Hi!
Most electronic devices have a lot of different parts: A computing part, telemetry, motors, maybe motor controllers and a battery. All parts have to live in harmony with each other – in other words being electromagnetic compatible. This means that each part should avoid generating bad signals, coupling them to other parts and if it does, the other parts need to be immune to these signals. At the moment, I do a university course on electromagnetic compatibility. Every once in a while, I need to get hands on and play around with the theory to make sure the university isn’t just telling fancy stories!
Measuring capacitive coupling #
Signals couple between devices in multiple different ways, one being capacitive. With the following experiment, I want to check whether capacitive coupling really exists:
- The signal generator outputs a square wave voltage signal. A square wave has steep edges, coupling well to other cables.
- The generators output is connected the oscilloscope directly for reference and to a long signal wire taped to a grounded aluminum sheet.
- Another long wire is placed closely to the signal wire and connected to another oscilloscope input. It therefore should pick up signals over the air, capacitively.
The video shows me varying the distance between the two wires. The oscilloscope shows two signals: The yellow one being the original reference output of the signal generator, and the green one being the victim cable that should pick up the signal.
…and indeed! As I am moving the cables more closely, the green signal changes into a similar shape of the yellow signal! Please note that the oscilloscope scales the green signal’s amplitude higher than the yellow one for a better visibility.
There are invisible capacitors #
Why do we have the coupling in the first place? Why do we see the signal from the signal generator in the oscilloscope, even though it is not connected? The following circuit shows the naive circuit - the signal generator and the oscilloscope are not connected. But the measurement results tell something different!
Now from school, we know that a capacitor was originally defined as two conducting plates in the first place. The capacitance can be calculated like this:
$$C = \epsilon \cdot \frac{A}{d}$$
The permittivity $\epsilon$ is the ability of the non-conducting material to polarize. $A$ is the area of the two plates and $d$ the distance. If a voltage change happens, electric fields are generated across the non-conducting material, resulting in electrical charges collecting at the plates, allowing electric displacement current to flow.
Now in this case, we don’t have two plates, only two wires. Two wires are similar to two plates, only the area $A$ is smaller and thus, the capacitance is smaller according to the equation above. (Actually, there are better models for two wires in my lecture, but let’s keep things simple). Now, we can model the circuit much more precisely by putting in capacitors for every cable-cable and cable-plate interaction:
But how do we receive a voltage exactly?
The voltage / current relationship of a capacitor can be modelled like this:
$$i(t) = C * \frac{du(t)}{dt}$$
In words, a voltage change across the capacitor results in a current. And if the capacitance is bigger, the current is also bigger.
The most important capacitor is $C_{12}$. If the voltage changes between the long oscilloscope wire and signal generator wire, it results in a current flowing through $C_{12}$. The current flows back through the components $C_{2G}$, $C_{input capacitance}$ and especially the $1MOhm$ resistor, and this finally can be measured as a voltage!
Now here are some ideas on how to maximize this voltage:
- Decrease distance $d$ between the wires, thus increasing $C_{12}$. You see this in the video above.
- Remove the aluminum plate and therefore removing $C_{2G}$ and $C_{C1G}$
- Increase the voltage change speed $du(t)/dt$ at the signal generator.
This extended circuit still ignores my hand moving the oscilloscope wire and also the second wire that connects the signal generator to another oscilloscope port.
Going further: Making music with interference! #
The experiment workflow gets extended:
- The oscilloscope measures peak-to-peak voltage automatically
- With a vibe-coded Python script on my computer, I retrieve the peak-to-peak voltage from my oscilloscope and translate it into a midi device outputting the same signal
- The VCV Rack modular synthesizer program received the midi signals makes some sounds!
As you see, I control the tone pitch using the amount of capacitance between the two cables, similar to a theremin. You can even add beats:
Btw., this synthesizer program is called “VCV Rack”. It’s very cool since you can just put modules together as you like. It’s a little difficult to get started, but regarding making music, you have the most freedom, especially regarding sound design. And it’s free!
I am interested in your thoughts! - Reply with a simple Email
Have a nice day,
Carl