The *RLC filter* that is the subject of this experiment has the property of tending to preferentially allow through frequencies at or near to its *Resonant Frequency*.

As with earlier experiments, you can use the buttons to adjust the values and discover what happens.

The arrangement used here is called a *Parallel Resonance* circuit as the inductor and capacitor are connected in parallel. This arrangement has an overall impedance which reaches its highest values around the resonant frequency. (A related circuit, called *Series Resonance* uses a capacitor and inductor connected in series to obtain an impedance which reaches a minimum value around the resonant frequency.) The buttons for this experiment include an extra row for 'fine control' of the input signal frequency. This is because the circuit can - depending on the component values - be quite *selective*. i.e. it's behaviour selects only passes a narrow range of frequencies.

First, experiment by plotting a graph of how the output/input voltage ratio *A*_{V} and output phase vary with the frequency.

Do this initially for the preset component values. (If you have already altered them to see what happens, just use the green 'reset' buttons to set them back to the starting values.) Then set the signal frequency as close as you can get it to *f*_{0} and see what happens when you change the resistor values, *R*_{1} and *R*_{in}. You should find that lowering either value will tend to increase *A*_{V} at resonance. Now try and discover the effects of altering these resistances on the 'width' of the range of frequencies passed by the circuit. You should find that reducing *R*_{1} tends to narrow the passed range, but reducing *R*_{in} widens the range.

Finally try changing the capacitor or inductor value and see what happens to the resonant frequency. You should find that *f*_{0} and hence the frequency where the largest fraction of the input is allowed through alters according to the equation given for the resonant frequency.

The results you obtain should be consistent with the parallel resonance arrangement having an impedance of

When combined with the input resistor this produces a potential divider whose voltage gain has the value

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University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.