### I. Introduction

### II. Antenna Design

*ɛ*

*= 4.4, tanδ = 0.02) with copper. Each of these antennas comprised a ground plane, a feed structure, and a radiating element. The size of the ground plane was 100 × 50 mm*

_{r}^{2}with a clearance of 20 × 50 mm

^{2}to set up an antenna. The feed structure was a parallel resonator that included a feed line, a shorting line, and a shunt capacitor line. The dimensions of the feed structure were 6 × 5.5 mm

^{2}, with a shunt capacitor.

### III. Operating Mechanism

*I*

_{1}comprises the loop of the shunt line and the source, and current

*I*

_{2}comprises the loop of the shorting line and the shunt line.

*I*

_{1}is excited by the source, and

*I*

_{2}is excited by

*I*

_{1}. The wideband performance can be achieved as the new loop current

*I*

_{2}resonance is added to the conventional PIFA. The magnitude of the loop current

*I*

_{2}can be controlled by the voltage across the shunt line, that is, by the overlap current in Fig. 2. The two loop circuits are represented by the following two-port impedance matrix [6]:

*Z*

*and*

_{f1}*Z*

*are the impedances of feeding loop 1 and feeding loop 2, respectively.*

_{f2}*Z*

*is the impedance of the shunt line. As seen in Eq. (1), the degree of coupling is determined by the magnitude of*

_{sh}*Z*

*. During the operation of the PIE feed structure, the resonant frequency of feeding loop 2 is set at the operating frequency of the antenna. However,*

_{sh}*Z*

*is included in feeding loop 2 and forms a series resonance because of the inductance and capacitance of the shunt line. Generally, the series resonant frequency is higher than the operating frequency because the shunt line is part of feeding loop 2. At*

_{sh}*Z*

*= 0, there is no coupling between the two feeding loops. As a result, power cannot be transferred from the feeding structure to the antenna element because*

_{sh}*I*

_{2}has barely been generated on feeding loop 2. Therefore, if this parasitic resonance of

*Z*

*= 0 is designed close to the operating frequency, the obtained impedance bandwidth and efficiency will be degraded.*

_{sh}*∂X*

_{sh}*/∂ω*represents the input reactance change in the resonant frequency of the shunt line. When the reactance changes rapidly at the resonance frequency, it has a high impedance characteristic and a narrow impedance bandwidth.

*L*

*is the distributed inductance on the shunt line, and*

_{sh}*C*

*is the lumped capacitor on the shunt line.*

_{sh}*ω*

*is the resonance frequency determined by the distributed inductance of the shunt line and the lumped capacitor. As can be seen from the equation, the impedance bandwidth characteristic of the parasitic resonance can be determined by controlling the ratio of the distributed inductance on the shunt line and the shunt capacitor. If the inductance is large and the capacitor is small at the parasitic resonance frequency, the variation of the stored energy becomes large and results in a narrow impedance bandwidth characteristic. Antenna 2 intentionally inserts a lumped inductor in the shunt capacitor line to control the impedance characteristic of the parasitic resonance. In antenna 1, the parasitic resonance demonstrates a wide impedance bandwidth characteristic by using a large capacitor of 6.5 pF without a lumped inductor. At the same frequency where the parasitic resonance of antenna 1 occurs, a 7 nH lumped capacitor of 2 pF was applied to the lumped inductor of antenna 2 to observe the change in the antenna characteristics when the parasitic resonance had only a change in the high impedance characteristic. A 7 nH lumped inductor and a 2 pF capacitor were used in antenna 2, so the parasitic resonance demonstrated a narrow impedance bandwidth characteristic.*

_{sh}