## 2 Design of Low-Pass Filter  
### Reconfigurable Structure of the Filter  
A wideband reconfigurable integrated LPF for SDR transceivers has to cover bandwidths ranging from several to hundreds of megahertz. The proposed wideband reconfigurable integrated LPF is designed to have a bandwidth tuning range from 2.5 MHz to 200 MHz, which allows it to work with all 5G NR FR1 and FR2 and nearly all LTE bandwidth configurations, excluding 1.4 MHz and 3 MHz options [16; 17]. The structure of the proposed wideband reconfigurable integrated LPF for SDR transceivers is shown in Figure 2. Due to high requirements for bandwidth tuning range, the LPF is split into two paths--low frequency path (LP) and high frequency path (HP), where each path can be tuned over a decade. Moreover, this approach of split LPF paths gives several advantages to the design:  
1. Optimization of the active stage. This feature allows optimizing layout size and power dissipation for each path, since size and current consumption of the LP active stage can be scaled in respect to HP, while maintaining same performance. 2. Compensation of each stage over the entire tuning range for each path can be optimized for large signal response. 3. Count of passive elements of the tuning banks in the LPF can be distributed in both paths, which reduces the size of the bandwidth control step over the entire LPF tuning range for the same bit count of the control word. Hence, size of the control step can be reduced without adding additional parasitic capacitance due to a large number of switching elements. 4. If the design requires, LP and HP can be split into two separate and independently controlled LPFs that can work with narrow and wide bandwidths simultaneously, for example in 5G NR NSA implementation. The configuration of the order of the proposed LPF is achieved by designing both LP and HP paths with two independently controlled, interconnected filter stages--a 2 nd and a 4 th order implementation with a low-pass response. As shown in Figure 2, they are respectively designated as MFB_LP and LAD_LP for LP path, and MFB_HP and LAD_HP for HP path. Each path can be configured to either one of the stages or their combination. This allows each path to be configured as 2 nd, 4 th, or 6 th order LPF. Design of the Filter Stages  
Active-RC topology is chosen for each stage of the filter, due to its high linearity and robustness with insensitivity to the parasitics compared to gm-C designs [18]. The 2 nd and 4 th order stages, respectively, use fully differential multiple feedback (MFB) topology and ladder filter (LAD) topologies. Their schematics are respectively shown in Figures 3 and 4. Since MFB topology uses a single operational amplifier (OA), as  
Figure 2: Structure of the proposed wideband reconfigurable integrated low-pass filter. opposed to two active stages in a biquad, it can be used for low power applications, while having excellent linearity performance. Ladder filter topology provides a more robust design for higher order filters against PVT. MFB stage has two differential inputs V\({}_{\text{ip1}}\), V\({}_{\text{in1}}\) and V\({}_{\text{ip2}}\), V\({}_{\text{in2}}\). The first differential input is used when the active filter path is configured as a 6 th order LPF, while the second differential input is used for 2 nd order LPF configuration. This dual input approach removes the need to have two bypass transmission gates for each stage of the filter path--only the 2 nd order stage is bypassed via a transmission gates under large signal conditions. These transmission gates in Figure 2 are marked as S1_LP and S1_HP for LP and HP paths, respectively. The S2 transmission gate in MFB topology (Figure 3) is placed at the summing node to achieve better linearity performance at large signal conditions. Butterworth approximation is used for all stages in both LP and HP. Butterworth is chosen due to lower Q, which in turn relaxes OA gain-bandwidth product (GBWP) requirement.