# A Novel Active Polyphase Filter Employing Frequency-Dependent Image Rejection Enhancement Technique
## 1 Introduction  
Nowadays, wireless communication systems pursue higher carrier frequency and wider channel bandwidth to achieve high data rates and low transmission delay [1, 2, 3, 4]. Among the current mainstream receiver architectures, the superheterodyne architecture receiver requires multiple down-conversion processing and off-chip high-performance filters. This does not meet the increasingly demanding size, weight, and power (SWaP) requirements for receivers in applications [5, 6]. In addition, superheterodyne architecture receivers are not suitable for broadband applications due to their inherent narrow-band characteristics. Direct down-conversion architecture receivers, consisting of zero intermediate frequency (zero-IF) and low intermediate frequency (low-IF) architecture receivers, are more in line with the requirements of existing and future wireless communication applications for receiver chips [7, 8, 9, 10]. The zero-IF receivers convert the incoming radio frequency(RF) signals directly to the baseband signals, while the low-IF receivers convert the RF signals to intermediate frequency (IF) signals. Zero-IF receivers face problems such as in-phase quadrature (I/Q) imbalance, local oscillator (LO) leakage, direct current (DC) offset, and flicker noise [11]. Furthermore, the zero-IF receiver has one more IF signal processing path that contains a broadband low-pass filter (LPF), a high-accuracy programmable gain amplifier (PGA), and a costly off-chip high-performance analog-to-digital converter (ADC) than the low-IF receiver. To sum up, compared to other architectures, the low-IF architecture receiver has excellent overall performance in terms of received signal quality, signal bandwidth, chip area, and power consumption [12]. The low-IF receiver must have a strong ability to reject image frequency signals. Otherwise, after down-conversion, image frequency noise and potential interfering signals will overlap with the desired signal, severely degrading the signal-to-noise ratio (SNR) of the receiver [13]. There are currently two schemes for image rejection in low-IF receivers. On the one hand, image rejection can be achieved by adding a band-pass filter (BPF) that places the desired frequency in the passband and the image frequency in the stopband before down-conversion. Due to the relatively low-quality factor of the on-chip BPF, the IF must be high enough to achieve a great image rejection ratio (IRR). For example, 7 GHz as in [14; 15] or up to 16 GHz as in [16]. However, such a high operating frequency poses significant challenges to the receiver IF module, including the channel selection filter, PGA, and ADC. Overall, the use of a BPF before down-conversion is not a cost-effective and high-performance solution for image rejection in low-IF receivers. On the other hand, image rejection can be achieved by using a complex filter after down-conversion. In the complex frequency domain, the complex filters can be configured as the complex band-pass filters (CBPFs) or the complex band-stop filters (CBSFs). Few CBPFs operate at frequencies above 100 MHz [17]. This cannot cope with the increasing IF frequencies of low-IF receivers. For example, several low-IF receivers have IF signals with frequencies up to hundreds of MHz or even several GHz [18]. On the contrary, several CBSFs have been proposed to meet the IRR requirements of low-IF receivers at relatively high IF frequencies [19; 20]. Almost all existing schemes are passive topologies based on multistage RC polyphase filters (RC-PPF) or transformer-based couplers. The passive topologies are relatively simple to achieve image rejection at high frequencies, but high insertion loss and a large silicon area are unavoidable problems [21; 22]. In addition, to address the possible IRR degradation due to process, voltage, and temperature (PVT) variations in the RC-PPF [23], conventional solutions for on-chip passive component tuning include capacitor or resistor arrays, which allow only discrete tuning and limited minimum resolution of tuning.