all types of filters are explained here! EX: low pass,high pass,band pass,band width and etc

1. 6.002 Fall 2000 Lecture 18
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 CIRCUITS AND
ELECTRONICS
Filters

2. 6.002 Fall 2000 Lecture 18
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Review
+
–
CvIv +
–
R
C
Reading: Section 14.5, 14.6, 15.3 from A & L.
+
–
cViV +
–
RZ
CZ
i
RC
C
c V
ZZ
Z
V ⋅
+
=
RCj1
1
R
Cj
1
Cj
1
V
V
i
c
ω
ω
ω
+
=
+
=

3. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
A Filter
RCj1
1
V
ZZ
Z
V i
RC
C
c
ω+
=⋅
+
=
“Low Pass Filter”
ω
1
( )
i
c
V
V
H =ω
Demo
with audio
+
–
cViV +
–
RZ
CZ

4. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
Quick Review of Impedances-
Just as
21
ab
ab
AB RR
I
V
R +==
LjR
I
V
Z 1
ab
ab
AB ω+==
1R
abI +
–
abV
2R
A
B
1R
abI +
–
abV
Ljω
A
B

5. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
Quick Review of Impedances
Similarly
L2C1AB ZR||ZRZ ++=
L
2C
2C
1 Z
RZ
RZ
R +
+
+=
Lj
CRj1
R
R
2
2
1 ω
ω
+
+
+=
1R
L
A
B
2RC

6. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
We can build other filters by
combining impedances
( )ωZ
L
R
C
ω
Z

7. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
We can build other filters by
combining impedances
HPF
High Pass Filter
ω
( )ωH
ω
( )ωH
LPF
Low Pass Filter
ω
( )ωH
HPF
( )ωZ
L
R
C ω
Z
+
–
+
–
+
–

8. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
Check out:
R
Cj
1
Lj
R
V
V
i
r
++
=
ω
ω
RCjLC1
RCj
2
ωω
ω
+−
=
( ) ( )222
i
r
RCLC1
RC
V
V
ωω
ω
+−
=
ω
+
–
L C
R
+
–
rViV
LC
1
o =ω
At resonance,
ω = ωo
and
ZL + ZC = 0,
so Vi sees
only R!
More later…
Intuitively:
i
r
V
V
1
L blocks high freq
C blocks low freq

9. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
What about:
+
–
L C
R
+ –lcV
iV
Band Stop Filteri
lc
V
V
ω
1 C open L open
Check out Vl and Vc in the lab.

10. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
Another example:
+
–
+
– L
R
iV C oV
i
o
V
V
oω ω
BPF
C shortL short
Application: see AM radio coming up shortly

11. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
AM Radio Receiver
crystal radio demo
Thévenin
antenna
model
+
– L
R
iV C
demodulator
amplifier
antenna

12. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
AM Receiver
“Selectivity” important —
relates to a parameter “Q” for the filter. Next…
+
– L
R
iV C
demodulator
amplifier
f
signal
strength
540 …1000 1010 1020 1030 … 1600 KHz
10 KHz
filter WBZ
News
Radio

13. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
Recall,
Selectivity:
Look at series RLC in more detail
+
–
L C
R
+
–
rViV
Cj
1
LjR
R
V
V
i
r
ω
ω ++
=
i
r
V
V
ω
oω
2
1
higher Q
1
Define quality factor
Δ
=Q o
ω
ω
ωΔ
bandwidth
⇒Qhigh more selective

14. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
ω
ω
Δ
= o
Q
LC
1
o =ω
Quality Factor Q
⎟
⎠
⎞
⎜
⎝
⎛ −+
=
++
=
CR
1
R
L
j1
1
Cj
1
LjR
R
iV
rV
ω
ω
ω
ω
?ωΔ
at =0ωο
ωο:

15. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
Note that abs magnitude is
2
1
when
1j1
1
CR
1
R
L
j1
1
V
V
i
r
±
=
⎟
⎠
⎞
⎜
⎝
⎛
−+
=
ω
ω
i.e. when 1
CR
1
R
L
±=−
ω
ω
0
LC
1
L
R2
=−
ω
ω ∓
:ωΔ
ω
ω
Δ
= o
Q
Quality Factor Q
Looking at the roots of both equations,
LC
4
L
R
2
1
L2
R
2
2
1 ++=ω
LC
4
L
R
2
1
L2
R
2
2
2 ++−=ω
L
R
=−=Δ 21 ωωω

16. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
R
L
L
R
Q oo ωω
==
The lower the R (for series R),
the sharper the peak
ω
ω
Δ
= o
Q
Quality Factor Q
LC
1
o =ω

17. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000 Lecture 18
Another way of looking at Q :
cycleperlostenergy
storedenergy
2π=Q
0
2
r
2
r
2
RI
2
1
IL
2
1
2
ω
π
π=
R
L
Q oω
=
Quality Factor Q