# University of Twente Student Theses

## Approximation of an ideal bandpass filter using an N-path filter with overlapping clocks and harmonic rejection

Fortgens, L.C.
(2012)
*Approximation of an ideal bandpass filter using an N-path filter with overlapping clocks and harmonic rejection.*

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Abstract: | N-path filters are switched filters that allow baseband transfer functions to be transformed to an arbitrary frequency. These filters have gained renewed interest after many years of absence due to the availability of high speed transistors enabling N-path filters to be used at gigahertz frequencies. Much research on N-path filters has been done already starting in the 1960s [1]. Most authors use a first-order RC low-pass filter as a baseband network to create a band-pass filter resembling a high-Q LC tank. Analytical solutions are available for such networks. Other functions such as notch filters and constant delays are possible. The focus of this thesis is the band-pass filter. The use of the N-path topology for a band-pass filter allows for narrowband filters which are easily tuned as the centre frequency is determined by a clock signal. The filter shape is dictated by the baseband transfer function. The tuneability of this filter makes it suitable for upcoming applications such as software defined radio (SDR). Practical N-path filters suffer from two problems that limit their applicability. The first is that it does not only pass the desired frequency content but also the contents that are present around the harmonics of the clock much like comb filters (harmonic transfer). This puts strong demands on any mixer in a subsequent stage which has to supress these harmonics. The second problem is that the filter will fold the harmonics and into the desired signal at the fundamental harmonic (harmonic folding). Strong interferers at these frequencies can corrupt the desired signal. This work aims to provide solutions to these problems. The proposed solution against harmonic transfer is the use of harmonic rejection mixers instead of the simple switches that are commonly used. This idea conserves the folding properties of typical Npath filters while effectively suppressing the band-pass filters at higher harmonics of the clock. These mixers can easily be implemented by impedance scaling at the cost of area in each path. The suppression of higher harmonics greatly relaxes the design of a subsequent mixer stage. Each harmonic rejection mixer requires roughly switches and impedances. This means that the area required for switches and impedances scales with which may be problematic for large . The harmonic folding can be resolved by increasing the number of clock phases. Creating nonoverlapping clocks with a high number of phases is difficult at RF as it generally requires very high frequencies. The option of using overlapping clocks was explored to allow for other clock generation techniques to be used such as ring oscillators. The idea is proven to be possible provided that a good adder is available. A filter combining harmonic rejection mixers and overlapping clocks has been simulated to show their potential. This filter uses 24 clock phases with a duty cycle of 0.125 . The harmonic rejection mixers use 12 phases with a switched capacitor low pass filter. The resulting filter has a bandwidth of 8MHz , a noise figure of 4.8dB and a gain of 7.2dB . The transfer function shows no harmonic transfer up to the 11th harmonic and the first folder is the 23rd harmonic. Although each application requires different specifications, the filter shows the potential of the two techniques. |

Item Type: | Essay (Master) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 53 electrotechnology |

Programme: | Electrical Engineering MSc (60353) |

Link to this item: | http://purl.utwente.nl/essays/69636 |

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