Vol. DIY Electronics Projects
Chapter 3 DC Circuit Projects

# DC Lab - An Analog Computer For Averaging

### Project Overview

Digital computers, such as personal computers (PCs), calculators and smartphones, perform mathematical operations in a series of discrete steps. Analog computers perform calculations in continuous fashion, exploiting Ohm’s and Kirchhoff’s Laws for an arithmetic purpose. The answer in an analog computer is computed as fast as voltage propagates through the circuit—ideally, at the speed of light!

In this surprisingly simple project, you will build and test the analog computer illustrated in Figure 1 to compute the average of three input voltages.

### Parts and Materials

• Three batteries, each one with a different voltage
• Three equal-value resistors, between 10 kΩ and 47 kΩ each. When selecting the resistors, measure each one with an ohmmeter and choose three that are the closest in value to each other. Precision is very important for this experiment!

### Learning Objectives

• Learn how a resistor network can function as a voltage signal averager
• Introduction to analog computing
• Illustrate that application of Millman’s Theorem

### Instructions

Step 1: Build the analog computer averaging circuit as shown in the schematic diagram of Figure 2. You can construct it using a breadboard as illustrated above in Figure 1 or using terminal strips as illustrated below in Figure 3. Pay careful attention to notice that the battery connected to resistor R2 is connected backward to the other two with the negative side up.

##### Figure 3. Analog computer for averaging calculation built on using terminal strips

Step 2:  Measure all battery voltages with a voltmeter and record the values. When you measure each battery voltage, keep the black test probe connected to the “ground” point (the side of the battery directly joined to the other batteries by jumper wires), and touch the red probe to the other battery terminal. Polarity is important here! The voltage of the second battery connected to resistor R2 should read as a negative quantity when measured by a properly connected digital meter, the other batteries measuring positive.

Step 3. Calculate the average of the three battery voltages: $$(V_1 + V_2 + V_3) / 3$$.

Step 4: Conntect the voltmeter iat the point shown in the schematic and illustrations and measure the voltage. It should register the algebraic average of the three batteries’ voltages. If the resistor values are chosen to match each other very closely, the output voltage of this circuit should match the calculated average very closely as well. This deceptively crude circuit performs the function of mathematically averaging three voltage signals together and so fulfills a specialized computational role. In other words, it is a computer that can only do one mathematical operation: averaging three quantities together.

Step 5: Disconnect one battery and remeasure the output voltage. It will equal the average voltage of the two remaining batteries.

Step 6: Connect the jumper wires formerly connecting the removed battery to each other to effectively create a 0 V input for that branch of the circuit as illustrated in Figure 4. The circuit will average the two remaining battery voltages together with 0 V, producing a smaller output signal.

##### Figure 4. Applying 0 V to one branch of the analog computer averaging circuit

The sheer simplicity of this circuit deters most people from calling it a computer, but it undeniably performs the mathematical function of averaging. Not only does it perform this function, but it performs it much faster than any modern digital computer can! At one time, analog computers were the ultimate tool for engineering research, but since then have been largely supplanted by digital computer technology. Digital computers enjoy the advantage of performing mathematical operations with much better precision than analog computers, albeit at much slower theoretical speeds.

With the addition of circuits called amplifiers, voltage signals in analog computer networks may be boosted and re-used in other networks to perform a wide variety of mathematical functions. Such analog computers excel at performing the calculus operations of numerical differentiation and integration, and as such may be used to simulate the behavior of complex mechanical, electrical, and even chemical systems.

### SPICE Simulation

We can also simulate our analog computer circuit in SPICE. We can force a digital computer to simulate an analog computer, which averages three numbers together. Obviously, we aren’t doing this for the practical task of averaging numbers, but rather to learn more about circuits and more about computer simulation of circuits!

Figure 5. Adding node numbers to the analog computer circuit for SPICE simulation

Netlist (make a text file containing the following text, verbatim):

Voltage averager
v1 1 0
v2 0 2 dc 9
v3 3 0 dc 1.5
r1 1 4 10k
r2 2 4 10k
r3 3 4 10k
.dc v1 6 6 1
.print dc v(4,0)
.end 

### Related Content

Textbook:

Worksheets:

#### Lessons in Electric Circuits

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