Lab 9 Frequency Domain

Transcription

1 Lab 9 Frequency Domain 1

2 Components Required Resistors Capacitors Function Generator Multimeter Oscilloscope 2

3 Filter Design Filters are electric components that allow applying different operations to signals based on specific frequencies. Example Operation: Gain, Attenuation, Phase Shift Examples of Filters: Equalizer on a stereo Allows you to apply different gains at different frequencies Car fuel gauge Display the level of fuel in the gas tank without changing the reading as the car drives over bumps and goes through corners. 3

4 Concepts needed to be understood Impedance Frequency Response Low-pass filter (LPF) High-pass filter (HPF) Band-pass filter (BPF) Band-stop filter (BSF) 4

5 Impedance Impedance of a Capacitor: Impedance of an Inductor Impedance of a Resistor Can you solve the circuit on the right? 5

6 Back to our Voltage Divider Solve using Ohm s Law and Impedance instead of Integrals, derivatives Solve it: Magnitude: Phase: 6

7 Build the Circuit, Measure Measure amplitude of Vout and phase difference from Vin to Vout Input: 10V rms sinewave For given Frequencies 7

8 Phase (deg) Magnitude Frequency Response Here we can see the circuit passes low-frequencies. High-frequency signals are reduced in magnitude (attenuated) and shifted - 90deg There is a transition region in between low and high, near the time constant of the circuit. This is called a low-pass filter Frequency (Hz) 8

9 AC Circuit Analysis LTspice has a mode which does circuit simulation one frequency at a time and does the measurements you just performed. Called AC Analysis (AC Sweep). Horizontal axis is frequency, not time. Important to realize: Circuit simulator first solves for DC operating point Then it finds how small AC signals get transferred through the circuit (in a linear manner for linear circuits) Circuit simulation then takes the AC small-signal source and passes it through the linearized circuit Important output data is magnitude or phase 9

10 AC Analysis Build the schematic from the previous page. Define the voltage source in the Small signal AC analysis portion of the voltage source window. In an AC analysis (AC sweep), all sources are treated as sine waves. 10

11 Setup an AC Analysis. AC Analysis Decade spacing means use an equal number of points from 1kHz to 10kHz as from 100kHz to 1MHz (in each decade) 11

12 Bode Plots Magnitude: often represented in decibels Magnitude db = 20 log 10 (Magnitude) Phase Magnitude 12

13 Bode Plot of Gain From the Plot Settings menu, choose Add Trace. Use the following expression in the box: V(vout)/V(vin) Magnitude of Gain Phase 13

14 Low Pass Filter(Simulation) Build the circuit shown below and determine the cut-off frequency (LTspice). Also plot Bode plots. 14

15 High Pass Filter (Simulation) Build the circuit shown below and determine the cut-off frequency (LTspice). Also plot Bode plots. 15

16 Band Pass Filter (Simulation) Build the circuit shown below and determine the center frequency (LTspice). Also plot Bode plots. 16

17 Band Stop Filter (Simulation) Build the circuit shown below and calculate the center frequency (LTspice). Also plot Bode plots. 17

18 Cut-off and Center frequencies Monitor V in and V out in the oscilloscope s channels 1 and 2, respectively. Make a Bode plot of the magnitude of V out /V in as a function of the frequency. Make sure to get data over several decades of frequency values. 18

19 Low Pass Filter (Hardware) Build the circuit shown below and determine the cut-off frequency. 19

20 High Pass Filter (Hardware) Build the circuit shown below and determine the cut-off frequency. 20

21 Band Pass Filter (Hardware) Build the circuit shown below and determine the center frequency. 21

22 Band Stop Filter (Hardware) Build the circuit shown below and calculate the center frequency. 22

23 Filters Do the results from LTspice and hardware match? 23