Circuit Models. Lab 5

Transcription

1 Circuit Models Lab 5 1

2 Equipment List DC power supply Decade resistance box (2) 1.5kΩ, 2.2kΩ, 560Ω 2

3 Circuit Models Any circuit can be modeled by either a Thevenin or a Norton model Any circuit whose output can be measured, can be represented by either model 3

4 Black Box The circuit can be represented as a black box with two terminals available for voltage and current measurements V I 4

5 Equivalent Circuit Measure V OC (open circuit voltage) and I SC (short circuit current) at the output terminals of the black box Construct the Thevenin and Norton model 5

6 Thevenin Model This model states that any circuit can be modeled as a voltage source in series with a resistance of a specific value (VSC series Rth) 6

7 Norton Model This model states that any circuit can be represented as a current source parallel to a resistance of a specific value (Isc//Rth) 7

8 Checking Equivalence The easiest method to check equivalence is to connect a load of the same resistance across the output terminals of the original circuit (black box) and the two models If the voltages across and currents through the load for each circuit are the same, the models are equivalent to the black box 8

9 Circuit Models for Complex Circuits Build the circuit shown below (using LTspice) 9

10 Open Circuit Voltage To calculate V OC (open circuit voltage) replace R 2 by a very high value as shown, so that no current flows through R 2. Measure voltage across R 3 V OC 10

11 Circuit Models for Complex Circuits Thevenin Resistance can be calculated as R Th = (V OC )/I sc, where I sc is measured across as shown (Isc is at right side of circuit) I sc 11

12 Simple Problem Find the Thevenin Resistance if The black box delivers 6V at the output terminals with an open circuit, and The black box delivers 5.11 volts when connected to a load resistance of 270 ohms You may wish to hand calculate Rth first. 12

13 Circuit Models for Complex Circuits Build the circuit shown below on the breadboard. 13

14 Measurements Using the multimeter, measure the open circuit voltage at the output terminals. This is V OC, the open circuit voltage. In addition, connect a decade box between the output terminals and set the values of the decade box as given in the grading sheet. Measure the voltage drop for each load setting and note it down on the table in the grading sheet. 14

15 Finding Thevenin Resistance To find Thevenin resistance, short all DC voltage sources, and open all DC current sources. Measure the resistance from the load terminals. The original circuit we built, becomes: Short Open 15

16 Thevenin Model Find the Thevenin resistance using a multimeter on your breadboard circuit. Using this resistance, build the Thevenin model (using decade resistance boxes) on your breadboard, and measure the voltage drop across the loads as given on your grading sheet. Do they match up with the measurements obtained previously? 16

17 Calculating Necessary Values Open circuit voltage and Thevenin resistance can also be calculated from the circuit very easily 17

18 Calculating Thevenin Resistance To calculate Thevenin resistance, short any DC voltage sources, and open any DC current sources The original circuit we built, becomes: Short Open R Th 18

19 Calculating Thevenin Resistance Looking in from the output terminals, hand calculate the equivalent resistance Show the steps clearly and legibly on your data sheet 19

20 Calculating Open Circuit Voltage To calculate V OC, it should be noted that resistance R2 does not draw any current Remove R2 from the circuit 20

21 Calculating Open Circuit Voltage The circuit is reduced to a simple voltage divider The voltage drop across the resistance R3 is the open circuit voltage (VR3 = Open Circuit Voltage) Show your calculations on the data sheet Does your calculated value match up with the measured value? 21

22 Norton Model Using the Thevenin resistance and the I SC measurement, Hand CALCULATE the voltage dropped across the loads as given in your grading sheet Do these values match up with the voltage measurements made on the original circuit? 22