Chapter 3
Analysis Techniques

m3.2 Mesh-Current Method

Apply the mesh-current method to determine the mesh currents I₁ to I₄ in the circuit of Fig. m3.2. From these results determine V ₁, the voltage across the current source. Use these component values: I_SRC = 12.5 mA, V _SRC = 15 V, R₁ = 5.6 kΩ, R₂ = 2.2 kΩ, R₃ = 3.3 kΩ, and R₄ = 4.7 kΩ.

NI Multisim Measurements

Enter the circuit of Figure m3.2 into NI Multisim. Use “Measurement Probes” and interactive simulation to measure the four mesh currents. Use the multimeter or a measurement probe to display the voltage across the current source.

• Place the measurement probe on wires that carry only a single mesh current; remember that many of the resistors carry two mesh currents.

NI myDAQ Measurements

Build the circuit of Figure m3.2. Use the myDAQ DMM (digital multimeter) as an ammeter to measure each of the four mesh currents; use the DMM voltmeter to measure the voltage across the current source.

• Place the resistors to match the resistor orientations shown in Figure m3.2. Use 1-inch jumper wires to establish the top connections between the resistors to facilitate measurement of the mesh currents.
• Implement the voltage source V _SRC with the NI myDAQ -15V power supply.
• Implement the current source I_SRC according to the circuit diagram of Figure B.4 in Appendix B. Use a 100 Ω resistor for the adjustment resistor R.
• Measure I_SRC with the myDAQ DMM ammeter and confirm that the current is close to 12.5 mA. If you desire more precision, use a 1.0 kΩ potentiometer for the adjustment resistor.

Further Exploration with NI myDAQ

Some types of digital-to-analog converters require binary-weighted currents that can be selectively summed together. With a slight modification to your existing circuit topology you can redesign it to produce mesh currents that meet your own specifications such as those required by the digital-to-analog converter.

1. Consider the modified circuit of Figure m3.2a. Apply mesh-current analysis to write a set of equations in terms of the indicated currents and resistor values.
2. Choose resistor values that will establish the binary-weighted current values I₂ = I_SRC/2, I₃ = I_SRC/4, I₄ = I_SRC/8, and I₅ = I_SRC/16, and that will limit the current source voltage V ₁ to 5 volts or less.
3. Note: The standard parts list of Appendix A includes resistors that are close to the calculated values you need.
4. Build the circuit and measure all five mesh currents I₁ to I₅.
5. Measure the current source voltage V ₁.
6. Evaluate your results to determine how well the circuit produces the desired binary-weighted currents.