## 3 System Implementation
### Baseband Trans-Impedance Amplifier (TIA)  
After the LNA a current mode passive mixer driven by a 25% duty-cycle LO was used, followed by a baseband TIA, as shown in Figure 5. The TIA introduces a pole at 22 MHz to attenuate large OOB interferers. The TIA is based on a three-stage operational transconductance amplifier (OTA). The OTA design is based on a similar concept as the one in [30] but it has a wider bandwidth and is designed in 40 nm (versus 28 nm in [30]), which makes the design more challenging. In order to achieve wide bandwidth for better linearity instead of using Miller compensation capacitors, stability is ensured by introducing zeros both within the OTA and in the feedback network. The first stage of the TIA consists of PMOS telescopic--cascode amplifier designed to have high gain in order to ensure high linearity, while the second stage is a full differential pair designed with both moderate gain and distortion, and the third stage work is a complementary class AB, to ensure very high output voltage swing.  
Analysing the stability of the TIA, the following critical poles and zeros are identified. The first stage has a dominant pole, \(\omega_{\rm p,OTA,1}\) at 32 MHz and a high frequency zero, \(\omega_{\rm z,OTA,1}=1/({\rm R_{\rm c}}{\rm C_{\rm c}})\). There is also a second pole at high frequency, \(\omega_{\rm p,OTA,2}\approx{\rm G_{m,L}}/{\rm C_{L,1}}\) that must be well above the unity-gain loop bandwidth. To extend the bandwidth of the second stage, a feed-forward path is introduced through Rz and Cz. This introduces a zero-pole doublet, in which the pole, \(\omega_{\rm p,OTA,3}\) at \(1/({\rm R_{\rm c}}{\rm C_{\rm z}})\) is placed two times the zero frequency, and the zero is used to cancel out the pole introduced by the  
Figure 9: Noise figure of LNA with canceler as function of the phase shift.  
second stage finite output resistance, r\({}_{\rm o,2}\) and its load capacitance, C\({}_{\rm L,2}\). Simultaneously, the pole of the second stage, \(\omega_{\rm p,OTA,3}\) is compensated for by the zero of the first stage \(\omega_{\rm z,OTA,1}\). A second dominant pole at 5 MHz, \(\omega_{\rm p,OTA,5}\) is created through the feedback network and the third stage at \(1/({\rm R_{d}}//({\rm R_{F}}+{\rm r_{o}}){\rm C_{in}})\), where R\({}_{\rm F}\) is the feedback resistor, R\({}_{\rm d}\) is the driving resistance seen looking to the mixer and r\({}_{\rm o}\) is third stage finite output resistance. In fact, a large C\({}_{\rm in}\) (20 pF in this design) helps to filter out the blockers at high frequencies. With two dominant poles, the loop would not be stable. R\({}_{\rm in}\) is a small valued resistance placed in series with C\({}_{\rm in}\) to introduce a high frequency zero, \(\omega_{\rm z,OTA,3}\) at \(1/{\rm R_{in}}{\rm C_{in}}\) (around 700 MHz), which is placed before the GBW (at 1.5 GHz) to ensure stability. From the loop gain simulations shown in Figure 11, the loop has a DC gain of around 70 dB, 1.5 GHz GBW and a phase margin of 85\({}^{\circ}\). To ensure a stable DC quiescent point, a common-mode feedback circuit is introduced, and its output is connected to the PMOS of the last stage OTA, as shown in Figure 10.  
Figure 11: Loop gain magnitude and phase of the trans-impedance amplifiers (TIA).  
Figure 10: (**a**) Schematic of the three-stage operational transconductance amplifier (OTA); (**b**) TIA schematic.