Resistors come in a wide range of resistances. For op-amp circuits, values in the range of 10 k ohm to 250 k ohm work best. For this lab, we will use primarily 10 k ohm and 100 k ohmresistors and maybe a few others. Resistors are color coded so that with some practice you can decipher resistance values from the color bands on the resistors you are using.

Capacitors also come in a wide range of values and are made using a variety of techniques. The capacitors that we will use for signal conditioning are fairly small and have capacitances measured in Pico farads or microfarads. Some capacitors are polarized and care must be taken to ensure that they are connected to a circuit with the proper orientation.

Figure 1: Trim Potentiometer Schematic

A trim potentiometer is a variable resistor. It has three leads.

The resistance of the trim pot is measured between the wiper and one of the other two leads. A trim-pot is depicted schematically in Figure 1. An adjustment screw moves the wiper along the length of a coil resistor. The resistance between lead 1 and the wiper increases or decreases as the wiper moves further or closer.

The output voltage (Vout ) is related to the input voltages by the following relationship:

Figure 2: equation (1)

For this lab, we will use the LM741 op-amp. The LM741 is a very common op-amp package, with one op-amp per integrated circuit (IC). (Many op-amp packages have two or four op-amps per IC.) A schematic representation of the LM 741 is shown in Figure 3. The semi-circular depression on the chip marks the top of the chip and the pins are numbered counterclockwise around the chip. The highest number pin is always opposite pin 1.

LM741 Pinout:

Data sheets for this and other integrated circuits (IC's) can be obtained from the National Semiconductor web site (www.national.com).

Figure 3: LM741 Connection Diagram

You will build circuits for this lab using a solderless prototyping board known as a proto-board or breadboard. Breadboards allow us to connect circuits by plugging in components and wires. No soldering is required. A drawing of a breadboard is shown in Figure 4 below. As indicated by the gray lines, horizontal rows of connectors in areas B and C are internally connected. When a chip is plugged into the board as shown, these strips give you four connections to each of the IC pins. The connections in regions A and D are intended as power and ground buses. As indicated by the gray lines, the columns in these regions are tied together vertically.

Figure 4: Breadboard

The breadboards are fairly robust; however they are susceptible to damage from wires that are too large. Do not use wires larger than 28 gauge. Components with leads that are too large can damage the breadboard as well.

You will use a Tektronix triple-output power supply. The power supplies should be set up when you come to lab. For your reference, set-up instructions are given below. Perform the following steps before you turn the power supply on.

The power supply has three dc-power outputs; one capable of 0-5 V, and two capable of 0-15 V. To power the electronic components for the lab, we will need a +12 V supply, a –12 V supply, and a ground connection. We will use the two 0-15 V outputs in series and adjust them to output approximately 12 V each.

In this configuration, the negative side of the “B” output is a –12 V source. The positive side of the “A” output becomes the +12 V source. The positive side of the “B” output and the negative side of the “A” output are the ground.

Incorrectly connecting an op-amp to the power supply will destroy the op-amp. Make sure that the op-amp is connected with correct polarity.

Your breadboard is now configured to power the circuits for this lab.

Use the function generator to create a sine wave with the following characteristics:

For such a small signal, the Attenuator button on the function generator must be depressed. This signal will be treated as the output of a sensor. We will condition this "sensor output" with a signal conditioning circuit.

In this lab, we will build on the skills that were developed in Introduction to Benchtop Equipment and Data Acquisition and Temperature Measurement and First-Order Dynamic Response. It is assumed that the student understands the concepts of a Front Panel, a Block Diagram, the Control Palette, and the Functions Palette. It is also assumed that the student can search the control and functions palette for necessary features. The student should be familiar with configuration options for voltage measurements using the DAQ Assistant.

The VI that you developed for Temperature Measurement and First-Order Dynamic Response can be easily modified to examine circuit inputs and outputs.

Figure 5: Modified Block Diagram

Before building a circuit to condition the signal, you will build a couple of simple op-amp circuits to get a feel for what to do.

5.1 Inverting Circuit

The inverter is one of the simplest op-amp circuits. This circuit simply changes the sign of a signal. The schematic diagram of an inverter is shown in Figure 6.

1. Build the inverter using two 10 k ohm resistors and an LM741 op-amp.
2. Input the signal from the function generator to the circuit.
3. Branch the input cable with a BNC T-connector. Connect this input to Channel 0 on Module 1 of the SCXI.
4. Connect the output signal from the circuit to the Channel 1 on module 1 of the SCXI.
5. When you run the VI, you may need to adjust the scales on the X and Y axes.

You should see that the output is an inverted version of the input.

Figure 6: Inverter and Inverting Gain Circuits

For the amplified signal to be read correctly, the 800 mV bias must be removed. A two step process will be used to remove the bias:

The result will be an 80 mV sine wave with zero mean.

6.1 Trim Potentiometer Adjustment

Use the 10 k ohm trim potentiometer provided to build a voltage divider as shown below.

1. Connect one end lead of the potentiometer to the +12 V bus.
2. Connect the other end lead to the –12 V bus.
3. Connect a voltmeter across the wiper lead and ground to measure the output.
4. Adjust the potentiometer resistance until the voltage on the wiper lead is 800 mV.

Figure 7: Voltage divider circuit

6.2 Differential amplifier

You will build a differential amplification circuit to subtract 800 mV from the sensor signal. A differential amplifier is shown in Figure 8 below.

1. Use four 10 k ohm resistors to subtract the voltage divider output from the sensor signal. It is unlikely that the resulting output signal will be a zero-mean sine wave as desired.
2. Adjust the screw on the potentiometer to "trim" the offset of the sine wave to zero.
3. Amplify the difference between the signals by replacing the R2 resistors so that R2 > R1. Replace the R2 resistors with 100 k ohm resistors.

The resultant signal should be an 800 mV sine wave with minimal offset.

Using the inverting gain circuit shown in Figure 8, amplify the output of the differential amplifier circuit by an additional factor of ten. This can be done with another op-amp and a 10 k ohm resistor and a 30 k ohm resistor. The resultant output signal should have a mean of zero and amplitude of ~2.4 V. Adjust the potentiometer to remove any offset.

Figure 8: Differential Amplifier Circuit

A low pass filter can be used to attenuate high-frequency noise in an analog signal and to minimize the portion of the signal that will be aliased. Later in this lab, you will see a demonstration of the damaging effects of aliasing.

Figure 9: First-Order Low-Pass Filter

7.3 Modifying Existing VI to Measure Magnitude Ratio

By measuring the magnitude of the input and output of a filter, you can determine the how much the filter attenuates the signal.

Figure 10: Completed Block Diagram

1. Delete the Amplitude and Frequency constants from the Block Diagram.
2. Hold Ctrl as you drag the Tone Measurements icon to make a copy.
3. Place a Split Signals icon to the left of the Tone icons.
4. Place a Divide function to the right of the Tone icons.
5. Create a numeric indicator at the x/y output terminal of the Divide function.
6. Rename the numeric indicator Magnitude Ratio. (The Magnitude Ratio represents the output amplitude divided by the input amplitude.)
7. Wire the Block Diagram as shown in Figure 10.
8. Save the VI.

7.3 Build a Passive Low-Pass Filter

The filter described in step 6.1 is an active filter, meaning it requires an external power source. Since it uses an op-amp, it must have a ±12 V power supply. Active filters can have a static gain greater than one. Active filters also have low output impedance, which means that they can pass up to 10 mA of current without any effects on the operation of the filter.

A passive low-pass filter does not require an external power source. A passive filter can be constructed with simply a resistor and capacitor as shown in Figure 11.

1. Build a filter using a 10 k ohm resistor and a 0.1 micro F capacitor.
2. Repeat section 6.2 (steps 4-11). Record your results in your lab book. You may use Table 2 to organize your data.

Figure 11: Passive First-order Low-pass filter

Table 2: Magnitude Ratio Data for First-order Low-pass Filter (Passive)

Table 2

frequency (Hz)	Input magnitude (V)	Output magnitude (V)	Magnitude ratio
10	1V
18	1V
32	1V
58	1V
110	1V
190	1V
340	1V
620	1V
1100	1V
2000	1V

7.4 Build a Second-Order Butterworth filter

Figure 12 below shows a second-order Butterworth low-pass filter. A second-order filter is superior to a first-order filter in many respects, as we will investigate.

1. Build the Butterworth filter circuit using R = 10 k ohm and C = 0.1 micro F.
2. Perform the sine wave and square-wave input tests from step 6.2. Record your results in your lab book. You may use Table 3 to organize your data.

How is the response of this filter different from that of the first-order filter?

Figure 12: Second-order Butterworth Low-pass Filter

Table 3: Magnitude Ratio Data for Second-Order Low-Pass Filter

Table 3

frequency (Hz)	Input magnitude (V)	Output magnitude (V)	Magnitude ratio
10	1V
18	1V
32	1V
58	1V
110	1V
190	1V
340	1V
620	1V
1100	1V
2000	1V

Aliasing is a generally undesired phenomenon that results when periodic signals are sampled too slowly. Aliasing causes high frequency periodic signals to be recorded as signals consisting of lower frequencies, as will be apparent in the following steps.

Estimate the damping ratio of the second-order Butterworth filter through experimentation. To do this, you will probably need to take more measurements near the expected cut-off frequency of the filter (which is near the natural frequency). Support your result with plots and discussion as necessary.