Lecture 6 Review: Circuit reduction Circuit reduction examples Practical application Temperature measurement Related educational modules: –Section 1.5, Lab assignment 2

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: R min 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 V out in the circuit below.

Circuit reduction – example 3 In the circuit below, find i 1, V S, and V O.

Example 3 – continued

Circuit reduction – example 4 In the circuit below, determine (a) the equivalent resistance seem by the source, (b) the currents i 1 and i 2

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 NTC 10K 25  C Negative temperature coefficient thermistor with (nominal) resistance of 10k  at 25  C Response:

Initial Design Concept Use voltage divider to convert resistance variation to voltage variation Design problem: choose V s and R to obtain desired variation in V out 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 V S Increasing V S 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