Uniform Linear Antenna Array Beamsteering Based on Phase-Locked Loops

Abstract

Phased arrays are extensively used in many modern beam-scanning applications such as radar and satellite communications. Electronic beam scanning makes phased arrays an important aspect of modern antenna array systems. This Tutorial aims to promote the basic understanding of the principle and operation of a phased array to general undergraduate students. This paper starts with a discussion on the theory of operation and some basic definitions of antenna parameters followed by derivations of two-element and N-element array patterns and, finally, a five-element array design. The essential hardware based on Phase-Locked Loops (PLLs) as phase controllable RF sources required to build an array and the basic tools required for software and measurement set-up to demonstrate the beam-scanning phased array operation are presented. This enables students to quickly understand and set-up an experiment to verify the phased array operation with commercial off-the-shelf components. In addition, the hardware and software necessary for autonomous control are discussed. By combining basic concepts of phase arrays with a series of simple coding and intuitive laboratory experiments, students can easily understand the Uniform Linear Array (ULA) scanning operation.

1. Introduction

Antenna selection is critical to any wireless system design [1]. Some of the design criteria for an antenna are its frequency, bandwidth, physical size, and directivity [2]. The application of the wireless system defines these criteria, for applications with long range or direction-finding (e.g., satellite communications, power transfer, radar, localization), a highly directive antenna allows for increased range and angular accuracy [3]. Antenna arrays allow a directional antenna to be created from individual elements which can be omni-directional [4]. Antenna arrays are composed of several antenna elements (often identical) arranged in a particular geometric configuration (linear or planar) [5].

This paper deals with Uniform Linear Arrays. Phased arrays can be steered electronically by use of controllable phase shifters. These phase shifters can be analogue or digital. This means that a linear array can electronically scan its beam quicker than antennas which have to be mechanically rotated. Removing the need for mechanical rotation can simplify the overall system design as well as reducing size and weight, therefore opening up more applications. In this paper, we explore the theory behind ULA antenna design, particularly in terms of how its physical size and directivity can be designed. We show how to create an ULA demonstrator that uses PLLs as independent sources for each element, we also explain how to measure the antenna radiation pattern and compare it to the theoretical results. A design example is used to illustrate the theory and practical techniques are discussed. This paper is organized as follows. In Section 2, we discuss the theory and the design aspects of ULAs using numerical examples and also give the specification of our example problem and use these criteria to discuss the basic definitions of antenna parameters with respect to arrays. In Section 3, we discuss electronic beam-scanning techniques as applied to ULAs. In Section 4, we implement these techniques on a fabricated antenna array and present the hardware required for demonstration on a 5-element linear array. In Section 5, we present basic requirements of the set-up for measurement and calibration along with the measurement results. Finally, we conclude in Section 6.

2. Antenna Basics

The example problem in this paper is to design an ULA antenna array at 2.4 GHz which has a gain of 10 dB and can be steered through $\pm {60}^{\circ }$ in azimuth. The full design criteria are given in

Table 1. Design parameters of ULA at 2.4 GHz.

Parameter	Desired Range	Value Single Element
Frequency (GHz)	2.4	2.4
Return loss (dB)	10	10
Gain (dB)	10	2.1
3 dB beamwidth (°)	21	Omni-directional
10 dB bandwidth (MHz)	100	100

.

The basic building block of an array is a single antenna, which is referred to as an element in array terminology. For simplicity, in this paper, we use a half-wave dipole positioned a quarter-wave over a ground plane (Ref. [1] gives details on dipole design and fabrication), other element types such as patches or slots are often used in printed arrays. The performance of this dipole will be stated by its frequency, return loss, and gain/radiation pattern. The frequency of the antenna is the frequency at which it has the highest return loss. (The return loss of the antenna is the dB ratio of the power applied to the antenna and the power reflected back from it.) The gain of an antenna is “the ratio of the intensity, in a given direction, to the radiation intensity that would be obtained if the power accepted by the antenna was radiated isotropically” [2]. The 3 dB beamwidth is the angle over which the power does not drop below 3 dB of peak power. Typically, antenna directivity is shown in the radiation pattern, often directivity is quoted as a single number in which case it is the peak directivity, which is defined as the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions [2]. The 10 dB bandwidth is the frequency span over which the return loss is greater than 10 dB.

2.1. Array Theory

There are six design parameters in an antenna array. They are the layout/geometrical configuration, and number of elements, spacing of elements, excitation amplitude, excitation phase, and element type/radiation pattern. In this paper, we are only interested in the number of elements and the relative phase of each element. The other parameters remain fixed as a linear array with each element spaced a distance of $(\lambda /2)$ apart and every element being a balun-fed dipole [1], all with the same excitation amplitude. To understand the theory of arrays, we first start with the special case of a two-element array with equal amplitude excitation [2]. The electric field at a point in the far-field from the two elements is the sum of the electric fields of each individual element. If we assume that there is negligible coupling between the elements, then we can consider each element independently (Figure 1). For two identical dipole elements separated by distance d as shown in Figure 1, their resultant electric fields at P is derived as shown from Equations (1)–(7).

$$\begin{array}{c}\hfill E_1=\frac{A_1({\theta }_1,{\varphi }_1)}{r_1}{e}^{-j(k{r}_1-\frac{\beta }{2})}{\rho }_1^{.}\end{array}$$

(1)

$$\begin{array}{c}\hfill E_2=\frac{A_2({\theta }_2,{\varphi }_2)}{r_2}{e}^{-j(k{r}_2-\frac{\beta }{2})}{\rho }_2^{.}\end{array}$$

(2)

Here, $A_1,A_2$ are the normalised field magnitudes at distances $r_1,r_2$ and polarization vectors ${\rho }_1^{.},{\rho }_2^{.}$, respectively. k is the phase constant given by $2\pi /\lambda$, $\beta$ is the phase difference between the two elements. ${\theta }_1,{\varphi }_1$, and ${\theta }_2,{\varphi }_2$ are the positions in azimuth and elevation, respectively, with reference to the array centre. Both elements are identical with the same excitation amplitude; therefore, $A_1=A_2$, they are both physically aligned, so the same polarization, therefore ${\rho }_1^{.}={\rho }_2^{.}$. If we make the assumption that point P from Figure 1 is sufficiently far away, then we can set ${\theta }_1={\theta }_1=\theta$ and ${\varphi }_1={\varphi }_2=\varphi$. This means that both $E_1$ and $E_2$ can be written as below in Equation (3):

$$\begin{array}{c}\hfill E_1=E_2=\frac{A_1({\theta }_1,{\varphi }_1)}{r_1}{e}^{-j(k{r}_1-\frac{\beta }{2})}{\rho }^{.}\end{array}$$

(3)

As mentioned, the resultant field is the summation of the fields from each element. The final simplified resultant far-field is given by Equation (7).

$$\begin{array}{c}\hfill E=E_1+E_2\end{array}$$

(4)

$$\begin{array}{c}\hfill E={\rho }^{.}\frac{A_1(\theta ,\varphi )}{r}\left[e^{-j(k(r-\frac{d}{2}cos\theta )-\frac{\beta }{2})}+e^{-j(k(r+\frac{d}{2}cos\theta )+\frac{\beta }{2})}\right]\end{array}$$

(5)

This can be simplified by moving the common factor of $e^{-jkr}$,

$$\begin{array}{c}\hfill E={\rho }^{.}\frac{A_1(\theta ,\varphi )}{r}{e}^{-jkr}\left[e^{j(\frac{kd}{2}cos\theta +\frac{\beta }{2})}+e^{-j(k\frac{d}{2}cos\theta +\frac{\beta }{2})}\right]\end{array}$$

(6)

and further simplified by using Euler’s formula

$$\begin{array}{c}\hfill ={\rho }^{.}\frac{A_1(\theta ,\varphi )}{r}{e}^{-jkr}\left[2cos\left(\frac{kdcos\theta +\beta }{2}\right)\right]\end{array}$$

(7)

2.2. Uniform Linear Array with N Elements

The form in Equation (7) can be seen as two different attributes. The left-hand side is related to the individual element and is called the $ElementFactor$ and the right is related to the array and is called the $ArrayFactor$.

$$\begin{array}{c}\hfill TotalField=Elementfactor(E.F)\times Arrayfactor(A.F).\end{array}$$

(8)

Hence, the total field E can be expressed as the product of field due to single element and array factor. This is termed as pattern multiplication. This method is applicable to any array consisting of identical elements. Therefore, the overall pattern can be controlled by controlling the E.F or A.F or both.

$$\begin{array}{c}\hfill A.F=2cos\left(\frac{kdcos\theta +\beta }{2}\right)\end{array}$$

(9)

A.F depends on the number of element (N), where N = 2, in the above Equation (9), distance between the elements d, and the amplitude and phase excitations of the array elements $\beta$. Having derived Equation (9) for the case of a two-element array, this can now be generalised to an N-element array. The derivation shows that the field strength in the far-field is given by the E.F times the A.F as from Equation (8). The A.F for an N-element ULA is derived as follows:

$$\begin{array}{c}\hfill A.F=1+e^{j\left(kdcos\theta +\beta \right)}+e^{j2\left(kdcos\theta +\beta \right)}+\dots \\ \hfill \dots +e^{j(N-1)\left(kdcos\theta +\beta \right)}.\\ \hfill =\sum _{n=1}^N{e}^{j(n-1)\left(kdcos\theta +\beta \right)}=\sum _{n=1}^N{e}^{j(n-1)\psi }\end{array}$$

(10)

where $\psi =kdcos\theta +\beta$. This is sufficient for calculating the A.F. and is the basis of the MATLAB code (source code is available [6]) used to plot the 2-element array in Figure 2.

However, a greater understanding of how the number of elements and progressive phase affect the A.F. can be gained by further simplifying Equation (10). Multiplying both sides by $e^{j\psi }$ results in Equation (11) [2]:

$$\begin{array}{c}\hfill A.F=e^{j\left(\frac{N-1}{2}\right)\psi }\left[\frac{sin\left(\frac{N\psi }{2}\right)}{sin\left(\frac{\psi }{2}\right)}\right]\end{array}$$

(11)

For small values of $\psi$, this can be approximated to

$$\begin{array}{c}\hfill A.F=\left[\frac{sin\left(\frac{N\psi }{2}\right)}{sin\left(\frac{\psi }{2}\right)}\right]\approxeq \left[\frac{sin\left(\frac{N\psi }{2}\right)}{\left(\frac{\psi }{2}\right)}\right]\end{array}$$

(12)

The peaks and nulls can be found by equating the A.F to 0 in (12). $sin\left(N\psi /2\right)=0$ when $\left(N\pi dcos\theta +\beta \right)/2\lambda =n\pi$. Peaks occur when $n\ne N,2N,3N,\dots$ and nulls occur when $n=1,2,3,\dots \dots$ [2]. The total number of nulls and peaks is dependent on the separation distance d and progressive phase $\beta$. The role of $\beta$ in beam steering is discussed in Section 2.3.

When A.F. $=0$, Equation (12) can be solved for $\theta$ (Equation (13)) and used to calculate the positions of peaks and nulls in the radiation pattern.

$$\begin{array}{c}\hfill {\theta }_n=arccos\left[\frac{\lambda }{2\pi d}\left(-\beta \pm \frac{2n\pi }{N}\right)\right]\end{array}$$

(13)

Depending on the direction of maximum radiation, we can classify the array into a broadside array (radiation maximum is perpendicular to the array length) and an end-fire array (radiation maximum is along the array length) [2].

2.3. Beam Steering

In order to scan the beam from one direction to the other, we have to change the relative phase $\beta$ between the elements [7]. To find the $\beta$ needed to get a maximum in a particular direction ${\theta }_0$, the term $\psi$ is set equal to zero, as given by Equation (14):

$$\begin{array}{c}\hfill \psi =kdcos{\theta }_0+\beta =0\end{array}$$

(14)

$$\begin{array}{c}\hfill \beta =-kdcos{\theta }_0=-\frac{2\pi }{\lambda }dcos{\theta }_0\end{array}$$

(15)

By solving the above equation for a given frequency and angle, the phase difference necessary for a given scanning angle (Figure 3) can be derived. In the next section, we apply these equations to design an array to meet the requirements of Table 1.

3. N-Element Array Design

Given the specification in Table 1, we now calculate the number of elements needed to meet those specifications. The total field of an array is a vector superposition of the fields radiated by the individual elements. To provide a directive pattern, it is necessary that the partial fields (generated by the individual elements) interfere constructively in the desired direction and interfere destructively in the remaining space.

The estimated far-field patterns for different N values from 1 to 6 are calculated using MATLAB [8] and are plotted in Figure 4. From Figure 4, it can be seen that at least 3 elements would be needed to get gain to meet the specification; however, more elements are needed to meet the beamwidth specification. So, we have selected N = 5 and the element spacing is chosen to be $\lambda /2$ to meet the gain specification of 10 dBi and 21° as the 3 dB beamwidth. These are now arranged along a straight line to from our ULA (Figure 5). The values of progressive phase $\beta$ for different beam scan angles is calculated using Equation (14). The progressive phase shift $\beta$ needed to steer the beam to angle $\theta$ is shown in

Table 2. Setting parameters of ULA at 2.4 GHz.

Scan Angle ($\mathit{\theta }$)	Progressive Phase ($\mathit{\beta }$)
0	−180
30	−155.9
45	−127.3
60	−90
90	0
120	90
135	127.3

.

Defining Array Parameters

The definitions for antenna-related parameters can be found in [2]. Some have already been defined in Section 2 and some which are relevant to arrays are defined below:

Beamwidth: In a plane containing the direction of the maximum of a beam, the angle between the two directions in which the radiation intensity is one-half value of the beam.

Side Lobe Level (SLL): A side lobe is a radiation lobe in any direction other than the intended lobe. Side lobes are normally the largest of the minor lobes. The level of minor lobes is usually expressed as a ratio of the power density in the lobe in question to that of the major lobe. This ratio is often termed the side lobe ratio or side lobe level.

Number of elements: This is the number of individual antennas that make up the array, we have chosen 5 elements for the array; the greater the number of elements the greater the directivity.

Phased array: An arrangement of antenna elements where the phase of each element is controlled to steer the beam.

Phase excitations: The phase input to the elements on the arrays is termed as excitation phase.

Maximum Beam scan angle: The maximum beam-scan angle for a linear array without much beam-shape degradation is around $\pm {60}^{\circ }$, in the absence of mutual coupling, from bore-sight.

4. Hardware Required

The radiating elements are 55 mm long with a balun of 33 mm connected to a rigid coax. The elements are mounted on a wooden platform which was covered in metal foil to create a ground plane (Figure 5a).

Each element is fed from a dedicated source provided by separate PLLs with a common 10 MHz reference connected to all PLLs. Phase-shifting is accomplished by shifting the 10 MHz reference signal fed to each PLL. Individual PLLs were chosen over a single common source with phase shifters at RF because phase shifters will have varying losses depending on the required shift; the power to each element decreases with the number of elements; turning on off output amplifiers could affect loading of the phase shifter leading to difficulty in calibration. A narrow-band phase shifter at the reference frequency allows for phase-shifting to be accomplished across the full frequency band of the PLL, to achieve this at RF, a wideband phase shifter would be needed. Multiple PLLs also remove the need for a corporate feed network [9].

The topology for each element is shown in Figure 6. A 10 MHz reference is applied to the PLL board and individually buffered to each PLL [10] by a CMOS hex inverter [11]. The phase of the 10 MHz reference to each PLL passes through a phase shifter based on a varactor diode [12]. The phase of the output, the RF signal from the PLL, is adjusted by varying the DC voltage on the varactor. Applying the phase shift before the PLL allows for a constant output power irrespective of phase shift applied, also the system can be expanded by adding more PLL boards. The output of the PLL is then connected to a digitally controlled attenuator [13]. This allows for the power level of each PLL to be adjusted to compensate for variance in PLL output power between circuits as well as allowing for future work, where the excitation level can be adjusted as well as the phase. The output of the attenuator is then connected to an amplifier; in this case, an LNA [14], as this demonstration does not require high power transmission. The LNA increases the power output of each circuit as well as providing 30 dB of isolation between PLL and element; this isolation reduces the effect of a neighbouring radiating element with different phase, changing the phase of a PLL oscillator. In addition, the PLLs selected have frequency dividers available between the internal oscillator and RF output, this allows the PLL to be configured with the internal oscillator running at twice the RF frequency; again, this aids in isolating one PLL from any signal coupled to it from the antenna or PCB affecting its phase. Each LNA can be switched off to allow the output of each PLL to be measured independently and adjusted while still being connected to the antenna array.

To control the array, each PLL, attenuator, LNA, and phase shifter are connected to a dedicated microcontroller [15]. All the microcontrollers are connected to a single RS485 network with a CAT5e cable used to connect this to control the computer via an RS485 to a serial adapter. A combination of custom firmware for the micrcontrollers and a Windows desktop application allow each PLL to be controlled individually from a remote computer. In this experiment, a 20 m cable was used to allow the control computer to be outside of the anechoic chamber. Schematics and production files for the PLL array along with source code and MATLAB [8] scripts can be found in the supporting material [6]. The PLLs are individually bench-tested to verify their power output and phase-shifting performance before integration with the ULA (Figure 7).

5. Measurement on ULA

A 10 m × 5 m × 5 m anechoic chamber was used for the experimental measurements of radiation patterns [16]. The linear array was used as the transmitter as shown in Figure 5a. A common 10 MHz reference was fed to all PLLs, the dual channel IF receiver, and LO signal generator (as seen in Figure 8). One channel of the IF receiver is fed with the output of one PLL via a directional coupler (to reduce the power level and remove any DC) mixed with the LO signal and the second channel comes from the receiving horn in the far field mixed with the LO. The radiation pattern measurement set-up in the anechoic chamber with all the hardware to test is shown in Figure 9. In the next section, we describe how we phase and power-align each PLL in the far field using the anechoic chamber acquisition system (Figure 8).

Calibration Process and Pattern Measurement

Calibration of the transmitter array is essential before measuring the patterns in order for all phases from the elements to be aligned with respect to the receiver. The procedure is to firstly mechanically align the transmitter with receiver so as the transmitter’s broadside is normal to the direction of the receiver. Each PLL is muted while leaving its oscillator on and its LNA turned off. Then, each PLL is turned on, one at a time, and the far-field power and phase resulting from each element are measured and adjusted. Once all PLLs/elements have been set, all LNAs are turned on and the pattern can be measured. As the antenna array is connected to the PLL array by coaxial cables, this allows for compensation for any phase differences resulting form cable length mismatches.

The entire procedure is depicted in the flowchart shown in Figure 10. The progressive phase settings corresponding to different beam-pointing angles is set using the custom Windows−based program [6]. Simulated patterns, created using source code from [6] based on Equation (10), are show plotted against the measured patterns in Figure 11 and the results are in good agreement. The minor discrepancies can be attributed to fabrication tolerances and mutual coupling effect, which is left for the students to understand in depth. This completes the entire process, right from the theory, design, fabrication, and demonstration of ULA and its beam-scanning ability.

The current hardware does not utilise any measurement of phase in the PLL array; however, the PLL used has a differential output with the negative terminal currently terminated with a 50 Ohm load. This second RF output of each PLL could be compared with a selected PLL as a reference through a phase comparator. As the micro-controller has multiple analogue inputs, the DC phase reference signal could be used to tune the DAC output controlling the 10 MHz reference phase shifter. This would allow the control software to send a desired phase offset instead of a voltage, thus allowing for different beam angles to be automatically configured without user interaction.

6. Conclusions

The principle operation of antenna arrays, in particular ULA, their theoretical foundation and understanding of beamforming, and then, scanning properties with hardware demonstration has been described by using concepts taught in undergraduate antenna theory. To promote a better understanding and visualisation of phased antenna arrays, a laboratory demonstrator involving off-the-shelf components that can be easily purchased and integrated are used in the experiments. This enables students to do some basic coding based on theory and realise the operation with a simple experimental demonstrator. In addition, the basic definitions of design parameters commonly associated with antenna arrays are described with simple mathematical equations to quantify them. The experimental hardware gives students the opportunity to explore the flexibility of the ULAs by varying other parameters of the array. The measured radiation patterns are in close agreement with the basic simulations carried out using MATLAB code. The reasons for the deviations are also discussed, such as mutual coupling, etc. The use of a conducting back-plate reflector for minimising back-radiation is also presented. By combining descriptive, analytical, and experimental teaching methods, the students can be motivated to explore further this antenna array field and reinforce their understanding of the principles of phased arrays and their use in communication and radars.