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Unformatted text preview: SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York The Effect of Varying Source Frequency
EE 203 Circuit Analysis 2
Lecture 28
Chapter 14.1
Frequency Selective Circuits
Kwang W. Oh, Ph.D., Assistant Professor
SMALL (nanobioSensors and MicroActuators Learning Lab)
Department of Electrical Engineering
University at Buffalo, The State University of New York
215E Bonner Hall, SUNYBuffalo, Buffalo, NY 142601920
Tel: (716) 6453115 Ext. 1149, Fax: (716) 6453656
Email: kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  1/10 Frequency
Frequency Response
Up to this point in our analysis of circuits with sinusoidal sources, the source frequency was
held constant.
In this chapter, we analyze the effect of varying source frequency on circuit voltages
and currents. Frequency Selective Circuit: Filter
The careful choice of circuit elements, their values, and their connections to other elements
enables us to construct circuits that pass to the output only those input signals that reside
in a desired range of frequencies.
Many devices that communicate via electric signals, such as telephones, radios, televisions,
and satellites, employ frequencyselective circuits.
Frequencyselective circuits are also called filters because of their ability to filter out
certain input signals on the basis of frequency
Loss pass
Hiigh pass
Hh
Band pass
Band reject EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  2/10 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Recall 13.7: Transfer Function and SteadyState Sinusoidal Response (3) Transfer Function H(jω)
Assumption
Assumption
Note that the approach just outlined assumes that we can vary the frequency of a
sinusoidal source without changing its magnitude or phase angle.
Therefore, the amplitude and phase of the output
th
will vary only if those of the transfer function vary
as the frequency of the sinusoidal source
s changed. Transfer Function: H(s) = Vo(s)/Vi(s)
which indicates how to use the transfer function H(s) to find the steadystate sinusoidal response yss(t) of a circuit.
The amplitude of the response equals the amplitude of the source, A, times
the magnitude of the transfer function, H(jω).
th
The phase angle of the response, φ + θ(ω), equals the phase angle of the
source, φ, plus the phase angle of the transfer function, θ(ω).
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  3/10 Most cases are where both the input and outputs are sinusoidal voltages.
The transfer function of interest to us will be the ratio of the Laplace transform of
the output voltage to the Laplace transform of the input voltage, or H(s) =
Vo(s)/Vi(s).
For a particular application, a current may be either the input signal or output
signal of interest. EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  4/10 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Ideal Freq Response Plot (1) Ideal Freq Response Plot (2) Passband & Stopband Cutoff Frequency: ωc
A lowpass filter passes
signals at frequencies lower
than the cutoff frequency from
ff
the input to the output
A highpass filter passes
signals at frequencies higher
than the cutoff frequency.
Thus
Thus the terms low and high
as used here do not refer to
any absolute values of
frequency, but rather to
relative values with respect to
the cutoff frequency. The signals passed from
the input to the output fall
within a band of
frequencies called the
passband. Frequency Response
Plot
Magnitude plot: a graph
of H(jω) versus
frequency ω.
Phase angle plot: a
graph of θ(jω) versus
frequency ω. EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  5/10 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  6/10 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Ideal Freq Response Plot (3)
EE 203 Circuit Analysis 2
Lecture 28
Chapter 14.2
LowPass Filter A bandpass filter passes a
source voltage to the output
only when the source
frequency is within the band
defined by the two cutoff
frequencies.
A bandreject filter passes a
source voltage to the output
only when the source
frequency is outside the band
defined by the two cutoff
frequencies. Kwang W. Oh, Ph.D., Assistant Professor
SMALL (nanobioSensors and MicroActuators Learning Lab)
Department of Electrical Engineering
University at Buffalo, The State University of New York
215E Bonner Hall, SUNYBuffalo, Buffalo, NY 142601920
Tel: (716) 6453115 Ext. 1149, Fax: (716) 6453656
Email: kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu The bandreject filter thus
rejects, or stops, the source
voltage from reaching the
output when its frequency is
within the band defined by
the cutoff frequencies. EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  7/10 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  8/10 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Two circuits that behave as lowpass filters The Series RL Circuit for LowPass Filter
Transfer function H(s)
R
V
R
RL
Vo =
Vi ⇒ H ( s ) = o =
=
sL + R
Vi sL + R s + R L
RL
RL
∴ H ( jω ) =
⇒ H ( jω ) =
2
jω + R L
ω + ( R L) 2 The series RL circuit
Transfer function
Cutoff frequency ω
ω
ω The series RC circuit
Transfer function
Cutoff frequency 0 : H(jω)
1
∞ : H(jω)
0
ωc : H(jωc)
1/√2 Cutoff Frequency (by definition)
⇒ H ( jωc ) = R
∴ωc =
L
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 28  Chapter 14  1/5  9/10 RL ωc + ( R L)
2 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo 2 = 1
1
H max =
1
2
2
H max = H ( jω ) ω =0 = 1
Lecture 28  Chapter 14  1/5  10/10 ...
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This note was uploaded on 10/19/2011 for the course EE 203 taught by Professor Staff during the Spring '08 term at SUNY Buffalo.
 Spring '08
 Staff

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