EE2302 Passive Filters and Frequency esponse Objective he student should become acquainted with simple passive filters for performing highpass, lowpass, and bandpass operations. he experimental tasks also provide an introduction to Complex Frequency esponse and Phasor Algebra. Discussion Filters are used to remove unwanted frequency components from a signal. Filters can be implemented using a combination of active elements (independently powered elements like operational amplifiers) and passive elements (nonpowered circuit elements like resistors, capacitors, and inductors). Filters can also be constructed solely using passive elements. In this experiment, you will construct several simple passive filters and evaluate their performance. he frequency response is a complex gain as a function of frequency. he frequency response magnitude is the amplitude gain for a sinusoidal input at the given frequency. he frequency response's argument is the phase shift obtained for a sinusoidal input at the given frequency. he frequency response can be obtained by replacing the capacitor with the impedance 1/jωC and the inductor with the impedance jωl. he circuit is then analyzed treating these impedances as normal resistors. he output voltage divided by the input voltage (jω)/v i (jω) (typically a complex number for given circuit element values) is the frequency response. Prelab Determine the frequency response, (jω)/v i (jω), for each of the following filters. Let, C, and L be variables in these frequency responses. V i C Filter 1
V i L Filter 2 V i L C Filter 3 Procedure 1. Select the following components: a 470 Ω resistor, a 1 µf capacitor, and a 20 mh inductor. hese values are only approximate. Measure the actual resistance, capacitance, and inductance of these components, and record your answers on the data sheet. 2. Construct each of the filters (one at a time) using the selected components. 3. Connect the NI 5411 Function Generator output to the input terminals of each filter and Channel 1 of the NI 5102 Oscilloscope. Connect the filter output to channel 2 of the oscilloscope. Select a sinusoid output for the NI 5411 Function Generator with an amplitude of 200 mv Vp. 4. Set the Vertical lts/div control and Horizontal seconds/division controls for ease of measurement. 5. Measure the voltage gain (magnitude) and the phase shift of the output of each filter for the frequencies indicated on the data sheet. he voltage gain is the amplitude of the output signal () divided by the amplitude of the input signal ().
o find the phase shift, measure the time difference between the zero crossing (going positive) of the two waves. his time difference is denoted. he sinusoid s period, denoted, is the time between successive zero crossings (going positive) of a single wave. his can be measured of computed from the frequency. he phase shift is to 360 in the same ratio as is to the period: phase shift = 360 /. If the input signal s zero crossing occurs before the output signal s zero crossing, the output signal is said to lag the input, and the phase shift will be negative. If the output waveform's zero crossing occurs before the input waveform s, it is said to lead and the phase shift is positive. Its important to note which signal s zero crossing occurred first when measuring. Filter 1: C 50 Hz 100 Hz 200 Hz 300 Hz 400 Hz 500 Hz 800 Hz 1500 Hz. Φ 50 Hz 100 Hz 200 Hz 300 Hz 400 Hz 500 Hz 800 Hz 1500 Hz. Filter 2 : L
Φ
Filter 3: L C Φ 4. Using your measured values, plot the amplitude gain verses the frequency and the phase shift (in degrees) verses the frequency. SemiLog graph paper can be very effective for this graph. Use the linear axis for the gain and phase data and the log axis for frequency. 5. Substitute the measured values for, C, and L into the theoretical frequency responses obtained in the prelab, plot the resulting theoretical amplitude gain verses the frequency and the theoretical phase shift (in degrees) verses the frequency. 6. Compare the results of the theoretical values with the experimental values. Note that phase shift is ambiguous with respect to phase shifts of 360, so you can add ±360 phase shifts into your experimental results to obtain better agreement. 7. he passband of the filter is defined as the range of frequencies where the amplitude gain exceeds 0.707. Use the equation you derived for the theoretical gain to compute the passband of each filter. Can you think of applications for these different types of filters?