lecture 6 review: circuit reduction circuit reduction examples practical application temperature...

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

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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:

• 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.

i1VO

+

-VS

+

-

6A 9W

3W 1W

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

• 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!

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