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RLC Series Circuit Negative frequency issue?

Hi all I have been working through a question ive been given, i have to find the Resonant frequency, current at resonance, Q factor, Bandwidth and upper and lower -3db frequencies.To my knowledge ive done this all correctly however when i work out the lower frequency I get a negative number, however is it possible to have a negative frequency and what does it mean to have one?I will show my working to show my understanding of the question. 10v AC supply, 300 Ohm resistor, 80 milli Henry inductor and 20 micro farad capacitor.

Resonant Frequency

Fr =

\frac{1}{2\pi \sqrt{LC}}

\frac{1}{2\pi \sqrt{(80\times 10^{-3})(20\times10^{-6})}}

Fr = 125.82 Hz

Current at Resonance

Z=\sqrt{R^{2}+(XL-XC)^{2}}

This cancels to Z=R

Z=300Ohms

V=IZ I=V/Z

I=33.33mA

Quality Factor

\frac{1}{R}\sqrt{\frac{L}{C}}

\frac{1}{300}\sqrt{\frac{(80\times 10^{-3})}{(20\times 10^{-6})}}

=0.21

BandWidth

\Delta f=\frac{Fr}{Q}

\Delta f=\frac{125.82}{0.21}

=599.14 Hz

Upper and Lower Limits

\frac{599.14}{2}=299.57

Lower Limit = 125.82 - 299.57 = -173.75Hz
Upper Limit = 125.82 + 299.57 = 425.39Hz

Its this lower limit I dont understand? is this possible and if so what does it mean to have a negative frequency in a RLC series Circuit?

Many thanks in advance
RamJam

Reply 1

Ramjam

Someone must know the meaning of the negative frequency?

Reply 2

uberteknik

Original post by Ramjam

Someone must know the meaning of the negative frequency?

Hello RamJam.

There is no such thing as negative frequency in the real world time domain. Negative frequency is a mathematical concept only, which cannot exist in reality.

Your working is correct, however, this is a classic case of a measurement which is used as an indicator of performance but which does not give the full picture and indeed can lead to misinterpretation as you have discovered.

Quality factor and bandwidth only gives a snapshot of two points on the whole frequency response. i.e. it says nothing about the shape of the curve running through the points. Indeed, the values of the series components given, produces a response which is not symmetrically disposed about the resonant frequency

The frequency response will in fact look something like:

i.e. below the resonant frequency, the response amplitude falls rapidly to zero at d.c. The rate at which the slope rises to resonance is governed by the q-factor and resonant frequency where the lower half power point is skewed closer to resonance w.r.t. the upper half power point.

Above resonance, the response rolls off as a decaying exponential function. In other words, be careful about how you interpret bandwidth and quality factor in the absence of other information.