How did they get these equations break down simply? Where is ra and rb disappearing to?

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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How did they get these equations break down simply? Where is ra and rb disappearing to?
Splidien :-
Vin (-) - Vin (+)
Rg
VIN (+) - VoUT (+)
RA
a)
= Vour l-) - VIN(-)
RA
=> VoUr (-) -VIN(-) = VIN (+) - VOUT (+)
> Nour(+)+をVouT (-) +)+ \I()
Nour (+) + VOUT (-) = 1
=>
%3D
VIN (4) + VIN (-)
い
Transcribed Image Text:Splidien :- Vin (-) - Vin (+) Rg VIN (+) - VoUT (+) RA a) = Vour l-) - VIN(-) RA => VoUr (-) -VIN(-) = VIN (+) - VOUT (+) > Nour(+)+をVouT (-) +)+ \I() Nour (+) + VOUT (-) = 1 => %3D VIN (4) + VIN (-) い
A2a
R.
A26
Figure Q3a
Figure Q3a shows the circuit schematic of part of an instrumentation amplifier.
Show that the differential and common mode gains of the circuit are given by:
(a)
Avdiff
2 Ra+Rb
%3D
and ACM = 1
%3D
Rb
Including the circuit fragment shown in Figure Q3a, draw the diagram of a
traditional three-opamp instrumentation amplifier. Write down expressions for
the differential and common-mode gains of the complete circuit.
(b)
Figure Q3b shows part of a schematic for controlling a cooling fan for a high
power transmitter amplifier. The fan is driven from a 0-12V variable voltage
power supply and the current through the fan is monitored. This monitoring is
important because if the fan stalls or is prevented from turning, excess current
will flow and damage both the fan and the Fan Power Unit. The current flowing
through the fan is monitored using series resistor RCM and the
Instrumentation amplifier, Al. The voltage at 'Vout' is proportional to the fan
current and is used by a control circuit to monitor for excessive current.
Transcribed Image Text:A2a R. A26 Figure Q3a Figure Q3a shows the circuit schematic of part of an instrumentation amplifier. Show that the differential and common mode gains of the circuit are given by: (a) Avdiff 2 Ra+Rb %3D and ACM = 1 %3D Rb Including the circuit fragment shown in Figure Q3a, draw the diagram of a traditional three-opamp instrumentation amplifier. Write down expressions for the differential and common-mode gains of the complete circuit. (b) Figure Q3b shows part of a schematic for controlling a cooling fan for a high power transmitter amplifier. The fan is driven from a 0-12V variable voltage power supply and the current through the fan is monitored. This monitoring is important because if the fan stalls or is prevented from turning, excess current will flow and damage both the fan and the Fan Power Unit. The current flowing through the fan is monitored using series resistor RCM and the Instrumentation amplifier, Al. The voltage at 'Vout' is proportional to the fan current and is used by a control circuit to monitor for excessive current.
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