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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 op-amp, 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 time-invariant circuits to periodic inputs. 1 Prelab 1. Determine the compact-form 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 co-sinusoidal 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