Beat Frequency: Can Inductive Coupling Work?

[Jdo300]

Hi, here’s my question. If I make an oscillator that resonates at 6kHz and a second oscillator that resonates at 5kHz, the magnetic field produced by the coils of the two oscillators would be 1000Hz (please correct me here if I have made an incorrect assumption). If I have a 1000Hz signal that I would like to inductively couple to the two oscillators, could this 1000Hz signal keep the two oscillator circuits running or would it have to be set to one of the two frequencies (5kHz or 6kHz)? So in general, can you use the beat frequency of two oscillator circuits to inductively couple to a signal source that resonates at the beat frequency of the two oscillators?

 

[berkeman]

You hear the beat because the *envelope* of the resultant waveform is varying at the difference frequency. You can only "use" this frequency for something if you first use an envelope detector circuit to give you a sine wave at the beat frequency.

Take a look at the sine wave addition plot that I posted part-way down this other thread where we were talking about what happens when you add two sine waves ...
https://www.physicsforums.com/showthread.php?t=118708

 

[Jdo300]

Hi Berkeman,

Thanks for the link. I think I see what you are talking about but I’m not sure if an envelope detector will work for my application. I’m trying to see if this will work for oscillator circuits which are only inductively coupled to the signal source. For simplicity, we can assume that the two oscillator circuits have been given an initial charge and have started to resonate and create the EM beat wave. I drew up a plot to show you which specific type of beat wave I’m looking at. I would want the beat wave to look as sinusoidal as possible which is why I was using two very high frequencies to create the low frequency wave. (See attached picture for example).

If the two oscillator circuits are initially resonating and producing the beat wave, would it be possible to back-feed the oscillator circuits by inductively pumping an input signal into the coils of the two oscillators at the beat frequency? Or would this only work the other way around? (Using the beat wave to resonate another oscillator tuned to the frequency).

 

[berkeman]

If the two oscillator circuits are initially resonating and producing the beat wave, would it be possible to back-feed the oscillator circuits by inductively pumping an input signal into the coils of the two oscillators at the beat frequency? Or would this only work the other way around? (Using the beat wave to resonate another oscillator tuned to the frequency).

I think the answer is b. You can't pump a 5kHz resonator with a 1kHz beat signal. But you can use the beat envelope to excite a third resonator that is tuned to 1kHz, if you feed the third resonant circuit with the envelope signal. You can make a simple envelope detector circuit with just a diode. Will that work for what you are trying to do?


EDIT -- more like 4 diodes, I think, to full-wave rectify the envelope.

 

[berkeman]

BTW, your plot is a bit non-physical. The red line that you've drawn is not the beat or the envelope. It is following the top of the envelope for one beat period, and the bottom of the envelope for the second beat period. What you hear as the beat is the overall amplitude envelope changing, and that is varying at twice the frequency of the red sine wave that you drew. Note also that the envelope amplitude is not sinusoidal -- it's more like like full-wave rectified in shape. To get a sinusoidal shape to the top and bottom envelope shapes, you need to have a carrier signal with AM (which is a non-linear process carried out by a mixer, not just from adding two sine waves).

 

[waht]

you can't simply add these frequencies in a linear circuit. What you need is a non linear device like a diode or transitor which is capable of producing the sum and a difference between your frequencies, like a mixer.

 

[Jdo300]

Hmmmm ok I see. Well, this raises another question. If I have the two oscillators (4kHz and 5kHz), and they are close to each other so that the EM fields generated from the coils mix, would they actually make a beating EM wave at all? Maybe I should have asked this first.

 

[Jdo300]

Also, when letting two oscillating EM fields interact with each other would their frequencies be added together or multiplied? or something else altogether?

 

[berkeman]

Adding is different from "mixing". Mixing implies multiplication, as in modulation. Adding is just the superposition of the two AC magnetic fields from the coils. As what says, you need non-linear mixing of the waves (multiplication or rectification) to get true modulation where there is a physical thing at the sum and difference frequencies. Using an envelope detector like I mentioned (the diode is the non-linear element) is a simple way to get the difference frequency. That's how simple unpowered crystal AM radios work, for example.

The best way to understand this better is to play around in Mathematica or some other math simulation software (or even Excel), and try out different additions versus different multiplications of two signals. Display the component waves, then the addition or multiplication resultant wave, and take Fourier transforms of all the signals. You'll see that just adding two waves together in superposition does not change their spectra. But multiplication (mixing) does.

 

[berkeman]

Also, when letting two oscillating EM fields interact with each other would their frequencies be added together or multiplied? or something else altogether?

Depends on how they interact. If they are in a linear medium like air or water or vacuum, they don't affect each other. If they are in a non-linear medium like a non-linear optics cell, then they can have an effect on each other. But non-linear optical media are rare, so most of the time the answer to your question is no, they don't interact. All you get is the superposition (addition) of the two waves.

 

[Jdo300]

Ok I think I see what you mean now. I multiplied a few waves together in my graphing program and can now see what you mean. As for my 'application' for this, I am just trying to understand more about oscillator circuits and how they interact in various ways.

I do have another semi-related question. Let’s say that we have a single oscillator that is resonating at 10Hz. Is is possible to make a tuned coil that will by itself oscillate at a harmonic of the 10Hz oscillator or would this lone coil need to be a tank circuit itself to work? In this setup, we are assuming that the second coil is not coupled to the oscillator in a transformer setup but simply sitting near the oscillator circuit. If this coil is assumed to be an air core coil, how does this effect things?

 

[waht]

I do have another semi-related question. Let’s say that we have a single oscillator that is resonating at 10Hz. Is is possible to make a tuned coil that will by itself oscillate at a harmonic of the 10Hz oscillator or would this lone coil need to be a tank circuit itself to work? In this setup, we are assuming that the second coil is not coupled to the oscillator in a transformer setup but simply sitting near the oscillator circuit. If this coil is assumed to be an air core coil, how does this effect things?

A coil sitting all by itself won't oscillilate, even when is near an oscillating field. If you complete the circuit, and add a resistor in parallel, then the coil will pick up the nearby oscillator and will oscillate only at the oscillator's frequency.

If you make a tuned tank circuit, a coil and a capacitor, then it will also pickup the nearby oscillator and start oscillating, but if you tune exactly your tank circuit with the nearby oscillator's frequency, then it will strongly oscillate at that frequency and weakly at multiples of the original frequency. Of course, this effect is greatly enhanced by adding a non linear element.

Hope that helps,

 

[Jdo300]

Thanks, that does help. How would one tune the tank circuit to oscillate strongly at harmonics of the oscillator? What do you mean by a nonlinear element?

 

[waht]

Thanks, that does help. How would one tune the tank circuit to oscillate strongly at harmonics of the oscillator? What do you mean by a nonlinear element?

a coil and a capacitor will oscillilate at a resonant frequency that depends on the coil and capacitor. So to tune it you have to adjust either the coil or capacitor to get it close to oscillate at your frequency of interest.

A nonlinear element is simply a diode or a transistor that are good at multipling frequencies.

Note, low frequencies are impractical to work with a tank circuit because of high values of capacitance or inductance required.