Experiment 3: Basic Electronic Circuits II (tbc 1/7/2007)

Transcription

1 Experiment 3: Basi Eletroni iruits II (tb /7/007) Objetive: a) To study the first-order dynamis of a apaitive iruits with the appliation of Kirhoff s law, Ohm s law and apaitane formula. b) To learn how to do data-logging using Labview 8 and the USB-6009 devie. I. apaitors A. Definitions and Units B. Symbols apaitane () ratio of eletrial harge (Q) to voltage () Units: farad (F) oulomb/volt apaitors are eletrial omponents with onstant apaitane: Q dq d dq d I d I d aution: some apaitors (speially eletrolyti types) are polarized. Figure. Symbols for apaitors.

2 II. Experimental Setup Figure. 0µF, MΩ II. Labview Setup Figure. Front Panel onfiguration

3 Figure 3. Blok Diagram onfiguration. Proedure to inlude the ead apaitor blok shown in Figure 3:. In the Blok Diagram window, aess the Funtions palette and expand the [Express] [Input] ion subdiretory. Selet the [DAQ Assistant] blok and drop into the While loop box.. A onfiguration window should pop out. [lik] the [Analog Input] item to expand the menu hoies, then selet [oltage]. (see Figure 4) 3. A menu of available hannels and devies should appear. ( Make sure the USB devie is onneted to the omputer). Selet the item ai0 then [lik] the [Finish] button to move on to the onfiguration window. lik this to expand the menu hoies. Figure 4. 3

4 4. In the onfiguration window, math the values given in Table. Table. Settings for DAQ Assistant blok. Settings Input ange Min -5 Max 5 Saled Units olts Terminal onfiguration Differential Task Timing Aquisition Model ontinuous lok Settings Samples to ead 0 ate (Hz) [lik] the [OK] button to finish. (You may need to move the onfiguration window to the left to show the [OK] button on the lower right orner of the window.) 6. hange to ion view and rename the blok as ead apaitor, if desired. III. Tasks/Proedure. onstrut both the experimental setup and the Labview I setup.. With the power supply off, run the Labview I. Make sure that the voltage reading of the apaitor voltage starts at zero. ( If not, wait until the voltage settles to zero then stop and repeat the Labview run ) 3. At a hosen elapsed time (e.g. 0 seonds), turn the power supply on 4. Wait until the voltage settles to a new steady state then stop the Labview run. 5. Load the data into an Exel spreadsheet similar to the one shown in Figure 5. The model for the estimated apaitor voltage will be a first order model: d τ ) final ( t ) 0) initial () where τ is the time onstant, and t ) is the time elapsed after step hange. Assuming ap initial for t ) <0, the solution is given by: final ( ) initial initial final if t < tstart t tstart exp τ if t tstart () 4

5 (8-D8)^ AEAGE(E8: E37) IF( B8<$$, $$3, $$4($$3-$$4)* EXP(-(B8-$$)/$$5) Figure 4. Sample spreadsheet. 6. Use SOLE to minimize the root mean square (MS) error, by modifying the values of t start, initial, final and τ. Plot the data together with the estimated voltages to see if the fit is visually aeptable. Fill-in the values in Table. 7. Using the voltmeter, measure: a) the atual resistane of the MΩ resistor b) the apparent resistane of the USB-6009 devie ) the atual apaitane of the 0 µf apaitor d) s the voltage of the power supply and fill-in the values in Table ompare the value of time onstant τ and final,obtained from the parameter estimation in step 6, with the alulated values uisng equation (5) below, whih are based on Kirhoff s law, Ohm s law and the apaitane formula. Let, and be the voltages aross the MΩ resistor, the USB-6009 devie and the apaitor, respetively. Likewise, let I, I and I be the urrent flowing aross the MΩ resistor, the USB-6009 devie and the apaitor, respetively. Thus, I I I d Sine s and, we have (3) 5

6 6 s s s d d d (4) After omparing the oeffiients of (4) with (), final s τ (5) Table. From Data Fitting alulated from Eqn (5) % elative Error τ final initial t start

7 Table 3. s alulation for τ and final using equation (5): 7