a)
b)
Figure 4.2. Effect of a Shunt Cap Self-Resonating at the Second Harmonic Together with a Parallel SMD Inductor Resonating
with the Shunt Cap at the Fundamental
The circuit shown in part A of the above figure has a moderate attenuation at the third harmonic frequency. Up to ~13 dBm output
power level, this limited third harmonic attenuation is enough for the EFR32 to comply with the ETSI and FCC standards. Therefore, a
low BOM two-element match formed by the L0-C0 elements can be used because the transmission line is not required for operation.
With this match, the impedance at the TX pin is usually not the optimum, but rather close to 50 Ω. Fortunately, the L0-C0 ratio variation
allows for limited impedance tuning. Even if some residual impedance does occur, the slight reduction of power can be easily compen-
sated for by higher power state settings with a minimal increase in total IC current at low power levels.
However, at higher power levels, EFR32 requires more harmonic suppression. For example, at a 20 dBm output power level, at least
30 dB third harmonic attenuation is required to comply with the 41.2 dBm limit of the US FCC standard. To resolve this issue, introduce
a second parallel capacitor denoted by C1, which has the self-resonance close to the third harmonic frequency. Unfortunately, the sec-
ond parallel capacitor mistunes the fundamental C0-L0 parallel resonator if it is connected directly parallel to it. Besides, the C1 alone
has a shunt effect, which again increases the insertion loss at the fundamental frequency. To resolve both issues, separate the C1
capacitor either by a series inductor or a transmission line to form a ladder network. Now, a series transmission line is used becacuse
of the higher cost and higher loss of applying a series inductor.
However, separation is not the only function of the transmission line. Because the C0-L0 parallel resonant circuit is invisible at the fun-
damental frequency, the series transmission line together with the C1 capacitor should also generate the optimum impedance at the TX
pin. As mentioned previously, the L0-C0 can be tuned in a limited fashion to get the right impedance. However, the main tuning element
is the transmission line because of the C0 and the C1 capacitor value variation limitation, which dictates that self-resonant frequencies
should be close to the critical harmonics. The transmission line is only several mm long, which is much shorter than the wavelength at
the fundamental frequency and can, therefore, be modeled as a lumped inductor with some parasitic parallel capacitance. The value of
C1 adds directly to this parasitic cap. Usually, the width of the transmission line has to be decreased close to the technological mini-
mum (~0.2 mm) to have sufficiently high inductance and to minimize the parasitic cap effect beside the C1. Because the width is more
or less fixed, the residual main tuning possibility is the length of the transmission line.
The matching network with 3.5 mm long and 0.2 mm wide transmission line and with 0.8 pF C1 value is shown in part A of the figure
below. Part B shows the transfer characteristic. The third harmonic is efficiently suppressed with the 0.8 pF C1 value. However, the
input impedance at the TX pin (at Port 2 in the schematic) is quite far from the optimum impedance as shown in
Figure 4.4 Impedances
of Differently Tuned Tline Matches on the 2G4RF_IOP Pins on page 30
part A. Here, some tuning is required to shift the impedance
closer to the targeted 23+j11.5 ohm. This can be done either by varying C1 and L0–C0 slightly or by tuning the transmission line length.
For example, with a C0 of 2 pF, L0 of 1.2 nH and C1 of 0.9 pF and with 5 mm long transmission line, the impedance is quite close to
the optimum (see
Figure 4.4 Impedances of Differently Tuned Tline Matches on the 2G4RF_IOP Pins on page 30
with good transfer
characteristic.
Based on the above experiences, the design steps of the transmission line match are as follows:
1. Choose a C1 capacitor value, which has its self-resonance, good suppression, and is nearly at the third harmonic. Additional layout
series parasitic inductances, such as via or trace inductance, shift down the resonant frequency.
2. Choose a transmission line with 0.2–0.25 mm width and with a length, which together with C1 tunes nearly the optimum impedance
(~23+j11.5 ohm) at the TX pin.
3. Choose a C0 value that has its self-resonance close to the second harmonic. Again, the series parasitic inductances, such as via
or trace, of the layout decreases the resonant frequency.
4. Choose a parallel L0 value that resonates with the C0 at the fundamental frequency and provides a low insertion loss. Slight tuning
of L0 can further improve the impedance optimization.
AN930: EFR32 2.4 GHz Matching Guide
Transmission Line (Tline) Match for Minimal BOM Solutions (U.S. Patent US9780757B1)
silabs.com
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