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UNIVERSITY OF CALIFORNIA, SAN DIEGO Department of Electrical and Computer Engineering Bang-Sup Song 1 ECE163 Lecture #5: Switched-Capacitor Filter All active filters can be implemented using biquads as building blocks. Biquad is made of two RC or G m -C integrators. Time constant of an RC integrator is set by resistor and capacitor values. Discrete components can be selected to be as accurate as within 1%, but in integrated circuit technologies, resistor and capacitor values vary by as much as +/ - 20%. As a result, filters implemented with such inaccurate RC components have widely-spread cut-off frequencies. The main motivation behind using switched-capacitor filter is the accuracy of its time constant, which is determined by the accurate crystal clock and the capacitor ratio. v o R C v i C S v i v o C φ 1 φ 2 Continuous-Time Discrete-Time on off on off on off on off on off on off on off φ 1 φ 2 Fig. 5.1: Switched-capacitor principle. Consider two ideal switches which can be turned on and off alternately at a switching rate of f S , using two non-overlapping clocks, φ 1 and φ 2 , as shown in Fig. 5.1. When the sampling capacitor C S is connected to the source during φ 1 , it is charged to v i . When it is connected to the output v o during φ 2 , some of the stored charge is transferred to the output capacitor C. As this charge transfer occurs at a rate of f S , it is in effect equivalent to a current flowing from the source side to the output as shown in Fig. 5.2. ( ) ( ) S S o i eff S S o i S S o i C f I v v R C f v v Qf I C v v Q 1 = - = - = Δ = - = Δ (5.1) Therefore, a capacitor switched back and forth works as an effective resistance, and it performs as a low-pass filter together with a capacitor. Since the effective resistance is defined as in (5.1), the filter cut-off frequency is independent of RC component values as shown below.
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Department of Electrical and Computer Engineering Bang-Sup Song 2 ECE163 R eff = 1/f S C S C S f S C C 1M Ω 1pF 100kHz 10pF 100pF Fig. 5.2: Switched-capacitor LPF. C C f C R f S S eff dB π 2 2 1 3 = = - (5.2) For example, to make a voice-band RC filter with a cut-off frequency of 1.6kHz, a 1M Ω resistor and a 100pF capacitor are needed. If switched-capacitor circuit is used, even a 10M Ω effective resistance can be implemented by switching a 1pF capacitor at 100kHz rate as explained in Fig. 5.2. Two capacitor values of 1 and 10pF are small enough to integrate in monolithic forms. Furthermore, the accuracy of the cut-off frequency is only set by the crystal frequency f S and the ratio of two capacitors, which can be closely matched within 0.1% in CMOS integrated circuits. Such an advantage is so dramatic both in the performance and size, and most monolithic filters for voice, audio, and video applications have been implemented using switched-capacitor filters. Fig. 5.3: Switched-capacitor integrator.
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