INTRODUCTION

This experiment contains a series of exercises to introduce analog computing concepts and computation using operational amplifier circuits. The laboratory analog computers provide basic analog capability in a small scale, simple arrangement. The machines operate with a range of voltage from -10 to +10 volts. You?ll quickly notice one peculiarity of analog computing notation - the voltage meter on the machine measures voltages in "machine units". Since one machine unit = 10 volts, when the meter shows 1.000, it means that the voltage is 10.00 volts.

EXERCISE #1: Unity Gain

Set up a single amplifier circuit with a "gain of unity" (equal resistors for input and feedback). Use a function generator to input a +/- 1 volt triangle wave at a frequency of about 1 Hz - be sure the bias is adjusted to zero. Use the VB-Scope to observe the input and output wave forms on channels 1 and 2 respectively. -- What do you see (#1)?

Now feed the output of your amplifier into an inverter (e.g. amplifier #7). Look at the output of the inverter on the VB-Scope. -- What do you see (#2)?
 
 

EXERCISE #2: Summing a Potentiometer Signal

Disconnect the inverter and return channel #2 to the amplifier output. Set up a potentiometer with an input of -10 volts and apply its output to a unity gain input on your amplifier. Momentarily disconnect your triangle wave. While watching the VB-Scope, adjust the pot to give an amplifier output of 1 volt. Reconnect your triangle wave input.-- What do you see on channel 2 (#3)?

Adjust the pot while watching the triangle waves on the VB-Scope. -- What do you see (#4)?
 
 

EXERCISE #3: An Integrator

Set up an amplifier to perform unity gain integration from a zero initial condition (ask for help as needed). Adjust the function generator to a +/- 1 volt square wave at 1 Hz (with bias adjusted to zero) and input this to the integrator. Monitor the input and output on the VB-Scope. Press the operate button. -- What do you see (#5)?

Push the IC button. Disconnect the square wave and input the 1 volt pot signal. Monitor scope channel 2 and press the operate button. -- What do you see (#6)?

EXERCISE #4: Solving a First Order Differential Equation

Set up one amplifier to solve the differential equation

Set the initial condition to 2 volts by connecting a pot supplied by -10 volts to the IC input and adjusting the pot appropriately. With all inputs disconnected, press the operate button while monitoring the output on the VB-Scope. -- What do you see (#7)?

Press the IC button and set the initial condition to zero. Connect the 1 volt square wave at 1 Hz. Press operate and observe the output on the VB-Scope. Adjust the frequency downward to 0.1 Hz. -- What do you see (#8)?
 
 

Exercise #5: A Landing Simulator

Adjust the function generator to a triangle wave of +/- 1 volt and a frequency of 20 Hz. Disconnect the function generator from the integrator input but apply it to channel 1 of the VB-Scope. Adjust the Scope to a full time scale of 100 msec. Place the Scope in X/Y plot mode. Put two integrators in series with the output of the first integrator connected directly to the second. Put the first integrator on an initial condition setting of +0.50 volts and the second integrator on an IC setting of zero. Connect the output of the second integrator to channel 2. Watch the VB-Scope and press the operate button. -- What do you see (#9)?

This analog computation is solving a form of the equation F=ma by integrating acceleration once to obtain velocity and integrating velocity to obtain position which is then displayed on Scope channel 2. An adjustable force can be applied by using potentiometer # 7 with +10 volts on one side and -10 volts on the other side. Connect the pot output to inverter #7 and connect that output to the first integrator. With the IC button depressed, set the pot to zero output (read this voltage from the analog volt meter by setting it to amplifier #7). Press the operate button and adjust the pot manually as necessary to gently "land the saucer" at -5 volts on the VB-Scope. -- Can you land it (#10)?
 
 

REPORT

Your group should have each exercise above checked by your TA. At the end of lab submit one group report containing brief answers to the ten questions above.