Experiments with LC circuits part 10
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Input resistance of measuring amplifier
In this measurement, the input resistance is determined of the
measuring amplifier which I use for measurements on LC circuits.
I have 2 versions of this amplifier; version 1 is the first design, version 2 is
the improved version.
During the measurements, a tuned circuit is used consisting of capacitor C6 (the 340 pF section), and coil L20.
Tuning capacitor C6 340 + 450 pF.  Coil L20 244 μH. 
The circuit Q of the LC circuit is measured with amplifier version1, with
version 2, and with both amplifiers parallel.

Table 1 Measured Q of the LC circuit when using different measuring amplifiers. 
For every Q measurement, the corresponding parallel resistance across the
circuit is calculated with the formula:
RP=2.pi.f.L.Q
The coil value L is 244 μH

Table 2 Parallel resistance (kΩ) of the LC circuit. 
RP1 is the parallel resistance of the LC circuit, when
using amplifier version 1.
RP2 is the parallel resistance of the LC circuit, when
using amplifier version 2.
RP3 is the parallel resistance of the LC circuit, when
using amplifier version 1 and 2 parallel.
Now we can calculate the input resistance of the amplifier, with the following formulas:
R1 = 1 / (1 / RP3)(1 / RP2) = Input
resistance of amplifier version 1
R2 = 1 / (1 / RP3)(1 / RP1) = Input
resistance of amplifier version
2

Table 3 Input resistance (MΩ) of the amplifier. 
Small changes in measured Q, have much influence on calculated value for
input resistance.
Through this, the values of R1 and R2 are maybe not very accurate, but we have
an indication of the range of value.
Parallel resistance of tuning capacitor
With the next measurement we determine the parallel resistance of a tuning
capacitor.
This parallel resistance is caused by the losses in the capacitor.
In the ideal case the parallel resistance is infinite high.
First the circuit Q is measured, one time with section 1 of the tuning capacitor
(340 pF), one time with section 2 (450 pF), and one time with both sections
parallel.
The used coil is L20.
The used amplifier is version 2.

Table 4 Q of the LC circuit when using different tuning capacitors. 
For every Q measurement, the corresponding parallel resistance across the
circuit is calculated with the formula:
RP=2.pi.f.L.Q
The coil value L is 244 μH

Table 5
Parallel resistance (kΩ) of the LC circuit. 
RP1 is the parallel resistance of the LC circuit, when
using capacitor section 1.
RP2 is the parallel resistance of the LC circuit, when
using capacitor section 2.
RP3 is the parallel resistance of the LC circuit, when
using capacitor section 1 and 2 parallel.
Now we can calculate the parallel resistance of the capacitor, with the
following formulas:
R1 = 1 / (1 / RP3)(1 / RP2) = Input
resistance of capacitor section 1.
R2 = 1 / (1 / RP3)(1 / RP1) = Input
resistance of capacitor section
2.

Tabel 6 Parallel resistance (MΩ) of the tuning capacitor. 