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Nonlinear Echo Cancellation
Published in Andrzej Borys, Nonlinear Aspects of Telecommunications, 2018
where c(i), i 0, 1, 2, ..., Mê 1 represent the complex-valued filter coefficients. Having the expressions describing the bandpass echo channel and echo canceller, we can illustrate a means of cancellation in the case of bandpass voiceband channel. This is shown in Figure 2.45. In Figure 2.45a, Re va(t) means the received realvalued signal, except for the echo signal; the latter signal is denoted by Re ea(t) in the figure. We assume that the effect of filtering through the received filter is already included in the signals mentioned above. The sum of these signals, that is, Re ea(t) va(t) , provides an input signal to the so-called phase splitter,24 whose behavior is explained in Figure 2.45b. As shown in this figure, the task of the phase splitter is to provide an analytic signal from a real-valued one; its implementation is through the use of the Hilbert transform filter. For more explanation, compare the scheme of Figure 2.45a with that presented in Figure 2.40. The complex-valued transversal filter in Figure 2.45a works with the input signal as a complex-valued data symbol stream provided by the encoder shown in Figure 2.38. The output signal of the complex-valued transversal filter in Figure 2.45a is given by
Design and implementation of 75~110 GHz elliptical dual balun in 90 nm CMOS for W-Band transceiver
Published in International Journal of Electronics, 2019
In a star double-balanced mixer or a four-way PA, the dual balun is applicable for four-way power splitting. Figure 2(a) exhibits the block diagram of the proposed four-way PA for achieving high Pout, small chip size, and high PAE. Instead of the area-consuming four-way Wilkinson power combiner, a miniature and high-performance dual Y-shaped combiner (in conjunction with a T-matched network) is used at the output of the PA (Lin & Nguyen, 2017). The outputs of the dual balun are two pairs of differential signals. In order to attain in-phase outputs, the PA units following ports 3 and 5 of the dual balun should be anti-phase with those following ports 2 and 4. Figure 2(b) exhibits the proposed two anti-phase PA units with the same gain, which can be applied to the PA in Figure 2(a). In addition, instead of the four-way Wilkinson power splitter, the proposed PA only takes one low-loss miniature dual balun to averagely split the input signals into four ways. The chip size of the dual balun (0.0256 mm2) is only 14.6% of the size (0.175 mm2) of the corresponding four-way Wilkinson power splitter (see Figure 1(b)), and is even smaller than the size of the single balun (0.0288 mm2) in Lin, Liu, and Wen (2014) and the Wilkinson-power-splitter-based two-way 180° out-of-phase splitter (0.15 mm2) in Lee, Chen, and Lin (2011). Therefore, high Pout, miniature chip size, and high PAE can be attained simultaneously.