(a) Perform a Monte Carlo analysis of the six-stage cascade amplifier design resulting from the exam- ple in Tables 12.4 and 12.5, and determine the frac- tion of the amplifiers that will not meet either the gain or bandwidth specifications. Assume the resis- tors are uniformly distributed between their limits. A, > 100 dB fu 2 50 kHz and (b) What tolerance must be used to ensure that less than 0.1 percent of the amplifiers fail to meet both specifications? The equation here can be used to estimate the location of the half-power frequency for N closely spaced poles, where fHi is the average of the indi- vidual cutoff frequencies of the N stages and f is the cutoff frequency of the ith individual stage. fH = FHIV2/N – 1 where THi =E fin n TABLE 12.5 Cascade of Six Identical Noninverting Amplifiers Av (0) GAIN PER fH1 SINGLE STAGE NUMBER N STAGE OF STAGES STAGE 1/B fH N STAGES GAIN B x fr Rin Rout 6.81E + 00 1.00E + 05 6.83E + 00 1.02E + 05 6.85E + 00 1.04E + 05 1.47E + 05 1.46E + 05 5.121E + 04 1.46E + 13 3.42E - 03 1.46E + 05 5.137E + 04 1.47E + 13 3.41E – 03 5.107E + 04 1.46E + 13 3.43E – 03 6.87E + 00 1.05E + 05 6.89E + 00 1.07E + 05 6.91E + 00 1.09E + 05 6.93E + 00 1.11E + 05 6.95E + 00 1.13E + 05 1.45E + 05 5.092E + 04 1.46E+ 13 3.44E – 03 1.45E + 05 6. 5.077E + 04 1.45E + 13 3.45E – 03 5.062E + 04 1.45E + 13 3.46E – 03 6. - 1.45E + 05 1.44E + 05 5.048E + 04 1.44E+ 13 3.47E –- 03 1.44E + 05 6. - 5.033E + 04 1.44E + 13 3.48E – 03 6.97E + 00 1.15E + 05 1.43E + 05 5.019E + 04 1.43E + 13 3.49E – 03 5.004E + 04 1.43E + 13 3.50E – 03 6.99E + 00 1.17E + 05 7.01E + 00 1.19E + 05 1.43E + 05 1.43E + 05 4.990E + 04 1.43E + 13 3.51E – 03 TABLE 12.4 Design of Cascade of N Identical Operational Amplifier Stages CASCADE OF IDENTICAL NONINVERTING AMPLIFIERS Ay (0) GAIN PER STAGE fн1 SINGLE STAGE NUMBER fy N STAGES OF STAGES 1/8 B x fr Rin Rout 1.00E + 05 3.16E + 02 4.64E + 01 1 1.00E + 01 1.000E + 01 2.00E + 09 2.50E + 01 3.16E + 03 2.15E + 04 2.035E + 03 1.098E + 04 3.17E+ 11 2.16E + 12 1.58E – 01 3 2.32E – 02 5.62E + 12 1.78E + 01 1.00E + 01 4 5.62E + 04 2.446E + 04 8.89E – 03 1.00E + 05 3.856E + 04 5.137E + 04 6.229E + 04 7.134E + 04 1.00E + 13 1.47E + 13 1.93E + 13 5.00E – 03 - 1.47E + 05 1.93E + 05 6. 6.81E + 00 5.18E + 00 4.22E + 00 3.41E – 03 2.59E – 03 8. 2.37E + 05 2.37E + 13 2.11E – 03 CASCADE OF IDENTICAL INVERTING AMPLIFIERS NUMBER OF STAGES Ay(0) fн1 SINGLE STAGE fH N STAGES (1/B) – 1 Rin Rout 1.00E + 05 3.16E + 02 4.64E + 01 R1 2.50E + 01 1.00E + 01 3.15E + 03 2.11E + 04 1.00E + 01 2.03E + 03 1 1.58E – 01 R1 R1 1.08E + 04 2.32E – 02 R1 1.78E + 01 1.00E + 01 6.81E + 00 5.32E + 04 2.32E + 04 3.51E + 04 4.48E + 04 4 8.89E – 03 - 9.09E + 04 1.28E + 05 R1 R1 5.00E – 03 6. 3.41E – 03 5.18E + 00 4.22E + 00 1.62E + 05 5.22E + 04 5.77E + 04 R1 R1 2.59E – 03 1.92E + 05 2.11E – 03
(a) Perform a Monte Carlo analysis of the six-stage cascade amplifier design resulting from the exam- ple in Tables 12.4 and 12.5, and determine the frac- tion of the amplifiers that will not meet either the gain or bandwidth specifications. Assume the resis- tors are uniformly distributed between their limits. A, > 100 dB fu 2 50 kHz and (b) What tolerance must be used to ensure that less than 0.1 percent of the amplifiers fail to meet both specifications? The equation here can be used to estimate the location of the half-power frequency for N closely spaced poles, where fHi is the average of the indi- vidual cutoff frequencies of the N stages and f is the cutoff frequency of the ith individual stage. fH = FHIV2/N – 1 where THi =E fin n TABLE 12.5 Cascade of Six Identical Noninverting Amplifiers Av (0) GAIN PER fH1 SINGLE STAGE NUMBER N STAGE OF STAGES STAGE 1/B fH N STAGES GAIN B x fr Rin Rout 6.81E + 00 1.00E + 05 6.83E + 00 1.02E + 05 6.85E + 00 1.04E + 05 1.47E + 05 1.46E + 05 5.121E + 04 1.46E + 13 3.42E - 03 1.46E + 05 5.137E + 04 1.47E + 13 3.41E – 03 5.107E + 04 1.46E + 13 3.43E – 03 6.87E + 00 1.05E + 05 6.89E + 00 1.07E + 05 6.91E + 00 1.09E + 05 6.93E + 00 1.11E + 05 6.95E + 00 1.13E + 05 1.45E + 05 5.092E + 04 1.46E+ 13 3.44E – 03 1.45E + 05 6. 5.077E + 04 1.45E + 13 3.45E – 03 5.062E + 04 1.45E + 13 3.46E – 03 6. - 1.45E + 05 1.44E + 05 5.048E + 04 1.44E+ 13 3.47E –- 03 1.44E + 05 6. - 5.033E + 04 1.44E + 13 3.48E – 03 6.97E + 00 1.15E + 05 1.43E + 05 5.019E + 04 1.43E + 13 3.49E – 03 5.004E + 04 1.43E + 13 3.50E – 03 6.99E + 00 1.17E + 05 7.01E + 00 1.19E + 05 1.43E + 05 1.43E + 05 4.990E + 04 1.43E + 13 3.51E – 03 TABLE 12.4 Design of Cascade of N Identical Operational Amplifier Stages CASCADE OF IDENTICAL NONINVERTING AMPLIFIERS Ay (0) GAIN PER STAGE fн1 SINGLE STAGE NUMBER fy N STAGES OF STAGES 1/8 B x fr Rin Rout 1.00E + 05 3.16E + 02 4.64E + 01 1 1.00E + 01 1.000E + 01 2.00E + 09 2.50E + 01 3.16E + 03 2.15E + 04 2.035E + 03 1.098E + 04 3.17E+ 11 2.16E + 12 1.58E – 01 3 2.32E – 02 5.62E + 12 1.78E + 01 1.00E + 01 4 5.62E + 04 2.446E + 04 8.89E – 03 1.00E + 05 3.856E + 04 5.137E + 04 6.229E + 04 7.134E + 04 1.00E + 13 1.47E + 13 1.93E + 13 5.00E – 03 - 1.47E + 05 1.93E + 05 6. 6.81E + 00 5.18E + 00 4.22E + 00 3.41E – 03 2.59E – 03 8. 2.37E + 05 2.37E + 13 2.11E – 03 CASCADE OF IDENTICAL INVERTING AMPLIFIERS NUMBER OF STAGES Ay(0) fн1 SINGLE STAGE fH N STAGES (1/B) – 1 Rin Rout 1.00E + 05 3.16E + 02 4.64E + 01 R1 2.50E + 01 1.00E + 01 3.15E + 03 2.11E + 04 1.00E + 01 2.03E + 03 1 1.58E – 01 R1 R1 1.08E + 04 2.32E – 02 R1 1.78E + 01 1.00E + 01 6.81E + 00 5.32E + 04 2.32E + 04 3.51E + 04 4.48E + 04 4 8.89E – 03 - 9.09E + 04 1.28E + 05 R1 R1 5.00E – 03 6. 3.41E – 03 5.18E + 00 4.22E + 00 1.62E + 05 5.22E + 04 5.77E + 04 R1 R1 2.59E – 03 1.92E + 05 2.11E – 03
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
Related questions
Question
![(a) Perform a Monte Carlo analysis of the six-stage
cascade amplifier design resulting from the exam-
ple in Tables 12.4 and 12.5, and determine the frac-
tion of the amplifiers that will not meet either the
gain or bandwidth specifications. Assume the resis-
tors are uniformly distributed between their limits.
A, > 100 dB
fu 2 50 kHz
and
(b) What tolerance must be used to ensure that less
than 0.1 percent of the amplifiers fail to meet both
specifications?
The equation here can be used to estimate the
location of the half-power frequency for N closely
spaced poles, where fHi is the average of the indi-
vidual cutoff frequencies of the N stages and f
is the cutoff frequency of the ith individual stage.
fH = FHIV2/N – 1
where THi =E fin
n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facd962c6-9466-40bb-8ed8-397d858d1161%2F415b18e0-378e-43d3-938b-d1fcf62e2bb5%2F7e7t9t.png&w=3840&q=75)
Transcribed Image Text:(a) Perform a Monte Carlo analysis of the six-stage
cascade amplifier design resulting from the exam-
ple in Tables 12.4 and 12.5, and determine the frac-
tion of the amplifiers that will not meet either the
gain or bandwidth specifications. Assume the resis-
tors are uniformly distributed between their limits.
A, > 100 dB
fu 2 50 kHz
and
(b) What tolerance must be used to ensure that less
than 0.1 percent of the amplifiers fail to meet both
specifications?
The equation here can be used to estimate the
location of the half-power frequency for N closely
spaced poles, where fHi is the average of the indi-
vidual cutoff frequencies of the N stages and f
is the cutoff frequency of the ith individual stage.
fH = FHIV2/N – 1
where THi =E fin
n
![TABLE 12.5
Cascade of Six Identical Noninverting Amplifiers
Av (0)
GAIN PER
fH1
SINGLE STAGE
NUMBER
N STAGE
OF STAGES STAGE 1/B
fH
N STAGES
GAIN
B x fr
Rin
Rout
6.81E + 00 1.00E + 05
6.83E + 00 1.02E + 05
6.85E + 00 1.04E + 05
1.47E + 05
1.46E + 05 5.121E + 04 1.46E + 13 3.42E - 03
1.46E + 05
5.137E + 04 1.47E + 13 3.41E – 03
5.107E + 04 1.46E + 13 3.43E – 03
6.87E + 00 1.05E + 05
6.89E + 00 1.07E + 05
6.91E + 00 1.09E + 05
6.93E + 00 1.11E + 05
6.95E + 00 1.13E + 05
1.45E + 05 5.092E + 04 1.46E+ 13 3.44E – 03
1.45E + 05
6.
5.077E + 04 1.45E + 13 3.45E – 03
5.062E + 04 1.45E + 13 3.46E – 03
6.
-
1.45E + 05
1.44E + 05 5.048E + 04 1.44E+ 13 3.47E –- 03
1.44E + 05
6.
-
5.033E + 04 1.44E + 13 3.48E – 03
6.97E + 00 1.15E + 05
1.43E + 05
5.019E + 04 1.43E + 13 3.49E – 03
5.004E + 04 1.43E + 13 3.50E – 03
6.99E + 00 1.17E + 05
7.01E + 00 1.19E + 05
1.43E + 05
1.43E + 05 4.990E + 04 1.43E + 13 3.51E – 03
TABLE 12.4
Design of Cascade of N Identical Operational Amplifier Stages
CASCADE OF IDENTICAL NONINVERTING AMPLIFIERS
Ay (0) GAIN
PER STAGE
fн1
SINGLE STAGE
NUMBER
fy
N STAGES
OF STAGES
1/8
B x fr
Rin
Rout
1.00E + 05
3.16E + 02
4.64E + 01
1
1.00E + 01
1.000E + 01
2.00E + 09
2.50E + 01
3.16E + 03
2.15E + 04
2.035E + 03
1.098E + 04
3.17E+ 11
2.16E + 12
1.58E – 01
3
2.32E – 02
5.62E + 12
1.78E + 01
1.00E + 01
4
5.62E + 04
2.446E + 04
8.89E – 03
1.00E + 05
3.856E + 04
5.137E + 04
6.229E + 04
7.134E + 04
1.00E + 13
1.47E + 13
1.93E + 13
5.00E – 03
-
1.47E + 05
1.93E + 05
6.
6.81E + 00
5.18E + 00
4.22E + 00
3.41E – 03
2.59E – 03
8.
2.37E + 05
2.37E + 13
2.11E – 03
CASCADE OF IDENTICAL INVERTING AMPLIFIERS
NUMBER
OF STAGES
Ay(0)
fн1
SINGLE STAGE
fH
N STAGES
(1/B) – 1
Rin
Rout
1.00E + 05
3.16E + 02
4.64E + 01
R1
2.50E + 01
1.00E + 01
3.15E + 03
2.11E + 04
1.00E + 01
2.03E + 03
1
1.58E – 01
R1
R1
1.08E + 04
2.32E – 02
R1
1.78E + 01
1.00E + 01
6.81E + 00
5.32E + 04
2.32E + 04
3.51E + 04
4.48E + 04
4
8.89E – 03
-
9.09E + 04
1.28E + 05
R1
R1
5.00E – 03
6.
3.41E – 03
5.18E + 00
4.22E + 00
1.62E + 05
5.22E + 04
5.77E + 04
R1
R1
2.59E – 03
1.92E + 05
2.11E – 03](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facd962c6-9466-40bb-8ed8-397d858d1161%2F415b18e0-378e-43d3-938b-d1fcf62e2bb5%2Ff1uwyin.png&w=3840&q=75)
Transcribed Image Text:TABLE 12.5
Cascade of Six Identical Noninverting Amplifiers
Av (0)
GAIN PER
fH1
SINGLE STAGE
NUMBER
N STAGE
OF STAGES STAGE 1/B
fH
N STAGES
GAIN
B x fr
Rin
Rout
6.81E + 00 1.00E + 05
6.83E + 00 1.02E + 05
6.85E + 00 1.04E + 05
1.47E + 05
1.46E + 05 5.121E + 04 1.46E + 13 3.42E - 03
1.46E + 05
5.137E + 04 1.47E + 13 3.41E – 03
5.107E + 04 1.46E + 13 3.43E – 03
6.87E + 00 1.05E + 05
6.89E + 00 1.07E + 05
6.91E + 00 1.09E + 05
6.93E + 00 1.11E + 05
6.95E + 00 1.13E + 05
1.45E + 05 5.092E + 04 1.46E+ 13 3.44E – 03
1.45E + 05
6.
5.077E + 04 1.45E + 13 3.45E – 03
5.062E + 04 1.45E + 13 3.46E – 03
6.
-
1.45E + 05
1.44E + 05 5.048E + 04 1.44E+ 13 3.47E –- 03
1.44E + 05
6.
-
5.033E + 04 1.44E + 13 3.48E – 03
6.97E + 00 1.15E + 05
1.43E + 05
5.019E + 04 1.43E + 13 3.49E – 03
5.004E + 04 1.43E + 13 3.50E – 03
6.99E + 00 1.17E + 05
7.01E + 00 1.19E + 05
1.43E + 05
1.43E + 05 4.990E + 04 1.43E + 13 3.51E – 03
TABLE 12.4
Design of Cascade of N Identical Operational Amplifier Stages
CASCADE OF IDENTICAL NONINVERTING AMPLIFIERS
Ay (0) GAIN
PER STAGE
fн1
SINGLE STAGE
NUMBER
fy
N STAGES
OF STAGES
1/8
B x fr
Rin
Rout
1.00E + 05
3.16E + 02
4.64E + 01
1
1.00E + 01
1.000E + 01
2.00E + 09
2.50E + 01
3.16E + 03
2.15E + 04
2.035E + 03
1.098E + 04
3.17E+ 11
2.16E + 12
1.58E – 01
3
2.32E – 02
5.62E + 12
1.78E + 01
1.00E + 01
4
5.62E + 04
2.446E + 04
8.89E – 03
1.00E + 05
3.856E + 04
5.137E + 04
6.229E + 04
7.134E + 04
1.00E + 13
1.47E + 13
1.93E + 13
5.00E – 03
-
1.47E + 05
1.93E + 05
6.
6.81E + 00
5.18E + 00
4.22E + 00
3.41E – 03
2.59E – 03
8.
2.37E + 05
2.37E + 13
2.11E – 03
CASCADE OF IDENTICAL INVERTING AMPLIFIERS
NUMBER
OF STAGES
Ay(0)
fн1
SINGLE STAGE
fH
N STAGES
(1/B) – 1
Rin
Rout
1.00E + 05
3.16E + 02
4.64E + 01
R1
2.50E + 01
1.00E + 01
3.15E + 03
2.11E + 04
1.00E + 01
2.03E + 03
1
1.58E – 01
R1
R1
1.08E + 04
2.32E – 02
R1
1.78E + 01
1.00E + 01
6.81E + 00
5.32E + 04
2.32E + 04
3.51E + 04
4.48E + 04
4
8.89E – 03
-
9.09E + 04
1.28E + 05
R1
R1
5.00E – 03
6.
3.41E – 03
5.18E + 00
4.22E + 00
1.62E + 05
5.22E + 04
5.77E + 04
R1
R1
2.59E – 03
1.92E + 05
2.11E – 03
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