Capacitively coupled RLC circuits

[SadStudent]

Homework Statement

Given a set of two capacitively coupled RLC circuits where each has a capacitor $C$ and they share a coupling capacitor $C^{'}$.
I'm trying to find nice organized material that will explain the various relevant
coefficients\concepts like $QF$, bandwidth etc. in relation to the above mentioned setup.
Or how to find the function of the maximal voltage as the function of frequency given a certain setup.

Homework Equations

The Attempt at a Solution

I do know how to solve the differential equations involved and get the voltage and current as the function of time but I can't find good sources that could explain all the aspects of coupling two circuits using a capacitor.

 

[berkeman]

Homework Statement

Given a set of two capacitively coupled RLC circuits where each has a capacitor $C$ and they share a coupling capacitor $C^{'}$.
I'm trying to find nice organized material that will explain the various relevant
coefficients\concepts like $QF$, bandwidth etc. in relation to the above mentioned setup.
Or how to find the function of the maximal voltage as the function of frequency given a certain setup.

Homework Equations

The Attempt at a Solution

I do know how to solve the differential equations involved and get the voltage and current as the function of time but I can't find good sources that could explain all the aspects of coupling two circuits using a capacitor.

How is the combination circuit driven?

Does the circuit look like any of these coupled RLC circuits? https://www.google.com/search?hl=en...urce=og&sa=N&tab=wi&ei=pnUGU-q6Ec_poATJqYHgAQ

.

 

[SadStudent]

It looks like this:

And the we've measured the voltage on the $R_{1}$ for various frequencies and $C^{'}$ coupling capacitors.

 

[SammyS]

It looks like this:

And the we've measured the voltage on the $R_{1}$ for various frequencies and $C^{'}$ coupling capacitors.

I couldn't see that image.

Use the "Manage Attachments" feature of PF .

Here is the image below.

 

[HalfLostAndSearching]

Can someone please provide me with some helpful resources or explain the concepts further?

As a scientist, it is important to have a thorough understanding of the concepts and equations involved in any experiment or setup. Capacitively coupled RLC circuits are commonly used in electronic circuits and understanding their behavior is crucial for designing and analyzing such circuits.

To begin with, let's first define the various coefficients and concepts involved in this setup. The quality factor (QF) is a measure of the damping in an RLC circuit and is defined as the ratio of the energy stored in the circuit to the energy dissipated per cycle. It is given by the formula Q = ω0L/R, where ω0 is the resonant frequency, L is the inductance, and R is the resistance.

The bandwidth of an RLC circuit is the range of frequencies over which the circuit can operate efficiently. It is related to the quality factor by the formula BW = ω0/Q. A higher QF results in a narrower bandwidth, meaning the circuit can operate at a specific frequency with less interference from neighboring frequencies.

Now, let's consider the function of the maximal voltage as a function of frequency in this setup. The voltage across the capacitor C is given by the formula Vc = Vmcos(ωt + φ), where Vm is the maximum voltage, ω is the angular frequency, t is time, and φ is the phase angle. The resonant frequency of the circuit is given by ω0 = 1/√(LC). At this frequency, the capacitor voltage is maximum and in phase with the source voltage.

The coupling capacitor C' plays a crucial role in this setup. It allows for the transfer of energy between the two circuits, resulting in a coupled resonance. The maximum voltage across the coupling capacitor occurs at the resonant frequency and is given by Vc' = Vm'cos(ωt + φ'), where Vm' is the maximum voltage across the coupling capacitor and φ' is the phase angle.

To find the function of the maximal voltage as a function of frequency, we need to consider the voltage across the two capacitors in series. This can be calculated using the formula Vtotal = Vc + Vc'. At the resonant frequency, the phase angle for both capacitors is the same, resulting in a maximum voltage of Vtotal = Vm + Vm'. As the frequency deviates from the resonant frequency, the