Page 67 - Circuit Analysis II with MATLAB Applications

Chapter 2

Resonance

T his chapter defines series and parallel resonance. The quality factor is then defined in terms
Q
of the series and parallel resonant frequencies. The half-power frequencies and bandwidth are
also defined in terms of the resonant frequency.

2.1 Series Resonance

Consider phasor series RLC circuit of Figure 2.1.

`
V S R jZL

I
1jZC
e

Figure 2.1. Series RLC phasor circuit

Z
The impedance is
1
Phasor Voltage
§
1 ·
Impedance = Z = --------------------------------------- = V S R + jZL + ---------- = R + j ZL – -------- (2.1)
------ =
Phasor Current I jZC © ZC ¹
or
2 2 – 1
Z = R + ZL – 1 ZC ‘ tan ZL1 ZC e R (2.2)
–

e
e
Therefore, the magnitude and phase angle of the impedance are:
2
Z = R + ZL – 1 ZC 2 (2.3)
e
and
T = tan – 1 ZL – 1 ZC e R (2.4)

e
Z
The components of Z are shown on the plot of Figure 2.2.

Circuit Analysis II with MATLAB Applications 2-1
Orchard Publications