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Resonant circuit that amplifies voltage

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cj5

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The lab exercise: A resonant circuit which amplifies a small 20kHz input voltage at least 20 times.

I've been quite stumped on this one for a while now. I basically started out with the components I have on hand 1kΩ resistor; 33mH inductor; and then calculated the needed capacitance (1/4π²f²L) based on those and the resonant frequency needed, and I got 1.92nF.

I have these set up in series, and set the generator to 20kHz, with scopes across the supply, and one on the resistor. The supply scope is reads 4.2V and the resistor reads 2.48V.

Do I have this set up correctly? If so why am I getting a higher voltage on the supply? Should I put one of the scopes across either the inductor or capacitor? I'm really unsure how to go about this.

I appreciate your help in advance.
 
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OK

A quick calculation shows that your value of capacitance is about right.

Why do you think that you need a resistor in series with the L and C, particularly one as high as 1k ohm?

A few hints:

Try connecting the L and C is series across the output of the generator, connect the scope across the L and adjust the generator frequency and see what happens to the voltage across the L compared with what comes out of the generator.

Now try adding various values of resistance in series with the L and C and repeat the exercise.
Start with a low value of resistance and increase it, see what happens.

JimB
 
My mains electricity is 120VAC. I found a European fan that needs 230VAC. So I connected a series capacitor so it resonates with the inductance of the fan at my mains frequency and the fan runs perfectly on my 120VAC mains electricity.
 
Try putting the inductor and capacitor in parallel.
 
cj5,

The lab exercise: A resonant circuit which amplifies a small 20kHz input voltage at least 20 times.

For a series circuit, make the reactance of either L or C 20 times the resistance. Then the voltage across the reactance will then be 20 times what it will be across the resistance. Its phase across the reactance will be 90° from the resistance voltage, however. At resonance, the voltage across the resistor should be close to what the voltage supply is, because the reactances cancel out.

Since you do not have about the same voltage across the resistance compared with the supply voltage, something is wrong with your measurement or setup. Check to see if your are getting a large increase of current at resonance. Are you measuring the voltages using the A-B differential voltage method? You shouldn't have to do that if everything is isolated, but we cannot see your setup. Try disconnecting both leads of each scope and see if the other scope changes its readings. If it does, they are coupled together in some way and your readings are being affected.

Ratch
 
Hi,

One of the key points hinted at by Ratch is that the inductor should be relatively large. The larger the inductance, the better the circuit works with a given resistance which eats up energy. It's a little hard to do in practice because you have to find an inductor that has enough inductance to cause a voltage boost, yet that very same inductor has to have low series resistance. Of course at 20kHz that might be much easier than at say 60Hz line frequency.
For example a 500uH inductor would probably work pretty nice at boosting the voltage at 20kHz with the appropriate capacitor value (around 0.127uf).
You have to be a little careful though, to watch the sensitivity of the circuit with respect to the component values. If the chosen LC pair create too sharp of a response, just like a filter it will not work as well if one or both of the components changes value by some percentage. This means you probably should not design it to have too sharp of a response. 500uH and 0.127uf might be too sharp so you may have to come down on the inductor value.
Lowering the inductance by a factor of 0.5 and increasing the capacitor value by a factor of 2 keeps the same center frequency, but lowers the boost by about 0.5 too, but also reduces the sensitivity to component variation.
 
Certainly you can tweak the resonant frequency, if needed, by using small capacitors in parallel and adding or removing them as needed to get the desired frequency.
 
Certainly you can tweak the resonant frequency, if needed, by using small capacitors in parallel and adding or removing them as needed to get the desired frequency.

Hi there Carl,

Yes that's true, but we dont want to have to keep adjusting it as the temperature changes :)
 
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