*3.2.4 Design of controller for reflection type phase shifter*

than 13.2 pF at 2.45GHz. That capacitance value is hard to be met by gaps or microstrip interdigital capacitors. For capacitor components, in practice, at microwave frequency, a capacitor component is equivalent to a series of inductor, resistor, and capacitor, so the impedance of DC Block changes in frequency. Above a certain frequency threshold, that DC Block will act as an inductor. Thus, DC Blocks are usually capacitors with its self-resonant frequency near operating frequency, 2.45 GHz. Finally, the DC Block is VJ0603D8R2CXP capacitor of Vishay/Vitramon

*Advanced Radio Frequency Antennas for Modern Communication and Medical Systems*

In contrast, the DC feed is usually an inductive element, which blocks high frequency waves and passes DC current. The impedance of DC Feed element must be very high compared with the reference impedance (50 Ω) at operating frequency, 2.45 GHz. Similar to DC Block, the DC Feed may be an inductance element with a self-resonant frequency near 2.45 GHz operating frequency. However, in practice, due to cost constraint and the availability of inductors, these inductors are replaced by another option, taking advantage of some special case in length of transmission lines. To minimize the whole structure, the quarter-wavelength transmission line used is shorted at the end, of which the equivalent impedance is positive infinity at operating frequency. In other words, a quarter-wavelength transmission line with shorted at the end can be treated as an open circuit at the beginning of that transmission line. Consequently, the DC bias can be replaced at the end of quarter-wavelength transmission line, so that high frequency waves do not reach the DC circuit while the DC currents can flow directly to varactors.

There exist two ways to short a circuit. The first way is to use via holes to create physical connection from electric lines to the ground; however, this method also shorts the DC bias. The other way is to employ open quarter-wavelength straight stubs or radial stubs. These two kinds of stubs do not physically connect to the ground, so they do not short the DC bias. In [28], Gardner and Wickert mentioned that radial stubs, possibly realized as shunt stubs with low characteristic impedance, may avoid the problems of transverse resonance and poorly defined point of attachment associated with straight stubs. In our DC Feed, the radial stubs are the suitable choice. Some research groups have studied about the equations for the formulation of microstrip radial stubs [27, 29–31]. Based on these studies combined

with optimization tool in Advanced Design System software, the optimized

**Figure 16.**

**114**

*Impedance of DC block VJ0603D8R2CXP.*

with impedance about 3.8 Ω at 2.45 GHz, as shown in **Figure 16**.

In phase array antennas, in order to be able to steer the antenna's main lobe in different directions, the phase-shift system must be placed in front of the antenna elements to generate the phase difference of the wave to each antenna so as to create the angle of beam. The phase shift entirely depends on the capacitance value of the varactors whereas every varactor always has its own C – V characteristic curve, representing the relationship between the input applied voltage and output capacitance. In other words, the phase shift is controlled by the voltage applied to the anode and cathode pins of varactors. For SMV1247 varactor, the voltage range of 0–5 V is applied. Thus, the controller is required to generate adjustable voltage in the range of 0–5 V, providing eight different voltages for eight RTPS and each voltage channel must meet the total power of four varactors in a RTPS.

To generate a DC voltage controlled by the microcontroller, popular methods are to modulate pulse width or control open angle of power semiconductor components such as Triac or Thysistor to convert AC to DC. These two methods are commonly used in power circuits, so we usually only care about the average power and voltage in a cycle, but in essence, the voltage generated is not flat over time but it is ripple. Obviously, these two methods will not be able to generate the control voltage for the varactors, which constantly changes the capacitance and results in undesired phase shifts. From the datasheet of SMV1247 varactor, the reverse current is very small, just a few nA to μA, so it is possible to use Digital to Analog Converter (DAC) units. Output current of these elements is about 20 mA. It is enough to satisfy the reverse currents of four varactors in a RTPS. In addition, the DACs have a variety of resolution options ranging from 8 bits to 24 bits. This facilitates flexible adjustment of the RTPS resolution. Therefore, the controller will be designed based on the eight DAC elements to generate bias voltages for eight RTPS. The controller model is described in **Figure 17**. The main components are DACs, and in order to increase the accuracy of the output voltage, the DACs are powered by a different source with a higher accuracy than the source for the microcontroller or can be adjusted for backup case when higher voltage range of varactors is demanded.

#### *3.2.5 Design of antenna element*

Because the positioning system is executed indoor, the WiFi or Wireless LAN should be the most suitable protocol to use in order to radiate power to indoor mobile devices; therefore the 2.4 GHz to 2.484 bands is chosen as the operating frequency. On the other hand, in order to communicate with the mobile devices for localizing the position of the object, the angel of main beam of phased array antenna should change from 45 to 45° to scan the desired object, hence antenna element must have half power beam width [15] greater than 90°. These requirements demonstrate that the radio signal strength comparison completely depends on the array factor. Omnidirectional antennas can satisfy both requirements; however, some omnidirectional antennas such as dipoles, … [15] still have some undesired effects, that is, radiating to the back side of the antenna array, which results in some high side back lobes due to the reflection. The microstrip patch antenna can both meet the above condition and have small back lobes. In our array, the microstrip patch antenna was designed to operate at Wi-Fi band frequency, 2.4 to 2.484 GHz with an input impedance of 50 Ω using a low cost FR4 substrate with dielectric constant ε = 4.3, loss tangent tanδ = 0.02 and thickness h = 62 mil = 1.58 mm. The antenna

**Figure 17.** *Block diagram of varactor diode controller.*

width *W* and length *L* are computed with the following Equation [15, 32, 33] where f is center frequency (2.45 GHz):

$$W = \frac{3 \times 10^{11}}{2 \times f} \sqrt{\frac{2}{\varepsilon + 1}} = 36.60 \, mm \tag{30}$$

**4.1 Array component design and evaluation**

In the two-wayWPD, theoretically, the total input power is equally divided into two output ports. Assume that the input port is port 1 and the output ports are port 2 and 3,

However, microstrip circuits on any substrate are affected by the loss tangent coefficient of the substrate and the microstrip discontinuities. The loss tangent represents the loss in the dielectric. The higher the loss tangent is, the more the loss is. For FR4 substrate, the loss tangent is about 0.025, so the forward gain of WPD on FR4 is less than theoretical one. Furthermore, the microstrip discontinuity phenomenon, as well as [22, 34, 35], appears in practice and generates parasitic

the transmission coefficient S21 = S31 = 3dB as shown in **Figure 18b**.

*Beamforming Phased Array Antenna toward Indoor Positioning Applications*

*4.1.1 Wilkinson power divider (WPD)*

*DOI: http://dx.doi.org/10.5772/intechopen.93133*

**Figure 18.**

**117**

*The simulated 2-way WPD: (a) schematic circuit; (b) forward gains S21, S31.*

$$L = L\_{\rm eff} - 2 \times \Delta L = 28.07 \, mm \tag{31}$$

$$\text{where}\begin{cases} L\_{\text{eff}} = \frac{3 \times 10^{11}}{2 \times f \times \sqrt{\varepsilon\_{\text{eff}}}} = 29.53 \, mm \\\\ \Delta L = 0.412 \times h \times \frac{\varepsilon\_{\text{eff}} + 0.3}{\varepsilon\_{\text{eff}} - 0.258} \times \frac{W}{\frac{W}{h} + 0.264} = 0.73 \, mm \\\\ \varepsilon\_{\text{eff}} = \frac{\varepsilon + 1}{2} + \frac{\varepsilon - 1}{2} \left[ 1 + 12 \frac{h}{W} \right]^{-\frac{1}{2}} = 3.9953 \end{cases}$$

with *Leff* is the effective length, *ΔL* is the length adjustment, *εeff* is the effective permittivity, and *h* is the substrate thickness.

## **4. Evaluation of phased array antenna performance**

To validate the design of the antenna, every component in the phased array structure is evaluated and measured. All the simulations are performed on Keysight Technologies's Advanced Design System (ADS) software and CST Microwave Studio. All the components are fabricated on the FR4 substrate with dielectric constant ε of 4.3, loss tangent tanδ of 0.02, substrate thickness h of 62 mil (1.58 mm), and the conductive copper thickness t of 1.4 mil (1 oz).
