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Lecture 6•Review:
•Circuit reduction•Circuit reduction examples•Practical application
•Temperature measurement •Related educational materials:
–Chapter 2.3
Checking parallel resistance results• The equivalent resistance of a parallel combination
of resistors is less than the smallest resistance in the combination• Resistance decreases as resistors are added in parallel
• Range of equivalent resistance:
• Rmin is the lowest resistance; N is the number of resistors
Circuit Reduction
• Series and parallel combinations of circuit elements can be combined into a “equivalent” elements
• The resulting simplified circuit can often be analyzed more easily than the original circuit
Circuit reduction – example 3• In the circuit below, find i1, VS, and VO.
i1VO
+
-VS
+
-
6A 9W
3W 1W
2W 5W
Circuit reduction – example 4• In the circuit below, determine
(a) the equivalent resistance seem by the source,(b) the currents i1 and i2
i1
i2
Practical application – temperature measurement
• Design a temperature measurement system whose output voltage increases as temperature increases
• In general, we will typically have other design objectives• For example, power and sensitivity requirements• We neglect these for now; lab 2 will provide a more
rigorous treatment of this problem
Temperature sensors: thermistors
• Thermistors are sensors whose resistance changes as a function of temperature• Thermistors are classified as either NTC (negative temperature
coefficient) or PTC (positive temperature coefficient)• Resistance increases with temperature for PTCs; Resistance
decreases with temperature for NTCs• A resistance variation is generally not directly useful;
information is generally relayed with voltage• We need to convert the resistance change to a voltage change
Example thermistor characteristics
• NTC 10KW @ 25C
• Negative temperature coefficient thermistor with (nominal) resistance of 10kW at 25C
• Response:
Initial Design Concept
• Use voltage divider to convert resistance variation to voltage variation
• Design problem: choose Vs and R to obtain desired variation in Vout for a given variation in temperature
Potential Design Issues• Sensitivity
• Our design requirements may specify a minimum voltage change per degree of temperature change (the sensitivity of the instrumentation system)
• We can affect the sensitivity with our choice of R• Power requirements
• We can increase the sensitivity by increasing VS
• Increasing VS increases the power required by the system; increasing power (generally) increases cost
• The above can cause us to modify or discard our initial design concept!
• Demo:– Change of thermistor resistance with temperature
(DMM)– Change of output voltage from voltage divider• R<<RTH• R>>RTH• Intermediate R