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Lecture 6

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:.

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Lecture 6

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

  2. Review: series resistors and voltage division • Equivalent resistance: Voltage divider formula:

  3. Review: parallel resistance and current division • Equivalent resistance: Current divider formula:

  4. 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

  5. Examples: Non-ideal “loaded” power sources • Loaded voltage source: • Loaded current source:

  6. 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

  7. Circuit reduction – example 1 • Determine the equivalent resistance of the circuit below

  8. Circuit reduction – example 2 • Determine Vout in the circuit below.

  9. Circuit reduction – example 3 • In the circuit below, find i1, VS, and VO.

  10. Example 3 – continued

  11. Example 3 – continued

  12. Circuit reduction – example 4 • In the circuit below, determine (a) the equivalent resistance seem by the source, (b) the currents i1 and i2

  13. Example 4 – continued

  14. 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

  15. 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

  16. Example thermistor characteristics • NTC 10K @ 25C • Negative temperature coefficient thermistor with (nominal) resistance of 10k at 25C • Response:

  17. 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

  18. 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!

  19. Effect of resistance change on voltage

  20. Demo: • Change of thermistor resistance with temperature (DMM) • Change of output voltage from voltage divider • R<<RTH • R>>RTH • Intermediate R

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