Operational Amplifiers

Purpose: Operational amplifiers (op-amps) are devices with a large number of uses in the measurement of electrical signals. In the current market, solid-state operational amplifiers of high quality are readily available from commercial sources at quite modest cost. Some of their applications include voltage gain, impedance matching, integration and analog computation. Some of these common applications will be explored in this experiment.

Equipment: Dual polarity +10 to +15 volt power supply, operational amplifier and prototype board, various resistors and capacitors, oscilloscope, variable frequency function generator

Procedure: The performance of amplifiers constructed with different input and feedback components will be monitored using a dual channel oscilloscope. The input signal will be monitored on channel one of the dual trace scope and the output signal will be monitored on channel two. Subsequently, direct visual comparison of the input and output signals can be made.

Pin diagram of a typical operational amplifier (301, 357, 741) in the "flatpack" package. The pin number sequence starts in the lower left hand corner (pin 1) and proceeding counter-clockwise when viewed from the top. Many operational amplifiers also have "balance" and/or "compensation" input pins. This laboratory does not address these features. Do not wire to the pins unlabeled in the figure to the left.

NOTE: In the following schematics, the V+ and V- power leads, and the common return are omitted for simplicity. All grounds are connected to power common. Be sure to connected the V+ and V- pins of the op-amp to the dual polarity power supply, else the circuit won't work. If the power leads are not connected correctly the circuit won't work; ever again!

Part 1 The voltage follower circuit

Non-inverting voltage follower. This configuration would serve as an impedance matching device, e.g. between a glass pH electrode and a chart recorder. Use about 0.5 V square wave for E_in. Note E_out as you increase the amplitude of E_in. Vary the input frequency from 10 Hz and note how well (or not) E_out tracks E_in. Does the amplifier introduce any noticeable distortion? Measure the input impedance of this device using the capacitor discharge method discussed in the electrical measurements laboratory.

The following circuits use resistors of various resistance values. The resistance value is indicated by the first three colored bands. The value is given by the number value of the first two bands multiplied by ten to the number value of the third band. The fourth band, usually silver or gold, indicates the precision of the resistor value silver is 10%, gold 5%. Color codes for resistors are given in Table I.

Part 2 Inverter circuits

2a) Unity gain inverter This configuration is used when it is desired to change only the sign (polarity) of a signal. To construct this circuit, refer to the general schematic diagram in Figure 2 and use 1 kilo-ohm resistors for both input and feedback resistors.

As above, vary both the magnitude and frequency (10 Hz to 1 MHz) of a square wave input and note whether input and output are faithfully related by E_out=­E_in. Is any discrepancy explainable by the tolerance specified for R_i and R_f? Measure the input impedance of this configuration using the capacitor discharge method. Does it follow your prediction? Change the input signal to a sine wave; set the scope for x-y operation and measure gain and phase shift over the 10 Hz to 1 MHz frequency range.

2b) Inverter with voltage gain Here, E_out=­E_in(R_f/R_i) Let E_in=0.5 V square wave and observe both E_in and E_out using the scope in the dual trace mode. How accurately does the relationship, E_out=­10E_in, describe your observations?

2c) Inverting adder Any number of input signals can be summed using this configuration and the ratio in which they are added can be selected by the choice of the input resistors. To construct this circuit, use two or more input resistors in parallel. The resistors are all connected to the common or summing point of the circuit. By using the basic design rules for operational amplifiers, it is easily shown that the output voltage will be

where n is the number of input resistors. The input resistors can have any values but this circuit generally uses the same values for the R_in. One problem with this circuit is that the input voltage sources are not isolated from each other. Subsequently, the circuit may "load down" the different voltage sources. This can be circumvented by using voltage follower circuits (Figure 2) for each input. While this may seem costly, it is not. Currently, four `high grade' op-amps in a single 14 pin flat pack package can be purchased for around 2$.

To test this circuit, use two 1 kilo ohm input resistors with R_f.=1.0 kilo ohm Using two different voltage sources for the two inputs check to see whether or not E_out is equal the sum of the inputs. You might try using a DC potential and an AC potential as the inputs.

Part 3 The integrator

3) Inverting integrator This configuration is known as the Miller integrator. Similar circuits were employed in older NMR spectrometers to obtain integrated peak areas. They are still employed today, as low pass filters, using a resistor is series with the capacitor. The circuit is similar to the voltage inverting amplifier, only the feedback resistor is replaced with a capacitor. First let E_in be a small dc voltage. Verify that E_out increases linearly with time and at the rate predicted from your choice of R and C. Remember to discharge the capacitor periodically.

Set up a signal of E_in=0.5 V pp (peak-to-peak) sine wave; monitor this on channel one and observe the output on channel two. What form do you expect for E_out? Does the observed signal match your prediction? How does E_out vary with input frequency? Set up a signal of ~0.5 V pp square wave; and monitor the output. Does the observed signal agree with your prediction?

Part 4 The differentiator circuit

4) Inverting differentiator An analog differentiator circuit can be constructed by using a capacitor as the input element and a resistor in the feedback position of the inverter circuit. Construct this circuit and design a test to insure that it operates as expected. What is the gain for a DC input? How does the gain change with input frequency?

Table I Resistor color codes