342lab1s (1)

342lab1s (1) - ECE-342 Fall 2008, Lab 1 Due Wed, Sept. 24,...

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Unformatted text preview: ECE-342 Fall 2008, Lab 1 Due Wed, Sept. 24, 4:00 PM Overview The schematic given below shows an op-amp active bandpass filter. You are to complete the design, and provide simulation and measured performance. Background The schematic above is called a ”Multiple Feedback Bandpass” (MFBP) active filter. It provides one possible method of using a single op-amp to implement the generic 2 nd order bandpass transfer function given by H ( s ) = K ω p Q p s s 2 + ω p Q p s + ω 2 p . (1) The values ω p and Q p are called the “pole frequency” and the “pole Q” respectively. The bandpass characteristic | H ( jω ) | is (roughly) centered at ω = ω p , where the filter gain is | H ( jω p ) | = | K | . Small values of Q p result in very broad frequency responses about the center frequency, while larger values give sharp filter characteristics. As Q p becomes large, the value of Q p reflect the ratio of the center-frequency to the 3-dB bandwidth. (So, for example, a 20 kHz 2 nd order bandpass filter with 3-dB bandwidth 1 kHz would require ω p ≈ 2 π (20 × 10 3 ) and Q p ≈ 20 .) Higher order filters can be formed by cascading MFBP sections, where each section is dedicated to implementing a complex-conjugate pair of poles. For conjugate-pole locations of p i = σ ± jω , the resulting values of ω p and Q p are ω p = q σ 2 + ω 2 Q p = 1 2 r 1 + ω 2 σ 2 (2) Tasks 1. Analysis (a) Assuming ideal op-amp characteristics derive the transfer function of the above active filter. (Both lab notebooks, and the lab report, should include the derivation.) You should be able to show that v o ( s ) v in ( s ) =- 1 R 1 C 1 s s 2 + 1 R 2 C 1 + 1 R 2 C 2 s + 1 R 1 R 2 C 1 C 2 (3) (b) To ease component matching requirements, most designers select a single convenient capacitor value C = C 1 = C 2 . Under this assumption, find the values of ω p , Q p and K in terms of R 1 , R 2 , and C . (You’ll find that for this circuit, the gain cannot be set independently from Q p . The gain can be lowered by using a resistor divider on the input, but increasing the gain would require a second amplifier stage.) Continued 2. Design: Each group is to complete the design of the filter under the restrictions given in the table below. In theEach group is to complete the design of the filter under the restrictions given in the table below....
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342lab1s (1) - ECE-342 Fall 2008, Lab 1 Due Wed, Sept. 24,...

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