# Quality factor of any circuit

1. Jul 7, 2012

Well If we talk about the quality factor of any circuit, we say that:

It is the ratio of natural frequency of any circuit and the band width.

Q = ω0 / Δω

Somewhere I read : It is the ratio of the P.D. across the capacitor or the inductor with the P.D. across the resistor in any circuit.

Q = P.D. across L or C / P.D. across R

My confusion is that what does Quality factor actually signifies ?

2. Jul 7, 2012

### sophiecentaur

It signifies how 'sharp' the resonance curve is. Bigger Q is sharper / narrower band. Also Q gives a measure of how fast the oscillations will die down because it represents (the inverse of) the fraction of energy lost each cycle.

3. Jul 8, 2012

### Staff: Mentor

The term probably originated in the early days of radio and tuned circuits. The higher the Quality of an experimenter's tuned circuit, the better the ability of his circuit to separate or discriminate between adjacent or interfering stations.

Mathematical analysis will turn up various equivalent statements of this measure, but you'll find they all relate back to the basic ratio of energy store to energy loss in a resonant system, whether electrical, mechanical or optical.

4. Jul 8, 2012

i.e. someone should choose a circuit having high quality factor because it will have greater efficiency of energy storage in its inductor or capacitor. ?

5. Jul 8, 2012

### Staff: Mentor

The fact that a tuned circuit has a high Q means that its impedance has a very sharp peak (or dip) at the circuit's resonant frequency. It has this response entirely due to having a high ratio of energy stored to energy loss. How to reduce energy loss? -- reduce the resistive losses.

6. Jul 10, 2012

Thank you very much friend.
The confusion has been cleared.

7. Aug 30, 2013

### anhnha

Hi,
I am reading about quality factor. I have searched a lot but all books and sites I read only talking about Q of a component (inductor, capacitor), or a resonant circuit (RLC in series and RLC in parallel). I don't see anywhere they mention about quality factor of an arbitrary circuit. Could you tell me why? Is that all other circuits can be transformed to said circuits above?

8. Aug 30, 2013

### f95toli

The concept of a quality factor only makes sense for some circuits, typically band-pass filters (where it defines how "sharp" the filter is) or resonators (where it tells you how quickly the resonance dies out). It is simply not useful for a generic circuit.

Also, note that an ideal inductor or capacitor does not have a Q value. However, real components are not ideal and it turns out that you can create useful circuit models of both inductors and capacitors, and the Q value tells you something about that circuit model (mainly how dissipative the element is).