Experiments with LC circuits   part 10

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.

 Measurement number. Used amplifier 600 kHz 900 kHz 1200 kHz 1500 kHz 88 Version 1 1160 1097 923 755 89 Version 2 1199 1140 992 857 90 Version 1 and 2 parallel 1132 1058 889 728

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

 Used amplifier 600 kHz 900 kHz 1200 kHz 1500 kHz RP1 Version 1 1067 1514 1698 1736 RP2 Version 2 1103 1573 1825 1971 RP3 Version 1 and 2 parallel 1041 1460 1636 1674
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

 Used amplifier 600 kHz 900 kHz 1200 kHz 1500 kHz R1 Version 1 18.6 20.3 15.8 11.1 R2 Version 2 43.1 41.1 44.4 46.8
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.

 Measurement number Tuning capacitor section 600 kHz 900 kHz 1200 kHz 1500 kHz 91 Section 1   (340 pF) 1199 1140 992 857 92 Section 2   (450 pF) 1200 1154 976 840 93 Section 1 and 2 parallel 1176 1085 923 802
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

 Tuning capacitor section 600 kHz 900 kHz 1200 kHz 1500 kHz RP1 Section 1   (340 pF) 1103 1573 1825 1971 RP2 Section 2   (450 pF) 1104 1592 1795 1932 RP3 Section 1 and 2 parallel 1082 1497 1698 1844
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.

 Used tuning capacitor 600 kHz 900 kHz 1200 kHz 1500 kHz R1 Section 1   (340pF) 56 31 24 29 R2 Section 2   (450pF) 54 25 31 41
Tabel 6

Parallel resistance (MΩ) of the tuning capacitor.