Break down simply how they got these equations?
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Break down simply how they got these equations?
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Vy(+)
R+A
A2
VOUT
R
R-A
Figure Q2a
Figure Q2a shows the circuit diagram of part of an instrumentation amplifier. The tolerance
of the two pairs of resistors is indicated by the symbolA, such that for resistors R having a
tolerance of T, (so that each resistor value lies in the range R:T), then A has a value 27.
Show that the differential and common mode gains of the circuit are given by:
(a)
Apirr = 1
ACM = 4/R
(b)
Draw the diagram of a traditional three-opamp instrumentation amplifier. Write down
expressions for the differential and common-mode gains of the complete circuit, including
the circuit fragment shown in Figure Q2a.
Sense
4750
Vout
700mH
21
Vc
A1
Ref
10mVrms
Figure Q2b
Figure Q2b shows the test setup in the manufacturing process of phono cartridges used to play
vinyl records. The electrical equivalent model can be represented by a voltage source in series
with a source resistance (475 ohms) and series inductance (700mH) driving a test resistance
(47kohms). Due to the test equipment configuration, there is a common mode voltage between
the cartridge ground and the instrumentation amplifier reference point of 10mV rms.
The electrical output of the phono cartridge is proportional to the stylus velocity and is described
by:
v(t) =2.nfa
Where: v(t) is velocity in ms',f= frequency in Hz, and a = the amplitude of the recorded grove
on the vinyl record in metres. The standard test used by the industry is f= 1000HZ and a vt) of
Scm/second (RMS). For a given cartridge manufacturer, the output voltage (Vc) under these test
conditions is 5mV (RMS).
The smallest detectable signal from the cartridge is 400nVrms. If the signal at the
instrumentation amplifier output, Vout, due to the CM signal should be no greater than
the smallest detectable signal, calculate the required common-mode rejection ratio.
(c)
(d)
During the design phase, the cartridge must be capable of reproducing a peak amplitude
on the vinyl record of 90um at 1000HZ. What is the corresponding peak electrical output
signal from the cartridge?
If additional test equipment attached to the above circuit at Vout requires a signal of
IVrms (+ 0.25dB) for an input signal of 5mVrms at AI, what gain is required in the
instrumentation amplifier? You should assume that the power supply for the systemis +
5V. [Note: you can ignore the effect of the series inductance within the cartridge]
(e)
(f)
Hence design an instrumentation amplifier showing all resistance values and tolerances.
The circuit you designed in part (f) has been optimised to drive production test
(g)
equipment. Considering the worst case peak signals appearing at the output of the
cartridge combined with an audio band covering 20HZ -20kHz, describe any limitations
this circuit might have when playing vinyl music records.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd84942ab-67a3-4593-8510-487f55a9ad56%2Ff932d8ee-6289-4999-956d-fda87fffa0fb%2Fwap48uk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q2
Vy(+)
R+A
A2
VOUT
R
R-A
Figure Q2a
Figure Q2a shows the circuit diagram of part of an instrumentation amplifier. The tolerance
of the two pairs of resistors is indicated by the symbolA, such that for resistors R having a
tolerance of T, (so that each resistor value lies in the range R:T), then A has a value 27.
Show that the differential and common mode gains of the circuit are given by:
(a)
Apirr = 1
ACM = 4/R
(b)
Draw the diagram of a traditional three-opamp instrumentation amplifier. Write down
expressions for the differential and common-mode gains of the complete circuit, including
the circuit fragment shown in Figure Q2a.
Sense
4750
Vout
700mH
21
Vc
A1
Ref
10mVrms
Figure Q2b
Figure Q2b shows the test setup in the manufacturing process of phono cartridges used to play
vinyl records. The electrical equivalent model can be represented by a voltage source in series
with a source resistance (475 ohms) and series inductance (700mH) driving a test resistance
(47kohms). Due to the test equipment configuration, there is a common mode voltage between
the cartridge ground and the instrumentation amplifier reference point of 10mV rms.
The electrical output of the phono cartridge is proportional to the stylus velocity and is described
by:
v(t) =2.nfa
Where: v(t) is velocity in ms',f= frequency in Hz, and a = the amplitude of the recorded grove
on the vinyl record in metres. The standard test used by the industry is f= 1000HZ and a vt) of
Scm/second (RMS). For a given cartridge manufacturer, the output voltage (Vc) under these test
conditions is 5mV (RMS).
The smallest detectable signal from the cartridge is 400nVrms. If the signal at the
instrumentation amplifier output, Vout, due to the CM signal should be no greater than
the smallest detectable signal, calculate the required common-mode rejection ratio.
(c)
(d)
During the design phase, the cartridge must be capable of reproducing a peak amplitude
on the vinyl record of 90um at 1000HZ. What is the corresponding peak electrical output
signal from the cartridge?
If additional test equipment attached to the above circuit at Vout requires a signal of
IVrms (+ 0.25dB) for an input signal of 5mVrms at AI, what gain is required in the
instrumentation amplifier? You should assume that the power supply for the systemis +
5V. [Note: you can ignore the effect of the series inductance within the cartridge]
(e)
(f)
Hence design an instrumentation amplifier showing all resistance values and tolerances.
The circuit you designed in part (f) has been optimised to drive production test
(g)
equipment. Considering the worst case peak signals appearing at the output of the
cartridge combined with an audio band covering 20HZ -20kHz, describe any limitations
this circuit might have when playing vinyl music records.
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