Experiments with LC circuits

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.

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.

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