## 2 Sensitivity and PSRR of Power Amplifier  
In an FDD system with an ET PA, the receiver's sensitivity is degraded by the PA output noise (\(P_{PMN}\)) from the SM noise (\(P_{SMN}\)), as shown in Figure 1. The receiver sensitivity is the minimum detectable input power (\(P_{in\_min\_dBm}\)), and it can be defined in the following equations:  
\[P_{in\_min\_dBm}=10 log_{10}\frac{P_{thermal+PAN}}{1m}+NF+SNR-Atten_{DP} \tag{1}\]  
\[P_{thermal+PAN}(mW)=10^{(-174\ dBm/Hz+10 log_{10}BW)/10}+10^{(P_{PAN}/10)} \tag{2}\]  
\[P_{PAN}=P_{SMN}-PSRR_{PA} \tag{3}\]  
where BW is the signal bandwidth in Hz, NF is the noise figure of the receiver path, SNR is the required signal-to-noise ratio of the system, and \(Atten_{DP}\) is the attenuation of the duplexer. If the specification for sensitivity degradation is lower than 0.4 dB and the attenuation of the duplexer is 45 dB, the required PA noise is under \(-139\ dBm/Hz\). The required SM noise is determined from the required PA noise and PSRR of the PA (\(PSRR_{PA}\)), as given in (2). The PSRR of the PA can be defined in the following equations:  
\[PSRR=20\times\log_{10}\frac{\Delta V_{CC\_un}}{\Delta V_{PAOUT\_avc\pm\omega m}} \tag{4}\]  
\[PSRR_{SSB}=PSRR+3 dB \tag{5}\]  
where \(\omega_{\rm n}\) is the TRX offset frequency of the FDD system, \(\omega_{0}\) is the RF carrier center frequency, \(\Delta V_{CC\_un}\) is the supply noise amplitude at \(\omega_{\rm n}\), and \(\Delta V_{PAOUT\_avc\pm\omega m}\) is the RF output noise amplitude at \(\omega_{\rm o}\pm\omega_{\rm n}\). Because the RF output noise due to the supply noise is located at a positive and negative offset frequency of \(\omega_{\rm n}\), the single-sideband PSRR (PSRR\({}_{SSB}\)) is a meaningful value that can be used to express RX-band noise. In this paper, the noise amplitude and noise power are calculated and measured with a 50-Ohm load impedance for convenience.  
Figure 1: RX-band noise transfer from ET PA in FDD system.  
Figure 2 shows the PSRR difference between the linear region and saturated region of the PA. In the linear region, the PA has a high PSRR because it has little gain variation due to the supply voltage change. In the saturation region, the PA has a much decreased PSRR due to the large gain variation over the supply voltage. To quantify and compare the PSRR of APT and ET, a mathematical PA model [14] is used to simulate gain and the PSRR at various supply voltages and input/output power values.  
Figure 3 shows the simulation results, and the simulated PSRR is well matched at a low frequency offset (tens of MHz) from the carrier frequency. For a large frequency offset (larger than 100 MHz), the PSRR increased due to the reduced gain caused by the limited PA bandwidth. In APT mode under 3.5 V, the PSRR\({}_{\text{SSB}}\) range is from \(-3\) dB to over 50 dB. The average PSRR\({}_{\text{SSB}}\) of APT is about 15 dB for the LTE signal, with a 6 dB PAPR. In ET mode, the PSRR\({}_{\text{SSB}}\) curve is located around 0 dB, and it is changed by an envelope-shaping function and the saturation level. The average PSRR\({}_{\text{SSB}}\) of ET is about 0 dB for LTE, and its slope is about \(-4\) dB per 1 dB of output power. From this result and the required PA output noise, the required SM noise is determined to be about \(-134\) dBm/Hz. If there is a margin in the SM noise, the ET PA system has many advantages such as better sensitivity, reduced requirement for duplexer attenuation, and higher PA efficiency due to having more saturated ET operation with a reduced PSRR. Therefore, noise reduction techniques are essential in SM design.  
Figure 3: Simulated gain and PSRRSSB curves of APT and ET.  
Figure 2: PSRR of PA in linear and saturated regions near P1 dB.