- To understand the basics of DC (direct current) circuits.
- To use a digital multimeter (DMM) to measure DC voltage, current and resistance.
- To understand the valid measurement condition for a digital multimeter.
- DC power supply
- Digital multimeter (DMM)
I. DC circuit basics
A DC circuit is an electrical circuit that consists of any combination of constant voltage sources, constant current sources and resistors. The voltages and currents in this circuit are invariant with time, in other words, constant. A DC circuit is usually powered by a DC voltage source or a DC current source.
There are basic concepts and laws that are fundamental to circuit analysis. These laws are Ohm’s law, KCL (Kirchhoff’s current law or Kirchhoff’s first law) and KVL (Kirchhoff’s voltage law or Kirchhoff’s second law). In addition, the voltage divider rule and the current divider rule are often applied to simplify the circuit analysis.
A breadboard is also referred to as a solderless breadboard or a plugboard. It is used to build temporary circuits for testing or to experiment new circuit ideas. It has many holes, which can be used to plug in resistors, capacitors, inductors, ICs, and etc. A typical breadboard is shown in Figure 1 – 1. The backside of the bread board, Figure 1 – 1 (b), has strips of metal connecting the holes on the front side. The holes connected by a same metal strip form one common node in a circuit. Different components at a given node are connected by pushing in a corresponding end of each component into holes connected to the same node. It is also noticed that some common nodes are longer than most of the five-hole nodes. They are typically used for power supply connections or for those nodes to which many components are connected. A jumper wire can also be used to combine two nodes into one.
The breadboard we are using for this lab also has four binding posts on one side of the board. They are used for DC or AC power supply connections. To connect a binding post onto the breadboard, a wire with long-enough metal exposed is inserted into the hole at the bottom of the post followed by tightening the plastic cap to ensure good connection. The other end of the wire is then plugged into one of the long common nodes on the breadboard.
Here are a few tips for using the breadboard.
- Never build your circuit without a breadboard, even for the easiest circuit configurations.
- Always use the binding posts and side-lines (long common nodes) for power supply connections.
- It is recommended to use black wires for ground and red (or other colors if there are multiple voltages needed) for positive voltage (or other DC/AC voltages).
- Keep the jumper wires short and flat on the board, so that the circuit doesn’t look cluttered.
- Route jumper wires around the chips, so that it makes it easy to change the chips.
- You could trim or bend the resistor/capacitor/inductor lead, so that they will fit in snugly and won’t get pulled out by accident.
- A wire should be used to connect the probe of an oscilloscope onto the breadboard, since the probe connection might loosen the existing connection of your components.
Figure 1 – 1 Breadboard. (top) front; (bottom) back.
III. DC power supply
A DC power supply is a device that supplies DC voltage and current to a circuit. The one we are going to use for this lab is an Agilent E3630A Triple Output DC Power Supply, as shown in Figure 1 – 2. It offers three output ratings: 0 to +20V (0 to 0.5A), 0 to -20V (0 to 0.5A) and 0 to 6V (0 to 2.5A), with a total maximum power of 35W. The +/-20V output have the ability to track each other by adjusting the Tracking Ratio knob, while the 6V output is adjusted separately. When setting each output, the corresponding range needs to be selected on METER section in order to have that particular output displayed on the LED. On VOLTAGE ADJUST section, the +6V knob is used to adjust the 6V output. The +/-20V knob adjusts both the +20V and the -20V output at the same time. Therefore, when two voltages with the same absolute value but opposite polarities are needed, the Tracking Ratio knob needs to be set at Fixed position, which means the tracking ratio is 1. However, when two voltages with different absolute values and polarities are needed from the +20V and the -20V output, one of the two (usually the +20V) needs to be adjusted first using the +/-20V knob, then by varying the Tracking Ratio knob, the other voltage is then set to the desired output. The COM knob in OUTPUT section is used as the common ground for all three outputs. The LED will show both the voltage and current for the voltage range selected, and when the current exceeds the maximum current rating during measurement, the OVERLOAD indicator will turn on.
Figure 1 – 2 Agilent E3630A DC power supply. (top) front; (bottom) back.
IV. Digital multimeter
A digital multimeter (DMM) is an electronic measuring instrument that combines several measurement functions, such as voltage, current and resistance measurement, in one unit, and displays its result digitally. The one we are going to use in this lab is a Tektronix DMM4050 6-1/2 Digit Precision Multimeter, as shown in Figure 1 – 3. This DMM is capable of measuring DC/AC voltages and currents, resistance, integrated frequency, period, capacitance and temperature measurement.
Figure 1 – 3 Tektronix DMM 4050
Here are a few tips for using the DMM.
- Voltage is measured by placing the DMM in parallel with the device under test (DUT) on which the voltage is to be measured, as shown in Figure 1 – 4 (a). First connect the DMM input connector (red probe) to 1000V/600V input, and select DCV or ACV. The ground probe (black probe) is connected to the corresponding LO input. Then place the probes on two sides of the DUT. Preferably, the red probed should be connected to the side with higher potential. But sometimes it is hard to decide in a circuit with multiple DC voltage sources as for which end of the DUT has higher potential. It is fine to just randomly pick a side. If the reading ends up being negative, that means the red probe is connected to the lower-potential end.
- Current is measured by inserting the DMM into the circuit and letting the current being measured go through the DMM, as shown in Figure 1 – 4 (b). First connect the DMM input connector (red probe) to 400 mA or 10 A input, and select DCI or ACI. The ground probe (black probe) is connected to the corresponding LO input. Then insert the probes into the branch being measured. Preferably, current should flow into the DMM from the red probed and flow out from the black probe. But sometimes it is hard to decide the current direction in a circuit with multiple DC voltage sources. It is fine to assume a direction. If the reading ends up being negative, that means the current flows in the opposite direction from your assumption.
- Resistance measurement is done similar to the voltage measurement by placing the DMM across the resistor to be measured, as shown in Figure 1 – 4 (c) and use the Ω The ground probe (black probe) is connected to the corresponding LO input. Note that the resistor being measured should be disconnected from the rest of the circuit during this measurement.
- A DMM usually has an internal resistance (typically of 10 MΩ), as shown in the circuit in Figure 1 – 6 (e). The measurement result will be inaccurate if the resistor for which the voltage or current being measured is comparable in value to the internal resistance.
Figure 1 – 4 Voltage, current and resistance measurement using DMM, (a) voltage; (b) current; (c) resistance.
Multisim is an electronic schematic capture and simulation program used to analyze circuit behavior. The DC/AC voltage, DC/AC current, resistance, frequency, time-domain waveform, etc, can be determined using this software. An example circuit simulation measurement is shown in Figure 1 – 5. In this simulation, all the components are laid out in a way that is the same as the circuit diagram. Each DMM is connected in the same way that a physical DMM would be connected on the breadboard. Results are obtained by running the simulation and then double clicking on each piece of equipment (DMM, oscilloscope, etc) to read the desired output values.
Figure 1 – 5 An example for using Multisim
VI. Standard resistor color code
Low-power resistors have a standard set of values. Color-band codes indicate the resistance value as well as a tolerance value. Refer to APPENDIX I on how to read the resistance using the color codes.
For the circuits in Figure 1 – 6, use VS = 9V as the input voltage and choose any resistor values within the range of
1 kΩ to 56 kΩ unless specified otherwise. Assign the same value to all resistors with the same name and different values to those with different names. Refer to APPENDIX II for available resistors.
A. Equivalent Resistance Calculation
- For the circuit in Figure 1 – 6 (a), calculate
- the equivalent resistance between nodes A & B, RAB;
- the equivalent resistance between nodes B & D, RBD;
- the equivalent resistance between nodes A & C, RAC.
B. Voltage and Current Calculation
- For the circuit in Figure 1 – 6 (b), perform the following steps.
- Calculate V1, V2, V3 and IS WITHOUT using the voltage division rule.
- Calculate V1, V2 and V3 again using the voltage division rule and compare the values with those determined in Part a.
- Is the addition of VS, V1 and V3 equal to the value of V2? Why? Explain your reasoning in detail.
- A practical voltmeter can be modeled by an ideal voltmeter in parallel with an internal resistor, RINT, as shown in Figure 1 – 6 (c). Assuming that the internal resistance is RINT = 10 MΩ, calculate VO for
- R = 10 kΩ;
- R = 10 MΩ.
Are the above results identical? Why? Explain your reasoning in detail.
- For the circuit in Figure 1 – 6 (d), perform the following steps.
- Calculate I1, I2, and I3 WITHOUT using the current division rule.
- Calculate I2 and I3 again using the current division rule and compare the values with those determined in Part a.
- Is the addition of I1 and I3 equal to the value of I2? Why? Explain your reasoning in detail.
Simulate all the circuits in Figure 1 – 6 using MultiSim.
- For the circuit in Figure 1 – 6 (a), use a DMM to read RAB, RBD and RAC.
- For the circuit in Figure 1 – 6 (b), use a DMM to read V1, V2, V3 and IS.
- For the circuit in Figure 1 – 6 (c), use a DMM to read VO for both cases considered in PREPARATION.
- For the circuit in Figure 1 – 6 (d), use a DMM to read I1, I2, and I3.
Compare all the simulation results with those determined in PREPARATION.
- Before you begin your experiment, flip over the breadboard and study the metal coating carefully so that you fully understand the connections on the breadboard. Ask your Lab TA if you cannot gain a full understanding.
- Refer to ‘Digital Multimeter’ in ‘BACKGROUND’ section on how to use a DMM to measure resistance, voltage and current.
A. Resistance Measurement
- Measure the resistance of each resistor used in this experiment using a DMM. Compare the nominal value with the measured value. The nominal value of a resistor can also be obtained from its color bands or color code.
- Construct the circuit in Figure 1 – 6 (a) on a breadboard and measure the equivalent resistances RAB, RBD and RAC. LEAVE THIS CIRCUIT IN PLACE for additional measurements.
B. Voltage and Current Measurement
- For the circuit in Figure 1 – 6 (a), perform the following steps.
- Measure the equivalent resistance RAB again using one DMM. At the same time, use a second DMM to measure the voltage across the first DMM (between nodes A & B). Then, use the second DMM to measure the current supplied by the first DMM.
- Repeat all the steps in Part a for RBD and RAC.
- For all three cases, determine the ratio of the measured voltage to the measured current. What observations or conclusions can be made based on the ratios?
- For the circuit in Figure 1 – 6 (b), measure V1, V2, V3 and IS.
- For the circuit in Figure 1 – 6 (c), measure VO for both cases considered in PREPARATION.
- For the circuit in Figure 1 – 6 (d), measure I1, I2, and I3.
- Compare all measured values with the calculated and simulated results.
C. Test of Knowledge
Using the 10 rows of holes between the 6 screws on either the top or bottom half of the breadboard, perform the following experiments. Adjust the range of values of the DMM if a measured value displayed on the DMM is out of range or has insufficient precision.
- Measure the resistance between any two holes on the 1st and 2nd row that are on the same column.
- Measure the resistance between any two holes on the 1st and 5th row that are on the same column.
- Measure the resistance between any two holes on the 1st and 6th row that are on the same column.
- Measure the resistance between any two holes that are on two different columns.
- Measure the resistance of a 10kΩ resistor without having it placed on the breadboard.
- Insert the two terminals of a 10kΩ resistor into any two holes that are on two different columns. Measure the resistance of the resistor.
- Insert the two terminals of a 10kΩ resistor into any two holes on the 1st and 5th row that are on the same column. Measure the resistance of the resistor.
For all seven experiments above, record your observations and provide a detailed reasoning to justify your observations.
Prepare your report as per the guidelines given in APPENDIX III.