LNA Matching

The LNA matching is required to adapt the complex input impedance of the input stage to a connected circuit like a SAW filter or a connected antenna. For this matching, the use of an NWA and the transformation to the system impedance of 50Ω is well-established. An advantage of the system impedance is that it is possible to change the connected component like the antenna without additional effort if it has 50Ω too. Besides input impedance, also consider parasitics from the board. If the matching is done with an NWA, it is possible to compensate for the parasitics in combination with the matching. The following figure shows the example of a simplified matching setup based on the layout.

Figure 1. ATA8510 Demo Board Footprint

Note: The LNA used in ATA8510 requires a DC path to GND. Therefore, the shunt element must be an inductor.

Figure 1 shows a theoretical routing for ATA8510 LNA matching, including the point of system impedance where the NWA is connected. Additionally, the parasitics are marked with gray-colored components. Every part of the circuit on the application board has a particular influence on the complex impedance. The pin, housing and bond of the chip can influence the complex impedance. If the build-in RF antenna switch is used, it must be considered during the matching process.

Measure the complex impedance with a 0Ω resistor mounted to the serial footprint. The parasitics from this component can be eliminated later in the matching process. It is important to activate the LNA of the ATA8510. Otherwise, the complex impedance that is measured with the NWA is wrong as the internal circuit is not activated. Once the complex impedance is known, either the transformation can be done by trying components that seem suitable for the matching or calculation tools can be used to get the values of the components. The following Smith Chart shows an example of the input impedance.

Figure 2. Complex Input Impedance

Note: The network analyzer must be calibrated to the frequency range and the system impedance point.

The complex input impedance of the LNA, including the parasitics from the board, chip and connector, is at (20.8j58.7)Ω . Applying the rules from the Smith Chart section, the shunt component must be an inductor and a serial capacitor. The theoretical matching, including the transformation, is shown in the following figure.

Figure 3. Theoretical Matching Input Impedance

Use open-sourced Smith Chart tools to calculate the required component values to illustrate the target values. For more details, see Reference Documentation.

Figure 4. Matching Calculation

The complex load impedance is set to the measured value (20.8j58.7)Ω . Further, the matching components must be added as a transformation network. A simple approximation can identify the required values to reach the system impedance. Based on the calculation, the required network to get (55.7j2)Ω is a 15 nH shunt inductor combined with a serial 4.7 pF capacitor.

With the 0Ω serial resistor and the 15 nH shunt inductor, the impedance is transformed to (84.4+j94)Ω , as shown in the following plot.

Figure 5. Matching 0Ω + 15nH

The calculated impedance is not reached but it is close to the value of 55Ω. The next step is to replace the 0Ω resistor with the 4.7 pF target capacitor.

Figure 6. Matching 4.7 pF + 15 nH

The complex impedance that can be measured with the calculated components mounted on the board is far from estimated due to the parasitic influences of the components. For every matching element, parasitic effects must be considered. An inductor element may also have capacitive influences, whereas, a capacitor component also adds inductive characteristics. In such scenarios, either add parasitics to the calculation model or use an approximation to continue with the matching process. Assume the values if not given. In the case of the adjustment of the calculation model, the real parasitics must be known from every part. Measured complex impedance is shown in Figure 6. The user must find this point in the Smith Chart by tuning the two matching components.

Figure 7. Matching Correction Calculation 4.7 pF + 15 nH

The measured complex impedance can be reached in calculation with a capacitor value of 6.2 pF and inductor of 9.1 nH. The inductor value is about 6 nH lower than initially calculated. The mounted inductor must be increased to improve the result, as shown in the next step.

Figure 8. Matching 4.7 pF + 22 nH

When using a 22 nH inductor, the resultant complex impedance is much closer to the target than with the initially-calculated values. As the value is already very close to the system impedance and the Voltage Standing Wave Ratio (VSWR) is below 2, a matching via approximation is constructive. For that, increase the inductor further to 27 nH.

Figure 9. Matching 4.7 pF + 27 nH

The complex impedance with 4.7 pF and 27 nH is, for most applications, good enough as the VSWR is in the range of 1.6 and S11 is better than -10 dB. For better values, continue the process, as shown in the following figures.

Figure 10. Matching 5.6 pF + 27 nH

Reach the complex impedance given in Figure 10 with a 5.6 pF capacitor and a 27 nH inductor. As the real part of the complex impedance is worse compared to the previous measurement, the other component is adjusted again. As shown in Figure 8 and Figure 9, an increase in the inductor value has increased the real part of the complex impedance. The value must be reduced to 5.6 pF and 22 nH, and the result is given in the following figure.

Figure 11. Matching 5.6 pF + 22 nH

As this value is almost real, the S-parameter is verified to get the quality of the chosen matching. The result is an input reflection factor of -21.6 dB. With that matching, >99% of the injected energy is routed through the matching circuit.

Figure 12. Matching S11 5.6 pF + 22nH

To achieve an optimum result or close to perfection, increase the capacitor value to 6.2 pF. The complex impedance is transformed from (20.8j58.7)Ω to (48.5+j4.5)Ω and an S11 of -26.4 dB is reached.

Figure 13. Matching 6.2 pF + 22 nH

Figure 14. Matching S11 6.2 pF + 22 nH

A successive approximation can be applied to find the best matching for the application, as shown in the matching procedure. If not all parasitics from the board, the components and the chip are known, and no simulation of the whole application can be done, the method described above is a suitable approach that can be used for the matching process.