# Seriously confused by my Lab results!

1. Feb 8, 2007

### tim_lou

I am enrolled in an electronics components experimentation class and we have just finished an experiment couple days ago regarding notch filter.

Basically, we set up a function generator, and measure voltage output using oscilloscope.

We set up a circuit with an inductor-capacitor in parallel, then the whole thing in series with a resistor.

we measure the amplitude of the input and output (across resistor) voltage while varying the frequency.

according to the mathematics, the ratio between output and input squared should be:
$$G^2=\frac{R^2}{R^2+(\omega L-\frac{1}{\omega C})^{-2}}$$

so that when,
$$\omega=\frac{1}{\sqrt{LC}}$$

the ratio goes to zero. and around that region, there is a spike. basically, G is pretty much constant (around 1) and shoots vertically down around notch frequency (which is what we tried to find out).

the resistance is 1k ohm
inductance is 1 mili-Henry

the theoretical notch frequency is around 15.9kHz. However, the result turned out to be around 17.5kHz. the weird thing is, not only did my group get off-results, all the people I asked got the same! around 17.5 kHz. and I checked and checked... the theory should be correct!

furthermore, the slope of the spike is much gentler as well.... in theory, it should be really really sharp (at least 100 times "sharper" or "narrower")

what has gone wrong? is something wrong with the equation? I think it might've been internal resistance but how could it have such a tremendous effects?

Anyone got any idea?

2. Feb 9, 2007

### AlephZero

What were the tolerances of the components you used? The difference betwee 15.9kHz and 17.5KHz is only 10%. Many capacitors and inductors have component tolerances bigger than that.

The sharpness of the spike will depend on the internal resistance of the inductor. Either measure the resistance, or look at the data sheet to see what the Q value is (and read up about Q values, if you haven't met them before). The internal resistance will also change the frequency of the spike.

3. Feb 9, 2007

### tim_lou

I don't know much about the tolerances of our equipments... but the thing is, the error is systematic. I've asked 5 other groups and they all got results like 17.5 kHz!

as for the Q factor... So you think that internal resistance could have a significant impact? from the data, the Q factor is at lesat 100 times greater (the width of the spike is at least 100 times wider)... very annoying.

Just one question, between a capacitor and an inductor, which one is more likely to have internal resistance that affect the results? or is it both?

Last edited: Feb 9, 2007