## 3 Designs  
Figure 3 shows the architecture of the MedRadio RF receiver. It is designed in an RF CMOS process. The receiver comprises a low-noise amplifier (LNA), transconductance (Gm) stage, quadrature down-conversion mixer with IM2 calibration, trans-impedance amplifier (TIA) with dc offset calibration (DCOC), three-stage variable gain amplifiers (VGAs), complex bandpass filter (BPF), fractional-N phase-locked loop (PLL) synthesizer, and a divide-by-4 local oscillator (LO) generator. The receiver takes a low intermediate-frequency (IF) architecture employing a quadrature single down-conversion scheme. The IF frequency is set equal to the channel bandwidth of 300 kHz so that the down-converted IF band resides in 150-450 kHz. The image band of the desired RF signal is rejected by the complex BPF. As shown in Figure 3, the complex BPF comprises two-stage complex biquads and three-stage VGAs. The detailed block diagram of the single-stage complex biquad is shown in Figure 4a. The unit biquad is based on a modified Tow-Thomas low-pass filter (LPF) structure in which the lossless integrator block (OPA\({}_{1}\), C\({}_{1}\)) is put before the lossy integrator block (OPA\({}_{2}\), R\({}_{3}\), C\({}_{3}\)). Since the second-order filtering is given by the unit biquad, the overall two-stage complex BPF presents a fourth-order bandpass filtering characteristics. Figure 4b illustrates how the low-pass characteristics of the unit biquad are translated to the complex bandpass characteristics. The cross-interconnecting resistors R\({}_{\rm xa}\) and R\({}_{\rm xb}\) that are placed between the I- and Q-path biquads as shown in Figure 4a shift the complex conjugate poles to real poles, resulting in the original low-pass filter response being shifted to the desired complex bandpass filter response, which gives the image rejection capability [25]. For optimal image rejection performance, the center frequency \(f_{o}\) is equally set to the channel bandwidth. As a result, the image component at the negative frequency band at \(-f_{o}\) is suppressed with respect to the wanted positive frequency band at \(+f_{o}\). To cope with process variability and also to support variable channel bandwidth modes, key performance parameters of the complex biquad are tunable by realizing the on-chip resistors and capacitors in a switched value structure. The resulting switched tuning ranges are given by 34-136 k\(\Omega\) with 2-bit control for R\({}_{1}\), 82-103 k\(\Omega\) with 3-bit control for R\({}_{3}\), and 0.6-7.35 pF with 4-bit control for C\({}_{1}\) and C\({}_{3}\), while R\({}_{2}\) and R\({}_{4}\) are fixed to 135 k\(\Omega\). Then, the overall complex BPF shows a tunable gain of \(-\)22-+45 dB, tunable center frequency of 0.25-3 MHz, tunable bandwidth of 0.23-2.7 MHz, and tunable quality factor of 0.9-1.1. In addition, the passband flatness is also tunable by independently controlling the on-chip R\({}_{\rm xa}\) and R\({}_{\rm xb}\) in the range of 78-106 k\(\Omega\) so that the band-edge gain difference is adjusted in the range of \(-\)1-+1 dB [25]. Figure 4c is the schematic of the operational amplifiers OPA\({}_{1}\) and OPA\({}_{2}\). It is a fully differential two-stage amplifier with a dc common-mode feedback (CMFB). The first stage is a differential pair having \(p\)-FET input pair of M\({}_{1,2}\) and \(n\)-FET active load of M\({}_{3,4}\), and the second stage is \(n\)-FET common-source stage of M\({}_{5,6}\). Designed parameters of the FET's gate width/length are 200/0.2 \(\upmu\)m for M\({}_{1,2}\), 80/0.5 \(\upmu\)m for M\({}_{3,4}\), 64/0.2 \(\upmu\)m for M\({}_{5,6}\), 192/0.5 \(\upmu\)m for M\({}_{7,8}\), and 480/0.5 \(\upmu\)m for M\({}_{9}\). The dc bias currents are 42 \(\upmu\)A for M\({}_{9}\) and 18 \(\upmu\)A for M\({}_{7,8}\). The frequency compensating R\({}_{\rm C}\) and C\({}_{\rm C}\) are 4 k\(\Omega\) and 0.9 pF, respectively. Figure 3: The MedRadio RF receiver architecture. The LO signal is generated by the fractional-N PLL frequency synthesizer.