Chapter 3, Sections Electrical Filters

Transcription

1 Chapter 3, Sections Electrical Filters

2 Signals DC and AC Components - Many signals can be constructed as sums of AC and DC components: =

3 DC Signals DC signals have an associated. V out (V) Time (s)

4 AC Signals AC signals have both and. out (V) V out Time (s)

5 - Depending on the what signals are summed, complex waveforms may be produced. V out (V) out (V) V out Time (s) Time (s) V out (V) out (V) V out Time (s) Time (s) V out (V) Time (s)

6 Filters A filter removes unwanted materials, oil filters remove metal particles from engines. An electrical filter is used to remove/reduce the amplitude of unwanted signals. Filters eliminate by allowing only certain frequencies to pass.

7 Filters Filters pass quantities according to some criteria: - Particulate filters hold back some sizes and pass on others - Coffee filters keep in the but pass through the. - Electrical filters have based on.

8 Types of (Electrical) Filters Low-pass: pass through frequencies, attenuate or reject frequencies. High-pass: pass through frequencies, attenuate or reject frequencies. Gain (db) Frequency Gain (db) Frequency

9 Types of (Electrical) Filters Band-pass: pass through a of frequencies, reject everything outside of the band. Band-reject: pass through everything outside of a, reject the band. Gain (db) Frequency Gain (db) Frequency

10 Why low-pass filters? Used in data acquisition to prevent aliasing high frequency signals pretending to be low frequency signals Most transducers act like low-pass filters at sufficiently high frequencies output cannot keep up with input bandwidth is the frequency when the magnitude ratio is -3 db (what s a db?!)

11 Signal Filtering 3 2 Original Data Filtered Data Data (units) Time (s)

12 Low Pass Filter - Magnitude Experimental gain found by Input and Output, volts Vi, p p V o, p p What is the gain for this experimental data? Time, sec

13 Low Pass Filter Phase Angle Low-pass filter s experimental phase angle 2.5 Input and Output, volts Zero crossing Time, sec T T

14 Input and Output Voltages, volts Example #1 - Experimental Data Estimate frequency, magnitude and phase from plot Input Output Time, sec

15 Active & Passive Filters Passive filters no power required, all power comes from the signal itself maximum (practical) gain is Active filters power provided, signal can be both filtered and amplified by an op-amp maximum gain can be

16 1 st Order, Low Pass, Passive Filter An ideal low pass filter allows low frequency to pass through, while high frequency signals. + - V i R C V o V V o i V V o i ωb = 2πf c ω = 2πf ωb = 2πf c Ideal and Actual Low-pass Filter Responses ω = 2πf

17 1 st Order, Passive, Low Pass Filter Magnitude Magnitude ratio is the theoretical gain Gain the = if we define + - V i R C V o + - break frequency: ω b = corner frequency: f c = Gain the =

18 Units if R has units of and C has units of then ω has units of ω b =

19 1 st Order, Passive, Low Pass Filter Magnitude A filter s theoretical gain is often expressed in units of decibels (db), Gain the (in db) = A filter s experimental gain can also be expressed in units of decibels (db), Gain exp (in db) =

20 1 st Order, Passive, Low Pass Filter Phase Angle Low-pass filter s theoretical phase angle V V o i the = Ranges from ~ degrees ( f << f c ) to degrees ( f = f c ) to ~ degrees ( f >> f c )

21 Example #2 What is the corner frequency, f c, for this filter? 22 kω V i (t) µf + - V o

22 Example #2 - Responses f Magnitude Phase Hz ratio db degrees

23 Example #2 - Answers f Magnitude Phase Hz ratio db degrees

24 Plot for Example # Magnitude, db Magnitude Phase Angle Phase Angle, degrees f, Hz -9

25 Linear Approximation - 1st Order 1 st order, Passive, Low pass Filter db -1 db -2 db Slope = Linear scale for decibels ω b 1ω b Log scale for frequency

26 Plot for Example # Magnitude, db Magnitude Phase Angle Phase Angle, degrees f, Hz -9

27 HW #2 Problems #1 & #2 1kΩ 1kΩ 1kΩ 1kΩ V i.1µf V o - 1kΩ 22kΩ 4.7kΩ V i.22µf V o -

28 Homework #2 For each of the problems: Determine the break and corner frequencies (use the appropriate units for each) Determine expressions for the magnitude and phase of the filter as a function of frequency. Verify that your expressions are correct by evaluating the magnitude and phase at the corner frequency. Create a plot of the magnitude and phase across some appropriate range of frequencies.

29 HW #2 Problems #3 and #4 47kΩ 22kΩ 1kΩ V i.1µf V o - 1kΩ 47kΩ 22kΩ V i.47µf V o -