TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant...
-
Upload
cuthbert-hutchinson -
Category
Documents
-
view
238 -
download
0
Transcript of TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant...
![Page 1: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/1.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
With the aid of a suitable diagram, explain
briefly what are meant by the following terms;
Q1
a) open-loop gain;
b) Loop gain
c) closed-loop gain
![Page 2: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/2.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
SolutionA
b
V e
V f
V sV o
+The open-loop gain is the gain of the operational amplifier without feedback. Referring to the figure, the open-loop gain is A and is expressed as;
e
o
V
VA
a)
![Page 3: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/3.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
A
b
V e
V f
V sV o
+The loop gain is the amplification (or attenuation) experienced by the signal as it travels from the input to the operational amplifier to the output of the feedback network. From the figure, the loop gain is Ab and is expressed as;
b)
e
f
V
VA b
![Page 4: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/4.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
A
b
V e
V f
V sV o
+
The closed-loop gain is the amplification of the input signal by the amplifier with feedback. From the figure, the closed-loop gain is Af and is
expressed as;
c)
s
of V
VA
Solution (cont’d)
![Page 5: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/5.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Q2 With the aid of suitable figures, describe the
term Barkhausen criterion as applied to
sinusoidal oscillators
![Page 6: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/6.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution
In the figure, it can be shown that the closed-loop gain, Af, is given by the expression;
A
b
V e
V f
V sV o
+
AA
V
VA
s
of b
1
![Page 7: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/7.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
When the magnitude of the loop gain is unity and the phase is zero i.e. when;
A
b
V e
V f
V sV o
+
01Abthe system will produce an output for zero input.
![Page 8: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/8.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
A
b
V e
V f
V sV o
+
Barkhausen criterion states that in order to start and sustain an oscillation, the loop gain must be unity and the phase shift through the loop must be 0
Solution (cont’d)
![Page 9: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/9.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
The following figure
shows a Wien-Bridge
oscillator employing
an ideal operational
amplifier A. Derive
an expression for the
frequency of
oscillation o in
terms of R and C.
Q3
.
RRC
C
R 2
R 1
+
v OA
![Page 10: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/10.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution
.
RRC
C
R 2
R 1
+
v OA
Z sZ p
v 1
v 2
1
1
11
sCR
RZ
R
sCR
sCRZ
p
p
![Page 11: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/11.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
.
RRC
C
R 2
R 1
+
v OA
Z sZ p
v 1
v 2
sCRZ s
1
sC
sCR 1
![Page 12: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/12.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
.
RRC
C
R 2
R 1
+
v OA
Z sZ p
v 1
v 2
ov
v2b
sp
p
ZZ
Z
![Page 13: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/13.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
sp
p
ZZ
Z
b
sCsCRsCRR
sCRR
/11/
1/
sCRsCR
13
1
![Page 14: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/14.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
1
21R
RA
.
RRC
C
R 2
R 1
+
v OA
Z sZ p
v 1
v 2
![Page 15: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/15.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
sCRsCR /13
1
b
1
21R
RA and
The loop gain;
1
21/13
1
R
R
sCRsCRAb
![Page 16: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/16.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
Substituting for s;
1
21/13
1
R
R
CRjCRjA
b
Since bA must be real at the oscillation frequency o, it follows that;
01
CRj
CRjo
o
![Page 17: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/17.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
or;RCo
1
![Page 18: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/18.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Q4For the relaxation oscillator shown in the figure, sketch and label the waveforms of vC and vR2 and
indicate in your sketch, the relevant mathematical equations describing various sections of the waveform.
![Page 19: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/19.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution
![Page 20: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/20.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution (cont’d)
![Page 21: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/21.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Q5 Design a phase shift oscillator in the following figure, to obtain a sinusoidal wave of 3 kHz. Use C = 22 nF and R1 = 50 k.
![Page 22: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/22.jpg)
TUTORIAL QUESTIONS – OSCILLATOR
Solution
RC
6oFrom the expression;
we obtain;C
Ro6
Substituting values;
kΩ 5.910221032
69-3
π
R
![Page 23: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/23.jpg)
Q1 A single-pole low-pass filter as shown in Fig.5-1 has a RC network with the resistance R of 2 kΩ and the capacitance C of 0.04μF. If the resistances of resistor R1 and R2 are 20 and 4 Ω respectively, determine:
i) cutoff frequency, fC
ii) pass band voltage gain or the gain of non-inverting amplifier, Acl iii) expression of output voltage, Vo
Figure 5-1.
a
![Page 24: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/24.jpg)
Sol1
kHzHzx
FxxRCfc
21099.1
)104)(102)(14.3(2
1
2
1
3
83
614
201
2
1)( R
RA NIcl
(a)
(b)
The cutoff frequency for a single-pole low-pass filter is
The pass band voltage gain or the gain of non-inverting amplifier is calculated as follows:
![Page 25: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/25.jpg)
fRCjv
RCjv
XR
jv
jRX
Xvv
inin
C
inC
Cina
21
1
1
1
1
1
C
Cin
C
Cina jXR
jXv
XR
Xvv
Applying the voltage divider rule, the input voltage, which is the voltage across the capacitor C, is determined as follows:
Sol1_Cont’d
Multiplying the numerator and the denominator by j and substituting for XC results in the following:
![Page 26: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/26.jpg)
Sol1_Cont’d
RCf
orRCf cc
21
2
1
At the cutoff frequency fc, the magnitude of the capacitive reactance XC equals the resistance of the resistor R.
Substituting for 2πRC in Eq. results in the following equation for va:
c
ina
ff
jvv
1
1
Where f is the operating frequency and fc is the cutoff frequency.
![Page 27: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/27.jpg)
Sol1_Cont’d
c
NIclinNIclao
ff
j
AvAvv
1
)()(
The output vo is the amplified version of vi.
where Acl(NI) is the pass-band voltage gain or the gain of the non-inverting amplifier.
![Page 28: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/28.jpg)
Q2
Determine the critical frequency critical frequency, pass-band voltage pass-band voltage gaingain, and damping factordamping factor for the second-order low-pass active filter in Fig. 5-2 with the following circuit components:
RA = 5 kΩ, RB = 8 kΩ, CA = 0.02 μF, CB = 0.05 μF, R1 = 10 kΩ, R2 = 20 kΩ
Figure 5-2.
![Page 29: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/29.jpg)
Sol2
Hz
xxxx
CCRRf
BABA
c
18.796
)105)(102)(108)(105()14.3(2
1
2
1
8833
The critical frequency for the second-order low-pass active filter is
![Page 30: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/30.jpg)
Sol2_Cont’d
5.1120
101
2
1)( R
RA NIcl
The pass-band voltage gain set by the values of R1 and R2 is
![Page 31: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/31.jpg)
Q3
Design a multiple-feedback band-pass filter with the maximum gain, Ao = 8, quality factor, Q = 25 and center frequency, fo =10 kHz. Assume that C1 = C2 = 0.01µF.
Draw the circuit design of the active band-pass
![Page 32: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/32.jpg)
kkCAf
QR
oo
97.4)8)(01.0)(10(2
25
21
kkCf
QR
o
58.79)01.0)(10(
252
32)8)25(2)(01.0)(10(2
25
)2(2 223 kAQCf
QR
oo
Sol3
![Page 33: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/33.jpg)
Sol3_Con’t
R 1
R 2
R 3
C 1
C 2
V inV out
The drawing of the circuit diagram :
![Page 34: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/34.jpg)
Q4Determine the center frequency, fc, quality factor, Q and bandwidth, BW for the band-pass output of the state-variable filter in following figure. Given that R1 = R2 = R3 = 25 kΩ, R4 = R7 =2.5 kΩ, R5 = 150 kΩ, R6 = 2.0 kΩ, C1 = C2 = 0.003µF
![Page 35: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/35.jpg)
Sol4_Con’t
i) Center frequency, fc
kHzkCRCR
f c 22.21)03.0)(5.2(2
1
2
1
2
1
2714
ii) Quality factor, Q
67.2510.2
150
3
11
3
1
6
5
k
k
R
RQ
![Page 36: TUTORIAL QUESTIONS – OSCILLATOR With the aid of a suitable diagram, explain briefly what are meant by the following terms; Q1 a)open-loop gain; b)Loop.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649f495503460f94c6b4ce/html5/thumbnails/36.jpg)
Sol4_Con’t
iii) Bandwidth, BW
The critical frequency, fo of the integrators usually made equal
to the critical frequency, fc
Hzk
Q
fBW
ff
o
co
65.82667.25
22.21