## 4 Results and Discussions  
The MedRadio receiver is fabricated in a 65 nm RF CMOS process. A micrograph of the fabricated chip is shown in Figure 7, in which the major building blocks are denotated. Note that the chip includes not only the RF receiver of Figure 3 but also an RF transmitter comprising a divide-by-4 circuit and a class-D power amplifier. However, the design details and measurement results of the RF transmitter are not discussed in this paper because they are out of the scope. Nevertheless, the total die size including the entire receiver and transmitter is 2.46 \(\times\) 1.26 mm\({}^{2}\). The fabricated die is mounted and directly wire-bonded on a printed circuit board for experimental measurements. A single supply voltage of 1 V is used. Figure 6: Simulation results of the IM2 calibration. Figure 8 shows the measured S\({}_{11}\) of the receiver. The input impedance bandwidth having S\({}_{11}<-10\) dB is 37.5 MHz between 389.4 and 426.9 MHz. It shows that the single series off-chip inductor L\({}_{\text{ext}}\) shown in Figure 5 is enough to achieve the satisfactory input bandwidth for the MedRadio applications. Note that this external L\({}_{\text{ext}}\) is not changed during the subsequent whole OOB blocker measurements. The measured gain and noise figure performances of the RF front end are plotted in Figure 9. The measurements were done by probing intermediate test ports at the TIA output. The gain is measured by applying the RF and LO signals by using signal generators and reading the output power level by using a spectrum analyzer (N9030B of Keysight Technologies Inc., Santa Rosa, CA, USA). The measured passband gain of the RF front end is +42.2 dB. As shown earlier in Figure 5, the on-chip feedback components R\({}_{1}\) and C\({}_{1}\) of the TIA are tunable. By controlling these, the TIA bandwidth is tuned between 3.4 and 9.5 MHz in eight steps. Among them, Figure 9 only displays three selected curves corresponding to the minimum 3.4 MHz, medium 4.9 MHz, and the maximum 9.5 MHz conditions for the TIA bandwidth. Figure 8: Measured S\({}_{11}\) of the receiver. Figure 7: Chip micrograph. For the noise figure measurement, the total output noise power \(P_{n,out}\) with the input port terminated by 50 \(\Omega\) is measured by using the spectrum analyzer. With \(P_{n,out}\) and the receiver's power gain \(G_{\mathrm{P}}\) are known, the receiver noise figure is calculated by (\(P_{n,out}+174\) dBm\(/\)Hz \(-\)\(G_{P}\)). This method is convenient because it does not need a noise source or noise figure meter and also ensures sufficient accuracy because the noise floor level of the spectrum analyzer is more than 30 dB lower than \(P_{n,out}\). The measured noise figure at the low-IF band of 150-450 kHz is given by 3.7-4.5 dB. Assuming that a non-coherent detection for binary frequency shift keying (BFSK) signal is adopted, the minimum required SNR should be 14 dB for achieving a bit error rate (BER) of \(10^{-6}\). In practice, the minimum BER required by a raw RF radio excluding a digital processor can be as high as \(\sim 10^{-3}\)[5], and the required SNR for this can be further lower by 3 dB, that is, only 11 dB. However, in order to take various practical errors and margins into account, we decide to use 14 dB for the minimum required SNR in the following discussions. Note that the receiver sensitivity \(P_{sens}\) is given by  
\[P_{sens}=-174(\mathrm{dBm}/\mathrm{FHz})+NF+10\log(B)+SNR_{min} \tag{9}\]  
where \(NF\) is the receiver noise figure, \(B\) is the signal bandwidth, \(SNR_{min}\) is the minimum required SNR. With \(SNR_{min}=14\) dB, \(B=300\) kHz, and \(NF=4.5\) dB, the receiver sensitivity \(P_{sens}\) is calculated to be \(-100.7\) dBm or 2.06 \(\mu\)Vrms. This sensitivity performance is comparable to [12; 15] and much better than [5; 13]. Figure 10 shows the measured frequency responses of the complex BPF. The measured curves exhibit the bandwidth tuning and image rejection performances at a medium gain condition.