# A Fully Integrated Low-Power Multi-Mode RF Receiver for BDS-3/GPS
## 4 Receiver Design
### RF Front-End  
The RF front-end includes LNA, ACTBA, and GMT circuits, shown in Figure 3. Considering the cost, this design aims to avoid using an off-chip LNA when the interference is weak. Therefore, the on-chip LNA must have sufficiently low NF and high gain. For navigation frequency, if the source inductor of LNA is spiral, a large area of 220 \(\upmu\)m \(\times\) 220 \(\upmu\)m is needed. An active inductor wastes voltage headroom, deteriorating the amplifier's large signal output capability, and introducing noise. Therefore, inductors \(L_{1}\) and \(L_{2}\) are realized by bonding wires [5], which are represented by dotted lines in Figure 3. The simulated values of \(L_{1}\) and \(L_{2}\) are 2 nH and 0.6 nH, respectively. The length of the bonding wire corresponding to 2 nH seems to be long, but \(L_{1}\) and the off-chip inductor \(L_{0}\) are connected in series; this long length can be reduced by increasing \(L_{0}\). The die position and the height of the bonding wires can be controlled on the package, thus controlling the length of the bonding wires in the range of \(\pm\)10%. At the matching frequency, (2) holds. \[\omega=2\pi\mathrm{f}=\sqrt{\frac{1}{\left(L_{\mathrm{g}}+L_{\mathrm{s}}\right) C_{\mathrm{gs0}}}}, \tag{2}\]  
\(L_{g}\) is the gate inductance, \(L_{s}\) is the source inductance, and \(C_{\mathrm{gs0}}\) is the parasitic gate-source capacitance of \(M_{0}\) in Figure 3. According to (2), \(\mathrm{f}\) varies from \(-\)1.98% to 2.17%, which is acceptable. The cascode circuit composed of \(M_{0}\) and \(M_{1}\) can effectively reduce the LO leakage to the antenna. The output-matching network is composed of \(R_{2}\), \(C_{1}\), and \(L_{3}\), where \(R_{2}\) and \(C_{1}\) are reconfigurable; the LNA has an improved in-band gain and higher out-of-band rejection than the traditional resistive load [8]. \(R_{2}\) is used to adjust the Q of the resonant network at the output of the LNA, thereby adjusting the gain. That is, if the measured maximum gain of the entire system is low or high, the gain of the LNA can be manually adjusted through \(R_{2}\) at the factory. We use an inductor instead of a current mirror, as the load consumes a very small voltage margin and achieves a higher resonant load, thus improving linearity and reducing power. \(L_{3}\) is a spiral inductor with a quality factor of 11.9 and a value of 5 nH. However, the resonant frequency of this output-matching network changes with the variation of the corner and temperature. Therefore, the resonant frequency needs to be corrected by adjusting \(C_{1}\) when leaving the factory. The simulation results show that the NF of the on-chip LNA is 1.3 dB with high gains of 23.7 dB and \(IP_{\mathrm{1 dB}}\) is \(-\)12.92 dBm. The ACTBA [8] shown in Figure 3 follows the LNA through the capacitor \(C_{2}\) with a value of 670 fF and converts the RF signals into differential signals, which are then down-converted to in-phase and quadrature low-IF differential signals by GMT. The cross-coupled structure composed of \(M_{3}\), \(M_{4}\), \(C_{3}\), and \(C_{4}\) can reduce the noise from \(M_{2}\)[14; 22], and further reduce the Miller effect from the input transconductor stage of the ACTBA [8]. Ignoring the channel length modulation and body effects, the differential signal with equal amplitude and phase difference of 180\({}^{\circ}\) can be obtained at output nodes \(output\) and \(output\), as long as \(\mathrm{g}_{\mathrm{m3}}R_{3}=\mathrm{g}_{\mathrm{m4}}R_{4}\) holds. In this design, \(R_{3}\) and \(R_{4}\) are equal to 1.144 k\(\Omega\). A certain phase error will be introduced. However, by reasonably adjusting the size of the devices in the ACTBA, the phase error between \(output\) and \(output\) can be controlled to less than 0.2\({}^{\circ}\)  
Figure 2: Receiver diagram. which does not affect the navigation performance. The simulation results show that the gain of the ACTBA is 18.2 dB, and the cascaded NF with LNA is 1.3 dB. The differential mixer is used to suppress common-mode interference.