# High Performance Receiver Design for RX Carrier Aggregation
## 2 Receiver Architecture
#### Single-\(g_{m}\) Receiver Architecture  
Figure 3 shows the conventional zero-IF receiver architecture with architectural implications. Low-noise amplifier (LNA) is the cascade of V-I (\(g_{m}\)) and I-V (load) conversion, and Mixer requires separate trans-conductance (\(g_{m}\)) to drive the passive switching mixer. A low-pass filter with I-V conversion is performed by the single block in either passive (\(R\parallel C\)) or active (trans impedance amplifier--TIA) implementation. The reason for having an LNA is best illustrated with the Friis equation [9] expressed in Equation (2). Due to the large gain and low noise figure of the LNA (\(G_{1}\) and \(NF_{1}\), respectively), system noise performance is improved with the suppression of subsequent noise coming from mixer and baseband amplifiers. On the other hand, large gain--which is desirable for noise performance--is detrimental to the linearity performance manifested by the cascade \(IIP_{3}\) equation given in Equation (3) [10]. Large gain due to the front-end amplifies the desired signal as well as large interferences in both in-band and out-of-band. Large interferences either saturate the baseband or worsen the linearity performance of the baseband without proper filtering. Then, low input impedance and the jammer filtering in a broadband IF frequency is highly desirable, both of which are not easily attainable with the current state of the art. On the other hand, the linearity of LNA itself is less of a concern compared to subsequent active stages. Then, we do not adopt the linearization technique, although there have been many efforts to improve the linearity of the LNA [11; 12; 13]. \[NF=NF_{1}+\frac{NF_{2}-1}{G_{1}}+\frac{NF_{3}-1}{G_{1}\cdot G_{2}}+\cdots \tag{2}\]  
\[\frac{1}{A_{IIP_{3}}^{2}}\approx\frac{1}{A_{IIP_{3},1}^{2}}+\frac{A_{v,1}^{2}} {A_{IIP_{3},2}^{2}}+\frac{A_{v,1}^{2}\cdot A_{V,2}^{2}}{A_{IIP_{3},3}^{2}}+\cdots \tag{3}\]  
The receiver architecture based on a single low-noise trans-conductance amplifier driving a current-mode passive mixer loaded by a low-impedance trans-impedance closed-loop amplifier has been widely adopted recently due to its beneficial features in terms of noise and linearity [8]. Figure 4 shows the conceptual diagram of the single-\(g_{m}\) receiver. I-V conversions of the LNA are eliminated, and thus the remaining V-I conversion is performing as LNTA. Since the output of LNTA is in the current domain, the trans-conductance of the mixer can also be eliminated. Due to the single-\(g_{m}\) prior to the baseband low-pass filter and I-V conversion, the large voltage swing present in traditional Gilbert-cell and voltage-mode mixers are eliminated. The virtual ground of the TIA minimizes the distortion caused by large in-band and out-of-band interferences. Low-pass filtering performed inside TIA improves the linearity of the receiver system. Due to the low-pass filtering prior to the first I-V conversion in the baseband, the receiver's robustness to the blocker is improved by the filtering effect. Assume for simplicity that the single blocker is present at the \(m\)th harmonic frequency of LO (Local Oscillator) frequency and the order of the low-pass filter is \(n\). Then, enhancement in the blocker tolerance (\(B_{\rm 1 dB}\)) is expressed as follows. \[B_{\rm 1 dB,enhancement}\approx n\cdot 20\cdot log_{10}\left(\frac{|f_{B}-m \cdot f_{LO}|}{BW}\right)+|HR_{m}| \tag{4}\]  
Figure 3: Conventional zero-IF (intermediate frequency) receiver architecture. where \(f_{B}\) is the blocker frequency and \(HR_{m}\) is the harmonic rejection ratio of the switching mixer. Due to the single-\(g_{m}\) of the receiver, large trans-conductance is essential to maintain low NF and low sensitivity. Inductor-degenerated LNA in common-source configuration is ideal in that respect due to the passive voltage gain coming from the impedance matching network. Moreover, simultaneous noise and power match is achieved by shifting the optimum noise impedance \(Z_{opt}\) to the desired value [14].