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Finding the resonant frequency of a LC circuit.

 

A previous post looked at a simple AM radio which I built using a ferrite coil antenna, TA7642 IC and a variable capacitor. After building this I thought it would be a good idea to see if I could determine the resonant frequency of its tuned circuit and therefore range.

 

Calculating Results

After some research I found that the resonant parallel LC could be determined with the formula:

f= 1/(2Pi Root LC)

                  

I used an LCR meter to take measurements from the variable capacitor [C] when both fully open and closed. I also measured the inductance [L] of both the long wave and medium wave coil.

 

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I used these measurements and the formula to calculate the minimum and maximum resonant frequency for the tuned circuit when using the long wave and medium wave coils. So in total this gave me four values.

 

Putting theory to the test

I didn't want to rely on only calculations and wanted to confirm the measured resonant frequency ranges. After some more research I found that this could be measured using a signal generator and oscilloscope. I connected the tuned circuit up for measurement as shown below.

 

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This was the first time I had used a signal generator or an oscilloscope, so to start out with I was given an older signal generator to use which only covered a frequency range of 1Hz – 260kHz.

 

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I soon realised that this signal generator would not cover the medium wave band (300 – 3000kHz) and so once I had got the hang of things I had to swap this out for a newer and more expensive signal generator, which covered a much larger range of 9kHz – 3.2GHz.

 

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I tested each coil with the variable capacitor vanes open and then fully meshed. I adjusted the settings on the oscilloscope to get the best view of the sine wave and altered the frequency on the signal generator accordingly until the wave peaked. Where the wave peaks this is the resonant frequency for that combination of capacitance and inductance.

               

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Comparing results

When I had collected all four sets of results I then compared these against the calculated results from earlier.

        

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I wasn't entirely sure why when the capacitor was open the results above differed so greatly from the calculated ones. To do further testing I continued taking measurements using different fixed value capacitors in place of the variable one.

                        

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I did this for both the long wave and medium wave coil using a range of fixed ceramic capacitors from 2.4pF to 22uF. I then compared the calculated results and actual measured results obtained using the signal generator and oscilloscope.

                                      

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*The highlighted area indicates values which should tune the circuit to frequencies within the long and medium wave bands.

                                       

From these results it appears that below a certain capacitance the effect on the resonant frequency lessens, until it reaches a point where the size of the capacitor can be reduced but this has negligible effect on the resonant frequency.

                                                       

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Long wave

                                           

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Medium wave

                                         

Evaluating the results

Why were some of the measured results far from those calculated? There could be many influencing factors, like:

- Variation in components due to tolerance.

- The way the circuit was assembled on breadboard loosely with wires which could create their own capacitance/inductance.

- Having the ferrite rod sat on the breadboard (which has a metal base) could also have influenced the results.

                                                 

Final thoughts

If I were to repeat this process again I would take into account all of the above factors and also simplify the layout of the components by using a smaller breadboard. Hopefully by limiting these influencing factors I would achieve results which were more accurate with minimum variance and closer to the calculated frequencies.

Trainee Electronics Engineer, currently studying towards my degree in Electronic Engineering at the University of Hudderfsield. Completed my HND in Electrical & Electronic Engineering from Bradford College 2017. Love to try new things and build interesting projects!
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