DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139
Battery Source Resistance
EVEREADY [Failed]
DURACELL [Fresh]
9.58 Volts Open Circuit
2.4 Volts with a 1kȍ load resistor
I = 2.4 mA
9.28 Volts Open Circuit
9.20 Volts with a 1kȍ load resistor
I = 9.2 mA
RS
RS
+
2.4 mA
1k :
9.58 V
+
9.2 mA
2.4 V
1k :
9.28 V
-
Rs
Isc
9.58V 2.4V
2.4 mA
9.58V
3kȍ
3.2mA
-
3kȍ
9.28V 9.2V
9.2 mA
Rs
3.2mA
Isc
3k :
Battery Source Resistance
9.2 V
9.28V
8.7ȍ
1.1 A
1 of 1
8.7ȍ
1.07A
8.7:
08/14/06
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139
COMPENSATE YOUR ‘SCOPE PROBES!
If you don’t, you won’t get accurate voltage measurements on the oscilloscope; they won’t agree
with the value displayed on your function generator!
1. To compensate your probes, hook the probe tip on to the metal terminal labeled “Probe
Comp = 5V Ȇ”, [or similar] located at the bottom of the right half of most ‘scopes. Adjust your
horizontal sweep until you can see 2 or 3 cycles of the square wave displayed horizontally.
2. Your display will probably look like either the second or third diagram below; if it looks like the
top diagram you need go no further.
CORRECTLY COMPENSATED
PROBE UNDERCOMPENSATED
PROBE OVERCOMPENSATED
3. Obtain a non-metallic screwdriver, or at least a plastic one with just a metal tip, and inserting
it into the screw slot on the probe, gently adjust the screw until the waveform looks “square” as
in the top figure above.
Oscilloscope input
10X Probe
One tenth of signal
(1 Vp-p) at input
9 MW
10 Vp-p
Signal
x pF
1 MW
20 pF
Probe compensation adjustment
Figure by MIT OpenCourseWare.
Ron Roscoe
1
2/3/2006
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139
Low-Pass Filter Basics [Integrator]
R
C
V1
j XC
R j XC
Av
V2
V1
Av
1
sCR 1
V2
1
j ZC
1
R
j ZC
1
j ZCR 1
AV (dB)
0
-3dB
slope = -6 dB / octave
slope = -20 dB / decade
log f
fHI or f-3dB
Degrees
PHASE LAG
0o
-45o
-90o
log f
fHI or f-3dB
Low-Pass Filter Basics
1 of 1
08/14/06
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139
High-Pass Filter Basics [Differentiator]
Av
C
V1
R
V2
V2
V1
R
R
1
j ZC
j ZCR
j ZCR 1
s CR
s CR 1
AV (dB)
0
-3dB
slope = 6 dB / octave
slope = 20 dB / decade
log f
fLO or f-3dB
Degrees
PHASE LEAD
90o
45o
0o
-45o
log f
fLO or f-3dB
High-Pass Filter Basics
1 of 1
08/14/06
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139
Transformer Derivation [for voltage step-UP transformer]
V2
V1
R2
1:n
For a perfect [lossless] transformer, the power in the primary will equal the power in the
secondary. Therefore:
V1 I 1
V2 I 2
substituting for the current, where R1 = the secondary resistance as reflected to the primary:
V1
R1
V1
V2
2
2
V1
R1
V2
R2
R1
V12 R2
V22
but V2
R1
V2
R2
nV1
V12 R2
nV1 2
V12 R2
n 2V12
so
R1
Transformer Derivation
R2
n2
1 of 1
9/09/02
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
f1 = 426.4 kHz
f2 = 483.6 kHz
BW = 57.2kHz
70%
I
fr
0 f
455kHz
Low Q current curve
100 %
90 %
80 %
70 %
Lower fco
Upper fco
f1 = 450 kHz
f2 = 460 kHz
BW = 10 kHz
60 %
50 %
40 %
30 %
20 %
10 %
fr
0 f
455kHz
High Q current curve
Bandwidth for high- and low- Q series circuit.
Figure by MIT OpenCourseWare.
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Frequency Effect
+j
Max
Increasing
e
anc
t
c
a
e re f L
v
i
t
uc
2π
Ind X L =
0
Min
Frequency
(Also called baseline)
Effect of frequency on inductive reactance.
XL
R
-j
+j
Increasing OHMS
Max
XC
Phase
Capacitive reactance
Min 0
XC =
1
2πfC
Frequency
(Also called baseline)
XC
R
-j
Effect of frequency on capacitive reactance.
XC = XL
Max
XL
+j
XC
XL
X
XC
Min
R
fr
0
F
Increasing
Relationship between XL and XC as frequency
increases.
-j
Figure by MIT OpenCourseWare.
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Eout
Q = 200
Q = 50
Q = 100
Frequency
f0
Frequency curve of single LC tuned circuit.
Figure by MIT OpenCourseWare.
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
1
2
H
max
H
max
B
0
wc1
w0
w
wc2
General bandpass and amplitude response.
Figure by MIT OpenCourseWare.
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Characteristic curves
Constant voltage input
Curve
no.
1
Voltage output
into open circuit
vi
4
dB 0
5
1
2
vo
Voltage output
into open circuit
vi
ii
io
1 + jωT
R 1+ jωT
jωT
1+ jωT
+
3
vo vi
Frequency
6
2
vi
vo vi
vo
vi
io
3
vo
R
vi
4
5
+90o
1
4
5
3
io
vi
2
io
6
vi
ii
io ii
io
1
1+ jωT
vo
R (1+ jωT)
ii
vo
jωL
io
1
jωL
io
1+ jωT
jωT
ii
jωC
6
io ii
vo
R
1 (1+ jωT)
R
f0
-90o
vi
1
1+ jωT
ii
1 1+ jωT
R jωT
ii
jωT
1+ jωT
vo
R
io
Current output
into short circuit
jωT
1+ jωT
ii
1
1
R 1+ jωT
1
1+ jωT
-
Constant current input
Current output
into short circuit
ii
vo
1
jωC
Diagrams, transfer function, and frequency responses for basic circuits
consisting of a resistor, capacitor, and/or inductor.
Figure by MIT OpenCourseWare.
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Sawtooth
Vn
V
(a)
A
A
Vn = nπ
t
f1
f2
f3
f4
f5
f
Square
V
(b)
A
Vn
2A
Vn = nπ (n ODD)
t
f1
f3
f5
4A
Vn = π
1
f
Sin2
Vn
V
(c)
A
4n2 - 1
t
f1
f2
f3
f4
f5
f
Triangle
Vn
V
Vn =
(d)
A
t
f1
4A
(n ODD)
(nπ)2
f3
f5
f
Figure by MIT OpenCourseWare.
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Amplitude
Time
Cycle
4
PR = π
1
3
1
5
Response DB
1
0
-10
3
5
7
-20
-30
100
9
11
200
400
800 1000
Frequency in cycles per second
13
15
17 19
2000
A rectangular wave, the equation of the wave, and the spectrum for a fundamental frequency
of 100 cycles, that is, t = 1/100 second for a complete cycle.
Figure by MIT OpenCourseWare.
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Amplitude
Time
Cycle
PR =
0
8
p2
cos wt +
1
1
cos 3 wt + cos 5 wt ----9
25
1
Response DB
-10
-20
-30
-40
3
5
7
9
11
-50
-60
100
200
400
800 1000
Frequency in cycles per second
13
15
17
19
2000
A triangular wave, the equation of the wave, and the spectrum for a fundamental frequency
of 100 cycles, that is, t = 1/100 second for a complete cycle.
Figure by MIT OpenCourseWare.
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139
Impedance/Admittance Notation
XL
j ZL
R
XC
1
j ZC
C
Z
L
Y
Z R j ZL 1
j ZC
1
1
1
j ZC
R j ZL
1
; BL
Z
Y G
1 º
ª
Z R j «ZL ZC »¼
¬
Z R j >X L X C @
1
; BC
XL
1
j ZC G j ZL
1
; G
XC
1
R
1 º
ª
j «ZC ZL »¼
¬
Y G j >B C B L @
______________________________________________
R
OHM’s LAW:
V
I R ;
V
ª 1 º
I«
;
¬ Y »¼
Where does the
V
2
L
C
I Z;
V Y
I
1
come from in –3dB point calculations?
2
or
2 1/
2
R
+j
45
-R
L
o
R
VS
R
VOUT
-j
Impedance-Admittance Notation
1 of 1
09/05/06
Cite as: Ron Roscoe, course materials for 6.101 Introductory Analog Electronics Laboratory, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].