# Being Above Resonance

What does it mean being above resonance? Does it mean that our frequency is more than the resonance frequency? In an LC circuit, why is circuit more inductive when frequency is above resonance?

-
A series L-C is predominantly inductive above resonance, but a parallel L-C is predominantly capacitive above resonance. – Olin Lathrop Dec 30 '13 at 13:07
I commend you for using the correct term "resonance frequency" rather than "resonant frequency". – Alfred Centauri Dec 30 '13 at 13:45

What does it mean being above resonance?
Does it mean that our frequency is more than the resonance frequency?

Yes - frequency > Fresonance.

Inductive reactance increases with increasing frequency.
Z = 2.Pi.f.L

Capacitive reactance decreases with increasing frequency.
Z = 1/ (2.Pi.f.C)

At resonance the capacitive and inductive reactances are, by definition of resonance, equal but of opposite sign.

So, above resonance the net reactance will be inductive.

...

-
Tset ................................................................. – Russell McMahon Dec 30 '13 at 13:02
As Olin correctly points out (see his comment to question) this only applies to series LC resonance case. Its not clear in the OQ if its series or parallel or both so really both circuit configurations need to be addressed. Also (small point) you either need to put in the (-) sign i.e. Z= -2.Pi.f.L or use the modulus (see Vasily's answer) – JIm Dearden Dec 30 '13 at 16:28
@JImDearden - That was meant to be a quick 2am answer without getting into the finer points of imaginary arithmetic. My "of opposite sign" was a hat tip in that direction which seemed, at the time, enough for the purpose. Without more hand waving you could argue that Olin's and Vasily's answer contradict each other while mine is vague enough to be uncertain :-). I think I'll leave it until next year :-). – Russell McMahon Dec 30 '13 at 22:14

Being above resonance = frequency above resonance.

As for the "more inductive/more capacitive", recall that:

Capacitor's impedance: $Z_{cap}=\frac{1}{j \omega C} = -\frac{j}{\omega C}$ (modulus of this impedance decreases with frequency).

Inductor's impedance: $Z_{ind}=j \omega L$ (modulus of this impedance increases with frequency).

In series LC circuit the resonance occurs when $Z_{ind}+Z_{cap}=0$. Thus, at resonance, the modulus' of the impedances are equal. Above resonance frequency inductor's impedance dominates, therefore you can say that the circuit is more "inductive". Consequently, below resonant frequency the circuit is capacitive.

Intuitively, you can think of it in this way: at very high frequencies the capacitor acts as a short circuit, therefore the circuit is entirely inductive. At DC the capacitor is an open circuit, therefore the inductor have no effect and the circuit is entirely capacitive. The inductor opposes the frequency behavior of the capacitor, therefore contributing to this picture.

-

In an LC circuit, why is circuit more inductive when frequency is above resonance?

For an inductor and capacitor connected in series, the equivalent impedance is:

$$Z_{eq} = j(\omega L - \frac{1}{\omega C})$$

Note that when $\omega > \omega_0 = \dfrac{1}{\sqrt{LC}}$, the term in parentheses is positive and increasing with frequency. Indeed, as the frequency becomes much larger than the resonance frequency $\omega_0$, we have:

$$Z_{eq} \approx j\omega L,\ \omega >> \omega_0$$

Thus, we say that for frequencies above the resonance frequency, the equivalent impedance of the series LC circuit is inductive.

For an inductor and capacitor connected in parallel, the equivalent impedance is:

$$Z_{eq} = j\omega L||\dfrac{1}{j\omega C} = j\dfrac{\omega L}{1 - \omega^2LC}$$

Note that when $\omega > \omega_0 = \dfrac{1}{\sqrt{LC}}$, the denominator is negative and becomes more negative with frequency. Indeed, as the frequency becomes much larger than the resonance frequency $\omega_0$, we have:

$$Z_{eq} \approx \dfrac{1}{j\omega C},\ \omega >> \omega_0$$

Thus, we say that for frequencies above the resonance frequency, the equivalent impedance of the parallel LC circuit is capacitive.

-