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### Lesson 13: Antenna Array with WiFi Measurement

This section is optional, and covers the actual construction and measurement of a circuit board. The unique aspect of this lesson is that the boards can be measured using relatively inexpensive equipment that would be commonly found in a lab (or house), rather than expensive measurement systems such as Network Analyzers. The measurements in this lesson take advantage of the Received Signal Strength Indicator built into WiFi sensors.

This lesson will avoid the use of the optimizers, attempting to calculate the correct values rather than guessing and tweaking.

## Section 1: Antenna Design

The first element to design is the antenna. Mason includes a folded dipole model which uses the Induced EMF method to approximate the impedance; this is not as good as a full 3D EM simulator, but is faster and reasonably accurate. The simplest way to design this component is using PrimCalc.

Use PrimCalc to load the folded dipole model, which is part of the antenna library. By default, this is located at: “C:\Documents and Settings\[YOUR USER NAME]\Local Settings\Application Data\CircuitMason\mason_models\antenna”; the actual location may vary depending on the installation.

We will model this circuit on a cheap FR4 substrate. For this lesson I will focus on a specific pcb manufacturer, Sunstone. I don't have a vested interest in Sunstone, however in my experience they are:

1. Reliable, helpful and relatively inexpensive

2. Accept the kind of Gerber files we're generating

3. Have an educational discount

Having said all that, most any board house will work, I just want to focus on one for the sake of procedure.

Sunstone uses an FR4 140 TG, which has the following (approximate) specs:

Permittivity (eps_r): 4.3

Loss Tangent (loss_tangent): 0.0165

Dielectric thickness (height_d): 62 mil

Copper thickness (thickness): 0.7 mil

Conductivity (conductivity): 4e6

The antenna will be designed for:

Frequency (frequency): 2.45 GHz

Dipole width (width): 20 mil

Length (length): start with 3 cm (we will use PrimCalc to calculate)

Feed point gap (gap): 20 mil

Ceiling (height_c): 1 m (no ceiling)

Figure 13.1: PrimCalc design of the folded dipole, before calculation

The antenna's impedance is made up of two parts. The real part is the resistance, which is the part of the impedance associated with the transmission of RF energy. The imaginary part is the reactance, which is “near field” energy that is not transmitted. The reactance causes a reflection and is undesired.

Load the model in PrimCalc with the numbers above. Calculate the length as follows:

1. Enter “0” for the Xfd property (folded dipole reactance)

2. Check the boxes next to the Xfd property and the length argument

3. Hit the “calc” button to solve for the desired length

The Rfd is 87 ohms, but we notice that the resulting Xfd is actually not zero. A local minimum is preventing us from actually reaching the zero reactance point; this is okay. We have calculated the folded dipole length which should maximize transmitted energy. Keep in mind this is an approximate model so the actual center frequency will likely be somewhat shifted.

Questions:

13.1: What is the optimal length?  What is the minimum reactance? Given the complex impedance of the folded dipole, what is the best case return loss given a purely real source impedance?

## Section 2: Balun Design

The folded dipole is a “balanced” or “differential” antenna- it requires two equal and opposite signals. Most electronics are, however, single ended. To transform a single ended source into a differential input, we need to use a balun, a balanced to unbalanced circuit. Many kinds of baluns exist, some widerband and some smaller, but the discrete balun will be a good fit for this application.

Figure 13.2: Balanced to Unbalanced transformer, from a 50-ohm port to a folded dipole

This balun circuit uses two inductors and two capacitors. The inductor L1 adds 90° to the voltage's phase, and the capacitor C1 subtracts 90° to the voltage's phase; the result is 180° of phase shift- equal and opposite signals. The capacitor C2 and the inductor L2 just act to cancel the reactance of L1 and C1, a resonant structure making this a relatively narrow band balun.

Based on our calculations for the folded dipole, the single-ended impedance is 87 ohms. The differential impedance is therefore 174 ohms. Therefore the two relevant impedances are:

The equations for the balun design are:

The closest approximate values of the Coilcraft and Murata parts are 0.7pF and 5.6nH, respectively.

Questions:

13.2: What are the actual calculated for the capacitance and inductance? How far off are we by percent?

## Section 3: Feed Design

Our folded dipole antenna requires a feed network- we will not be driving the antenna directly. We need some type of transmission line to bring power from the balun to the antenna. This brings up an interesting problem. Standard construction (read: cheap) for most processes generally assumes a 62-mil board. This is why we designed our folded dipole at this height_d. However, the microstrip widths at this dielectric height are impractically wide (using PrimCalc, the width is around 120 mils). We need a thinner dielectric between layers 1 and 2. It turns out that in order to get a thinner substrate for the microstrip lines, it is cheaper to use a standard 4-layer process rather than a custom 2-layer process.

Sunstone's 4-layer process uses the following stack-up (different vendors may vary):

Layer 1: 1.7mil copper (plated 0.5 oz)

11.9 mil FR4 (eps_r = 4.3 @ 2.45 GHz)

Layer 2: 1.4mil copper (1 oz)

28 mil FR4 (eps_r = 4.3 @ 2.45 GHz)

Layer 3: 1.4mil copper (0.5 oz)

11.9 mil FR4 (eps_r = 4.3 @ 2.45 GHz)

Layer 4: 1.7mil copper (plated 0.5 oz)

We will keep the folded dipole with the 62-mil dielectric height, but the microstrip will be designed for a height of 11.9 mil. This will keep the design relatively simple and inexpensive.

Figure 13.3: Folded dipole with feed

Twin-line carries an odd-mode (differential) signal; no even mode can be transmitted. Since there is no ground plane, no common mode energy can be coupled onto this transmission line. This is the “pure” odd mode. If a ground plane is present, then the energy can transmit in either the odd mode or the even mode. Each mode has a separate impedance associated with it.

Figure 13.4: Three types of transmission lines

We do not want a ground plane beneath the transmission lines running to the antenna.  These would permit undesirable modes.  Mason has a coplanar strip model to simulate the twin lines without a ground plane, which is more representative of this structure.  The coplanar strip model is located at "coplanar/coplanar_strip4.xml".  Use the following parameters:

Frequency: 2.45 GHz

Permittivity (eps_r): 4.3

Loss Tangent (loss_tangent): 0.0165

Copper thickness (thickness): 1.7 mil

Conductivity (conductivity): 4e6

Gap: 30 mil

Width: 18 mil

Length: 1.9 cm

The odd-mode impedance is 174-ohms.

Another way to calculate the gap and width for the twin-line is to use the stripline method of relaxation code, which is flexible enough to model the twin-line. This model is much slower, especially because the grid needs to be very large to keep the boundaries away from the transmission lines. The model can be found at “stripline/smorcoupled.xml”.  Using this method is more flexible because one can incorporate more complicated dielectric stack-ups, layers of board materials that have different dielectric properties.

## Section 4: Combiner Design

The next component for design is the combiner. As a narrow band design, a single loop Wilkinson will be sufficient. The loop to be used in the Wilkinson will be electrically 90-degrees at 2.45GHz, but geometrically will cover an arc of 180-degrees. We will design the loop using the “microstrip\mcurve.xml” model:

The Wilkinson will use a 100-ohm resistor and be designed for 50-ohm inputs and outputs, leaving the width and length of the 70-ohm line the major part of the design.

Arguments:

Frequency: 2.45 GHz

Permittivity (eps_r): 4.3

Loss Tangent (loss_tangent): 0.0165

Dielectric thickness (height_d): 11.9 mil

Copper thickness (thickness): 1.7 mil

Conductivity (conductivity): 4e6

Height_c (ceiling height): 1 m

angle (arc length, not electrical): 180

Fixed Properties:

Z0 (impedance): 70.71

BL_d (electrical length): 90

## Section 5: Connector Design

The SMA connector used on this board has an associated inductance. This inductance is not well characterized, but having a lumped element capacitor in series with the connector will help tune out the reactance, not just of the connector but also any stray reactance in the rest of the circuit. In the final circuit design, we will use the optimizer to estimate the desired value, but we will be open to changing this value when we actually build the circuit.

## Section 6: Practical Considerations

The next stage is adding the practical elements into the layout: the actual structure of the Wilkinson, the physical layout of the balun, fixing the antenna spacing, and so on. The actual Circuit Mason file describing the folded dipole array (“folded_dipole.dsn”) can be found at: https://sites.google.com/site/circuitmason/home/test_cabinet. The PADS layout file is also included (“folded_dipole.pcb”).

Figure 13.5: Actual layout of the folded dipole array

## Section 7: Measurement (professional)

The existing Mason model does not predict the gain, but will optimize for the match.  Therefore, the model and measurement of the match are compared below, and the measured realized gain from 2.3GHz - 2.6GHz are displayed in Figure 13.6.  The 30 degree beam width observed in Figure 13.7 is consistent with a 4-wide dipole array.  I expect the discrepancy between the expected realized gain of the system and the measured realized gain is the loss in the board- the FR4 used is fairly lossy at 2.4GHz, especially factoring in the metal loss.

This was the first prototype board for the folded dipole array, using a common FR4 substrate and process compatible with many general projects.  A second design will be considered in the next section.

Figure 13.6: Measured and modeled data versus frequency
Figure 13.7: Measured realized gain versus angle

## Section 8: Measurement (amateur and class room)

In order to bring this to the "classroom", a combination of software and hardware have been designed for a low budget antenna experiment.  This lab can be performed with the following kit:

1) A WiFi USB adapter with external antenna such as this, or this; most are probably comparable

2) An adapter cable: "CSA-RPSM-216-SAFB-ND" from Digikey

3) An SMA cable: "ACX1574-ND" from Digikey

4) A dipole antenna such as above (I'm currently working on a new, affordable design)