Electronics in a phy ...

As part of this exercise, impedance measurements were performed on various devices:

- MQL-5 Q-meter by INCO (resonance method)

- E-302 type C bridge from Eureka (bridge method)

- LC type HM8018 from Hameg (technical method)

Below are tips on how to convert the values ​​obtained for various measuring instruments:

1) Q meter:

On the Q-meter, we bring to resonance a system that looks like this:

When examining an unknown capacitor, the formula for the resonant frequency is as follows

\( f = \frac{1}{2\pi \sqrt(LC_z)} \)          (1)

where:

L - is the inductance of the reference coil used for the measurements,

\(C_z\) - is the equivalent capacitance of the entire circuit.

In this circuit, we have an unknown capacitor (\(C_x\)) and a built-in adjustable capacitor ((\C_{reg}\)) connected in parallel. The capacitance of such a system is: \(C_x + C_{reg} \). This arrangement of parallel connected capacitors is connected in series with the capacitance \(C_1=9500 pF \). Therefore, the equivalent capacitance of the entire circuit will be:

\(\frac{1}{C_z} = \frac{1}{C_1}+\frac{1}{C_x + C_{reg}} \)           (2)

In order to determine the capacitance of an unknown capacitor (\(C_x\)), formula no. (2) should be transformed so as to obtain the formula for \(C_z\) and then substitute the obtained formula for  \(C_z\) into formula (1). From this (formula  (1)) one can then obtain the formula for (\(C_x\)) .

In order to determine the inductance of an unknown coil, in the formula no. (2) you should put  (\(C_x=0\)). The obtained formula for \(C_z\) is inserted into formula no. (1) and transformed to obtain the formula for L.

2) E-302 type C bridge:

In the Q-meter, we measured the quality of the system (Q). In contrast, a C-type bridge returns \(tg \delta \). To determine the goodness, use the formula:

\( tg \delta = \frac{1}{Q} \)          (3)

3) LC type HM8018

In turn, LC type HM8018 returns:

- G (parallel conductance) when measuring an unknown capacitor

- \( R_s \) (series resistance ) when measuring an unknown coil.

To convert these values to Q, use the following formulas:

 - for unknown capacitor:

\( tg \delta = \frac{G}{\omega \cdot C_x} \)

where: \( tg \delta = \frac{1}{Q} \)

- for unknown coil:

\( tg \delta = \frac{R_s}{\omega L} \)