DC voltage and current measurements

DC voltage and current measurements Manual for the laboratory exercise Edited by: Łukasz Śliwczyński Witold Skowroński Karol Sawik ver. 3, 05.2018

1. Aim To get acquainted with the methods of DC voltage and current measurements and influence of internal impedance of used equipment on measured results. Measurement and calculation of the resistance of parallel-serial circuits. Calculations of output impedance of voltage source. Derivation of measurement accuracy. To learn how to correctly write down and process measurement data. 2. Setup description The block diagram of the measurement setup for DC voltage and current measurements is presented in Fig. 1. Printed circuit board (PCB) setup consist of three parts: DC voltage, DC currents and source resistance measurement. In addition, the following equipment will be used: 9V AC power supply Table digital multimeter Agilent U3401A Portable digital multimeter MU-02D Analogue voltmeter and ammeter YX-360TR Fig. 1. Simplified schematics of the measurement system. Schematics with all elements together with the PCB layout is attached in the Appendix section. 2

3. Exercise preparation 1. Print (or redraw) appendix 2 from the manual, including tables 1-6 2. Sketch a schematics of simple voltage divider with resistors RL and RH. Write down a formula for the voltage drop on one of them including its uncertainty, by taking into account the uncertainty of measured voltage and tolerance of the resistance values. 3. Sketch a voltage divider circuit with a voltmeter with a finite internal resistance RV (read the internal resistance from the datasheet of Agilent U3401A multimeter). Give the formula for the voltage drop across the resistor and the uncertainty of the measured voltage considering the resistance tolerance (5%) divider RL and RH and internal resistance of the multimeter RV and the uncertainty of the measurement voltage divider. 4. Calculate the correction taking into account the effect of the internal resistance of the voltmeter on the measurement result in the voltage divider. Determine the uncertainty of this correction on the basis of tolerances of resistors. 5. From the datasheet of Agilent U3401A multimeter (available on the website of the course) read values: internal resistance of ammeter at various measuring ranges, the uncertainty of measurement of DC voltage, current and resistance at various ranges. 6. Refer to the three-state logic gate operation and the meaning of the term "high impedance". 7. Write the formula for the resistance of the parallel connection of three resistors and its uncertainty by taking into account the resistance tolerance (assume 5%). 8. Write down the equation for current and it s uncertainty from Ohm s law. 9. Calculate the resistance of the copper wire on the PCB with length of 120 cm, width of 0.5 mm and the thickness of 35 m (assuming copper resistivity at room temperature). 10. Get familiar with following terms: standard uncertainty, extended uncertainty. Learn about proper correct measurement data writing. 4. Measurement plan Connect AC power supply to the measurement setup. Proper operation will be indicated by LED operation. 1. DC voltage measurements 1.1. Using Agilent U3401A multimeter measure voltage drop on three voltage dividers (using measurement points TP7-TP9 with respect to GND). Write down measured values together with their uncertainties (use accuracy data from the multimeter manual) in Table 1. Measure the supply voltage (Vcc) and include it in the Table 1. Repeat this procedure for portable multimeter MU-02D and analogue voltmeter YX-360TR. 1.2. Read resistance values of voltage dividers R9-R11 and R17-R19, write them down in Table together with uncertainties. 3

1.3. Measure the voltage on the outputs of buffer gates 74HC125 using measurement points TP11 TP14 with respect to GND and voltage supply (Vcc) using both Agilent U3401A and analogue voltmeter YX-360TR. Voltage values and their uncertainty put in Table 2. 2. DC current measurement 2.1. On the basis of resistors color code (in Appendix) read values of three resistors in the current measurement circuit (R2, R5, R6) and write them down with uncertainties in Table 3. 2.2. Disconnect jumper JP1, connect jumper JP2. Using ohmmeter measure load resistance of voltage stabilizer U1 between points TP2 and TP18. Measured values with uncertainties write down in Table 3. 2.3. Using potentiometer R3 set output voltage of stabilizer U1 between 1 and 4 V, by measuring is on TP1 point with respect to ground. Voltage value and its uncertainty write down in Table 4. 2.4. Measure current that flow through the load using measurement points TP1 and TP2 and two different ammeter ranges: 500 ma and 10A (change both the range on the front panel of the multimeter and input connectors). Repeat this measurement with jumper JP2 disconnected. Measure the resistance of the meander wire between TP18 and GND. All values with their uncertainties write down in Table 4. 2.5. Changing the load current using R3 potentiometer, measure 10 pair of points: voltage on the load resistance (between points TP2 and TP18) and the output voltage of U2 Hall meter ACS712. Voltage values with their uncertainties write down in Table 5. 2.6. Check and comment and influence of metallic and magnetic elements in the proximity of the Hall meter on measurement results. 3. Measurement of output resistance of the voltage source 3.1. Measure load resistance of the voltage source: three resistors R13-15 connected in parallel and resistor R16. Write down their values together with uncertainties. 3.2. Measure output voltage of stabilizers: regulated (U1 NCP5662, jumper JP3), LDO (Low- Dropout*, U4, jumper JP4) and reference voltage source (parallel stabilizer, band gap * U6, jumper JP5) with different load resistance connected (jumper JP6 or JP7). Voltages and their uncertainties write down in Table 6. *) stabilizer models may be different for each setup 3.3. Using the differential method described in the Appendix, based on necessary measurements calculate output resistance of three different voltage stabilizers. Values together with uncertainties write down in Table 6. 3.4. Observe and comment and influence of the cabling on measurement results (on the measurement setup an additional cabling is mimicked by folded wire installed on the PCB connected via JP8) 4

5. Data processing 1. Values of resistances R9-R11 and R17-R19 (localize them using schematics attached in the Appendix) together with their tolerance write down in Table 1. Calculate theoretical values of voltage on measurement point TP7 and TP9 with respect to ground. Compare measured values with the theoretical calculations. Comment any discrepancies. R9-R17, TP7 R10-R18, TP8 R11-R19, TP9 RH RL Vtheory VAgilent Vportable Vanalogue Table 1. 2. Based on the model prepared before the exercise, calculate voltage correction value, which has to be taken into account due to a finite resistance of the voltmeter (given in the multimeter manual). Compare calculations with measurements using this correction. 3. Compare measured results of the output voltages of 74HC125 buffer gates with theoretical model, assuming that input of gates connected to TP11 and TP13 are low, the ones connected to TP12 and TP14 are high and outputs of TP13 and TP14 are enabled and for TP11 and TP12 are disabled. Measured V with respect to GND Measured V with respect to Vcc Comment U3401A YX-360TR U3401A YX-360TR TP11 TP12 TP13 TP14 Table 2. 4. Calculate load resistance RL of current measurement setup (R2, R5, R6 connected in parallel) including resistance tolerance. Compare it with measured values (with jumper JP2 connected). R2 R5 R6 RL measured RL= R2ǁR5ǁR6 - theory 5

Table 3. 5. Calculate theoretical value of current that flows through the resistive load using Ohm's law. Compare it with measured values Table 4. Compare measured resistance of meander wire with theoretical calculations of copper path from the preparation part. Voltage set using potentiometer R3: VTP1 =... I ma range JP2 connected I A range JP2 connected I ma range JP2 disconnected I A range JP2 disconnected I theoretical Tabela 4. Meander resistance measurement: Rmeander =... 6. Calculate internal resistance of ammeter set to 10A and 500mA range, respectively. Compare calculated values with the manual of Agilent U3401A. 7. Using Ohm's law calculate current flowing through the resistive load (three resistors R2, R5 and R6 connected in parallel) and write it down in Table 5. Next, using two-parameter liner regression method calculate Hall sensor ACS712 sensitivity, defined as the ration between output voltage and input current. No. 1 2 3 4 5 6 7 8 9 10 VRL IL VHall Table 5. 8. Measured values of stabilizers' output voltage with different loads write down in Table 6 together with their uncertainties. Comment any discrepancies. 6

U5 TL431ACT regulated VO JP6 and JP7 disconnected VJP6 JP6 connected (RL2) VJP7 JP7 connected R16 V1 TP5 TP6 V2 TP5 TP6 Rw (to be calculated) U1 NCP5662 regulated U4 LDO unregulated U6 band gap unregulated Table 6. R16 =... RL2 =... 9. For advanced students: calculate the output resistance of voltage stabilizer U6 for jumper JP8 disconnected. Comment obtained results. Can one expect similar effect for stabilizer U6 (add comment why or why not). Appendix 1 Derivation of output resistance of voltage source using differential method. Low value of voltage source output resistance VS can be derived by comparing a voltage drop on resistance RL, which is connected in parallel with an alternative, reference voltage source VR which supplies similar output voltage. Simple diagram of such setup is sketched in Fig. 2. Fig. 2. Diagram of differential method for voltage source output resistance measurement. When the load resistor RL is disconnected, voltmeter indicates the difference between voltages supplied: V1 = VS VR (1) When one connects load resistor RL, voltmeter indicate voltage, which is the difference between voltage drop on RL : VRL = VS*(RL/Rout+RL) (2) and voltage on the reference voltage source VR: V2 = VS*(RL/Rout+RL) VR (3) Reformulating equation (3) one can calculate the output resistance of voltage source Rout. 7

Appendix 2 Measurement tables: Supply voltage: VTP4= RH RL Vtheory VAgilent Vportable Vanalogue R9-R17, TP7 R10-R18, TP8 R11-R19, TP9 Table 1. Measured V with respect to GND Measured V with respect to Vcc Comment U3401A YX-360TR U3401A YX-360TR TP11 TP12 TP13 TP14 Voltage set using potentiometer R3: VTP1 = Table 2 I ma range JP2 connected I A range JP2 connected I ma range JP2 disconnected I A range JP2 disconnected I theoretical Table 4. Meander resistance measurement: Rmeander = No. 1 2 3 4 5 6 7 8 9 10 VRL IL VHall Table 5. 8

Fig. 4. Schematic of the measurement setup PCB 10

Fig. 5. PCB with element layout. 11