# Frequency vs. Amplitude modulation in a circuit?

I'm trying to create two circuits that will eventually be added to a larger circuit in a custom PCB. A basic radio transmitter needs to hook into my computer via USB, and transmit data to a rudimentary radio receiver, which connects to the UART of a micro-controller. (As far as I understand, I should be able to send, receive, and translate serial data this way.)

I've done quite a bit of research, and even discovered a post on this site asking a similar question here...

How exactly are radio waves produced from a current in a circuit itself?

I would LIKE to know exactly how RF propagation works, but I'll settle for at least knowing how to build the circuit.

I found a site here that was the most helpful...

http://www.intuitor.com/resonance/circuits.html

But, it leaves some things to be desired. As far as I understand, a capacitor is charged, and used to store and release energy into an inductor. The inductor then builds up its electromagnetic field gradually until all the current is out of the capacitor, then releases the energy stored in the field back to the capacitor in the opposite polarity, forming one wave. Unfortunately, the capacitor and the inductor MUST have a resistance value, so the current will gradually diminish with each wave.

Is amplitude of the waves modulated by the amount of current? Frequency is modulated by the frequency of the capacitor release of energy, correct? That would mean that using a capacitor with a lower farad rating should produce a higher frequency?

How would one go about keeping a sustained current to the inductor since it's constantly losing current without messing up the cycle?

• What bit rate do you expect to run your UART at? – WhatRoughBeast May 4 '15 at 0:47
• Around 200 bytes per second, so around 16 kbit/s. – Allenph May 4 '15 at 2:03

## 1 Answer

Is amplitude of the waves modulated by the amount of current?

The amplitude of the current signal is half of the difference between the maximum and minimum of the current in each cycle of the oscillation.

For example, if the current over time is described by the equation

$$i(t) = A \sin(\omega{}t+\phi)$$

then A is the amplitude of signal because the current oscillates between +A and -A (and A has units of amps).

In the circuit shown, there is nothing modulating the current. Modulation happens when some other signal (like an audio waveform) changes the amplitude (for example) of the current waveform. This would require a more complex circuit than what is shown in your example.

Frequency is modulated by the frequency of the capacitor release of energy, correct?

Again, your circuit shows no mechanism for modulating the frequency. If you used a variable capacitor and the capacitance was controlled by another signal, that would cause frequency modulation. But it would probably also cause some undesirable parasitic amplitude modulation. To see some typical frequency modulator circuits, you can do a google image search for "frequency modulator" and look at the schematics that are found.

That would mean that using a capacitor with a lower farad rating should produce a higher frequency?

Generally the resonance of an LC tank circuit like in your example is given by

$$\omega_0=\frac{1}{\sqrt{LC}}$$

So the oscillation frequency can be increased by reducing either the capacitance or inductance value.

How would one go about keeping a sustained current to the inductor since it's constantly losing current without messing up the cycle?

You can use an oscillator circuit. Generally this means adding some kind of amplifier to the circuit to add energy to the waveform as quickly as it is lost to parasitic resistance and to feeding the load.

• Ahh, so the circuit on that site is simply producing a sin rf wave. There's no way to transmit data on that without modulating it. So, in order to transmit data, I would need to modulate either amplitude or frequency, then interpret that modulation as binary to feed into the UART. Amplitude modulation is accomplished by modulating the amperage passed to the inductor, while frequency would be modulated by affecting the capacitance or inductance of the inductor circuit. The base frequency would be controlled by the capacitance of the capacitor in the circuit I linked. Everything correct? – Allenph May 4 '15 at 2:25
• Do the width or number of loops on the inductor make a difference? Does it matter what core I use for the inductor? – Allenph May 4 '15 at 2:27
• An FM modulation circuit is more complex than what you said, but other than that, you mostly have it right. – The Photon May 4 '15 at 2:27
• How would you modulate frequency then? Also, how do you go about calculating the range of your wave? – Allenph May 4 '15 at 2:32
• @Allenph, both the number of coils and the core material affect the inductance. You can see some formulas in the Wikipedia article on inductors. The inductance affects the resonant frequency according to the formula I mentioned. – The Photon May 4 '15 at 2:34