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Unformatted text preview: L3 Frequency response and Fourier series In this lab you will build an active bandpass filter circuit with two capacitors and an opamp, and examine the response of the circuit to periodic inputs over a range of frequencies. The same circuit will be used in Lab 4 in your AM radio receiver system as an intermediate frequency (IF) filter, but in this lab our main focus will be on the frequency response H ( ) of the filter circuit and the Fourier series of its periodic input and output signals. In particular we want to examine and gain experience about the response of linear timeinvariant circuits to periodic inputs. 1 Prelab 1. Determine the compactform trigonometric Fourier series of the square wave signal, f ( t ) , with a period T and amplitude A shown in Figure L3.1. That is, find c n and n such that f ( t ) = c 2 + n =1 c n cos( n o t + n ) , where o = 2 T . Notice c 2 = 0 . How could you have determined that without any calcula tion? f ( t ) T A A t Figure L3.1: Square wave signal for prelab. 335 L3 Frequency response and Fourier series 5 k v o ( t ) v i ( t ) + 1 k 1 . 7 k 3 . 6 k 3 . 6 k . 01 F . 01 F v o ( t ) / 2 Figure L3.2: Circuit for analysis in prelab and lab. 2. Consider the circuit in Figure L3.2 where v i ( t ) is a cosinusoidal input with some radian frequency . a) What is the phasor gain V o V i in the circuit as ? (Hint: How does one model a capacitor at DC?) b) What is the gain V o V i as ? c) In view of the answers to part (a) and (b), and the fact that the circuit is 2nd order (it contains two energy storage elements), guess what kind of a filter the system frequency response H ( ) V o V i implements lowpass, highpass, or bandpass? The amplitude response  H ( )  of the circuit will be measured in the lab....
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 Spring '08
 Staff
 Fourier Series, Frequency, Wavelength

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