output impedance of the amplifier, but rather to maximize the power delivered to the antenna without exceeding the amplifier's capability to deliver current (i.e., without driving it into clipping). When an amplifier is "rated for" 4Ω or 8Ω or whatever, it simply means that its voltage output and current output capabilities both max out at about the same time with loads in that range.

It would be far more interesting to take a portable 2-channel oscilloscope (e.g., a USB device plugged into your laptop) and a current probe along on your field trip so that you can simultaneously measure both the voltage and current at the feedline input — and also do an instantaneous power calculation, assuming that your scope has the appropriate math features.