Giving up on low pass filters

# Soil Moisture Project

## Giving up on low pass filters

When I started this project, most of my electronics knowledge came from “Dick Smith’s Fun Way into Electronics”. Eventually I added to my knowledge and borrowed a copy of “Art of Electronics” from the university library. This book is well recommended by electronics hobbyists and professionals.

After some reading and returning to what I had already learned about low pass filters, it suddenly dawned on me why this may not work.

Recall that instead of resistance (opposition to the flow of electricity), we have to think in terms of reactance because we are using AC instead of DC. Reactance is the opposition to the change in voltage or current in a circuit. In other words, it is opposition to the alternating part of the AC. The reactance of a component changes according to the frequency of the AC.

The reactance of a capacitor is inversely proportional to the frequency. When the frequency increases, the reactance decreases, and vice versa. This image shows the relationship between reactance and frequency. Both reactance and resistance are measured in ohms. If you want to learn more about capacitive reactance, have a read of this site.

## So what does this mean?

Since I am using a relatively high frequency, the reactance of the soil capacitor will get lower as soil moisture increases. This is because increased soil moisture leads to increased capacitance, which in turn leads to decreased reactance.

In a voltage divider, the voltage across a component depends upon the amount of resistance of that component in relation to the resistance of the circuit. Have a quick re-read of the write up about voltage dividers if you need to.

I won’t go into the maths and my assumptions about the capacitance of the soil capacitor here. What I worked out was that the reactance of the soil capacitor will only be a few ohms if the soil was dry. If the soil is wet, the reactance could easily be less than one ohm.

This means that if I want to make a useful filter using a resistor and the soil capacitor, I would need resistors that are only a few ohms. Just as an example, the smallest resistors that Jaycar (the Bunnings of the electronics world) sell are 11Ω.

## Enter the inductor

At high frequencies it is more common to use inductors instead of resistors in filter circuits. This is because the reactance of capacitors and inductors change in opposite directions when they are exposed to alternating current. Where the reactance of a capacitor decreases at higher frequencies, the reactance of the inductor increases. While this sounds like it could be an alternative to using very small resistors, I would need very small inductors which I can’t buy at Jaycar.

## To make matters worse…

Since this was starting to get beyond my ability, it was time to ask the internet whether it was possible to create a low pass filter for high frequencies using a variable capacitor.

The best answer I got was that the changes in the filter would interact with the other parts of the circuit and that in order to start to understand this I would really need to learn some complex number algebra.

I also could not find any examples of high frequency filters that use a variable capacitor. Perhaps they are out there somewhere, perhaps I could invent one.

So far, designing a soil moisture sensor is hard enough, without developing a new way of interacting with alternating current. I think this pathway is best left for now.