Lecture 6
•Review:
•Circuit reduction
•Circuit reduction examples
•Practical application
•Temperature measurement
•Related educational materials:
–Chapter 2.3
Review: series resistors and voltage division
• Equivalent resistance:
Voltage divider formula:
Review: parallel resistance and current division
• Equivalent resistance:
Current divider formula:
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
Examples: Non-ideal “loaded” power sources
• Loaded voltage source:
• Loaded current source:
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 1
• Determine the equivalent resistance of the circuit below
Circuit reduction – example 2
• Determine Vout in the circuit below.
Circuit reduction – example 3
• In the circuit below, find i1, VS, and VO.
3W
+
6A
VS
-
9W
i1
1W
+
VO
-
2W
5W
Example 3 – continued
Example 3 – continued
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
Example 4 – continued
•
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
• Response:
• NTC 10KW @ 25C
• Negative temperature
coefficient
thermistor with
(nominal) resistance
of 10kW at 25C
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!
Effect of resistance change on voltage
• Demo:
– Change of thermistor resistance with temperature
(DMM)
– Change of output voltage from voltage divider
• R<<RTH
• R>>RTH
• Intermediate R