## 4.2 Front End Receiver Noise Figures

**Figure 1. Block diagram of receiver front-end**

__Front End Receiver__

__Front End Receiver__

Consider the typical front-end of a receiver shown in Figure 1, where the output impedance of the signal source is denoted as Z_{ss}. The **low-noise amplifier **(LNA) represents the device that is modeled with noise parameters. **Zin denotes LNA input impedance**. A passive matching network is in general needed between the signal source and the LNA. This network has a different purpose in different systems. However, it is most often used to convert Z_{ss} to Z_{s} such as Z_{s} is complex conjugate of Z_{in}.

In such a case, all output power of the signal source is delivered to the LNA. In other words, no power is reflected back to the signal source, and the reflection coefficient of the Matching Network and LNA is near zero. If Z_{opt} of the LNA is known, we can determine whether the LNA noise figure (NF) comes close to NF_{min}. If it happens that Z_{s} = Z_{opt}, then NF does equal to NF_{min} and the LNA is **both power matched and noise matched**!

__Matching Challenges__

__Matching Challenges__

If, however, this matching network creates **Z**_{s}**≠Z**_{opt}, then the LNA noise figure will be larger than NF_{min} and the LNA is power matched but not noise matched. Alternatively, the matching network could noise match the LNA but cause a power mismatch, which results in some input power reflected back into the signal source and a reduction in power gain. When this occurs, the power gain is referred in datasheets as the “**associated gain**.”