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 EE 203 Circuit Analysis 2
Lecture 37
Chapter 15.1
FirstOrder LowPass and
HighPass Filters
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: [email protected], http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Lecture 37  Chapter 15  1/2  1/12 Passive Filters vs. Active Filters
Passive Filters
Up to this point, we have considered only passive filter circuits, that is, filter
circuits consisting of resistors, inductors, and capacitors. Active Filters
There are areas of application, however, where active circuits, those that employ
op amps, have certain advantages over passive filters.
For instance, active circuits can produce bandpass and bandreject filters without
using inductors. This is desirable because inductors are usually large, heavy,
and costly, and they may introduce electromagnetic field effects that compromise
the desired frequency response characteristics. EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Lecture 37  Chapter 15  1/2  2/12 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 If General OP Amp Circuit / LowPass Filter
Is + I f = In Is Vi − Vn Vo − Vn
+
= In
Zi
Zf
Zf
Vi − 0 Vo − 0
+
= 0 ∴Vo = −
Vi
Zi
Zf
Zi In Active
Active LowPass Filter
H (s) = R2
sC Vn Vp= zero where K = 1
R2
, ωc =
R1
R2C if 1 < K then 1 < H ( jω ) Passive LowPass Filter
Filt R2 1
s
ωc
R RC
R1 R2
=−
= − 1 2 = −K
1
s
1
s + ωc
R1 ( R2 + )
s+
sC R1 R2
R2C
R2
sC H (s) = Vo ( s )
ωc
=
Vi ( s ) s + ωc where ωc = R2
1
, ωc =
R1
R2C EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Vo ( s ) − Z f
ωc
=
= −K
Vi ( s )
Zi
s + ωc 0 < H ( jω ) 1
1
R2  ( )
R2 +
Vo ( s ) − Z f
sC = −
sC
H (s) =
=
=−
Vi ( s )
Zi
R1
R1 where
where K = Gain K 1
RC 0 < H ( jω ) < 1
Lecture 37  Chapter 15  1/2  3/12 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Lecture 37  Chapter 15  1/2  4/12 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 Active HighPass Filter Frequency Response Plots: Bode Plots Vo ( s ) − Z f
R2
=
=−
1
Vi ( s )
Zi
R1 +
sC
s
R2
s
R2
s
R1
R1
=−
⋅
=−
= −K
1s
1
s + ωc
R1 +
s+
sC R1
C
R1C
0 < H ( jω )
R
1
⇒
where K = 2 , ωc =
R1
R1C
if
if 1 < K then 1 < H ( jω )
then Bode Plots H (s) = Named in recognition of the pioneering
work done by H. W. Bode
Decibels (dB) versus the log of
frequency
Made on semilog graph paper for
greater accuracy in representing the
wide range of frequency values A dB = 20 log10 H ( jω )
A dB = 0 ⇒ H ( jω ) = 1 Passive HighPass Filter A dB < 0 ⇒ 0 < H ( jω ) < 1 H ( s) = A dB > 0 ⇒ 1 < H ( jω )
A dB = −3 dB ⇒ H ( jω c ) = 1 where ωc = 2 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Vo ( s )
s
=
Vi ( s ) s + ωc Lecture 37  Chapter 15  1/2  5/12 1
RC 0 < H ( jω ) < 1 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Lecture 37  Chapter 15  1/2  6/12 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 Example 15.2 (1) Example 15.2 (2)
Gain Figure
Figure 15.5 shows the Bode
magnitude plot of a highpass filter. Using the active
highpass filter circuit in
Fig.15.4, calculate values of
R1 and R2 that produce the
desired magnitude response.
Use a 0.1 μF capacitor. If a
If
10 kΩ load resistor is added
to this filter, how will the
magnitude response
change?
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] 20 dB
dB 20 = 20 log10 H ( j∞) ∴ H ( j∞) = 10
⇒ K = 10 = R2 R1
3 dB point 500 rad/s ωc = 500 rad/s = 1 R1C
500
∴ R1 = 1 ωc C = 20 kΩ, R2 = 200 kΩ
Because we have made the assumption that
th
th
the op amp in this highpass filter circuit is
ideal, the addition of any load resistor,
regardless of its resistance, has no effect on
has
the behavior of the op amp. Thus, the
magnitude response of a highpass filter with a
lload resistor is the same as that of a highpass
oad
filter with no load resistor.
Lecture 37  Chapter 15  1/2  7/12 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Lecture 37  Chapter 15  1/2  8/12 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 OP Amp Bandpass Filters: Bode Plot EE 203 Circuit Analysis 2
Lecture 37
Chapter 15.3
OP
OP Amp Bandpass and
Bandreject Filters We
We can see from the plot
that the bandpass filter
consists of three separate
components: 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: [email protected], http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Lecture 37  Chapter 15  1/2  9/12 1. A unitygain lowpass filter
whose cutoff frequency is
ωc2, the larger of the two
cutoff frequencies;
2. A unitygain highpass filter
whose cutoff frequency is
ωc1, the smaller of the two
cutoff frequencies; and
3. A gain component to provide
the desired level of gain in
the passband.
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Lecture 37  Chapter 15  1/2  10/12 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 Cascaded OP Amp Bandpass Filter Cascaded OP Amp Bandpass Filter These three components are cascaded in series Transfer
Transfer Function The resulting filter is called a broadband bandpass filter, because the band of
frequencies passed is wide.
The formal definition of a broadband filter requires to satisf the equation
fy UnityGain LowPass Filter
it
Filt UnityGain Hi hPass Filter
it
Filt
High ωc 2
≥2
ωc1 Gain Component V⎛
ωc 2 ⎞⎛
s ⎞⎛ R f ⎞
H ( s) = o = ⎜ −
⎟
⎟⎜
⎟⎜
⎜ s + ω ⎟⎜ − s + ω ⎟⎜ − R ⎟
Vi ⎝
c 2 ⎠⎝
c1 ⎠⎝
i⎠
ωc 2 s
ωc 2 s
= −K
= −K 2
( s + ωc 2 )( s + ωc1 )
s + (ωc1 + ωc 2 ) s + ωc1ωc 2
If ωc 2 >> ωc1 then (ωc1 + ωc 2 ) ≈ ωc 2 H ( s) = − K ωc 2 s
s 2 + ωc 2 s + ωc1ωc 2 Two Cutoff Frequencies
ωc 2 = Gain 1
1
, ωc1 =
RL C L
RH C H ω c 2 ( jω o )
H ( jω o ) = − K
( jωo ) 2 + ωc 2 ( jωo ) + ωc1ωc 2
=K=
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Lecture 37  Chapter 15  1/2  11/12 Rf
Ri H(s) for UnityGain LowPass
Filter
H(s) for UnityGain HighPass
Filt
Filter
H(s) for Gain Component SMALL for Big Things nanobioSensors & MicroActuators Learning Lab University at Buffalo
The State University of New York Two RLC Bandpass Filters
2 ωc1 = − R
1
⎛R⎞
+ ⎜ ⎟+
2L
⎝ 2 L ⎠ CL
2 ωc 2 =
ωo = R
1
⎛R⎞
+ ⎜ ⎟+
2L
⎝ 2 L ⎠ CL
1
LC R
β=
L
Q= H (s) = βs
2
s 2 + β s + ωo
2 ωc1 = − 1
1
⎛1⎞
+⎜
⎟+
2 RC
⎝ 2 RC ⎠ CL
2 L
CR 2 ωc 2 = 1
1
⎛1⎞
+⎜
⎟+
2 RC
⎝ 2 RC ⎠ CL 1
LC
1
β=
RC ωo = Q= R 2C
L Lecture
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  [email protected] Spring 2007  Prof. Kwang W.LOh  [email protected] 15  15 Chapter 1412/89/8
ecture 37  38  Chapter 1/2 2/2  5/5 
 12/12
EE 203 Circuit Analysis 2
Lecture 32 ...
View
Full Document
 Spring '08
 Staff
 Highpass filter, Lowpass filter, State University of New York, Prof. Kwang W. Oh, MicroActuators Learning Lab

Click to edit the document details