International Journal of Microwave Science and Technology

Volume 2008, Article ID 287627, 7 pages

http://dx.doi.org/10.1155/2008/287627

## Design of PCB Impedance Matching Inductors and Antennas for Single-Chip Communication Systems

Electrical Engineering Department, San José State University, San José, CA 95192, USA

Received 15 April 2008; Revised 25 July 2008; Accepted 25 November 2008

Academic Editor: Chang-Ho Lee

Copyright © 2008 J. Chung and S. Hamedi-Hagh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents the design of an inductor and an antenna for a portable device with GPS and FM capabilities. The inductor is designed to operate at the lower frequency FM band as part of a matching network and the antenna is designed to operate at the higher frequency GPS L1 band. The FR4 PCB used has a thickness of 1.6?mm with a dielectric constant of 3.8 and has two metallization layers. The inductor is designed with 1.5?mm trace width, 3.5 turns, and has a dimension of 14.5?mm 14.5?mm. It has an inductance of 95?nH, a resistance of 2.9?, a self-resonance frequency of 500?MHz, and a maximum *Q* of 51 from 100?MHz to 200?MHz (FM band). The antenna has a dimension of 49?mm 36?mm and is designed to operate at 1.5754?GHz L1 band. It also has a return loss of -36?dB and a measured bandwidth of 250?MHz.

#### 1. Introduction

Advances in portable handheld wireless devices create a demand for combining many features onto a single PCB. Our aim is to design RF PCB components for a portable device with both FM and GPS capabilities. Each wireless path in such a device consists of an antenna, a matching network, as well as the receiver IC, as shown in Figure 1.

The front-end antennas and the impedance matching inductors, shown in Figure 1, are optimized for the GPS L1 band at 1575.42?MHz and the FM band at 100?MHz. The absence of transmitting signals in the handheld device and the large spectral and physical distances between the FM and GPS receiver front-ends keep their interactions and coupling at minimal.

To achieve the same impedance transformation ratio, the size
of the impedance matching inductor in the FM band is larger than that in the GPS
band due to the much lower operating frequency. The large size of the FM
inductor increases its parasitic capacitors and decreases its self-resonance
frequency. Maintaining high *Q*-factor below the already reduced self-resonant
frequency in FM inductor requires more design challenges when compared with the
GPS inductor and will be the focus of Section 2 in this paper.

The FM stations have limited area coverage compared with the GPS satellites which are located much farther. As a result, the received FM signals are much stronger due to the proximity of the transmitting stations and users. The low GPS signal power levels received at the user handhelds make design of the GPS antenna very challenging compared with the FM antenna and will be addressed in Section 3 of this paper.

Our paper is organized to correlate the design of the GPS antenna through characterization of the FR4 PCB obtained by the design of the FM impedance matching inductor. Section 2 presents the simulation and measurement results of the FM matching inductor that will lead to determination of the PCB traits. Section 3 discusses the design and measurement of the “L-ground h-type configuration with cornered patch” GPS antenna and, finally, Section 4 concludes the paper.

#### 2. FM Impedance Matching Inductor

##### 2.1. Performance of the PCB Inductors

Planar inductors can be created on either a silicon substrate
or an FR4 PCB. Silicon integrated inductors have higher cost and lower
*Q*-factor. Extra processing steps such as creating trenches in silicon [1] or
using suspension methods [2] are required to increase the *Q*-factor of the
silicon inductors which is typically lower than 25 [1, 2]. Inductors designed in
the standard PCB process with FR4 substrate inherently have the capability of having
higher inductance and Q-factor. Low temperature cofired ceramic, LTCC, is another
process that has higher cost and higher *Q*-factor compared with PCB. However,
LTCC inductors need a ferrite core to yield large inductance which, in turn,
reduces their self-resonance frequency [3, 4]. A summary of comparison among
silicon, FR4 PCB, and LTCC inductors is provided in Table 1.

The model of an inductor on FR4 PCB is shown in Figure 2 [5].
The PCB inductor has a resistance *R*, inductance *L*, and an interwinding
capacitance *C*. Compared to the well-known silicon inductor model [6], the PCB
inductor only represents a parasitic capacitance (). The is relatively large compared to the silicon parasitic, however, the inductance,
*L*, in PCB is much larger than that in silicon which improves the *Q*-factor
significantly.

The calculated for the inductor shown in Figure 3 is about 4?pF with an interwinding capacitance of 95?fF. For a similar *Q*-factor
of 50, LTCC inductors exhibit a smaller parasitic capacitance of 100?fF [3]
which improves
their performance; however, the advantages of realizing PCB inductors are their lower cost and fabrication
simplicity.

##### 2.2. Analysis and Design

It is possible to determine the overall inductance of a
planar structure by combining its distributed mutual and self-inductance
components [7]. The inductance of a rectangular inductor, in nanohenries, can
be approximately determined through where *D* is
the distance between the two outer edges of the inductor, in centimeters, and *N* is the number of turns within the
inductor. For a 100?nH inductance with 3 and , *D* is calculated to be 14.5?mm after grid
adjustment. The dimensions of the rectangular PCB inductor are shown in Figure 3.
The width of the conductive trace is selected to be 1.5?mm, the spacing between
the two metal trances is selected to be 254?m and the distance between the two
innercenter edges is selected to be 2.5?mm to attain a reasonable fit within
the distance between the two outer edges.

The designed
inductor is simulated using ADS and Sonnet CAD tools to obtain *S*-parameters
which are converted to *Z*-parameters to extract the *L*-*R*-*Q* parameters of the
inductor. The goal of the parameter extractions is to cross check the results
with calculations and measurement results that will be described in Section 2.3.
This will aid us in better characterizing the FR4 PCB substrate before starting
the antenna design.

The conductivity of the metal trace is determined to be 1.36
10^{6}?S/m, within the 100–200?MHz operating frequency, through fitting
simulation and measurement results that will be presented in Section 2.3. With
the consideration of skin depth, the resistance of the inductor metal trace is
2.4? at the operating frequency. For the designed inductance of 100?nH, the determined
*Q*-factor is 52.

##### 2.3. Calibration and Deembedding

The implemented PCB inductor test structures are measured after
calibrating the Agilent E8364B network analyzer using SOLT (short, open, load,
thru). Essentially the calibration process adjusts the 12 internal error terms
of the network analyzer by removing the effects of the cables [8]. The
calibration process increases the accuracy of the measured *S*-parameters of the
DUT, device under test [9].

The effects of the extra conductive traces, connecting the
main PCB inductor to SMA connectors, are removed with deembedding using separate
open and short structures [10]. The exclusion of the extra conductive traces and
connectors is achieved by measuring the *S*-parameters of the DUT, the open and the
short structures, followed by subtracting the corresponding admittance and impedance
parameters, as expressed in [11]: The implemented inductors and the deembedding test structures
are shown in Figure 4. The inductor used for matching the FM chip to antenna is
labeled “DUT” and is shown along with “open” and “short” test structures.

The impact of the deembedding can be clearly seen in Figure 5 where the original measured data for inductance, resistance, quality factor, and the self-resonant frequency is corrected using (2).

##### 2.4. Comparison of Simulation and Measurement Results

The frequency-dependent inductance at port 1, determined from
the measured deembedded *Z*-parameters and the inductance equation in [12], is
shown in Figure 6. This figure shows that the measured inductance peak occurs
slightly sooner than simulated peaks, however, the overall measured inductance
values are inline with the simulation profile. Both measurement and simulation
results show only slight variance from the 100?nH.

The frequency-dependent resistance of the PCB inductor at
port 1, calculated from deembedded *Z*-parameters using resistance conversion
equation in [12], is shown in Figure 7. This figure shows a spike of resistance
due to the open circuit characteristic at resonant frequency. Although the
measured and simulated results show a slight offset of the peak at the self-resonant
frequency, the results agree very closely at the 100–200?MHz operating
frequency of interest.

Finally, the inductor *Q*-factor is obtained from the measured deembedded
*Z*-parameters and using the conversion equation in [12]. The inductor quality
factor is shown in Figure 8. The results show that the designed inductor has a
maximum *Q*-factor of 50 at 100–200?MHz operating frequency.

The measured profiles of Figures 6, 7, and 8 follow the
simulation results, obtained from ADS and Sonnet CAD tools, fairly closely in
terms of the magnitudes and the operating frequency for the inductance, the
resistance, and the quality factor. These results are summarized in Table 2. From the table, Qmax
obtained from ADS is closer to the measured value while Sonnet's *L*-*R* parameters
are closer to measured values.

##### 2.5. Inductor Extracted PCB Characteristics

The inductor design process using calculations, simulations,
and measurements allow characterization of the FM impedance matching inductor as
well as the FR4 PCB. Accurate determination of the PCB substrate is very important
before design of the crucial GPS antenna. The dielectric constant, ,
of the FR4 is experimentally refined to be of 3.8. The PCB substrate thickness
of 1.6?mm and the conductor trace thickness of 36?m are both experimentally verified to be accurate. The
original simulations were based on the theoretical conductivity of pure copper to
be 5.8 10^{7}?S/m [13]; however, the inductor design iteration
determined that metal trace conductivity is 1.36 10^{6}?S/m. The
simulators are accordingly optimized for the GPS antenna design.

#### 3. GPS Antenna

The GPS for civilian purposes is called the Standard Positioning Service, SPS [14]. SPS transmits messages on to the L1 signal at the carrier frequency of 1575.42?MHz with a bandwidth of 2.046?MHz and with right-hand circular polarization [14]. We propose an “L-ground h-type configuration with cornered patch” GPS antenna for the L1 civilian frequency.

##### 3.1. Performance of the PCB Antenna

Patch antennas can be realized over FR4 PCB, silicon, and LTCC substrates. High performance silicon and LTCC antennas are more costly and need more complex fabrication steps compared with the PCB antenna. The typical range of the PCB dielectric allows acceptable radiation [15, 16] while offering lower cost, as listed in Table 3.

The antenna design and analysis on FR4 PCB are presented in the next section.

##### 3.2. Analysis and Design

The radiation patterns of an antenna can be studied based on a variety of models including the electric field characteristics. One particular method to determine the radiation pattern is based on the electric surface current model with rectangular patches [17]. In this antenna, the current characteristic, the ground planes, and the substrate contribute to the radiation patterns.

The starting point to design a reasonably compact antenna for the GPS applications can be the classic inverted-F structure [18, 19]. After analyzing antenna parameters such as polarization and radiation patterns, we propose the “L-ground h-type configuration with cornered patch” antenna, as shown in Figure 9.

The left vertical side of the “L” shaped ground plane
along the *Y* axis in Figure 9 acts as a unique reflector to create a strong
front beam in the direction. The proposed reflector influences the antenna
directivity at by reflecting the opposite fields at
direction, creating an intense forward power and focused gain. Our goal is also
to create a beam in the radiation direction of , above the *x-y* plane,
so that the additional tilt from the use of the FM-GPS portable device would
point to the sky.

In order to provide a patch antenna design with
circular polarization, the two opposite corners of a square patch under the
antenna are removed [19–21]. Removing the two diagonal opposing corners of the
square patch creates a phase shift in the excited wave mode creating less
capacitance compared to the standard square edges [21]. The patch creates
right-hand circular polarization [13], where the signal alignment is on the *Z*-*Y*
axes and the propagation is in the direction.

Similar to the inverted-F
antenna [20, 21], the h-shape portion of our designed antenna provides an
adjustment for the input impedance. The h-shape portion, just as the classic inverted-F,
is sensitive to the center frequency so that any process variation affecting
the trace dimensions will create a drift in the center of the operating
frequency. Therefore, although the GPS specifications require only a bandwidth of
2.046?MHz, our designed bandwidth is greatly increased as a safeguard to ensure
full antenna functionality after including 20% process variation. The first
antenna iteration is designed with a wide bandwidth of 300?MHz to ensure that
the ideal center frequency of 1.5754?GHz is covered even in the worst process
variation case. The bandwidth is determined relative to the frequency and the
geometry through the altered square patch portion of the antenna in Figure 9,
which can be determined through [20] where *h* is
the height of the patch in centimeters, *f* is the frequency in gigahertz, and BW is the bandwidth in megahertz. After reiterating the bandwidth calculation from
grid adjustment, the patch height is selected to be 24?mm and the final
calculated bandwidth is 297?MHz using 1.5754?GHz as the center frequency.

##### 3.3. Simulations and Measurement Results

The implemented “L-ground h-type configuration with cornered patch antenna” is shown in Figure 10.

The simulated and measured radiation patterns of the designed
antenna are shown in Figure 11(a) for the *xy*-plane and Figure 11(b) for the *yz*-plane.
As expected, the main beam in the *xy*-plane, shown in Figure 11(a), is at with high intensity between and
created by the reflectors in the *xy*-plane. Also, the simulated and measured
area of interest at is in close agreement. In relation to the functionality of the
FM/GPS handheld device, the measured angle of radiation for the antenna in the *yz*-plane
from Figure 11(b) shows a relatively
higher intensity around above the *xy*-plane to assist the user, holding
the handheld device, in pointing the maximum antenna beam toward the sky
direction.

The directivity and gain for the maximum radiation intensity,
obtained from both ADS and Sonnet CAD tools, is at and which correlates to the
radiation pattern because the difference from the *Z*-axis results in the tilt
angle of . At the mentioned angle where the maximum radiation intensity
occurs, the directivity is 5.0?dBi and the gain is 5.01?dBi.

Another important antenna parameter is the axial ratio, shown in Figure 12, where 0?dB indicates ideal circular polarization. Figure 12 shows that at 1.5754?GHz, the axial ratio is close to 1.2?dB in the direction of maximum radiation.

The maximum power is transferred from the antenna to the receiver IC when their impedance is matched. The simulated and measured parameters of the antenna are shown in Figure 13 and listed in Table 4. The measured results show that the antenna at 1.5754?GHz is ?dB, which is sufficient for GPS applications. Compared to the measurement, the ADS simulator presents accurate results in terms of center frequency and the Sonnet simulator presents accurate results in terms of bandwidth profile due to different modeling of metal traces.

#### 4. Conclusion

The design and measurements of antenna and inductor components of a GPS/FM receiver system were presented in this paper. The FM matching inductor was designed to correlate to the GPS antenna through the PCB characteristics, covering both frequencies. The measured results of the FM matching inductor allowed feedback to optimize the simulator in order to design the proposed GPS antenna.

The inductor was designed with 1.5?mm trace width, 3.5 turns,
and a dimension of 14.5?mm 14.5?mm. It yielded an inductance of 95?nH, a resistance of 2.9?, a
self-resonance frequency of 500?MHz, and a maximum *Q* of 51 from 100?MHz to 200?MHz
(FM band). The antenna has a dimension of 49?mm 36?mm and was designed to operate at 1.5754?GHz L1 band.
It yielded a return loss of ?dB and a measured bandwidth of 250?MHz.

#### Acknowledgments

This work was measured at RFICS laboratory at San José State University. The authors would also like to thank Sonnet Software Inc. and Agilent ADS for providing the use of their tools.

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