The temperature of a pressure relief valve at a nuclear power station is being monitored with a thermocouple. The thermocouple and its leads may be represented by a Thevenin generator of 100 ohm and 100 mV at standard operating temperature.
The voltage of the thermocouple must be monitored by an oscilloscope a long distance from the reactor. Thus a 30dB amplifier is selected to amplify the voltage for transmission to the scope. The amplifier's input impedance is 100 k and its output impedance is 50 ohm.
The coax cable connecting the amplifier to the scope is properly terminated. What voltage does the oscilloscope display?
The general configuration of an amplifier is shown below, with the transducer represented as a Thevenin generator.
From the quiz statement,
|RTh =||100 ohm|
|VTh =||100 mV|
|Rin =||100 k|
|Av =||30dB = 31.6|
|Rout =||50 ohm|
|Rload =||50 ohm for a properly terminated coax cable|
Vin =(Rin)/(Rin + RTh) VTh = (100k/100.1k)(100 mV) = 99.9 mV.
V2 = AvVin = 31.6 (99.9 mV) = 3.16 V.
Vout =(Rload)/(Rload + Rout) V2 = (50/100)(3.16 V) = 1.58 V.