How to Match a Chip Antenna with a Pi Network

The synthetic $2.45\,\mathrm{GHz}$ chip antenna is $10.64 + j5.56\,\Omega$. A Pi at loaded Q $= 5$, the default above this load’s L-network minimum of $1.64$, is a shunt $6.496\,\mathrm{pF}$ at the source, a series $931.7\,\mathrm{pH}$, and a shunt $14.3\,\mathrm{pF}$ at the antenna. Nearest E24 of those three, each part rounded on its own, is $6.8\,\mathrm{pF}$, $910\,\mathrm{pH}$, and $15\,\mathrm{pF}$, and the return loss is still $22.56\,\mathrm{dB}$. The sweep search over $2$–$3\,\mathrm{GHz}$ does not stay there. It walks off to $7.5\,\mathrm{pF}$, $750\,\mathrm{pH}$, and $12\,\mathrm{pF}$, and the return loss at $2.45\,\mathrm{GHz}$ falls to $5.16\,\mathrm{dB}$. Lay the footprint as a Pi so one shunt can stay empty. Start from the NanoVNA plane you will actually solder to, not from the connector you calibrated.

The antenna is the same synthetic model as the L-section note. It is not a vendor part and not a captured .s1p.

Why a Pi footprint instead of an L?

An MCU RF pin and a chip antenna rarely meet at $50\,\Omega$, and you will not know the number until the board exists. The footprint that survives that fact is three pads: shunt at the pin, series, shunt at the antenna. Populate both shunts and you have built this Pi. Leave the antenna-side shunt empty and you have built the L-section, which for this impedance is the only L topology available: shunt capacitor at the source, series inductor toward the load. A $0\,\Omega$ in the series pad and both shunts empty is the measurement, not a match.

The L-section on this model is a shunt $2.499\,\mathrm{pF}$ and a series $968.4\,\mathrm{pH}$, nodal Q $1.92$, and the $\ge 10\,\mathrm{dB}$ span on the antenna is $273\,\mathrm{MHz}$. The Pi at Q $= 5$ does not narrow that. Its span on the same model is $2.243$–$2.575\,\mathrm{GHz}$, $333\,\mathrm{MHz}$. The antenna is moving faster than the extra resonator can squeeze. Loaded Q is not the bandwidth you will measure here. What the Pi does buy, on a load that holds still, is harmonic rejection. That case is Pi vs T vs L. On this element model continued to $4.9\,\mathrm{GHz}$, where the impedance has become $243 + j295\,\Omega$, the bare transducer gain is $-5.51\,\mathrm{dB}$, the L-section is $-17.1\,\mathrm{dB}$, and this Pi is $-44.3\,\mathrm{dB}$. The model’s file stops at $3\,\mathrm{GHz}$. Past that, you are looking at the elements, not at a measured harmonic.

Put the Pi in when the pin is a transmitter and the second harmonic is in the specification, or when you want both pads present so the next spin can change its mind. Put an L in when you already measured the antenna and two parts are enough. Do not put a Pi in because someone said chip antennas need one.

What does the NanoVNA file actually fix?

A one-port Touchstone file is the reflection coefficient at the calibration plane, in the file’s reference impedance. IndieRF Match reads $\Gamma$ and interpolates in $\Gamma$. It does not remove fixture delay, and it does not invent samples past the ends of the file. Fifty picoseconds of line still in the fixture moves this antenna from $10.64 + j5.56\,\Omega$ to $24.6 + j54.8\,\Omega$, and the parts change with it. That arithmetic is in the L-section note. The rule does not get kinder because the network has three pads.

Calibrate at the plane you will solder, or port-extend on the instrument until the plane is that pad, then export. Matching the connector gives you a beautiful $S_{11}$ on the cable and a different impedance on the board. Plotting the file without proposing parts is the S-parameter viewer. The match tool is the one that turns the marker into a Pi.

Which E24 values, and why did the search miss?

Round each ideal part to E24 and stop. $6.496\,\mathrm{pF}$ becomes $6.8\,\mathrm{pF}$, $931.7\,\mathrm{pH}$ becomes $910\,\mathrm{pH}$, $14.3\,\mathrm{pF}$ becomes $15\,\mathrm{pF}$. With infinite component Q that network is $-0.024\,\mathrm{dB}$ transducer gain and $22.56\,\mathrm{dB}$ return loss at $2.45\,\mathrm{GHz}$. That is a match. You do not need a closer series.

The combined search is a different operation. It may leave the nearest step when a neighbor wins on the sweep. On this antenna, with E24 selected and the sweep running from $2$ to $3\,\mathrm{GHz}$, the search lands on $7.5\,\mathrm{pF}$, $750\,\mathrm{pH}$, and $12\,\mathrm{pF}$. Return loss at the marker is $5.16\,\mathrm{dB}$. The $\ge 10\,\mathrm{dB}$ band is gone. Open that link if you want to see the miss. Then type the nearest values back in. The search optimized a moving load over a gigahertz and gave up the frequency you asked for.

E96 of the same ideal parts is closer and not the point. The reel in a lab drawer is E24. Snap after you have picked the Pi, not before, and read the marker. A sweep that looks flatter while the marker falls through $10\,\mathrm{dB}$ is not a better match.

Does 0402 or 0201 change the answer?

Not inside this solver. $910\,\mathrm{pH}$ and $6.8\,\mathrm{pF}$ are the same nominal in 0402 and in 0201. The solver adds neither the pad capacitance nor the self-resonant frequency printed on the reel. Both are the difference between those packages at $2.45\,\mathrm{GHz}$.

An 0402 pad is a larger shunt capacitor than an 0201 pad. On the $14.3\,\mathrm{pF}$ arm that is a correction you can absorb, because the part is already many picofarads. On a $0.3\,\mathrm{pF}$ arm it would be the part. This Pi is the first situation. The series $910\,\mathrm{pH}$ is the second kind of problem: it is a small inductor, and a chip inductor that small lives near the edge of what the package can still look like an inductor. Read the SRF and the Q at $2.45\,\mathrm{GHz}$ on the exact part number. If that SRF sits on the channel, the 0201 or a smaller geometry is the one to measure. If you are going to swap three values with a soldering iron, 0402 is the one you will finish. Neither sentence is a license to skip the measurement.

The Q you are allowed to type is the Q of that part at $2.45\,\mathrm{GHz}$, not the minimum Q at $100\,\mathrm{MHz}$ and not the Q of a different construction. The catalog comparisons are in why an L-match is narrow.

What inductor Q costs on this Pi

Q is applied after the values are chosen. Series resistance of an inductor is $\omega L/Q$. Capacitor ESR is $1/(\omega C Q)$. On the ideal $6.496\,\mathrm{pF}$, $931.7\,\mathrm{pH}$, $14.3\,\mathrm{pF}$, with capacitor Q held at $300$:

Inductor Q of $50$ gives $-0.73\,\mathrm{dB}$ transducer gain and $22.05\,\mathrm{dB}$ return loss. Q of $30$ gives $-1.12\,\mathrm{dB}$ and $18.47\,\mathrm{dB}$. Q of $15$ gives $-2.02\,\mathrm{dB}$ and $13.72\,\mathrm{dB}$. The step from Q $50$ to Q $15$ is $1.29\,\mathrm{dB}$.

The same inductor-Q step on the L-section for this antenna costs $0.28\,\mathrm{dB}$. The Pi is a higher-Q network, Q $= 5$ against nodal Q $1.92$, and it has two capacitors carrying current. A mediocre coil hurts more here than it did in the two-element match. If the harmonic specification is what forced the Pi, spend the Q on the $931.7\,\mathrm{pH}$ inductor before you spend it on a closer E24 step. The $0.024\,\mathrm{dB}$ from rounding is not the term in the budget.

What this is not

No vendor antenna, no measured .s1p, no pad, no via, no ground inductance under the shunt, no package model for 0402 or 0201. The $4.9\,\mathrm{GHz}$ figures continue the same four elements past the $3\,\mathrm{GHz}$ end of the file. A real antenna will not follow them. The reference plane is whatever plane you export. If the file is the connector, these parts are a precise match to the connector.

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References

• C. Bowick, RF Circuit Design, the chapter on Pi-network matching. Loaded Q sits above the L-section minimum.
• D. M. Pozar, Microwave Engineering, the chapter on impedance matching and tuning.
• The element values are the synthetic demo in IndieRF Match, the same model as the L-section note, not a manufacturer’s measured antenna.

Related

• Match a 2.4 GHz chip antenna to 50 Ω
• Pi vs T vs L: which matching network
• Why an L-match is narrow, and what Q costs
• Ideal Pi on the demo antenna

FAQ

How do you match a chip antenna with a Pi network?

On the synthetic 2.45 GHz antenna, 10.64 + j5.56 Ω, a Pi at loaded Q = 5 is 6.496 pF at the source, 931.7 pH in series, and 14.3 pF at the antenna. Nearest E24 is 6.8 pF, 910 pH, and 15 pF, still 22.56 dB return loss. Lay out both shunts so one can stay empty and the board becomes an L-section.

Why did E24 rounding ruin the match?

Nearest-value rounding did not. 6.8 pF, 910 pH, and 15 pF are 22.56 dB at 2.45 GHz. The combined sweep search from 2 to 3 GHz left those values for 7.5 pF, 750 pH, and 12 pF, and the return loss fell to 5.16 dB. Read the marker after a search. A flatter sweep that misses the channel is not a better match.

Should the matching network be 0402 or 0201?

The solver does not know. 910 pH and 6.8 pF are the same nominal in either package. An 0402 pad is a larger shunt capacitor than an 0201 pad, and a chip inductor that small may be near its self-resonant frequency. Read the SRF and the Q at 2.45 GHz on the part number. Use 0402 if you will rework the match with a soldering iron and the SRF is still above the band.

Where do I put the reference plane for a NanoVNA match?

At the pads you will solder. A .s1p file is the calibration plane. Fifty picoseconds of leftover line moves this antenna from 10.64 + j5.56 Ω to 24.6 + j54.8 Ω, and both the L-section and the Pi change with it. IndieRF Match does not remove fixture delay.