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# Wideband Behaviour of Parallel-Tuned LCR Circuits (also known as RLC Circuits)

Author: R.J.Edwards G4FGQ © 7th July 2000

Parallel-Tuned LCR Circuits C is in parallel with L and R in series. Z is the impedance measured across C. This deceptively simple circuit is found in narrow-band tuned amplifiers, wideband video amplifiers, impedance-matching L-networks and in filters, etc.

When R is less than 1.554*Sqrt(L/C) there is a hump, Zmax, in the Z vs frequency response. As R decreases, Zmax increases and moves to higher frequencies.

When R > Sqrt(L/C) the angle of Z is always -ve and unity power, commonly defined as the resonant condition, does not occur at any frequency.

For smaller values of R the angle of Z is +ve at low frequencies and passes through zero (unity power factor) on the LF side of the frequency of Zmax which is itself lower than the LC series resonant frequency. At much smaller values of R, giving high Q, all three frequencies converge on a common value.

L/(C*R) is the simple formula often used to estimate Zmax when Q > 3. Decibels refer to relative amplifier voltage gain when Z = load impedance. The greatest +ve value of the angle of Z and its frequency are also computed.

Program Operating Notes
Enter all data and menu selections against the prompt on the bottom line 25.

Follow any instructions displayed on bottom line.

After one set of input data L,C,R & F has been entered and results displayed, any input data item may be changed on a "what if?" basis.

Input parameter values can be swept over wide ranges, in small increments from the keyboard, by pressing 'up-down' pairs of adjacent keys as indicated on line 24 of the data screen. Left key is down, right key is up.

It is instructive to observe how Z and its angle vary with frequency in the vicinity of very broad resonances. Also when the value of R is swept through its two critical values.

Indicated measurement units are micro-henrys, pico-farads, ohms, megahertz. If milli-henrys and nano-farads are entered, frequencies are in kilohertz.