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I would like to know how and why the tuner works in a crystal set radio. I already know all the theory and the "formal definitions" (this creates a resonant circuit which responds to an alternating current at one frequency) and I have read all the already given answers on the subject. But I can't seem to understand how a resonant circuit "filters" the frequency of a specific radio station.

I already know how induction works and how a LC circuit (capacitor+inductor) works so you can start from there.

fig a

Please do not be afraid to give very "deep" explanations.

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    $\begingroup$ Welcome to Physics Stack Exchange. On this site we require that questions are focused and specific. This post essentially asks a would-be answer writer to give a complete circuit analysis of a crystal set. That's not a specific question. It seems you've already identified some specific pieces you'd like to understand, e.g. how does an $LC$ circuit act as a filter. Why don't you post another question asking just that? You're much more likely to get a good answer that way. As worded, this question is too broad: I could explain crystal oscillators, resonant circuits, or a lot of other things. $\endgroup$ – DanielSank Dec 11 '15 at 6:59
  • $\begingroup$ Maybe it is worth looking at a very simplified explanation, if you have no problem with LC circuits. crystalradio.net/howitworks . The specific frequency is picked up by the tuner by rejecting all others which cannot set up a resonance. Their (rejected frequencies) energy goes to the ground and to heat. $\endgroup$ – anna v Dec 11 '15 at 12:56
  • $\begingroup$ Would Electrical Engineering be a better home for this question? $\endgroup$ – Qmechanic Dec 11 '15 at 14:02
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From your question is sounds as if you understand how parallel LC circuits work, in which case it's easy to explain how an LC circuit works as a tuner.

Any particular parallel LC circuit has a natural resonant frequency. If we assume the LC circuit is perfectly lossless, then if we apply a driving voltage at the resonant frequency the energy stored in the LC circuit will increase without limit and the voltage will become arbitrarily large. So the LC circuit amplifies the driving voltage in a frequency dependant way. The gain is highest at the resonant frequency and falls rapidly away from it.

At that's how the tuner works. The aerial develops a (very) small oscillating voltage by absorbing energy from a radio wave. The LC circuit amplifies the voltage with the amplification being greatest at the resonant frequency. That boosts signals that match the resonant frequency compared to all other frequencies.

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  • $\begingroup$ "if we apply a driving voltage at the resonant frequency the energy stored in the LC circuit will increase without limit".. why? $\endgroup$ – d0bz Dec 12 '15 at 6:05
  • $\begingroup$ @dobs: if a resonant system is lossless then any energy stored in it doesn't leak away. So if you apply a driving force in phase with the oscillation then that can only add to the energy in the system. It's like pushing a swing. As long as you time your pushes to be at the right moment even small pushes can make the swing move a long way. Real systems (like swings) aren't lossless so their energy doesn't keep increasing. However it can build up to be large compared to the driving force. $\endgroup$ – John Rennie Dec 12 '15 at 6:22
  • $\begingroup$ but how does the current reaches the speakers if its "trapped" into the LC circuit? $\endgroup$ – d0bz Dec 12 '15 at 6:26
  • $\begingroup$ @dobs: in an ideal world the rest of the radio, whether it's the headphones in a crystal set or the amplifier in a modern radio, would have an infinite impedance and draw no power from the LC circuit. In the real world some power is drawn from the LC circuit but the power loss is equal to the power coming in from the aerial. The energy stored in the LC circuit reaches an equilibrium and a constant (peak) voltage. That voltage is still far greater than the EMF developed in the aerial. $\endgroup$ – John Rennie Dec 12 '15 at 6:33
  • $\begingroup$ I am so sorry but this answer confuses me even more. How does one electron goes from the antenna to the speaker if it goes into an "infinite loop" in the LC Circuit? $\endgroup$ – d0bz Dec 12 '15 at 6:40
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The incoming radio wave creates a small oscillating voltage in the antenna. That voltage can drive a current. But how much current will it drive? And how much power can it deliver to a speaker?

The power it can deliver must come from the incoming radio wave. There is no other source for the power. So the wave must be weakened when it passes by the antenna. How can this be accomplished?

When current flows in the receiving antenna, it becomes a transmitting antenna. It radiates power spherically in all directions. So in addition to the power you want to deliver to the speaker, you are also wasting power that the antenna is re-radiating to the universe. So where does the energy come from?

Here is a diagram, looking from above, of the incoming plane waves (straight lines) and the outgoing spherical waves of the receiving antenna:

enter image description here

In the shaded region, the difference between the two sets of waves is less than half a wavelength. So it is just possible, if the phase of the outgoing waves is correct, that the two sets of waves could be 180 degrees out of phase with each other...destructive interference. Yes, there is still power wasted by the outgoing waves in all other diretions, but it can be less than the power absorbed in the shadow region. Leaving a residual excess of power that can be delivered to the radio speaker.

The job of the tuning circuit is to adjust the relative phase of the outgoing waves so that this maximum of interference is acheived. A careful analysis shows that under this condition, the power absorbed from the wave is in linear proportion to the amount of current flowing in the antenna. The spherically wasted power is, of course, proportional to the square of the current. Any time you have a linear relation competing with a quadratic relation, there is an optimization whereby the difference is a maximum. This is the condition of matched impedance and it tells you the limit to how much power you can draw from the wave.

It is interesting (and obvious from the explanation given above) that the maximum theoretical power has nothing to do with the size of the receiving antenna. I explain this seeming paradox in more detail in my blogpost, "The Crystal Radio".

As I explain the optimization:

Now, whenever you have two quantities, and one is linear and the other is quadratic, the linear one dominates at first; but then the quadratic grows faster, so it catches and overtakes the linear term. What this means for the antenna is that as you draw current and deliver it to the load, at first you have power available because the power you remove from the shadow zone is greater than the power you waste re-radiating into the rest of space. But as you try to draw more power from the antenna, the wasted power grows much faster than the useful power. The maximum current in the antenna flows when the load is short circuited; in that case, the power removed from the shadow zone is exactly equal to the power re-radiated to the rest of space. The maximum absorbed power is obtained at exactly one-half of this short-circuit current.

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  • $\begingroup$ On your blog you ask if anyone has heard anything through a crystal set. Well yes, I have at school in the late 60s. Our science teacher put up quite a long antenna (20 or 30 metres of wire) and used some science kits that had been "liberated" from Germany at the end of WW2, and other bits of army surplus gear. It was faint but perfectly audible. It was probably a long wave signal we heard - likely a 198m wavelength, which has a powerful signal in the UK. $\endgroup$ – Dr Chuck Dec 11 '15 at 15:37
  • $\begingroup$ The one thing i just don't understand is how does energy comes OUT of the LC circuit ? Isnt a LC Circuit suppose to create an "infinite loop" ? $\endgroup$ – d0bz Dec 12 '15 at 7:14
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There are two ways of filtering a desired signal out of all the noise. You can decrease the strength(or the required parameter for example voltage) of all the other signals or increase the strength of the required signal to such an extent that other signals do not matter( that is their strength is negligible). The second one is what is used in the LC resonant circuit in the tuner. The tuner resonant frequency is adjusted such that it is matched to the frequency of the required signal. Then the strength of the required signal is increased which overwhelm s the other signals.

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