After the introduction of the SMU ADALM1000 in our Analog Dialogue December 2017 article, we want to start with the first of some small, basic measurements. You can find the previous ADALM1000 article here.
Now let’s get started with the second experiment.
Topic 2: Proportionality and Superposition
Objective
The objective of this lab activity is to verify the proportionality and superposition theorems.
Background
In this activity, the proportionality and superposition theorems are examined by applying them to the circuits shown in the following figures.

The proportionality theorem states that the response of a circuit is proportional to the source acting on the circuit. This is also known as linearity. The proportionality constant A relates the input voltage to the output voltage as:
The proportionality constant A is sometimes referred to as the gain of a circuit. For the circuit of Figure 2, the source voltage is V_{IN}. The response V_{OUT} is across the 4.7 kΩ resistor. The most important result of linearity is superposition.

The superposition theorem states that the response of a linear circuit with multiple independent sources, such as in Figure 3, can be obtained by adding the individual responses caused by the individual sources acting alone.
For an independent source acting alone, all other independent voltage sources in the circuit are replaced by short circuits and all other independent current sources are replaced by open circuits, as shown in Figure 4.
Materials
 ADALM1000 hardware module.
 Various resistors: 1 kΩ, 2.2 kΩ, and 4.7 kΩ.
Procedure

Verify the voltage division:

Construct the circuit of Figure 2. Using the Voltmeter tool, accurately measure V_{OUT} for the three input voltages (using the ALM1000 fixed power supply voltages) as shown in Table 1. You should measure and record the actual fixed power supply voltages as well.
Table 1. Enter Your Results V_{IN} (volts) V_{OUT} (volts) A (no units) 2.5 V 3.3 V 5.0 V  Calculate the value of A in each case using Equation 1.
 Plot a graph with V_{IN} on the xaxis and V_{OUT} on the yaxis.


Verifying the superposition theorem:
 Construct the circuit of Figure 3. Measure and record the voltage across the 4.7 kΩ resistor.
 Construct the circuit of Figure 4. Measure and record the voltage across the 4.7 kΩ resistor.
 Calculate the total response V_{OUT} for the circuit of Figure 3 by adding the responses from Step 1a and Step 2b. Compare your calculated result to what you measured in Step 2a. Explain any differences.
Questions
 Is the graph obtained a straight line? Compute the slope of the graph at any point and compare it to the value of K obtained from the measurements. Explain any differences.
 For each of the three circuits you built for the superposition experiment, how well did the calculated and measured outputs compare? Explain any differences.
You can find the answers at the StudentZone blog.
Notes
As in all the ALM labs, we use the following terminology when referring to the connections to the ALM1000 connector and configuring the hardware. The green shaded rectangles indicate connections to the ADALM1000 analog I/O connector. The analog I/O channel pins are referred to as CA and CB. When configured to force voltage/measure current, –V is added as in CAV or when configured to force current/measure voltage, –I is added as in CAI. When a channel is configured in the high impedance mode to only measure voltage, –H is added as CAH.
Scope traces are similarly referred to by channel and voltage/current, such as CAV and CBV for the voltage waveforms, and CAI and CBI for the current waveforms.
We are using the ALICE Rev 1.1 software for those examples here.
File: alicedesktop1.1setup.zip. Please download here.
The ALICE desktop software provides the following functions:
 A 2channel oscilloscope for time domain display and analysis of voltage and current waveforms.
 The 2channel arbitrary waveform generator (AWG) controls.
 The X and Y display for plotting captured voltage and current vs. voltage and current data, as well as voltage waveform histograms.
 The 2channel spectrum analyzer for frequency domain display and analysis of voltage waveforms.
 The Bode plotter and network analyzer with builtin sweep generator.
 An impedance analyzer for analyzing complex RLC networks and as an RLC meter and vector voltmeter.
 A dc ohmmeter measures unknown resistance with respect to known external resistor or known internal 50 Ω.
 Board selfcalibration using the AD584 precision 2.5 V reference from the ADALP2000 analog parts kit.
 ALICE M1K voltmeter.
 ALICE M1K meter source.
 ALICE M1K desktop tool.
For more information, please look here.
Note: You need to have the ADALM1000 connected to your PC to use the software.