Calculating Q-Factor and Resistance for Series LC Filters

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In summary, when calculating the correct component values for a simple series LC filter, both the resistance of the inductor and capacitor and the load resistance further down the line in the circuit must be considered. It is important to create an equivalent circuit using the DC resistance of each component, load, and source resistance, and then calculate the effective DC resistance of all series and parallel branches combined. This resistance is then used to calculate the Q factor, which is defined only around the resonant frequency. However, when dealing with real-world scenarios, it is important to use the resistance at the operating frequency rather than just the DC resistance.
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I am trying to calculate the correct component values to use in a simple series LC filter, however I am not sure which value of resistance is to be included in these equations. When talking about a series LC filter, is the resistance required for calculating q factor the resistance of the inductor and capacitor? Or is it what ever the load resistance is further down the line in the circuit?

Thanks!
 
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Mzzed said:
the resistance of the inductor and capacitor? Or is it what ever the load resistance is further down the line in the circuit?
Both.
Create an equivalent circuit using the DC resistance of each component, load, and source resistance.
Calculate the effective DC resistance of all series and parallel branches combined (Thevenin Equivalent). Use that resistance to calculate the Q.
Note that in this sense, Q is defined only around the resonant frequency.

Cheers,
Tom
 
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Normally, the capacitor has a loss resistance Rp in parallel to the capacitance.
Therefore, in order to combine this resistance Rp with the series loss resistance of the inductor Ri, the value of Rp (relatively large) must be transferred into an equivalent (small) series loss resistance Rs.
 
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Thankyou both, exact answers I needed, really appreciate it!
 
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Tom.G said:
Both.
Create an equivalent circuit using the DC resistance of each component, load, and source resistance.
Calculate the effective DC resistance of all series and parallel branches combined (Thevenin Equivalent). Use that resistance to calculate the Q.
Note that in this sense, Q is defined only around the resonant frequency.

Cheers,
Tom
Apart from simple textbook questions, I think you need to use the resistance at the operating frequency, because DC and AC resistance differ due to skin effect and dielectric losses.
 

1. What is Q-Factor and why is it important in science?

Q-Factor, also known as quality factor, is a measure of the efficiency of a resonant system. It is important in science because it helps to quantify the amount of energy that is lost or dissipated in a system. This can be useful in understanding and optimizing the performance of various systems, such as electronic circuits, mechanical structures, and chemical reactions.

2. How is Q-Factor calculated?

Q-Factor is calculated by dividing the resonant frequency of a system by its bandwidth. The resonant frequency is the frequency at which a system naturally oscillates, and the bandwidth is the range of frequencies over which the system's response is considered significant. This can be expressed mathematically as Q = ω0/Δω, where ω0 is the resonant frequency and Δω is the bandwidth.

3. What factors affect Q-Factor?

The main factors that affect Q-Factor are the material properties of the system, such as its density, stiffness, and damping, as well as the geometry and design of the system. In general, a higher Q-Factor is desirable as it indicates a more efficient system with lower energy losses. However, there can also be benefits to having a lower Q-Factor, such as in the case of shock absorbers where damping is necessary to dissipate energy.

4. What is the relationship between Q-Factor and resistance?

Resistance is a measure of how much a system resists the flow of energy. In the case of Q-Factor, resistance is one of the factors that can affect the efficiency of a system. A higher resistance can lead to a lower Q-Factor, as more energy is lost in the system. However, the relationship between Q-Factor and resistance is not always straightforward and can vary depending on the specific system and its design.

5. How is Q-Factor used in real-world applications?

Q-Factor is used in a wide range of real-world applications, including electronic circuits, mechanical structures, and acoustic systems. In electronic circuits, a high Q-Factor can lead to more stable and efficient oscillators, while in mechanical structures, a high Q-Factor can indicate a more resilient and responsive system. In acoustic systems, Q-Factor is used to characterize the performance of musical instruments and to design sound systems with optimal sound quality.

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