Experiment 7 - Frequency Response of Filters | ECE 1201, Lab Reports of Electrical and Electronics Engineering

Download Experiment 7 - Frequency Response of Filters | ECE 1201 and more Lab Reports Electrical and Electronics Engineering in PDF only on Docsity! ECE 1201 – Electronic Measurements and Circuits Laboratory-Fall 2008 Experiment #7 -- Frequency Response of Filters INTRODUCTION With circuits containing energy storage elements, we are often interested in the steady state response rather than the transient response. An important special case arises when the sources in a system are periodic. Periodic sources are either sinusoidal or can be modeled as a linear sum of sinusoids. An analog signal is filtered by using it as the input to a circuit that changes the signal’s frequency content. Some examples of analog filtering are the use of filters to to attenuate 60 Hz or 120 Hz “noise” due to the power line or low-pass filtering to reduce “hiss” in audio. Usually, we think of filter circuits in a 2-port sense, where we have an input and output port with input and output signals represented by voltages or currents. The circuits shown on the following page are 2-port circuits with the function generator (FG) providing the input. In this lab, we’ll focus on voltage signals. We characterize a filter by its “frequency response” i.e. the transfer function as a function of frequency. The transfer function is the output voltage divided by the input voltage. The transfer function has two independent parameters: magnitude and phase. A plot of the frequency response or transfer function of a circuit shows the variation of its magnitude and phase with frequency. For a variety of reasons, both magnitude and phase are usually plotted against the log of frequency (usually in radians). Further, the magnitudes are also typically plotted on a log scale (i.e., in terms of decibels (dB) =20*log10[magnitude]). Phase is usually plotted in units of degrees (not radians) over the range (-180, +180] degrees. EXPERIMENT A. Single Stage Filters Three single stage filter circuits are given on the following page. The first two are passive and the third is an active filter (so-called because it employs an op- amp).. The third filter is an active filter and is particularly easy to analyze since the transfer function can be expressed as Vo (jω) / Vω) / V) / Vi (jω) / Vω) / V) = - Z2 (jω) / Vω) / V) / Z1 (jω) / Vω) / V), where Z2 is the impedance in the feedback loop (i.e. C in parallel with R2) and Z1 is the impedance in the input leg of the circuit (i.e. R1). For each of these three circuits, do the following: 1. For the pre-lab derive the transfer function: H(jw)=Vo(jw)/Vi(jw) for each of the three filters. Use impedance notions and voltage divider relationships. Include inductor resistance in your calculations (this will require you to measure the resistance of the inductors before you do the prelab). For each circuit plot the magnitude and phase responses using linear axes. Then plot these more carefully using a log scale for frequency, a log scale for magnitude and a linear scale for phase (Bode plots). MatLab can do these calculations automatically (FREQS function). To use this function the transfer function must be written as a quotient of two polynomials in power of s = j, These amplitude and phase plots from FREQS should be included in the prelab. Please plot the frequency scale as a linear scale. Next, use Pspice to generate plots of the amplitude of the transfer functions versus frequency. The Pspice calculations can be done either as part of the pre-lab or as part of the work that you do in lab. Characterize the kind of filter each seems to represent: e.g. low-pass, high-pass, band-pass, band-reject, etc. 2. Design an experimental procedure, applicable to all three circuits, to determine the frequency response of each of the circuits. (Have this design included in your pre-lab. The design should suggest the frequency range to be scanned and the voltage amplitudes to be used.) In the lab build each circuit and evaluate its magnitude response over an appropriate range of frequencies. Be sure to take a large number of data points over the frequency range where the filters’ responses are changing rapidly. You may assume that the capacitors are ideal, but you will want to make separate DC measurements of the resistance of all inductors. In this part you may use any available Labview programs to facilitate your data acquisition (e.g., the automatic measurement of a magnitude response). The link to the sweep demo (instrument interface) is found on under-ee on “conmael1.ee.pit.edu” (L), ee1201. You will need to follow the Labview instructions in order to use this link. Filter 1: R = 510  ; L = 1mH Filter 2: C = .1 F ; L = 27 mH; R = 2 K FG Vi Vo R L + - FG Vi C L R Vo