Raspberry Pi Antenna Design

The Raspberry Pi has a 2.4GHz WIFI antenna that is part of the PCB (Printed Circuit Board). The design is unique, but also illustrative of how antenna design can be done under constraints. Chip Antennas Chip antenna designs are often used to simplify things; you can find many 2.4GHz chip antennas from distributors such as digikey, mouser or a google search. The raspberry pi up until the model 3 used this solution: Figure 1. Raspberry Pi 3 Antenna. 2.4 GHz chip antenna on the left side of the board. PCB Trace Antenna Sometimes after the Raspberry Pi 3, they started to ditch the chip antenna (presumably for cost). By doing a trace antenna they can reduce their overal BOM (bill of materials). Pictured below is the antenna designed into the Raspberry Pi Zero W, which is similar to the antenna used on the Raspberry Pi 4 as well. Figure 2. Raspberry Pi Zero W Antenna. 2.4 GHz PCB antenna. How would we go about designing this antenna? As (almost) always, let's start with a half-wave dipole antenna, the fundamental building block of many antennas. At 2.4GHz, the half-wavelength is about 6cm, which is close to the length of the raspberry pi zero of 6.6cm. In Figure 3 below, I sketch a half-wavelength dipole antenna for 2.4GHz next to a Raspberry Pi. We can assume most of the RPi is ground, and draw an "antenna keepout" triangle that will be used for the antenna feed. Figure 3. A Half-Wavelength Dipole is About the Size of a Raspberry Pi Zero. On the left side of Figure 3, note the battery symbol represents the antenna feed, or where the RF+ pin of the radio connects to one side and the RF- pin (typically ground) connects to the other side. Next, we fatten up our original dipole to close to the size of the raspberry pi, essentially making a Vivaldi antenna: Figure 4. A Fat Dipole (left) and a Shorted Fat Dipole (Right). In Figure 4, we see that a shorted fat dipole is essentially a fat vivaldi antenna with a small value of inductance across the feed. This means the inductor is in parallel with the antenna, which shorts it out at DC (0Hz), but because the impedance is Z=2*pi*f*L, it is not completely shorted out at RF (2.4GHz). Now we can see that the raspberry pi zero antenna is essentially a modified version of what is shown in Figure 4. Then we just have to add some impedance matching, as we will see shortly. Figure 5. The Raspberry Pi Zero W Antenna - Before Impedance Matching I went ahead and removed the impedance amtching components nad measured the impedance of the Raspberry Pi Antenna with a VNA on the Smith Chart: Figure 6. Smith Chart for RPi Zero Antenna without Impedance Matching. As you can see in Figure 6, the impedance is almost purely inductive at 2.4GHz. The antenna is not tuned at all near 50 Ohms, so in this state most power would be reflected. However, with some series C and shunt C (capacitors) impedance matching, we can tune this antenna into band: Figure 7. Smith Chart for RPi Zero Antenna with Impedance Plan. Using 1pF series and 2.8pF shunt caps with a circuit simulator, the impedance can be tuned as shown on the Smith Chart below. Note the target band (2.4-2.48GHz) is shown in red. The rapid movement of the antenna impedance is indicative of a narrowband antenna design, which is expected given the inductance across the feed: Figure 8. Smith Chart for RPi Zero Antenna with Impedance Matching. Now - the analysis is done. This antenna is a wideband dipole, heavily shorted with inductance, that is rematched ot the center with series and shunt capacitors. I removed part of the RF matching components near the radio and cabled into the antenna with a SMA pigtail as shown in Figure 9: Figure 9. SMA Pigtail measuring Raspberry Pi Zero W Antenna. I can then measure the VSWR on a VNA as shown in Figure 10: Figure 10. VSWR of Raspberry Pi Measured on VNA. The VSWR (or S11) of the antenna shows good tuning, although slightly lower in frequency than optimal. This is likely due to the impedance matching component's tolerance, as discussed later. Next, we measure the antenna efficiency of this antenna and plot that in Figure 11: Figure 11. Antenna Efficiency of Raspberry Pi Measured in an Anechoic Chamber. The peak efficiency in Figure 11 is above -2 dB, which at about 70% is a pretty good antenna. The efficiency falls off rapidly due to the heavily shorted nature of the antenna and associated matching required. Lastly, with anechoic chamber measurements I can get both the efficiency and the antenna gain, which is plotted in Figure 12: Figure 12. Antenna Gain of Raspberry Pi Measured in an Anechoic Chamber. If you zoom in on the antenna in the left side of Figure 2, you will see two series matching capacitors and 1 shunt (parallel) matching capacitor. I measured these components on a VNA, and found the values to be Cser1 = 1.2pF, Cser2 = 2pF, and Cshunt = 2.6pF. As for why these used two series capacitors, the answer is likely because they needed a capacitor with a matching value of about 0.75pF. The capacitors are sold in 0.1pF increments, and also have a +-0.1pF tolerance. This explains the reasons for two series caps, as well as the shift in frequency as measured for efficiency and vswr in Figures 10 and 11. There you have it! That is the design and analysis of the Rapsberry Pi PCB antenna. Finally, I also have a video to describe this if learning in that format is useful to you: