# Analysis of Parallel LC Tuned Circuits including the Q's of Both L and C

Author: R.J.Edwards G4FGQ © 22th July 2005This program analyzes the behaviour of a parallel L & C tuned circuit. Losses in both components are taken into account by means of resistance in series with L and C.

There are two definitions of resonant frequency: the frequency at which the impedance is a maximum and the frequency at which the impedance is purely resistive, i.e., the impedance angle is zero. The two frequencies are not the same.

The usual calculated resonant frequency, F = 159.1549/Sqrt(L*C) MHz, is an approximation which has no special functional significance. As Q increases above very low values, all three frequencies converge on each other. They also converge when capacitor Q and coil Q are equal, i.e., L and C losses are equal.

After entering L, C and Q values, to obtain exact impedance versus frequency response use the fast and slow test frequency-sweeping facility.

As a memory aid, when L microhenrys = C picofarads the reactance at their resonant frequency is always 1000 ohms.

Typical Q Values at MF and HF

Q of coils at IF frequencies such as 455 KHz are in the range 40
to 80. Small medium wave receiver coils are in the range 50 to 100. Larger
medium wave solenoids are roughly 100 to 200. At 2 MHz, a 4" by 1.5" diameter,
90 turn solenoid, L=100uH, has a Q of 220. Slightly larger 100 watt transmitting
solenoids at 2 MHz have Q 220 to 270.

A transmitter tank coil rated at a few hundred watts, at 3.5 MHz, has a Q of about 350. At HF, for coils of similar shape and occupied volume, Q increases approximately in proportion to the square root of frequency. Also, when physical size is doubled, Q doubles. It is reduced by 10 or 15 % when enclosed in a screened compartment or wire mesh cage.

Q can be crudely calculated. The loss resistance of a solenoid is the RF resistance of the wire taking into account skin effect and then multiplying by 4 to take into account proximity effect. Q = (Coil reactance/Loss resistance).

Q of capacitors is less predictable except that it can be a magnitude greater than that of the coil it is used with. Loss depends on the dielectric material. In the case of air spacing, Q depends on the quality of insulating materials in contact with and in the vicinity of the plates.

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