Objectives:

1. To understand how to design and build a basic amplifier circuits with nearly any chosen gain, using an integrated circuit op-amp as a basic component of the amplifier circuit.

2. To determine the difference between the two basic configurations of amplifier circuits - inverting and non-inverting.

3. To understand the characteristics of an ideal op-amp used in an amplifier circuit and some of the different types of circuits derived from the two primary amplifier configurations.

Parts and Equipment:

Resistors: 560 Ohm, 1 k Ohm (2 ea.), 1.5 k Ohm, 10 k Ohm
Integrated Circuit Operational Amplifier: LM348 or equivalent

Down load and print a copy of the data sheet for the LM348 op-amp from one of the manufactures web sites before coming to class.

Signal Generator
Bi-Polar D.C. Power Supply (±15 VDC) with additional adjustable output.
Oscilloscope
Digital Multi-meter
Breadboard and wire

Textbook Reference:

Allan R Hambley, "Electronics", Prentice Hall, 2nd Ed., 2000, pp. 61-130
Serda and Smith, "Microelectronic Circuits", Oxford University Press, 4th Ed., 1998, pp. 60-122.

Material Review:

A basic model of an ideal operational amplifier is shown in Fig. 1. An op-amp is a direct-coupled device with differential inputs and a single-ended output. The op-amp responds only to the difference voltage between the two input terminals, not to their common potential. A positive-going signal at the inverting (-) input produces a negative-going signal at the output, whereas the same signal at the non-inverting (+) input produces a positive-going output. With a differential input voltage, V_in, the output voltage, V_o, will be A_voV_in, Where A_vo is the open loop gain of the op-amp.  Both input terminals of the op-amp will always be used, regardless of the application. The output signal is single-ended and is referred to ground. Bipolar (±) power supplies are most commonly used, which allows both positive and negative output voltages.

Properties that are useful in describing the operation of operational amplifiers are listed below and the ideal values given. The diagram illustrates the relationships between the op-amp and these properties.

1. The voltage gain is high - Ideal value A_vo = infinite.
2. The input resistance is high - Ideal value r_in = infinite.
3. The output resistance is low - Ideal value r_o = 0.
4. The bandwidth is high - Ideal value BW = infinite.
5. There is low input offset voltage  - Ideal value V_o = 0 if  V_in = 0.

Fig, 1 Equivalent Circuit of an Operational Amplifier

From these ideal characteristics, we can deduce two very important additional properties of the operational amplifier.  Since the voltage gain approaches infinite, any output signal developed will be the result of an infinitesimally small input signal. Thus, in essence:

1. The differential input voltage is zero.

2. There is no current flow into either the inverting or the non-inverting signal input terminal.

The Inverting Amplifier

Fig. 2 shows the first of the two most common amplifier configurations using an op-amp as the active component.  This circuit produces an inverting amplifier.  The ideal properties of this type of amplifier are:

1. Closed loop amplifier Gain = A_v = -R_f / R_a, unlimited in range ( R_f  may be 0 for 0 gain).
2. Input impedance = V_in / I_in = R_a.
3. I_f = I_in, regardless of R_f, since I_s = 0 for an ideal op-amp and is negligibly small for real op-amps.

In this amplifier circuit the signal input is between the left end of the resistor R_a and ground.  The non-inverting input terminal of the op-amp is connected directly to ground (the reference node).  The inverting input of the op-amp forms a summing point node, SP, since the sum of the currents entering this node must be zero by Kirchoff's current law.   

V_o =  -A_vo V_SP, since V_SP is applied to the inverting input of the op-amp and the non-inverting input is connected to ground and the output of the op-amp is A_vo times the difference of the difference between the voltages at it's  non-inverting input and it's inverting input.  solving that equation for the summing point voltage gives, V_SP = - V_o /A_vo.  Since A_vo is very large the voltage at the summing point must be very small for a typical finite output voltage.  for an ideal op-amp A_vo is infinite which would give V_SP = 0 for any finite output voltage.  This causes the summing point to act like a virtual ground.  in this circuit.  In circuits where the non-inverting input is not connected to ground it causes the summing point to be at the same potential as the non-inverting input.  This effect is caused by negative feedback of the output voltage to the inverting input through the feedback resistor R_f.  For real op-amps the open loop gain, A_vo, or gain with no negative feedback is typically about 200,000.  This leaves a finite but very small voltage at the summing point.  

The (-) signal input to the amplifier, or the junction of the input and feedback signals, is a node of zero voltage, regardless of the magnitude of I_in. Thus the junction is a virtual ground, a point that will always be at the same potential as the (+) signal input. Since the input and output signals sum at this junction, it is also known as a summing point (SP). This final characteristic leads to a third basic op-amp axiom, which applies to closed-loop operation:

3. With the loop closed, the (-) input will be driven to the potential of the (+), or reference, input.

If a second input resistor is added to the inverting amplifier circuit then the current through this resistor must be added to the total input current to the summing node. The resultant output is then a weighted sum of the input voltages. Additional input resistors can be added to the circuit adding additional terms to the sum. Note the gain formula for the summing amplifier:

V_out = - [V₁( R_f / R₁) + V₂( R_f / R₂) + V₃( R_f /R₃) + ...]

The Noninverting Amplifier

Fig. 4 shows the second of the common amplifier circuits using an op-amp as the active component which is the non-inverting amplifier.  The ideal properties of this type of amplifier are:

1. Gain = (R_a + R_f )/ R_a = A_v =  1 + R_f / R_a, with a lower limit of unity gain where R_a is infinite, R_f = 0, or both.
2. The input impedance is infinite for an Ideal Op-Amp.  For a typical real Op-Amp used in this circuit the input impedance is usually > 10¹¹ ohms.
3. I_f = I_a, regardless of R_f.

With this amplifier configuration, the lower limit of gain occurs when R_f = 0, which yields a gain of unity. This type of configuration is known as a unity gain buffer amplifier. With the inverting and noninverting amplifier, current I_a always determines I_f, which is independent of R_f. Thus, R_f may be used as a linear gain control, capable of increasing the gain from a minimum of unity (for the noninverting amplifier) or zero (for the inverting amplifier) to a maximum of infinity (although the practical limit of gain is about 100). The input impedance is infinite, since an ideal amplifier is assumed.

SUMMARY

In this lab we have examined the op-amp concept only in a general sense, assuming idealized parameters. In a real-world situation, the ideal amplifier does not exist. However, it is important to stress the idealized line of thinking because, in many applications, the differences between ideal and actual are negligible. Furthermore, we should always be aware of how closely we actually approach "idealized" performance.

Procedure 0: Obtain the data sheet for the Op-amp.

Down load and print a copy of the data sheet for the LM348 op-amp from one of the manufactures web sites before coming to class.

Procedure 1: Inverting Amplifier configuration

1. Using power supply voltages of ±15 VDC for the op-amp, construct an inverting amplifier circuit (Fig. 2.) with a gain of -10 using an input resistor of 1 K. Note: The pin connections for the LM348 Op-Amp are given on the manufactures data sheet.  Record both the positive and negative power supply voltages.

2. Connect an ac signal source set at 100 Hz (sinusoidal) to the input. Set the oscilloscope for X-Y display. Connect the input voltage to the x input and the output voltage to the y input using dc coupling. Increase the input voltage until considerable limiting is observed at both the positive and negative sides. The curve you are observing is the voltage transfer function of the circuit. Print this curve and label the upper and lower saturation voltages.  The central part of the curve is the linear voltage gain operating region.  The slope of this portion is the voltage gain. Determine the slope,  dV_out/dV_in, of the line in the linear central region. Do this by expanding the scale so the straight line portion fills the screen as much as possible and setting the top part of the line to cross through the intersection of a grid line at the top of the screen. Then measure the delta V_out and delta V_in to the point where the line crosses the bottom of the screen. Compare this slope to the gain calculated from your measured resistor values.

3. Switch the oscilloscope to voltage vs. time display.  The input voltage should appear as a sine wave.  The output voltage should be clipped at both the top and the bottom of the waveform.  The voltages at which the output is clipped are the saturation voltages.  Set the horizontal sweep for about one full cycle on the screen.  Measure the saturation voltages as accurately as possible by using the cursors.  Remember to set the Acquire mode to average in order to eliminate the noise and get as clean a waveform as possible.
 

4. Change the input to a  voltage of about 500 mV_RMS at a frequency of 1 KHz.  You will probably have to use the 20 dB attenuator button on the BK Precision Function Generator to get the voltage this low.  Adjust the sweep for one and one half to three cycles on the screen. In order for the oscilloscope or Wavestar to be able to calculate cycle rms values there must be at least three zero crossings of an ac waveform on the display.  For maximum accuracy of the calculations the maximum on screen display is also needed.  Measure v_in and v_out using the measure mode on the oscilloscope or the Wavestar software to measure the peak to peak and rms value of each voltage,  making sure the output level is well below the saturation level. Calculate the AC voltage gain from the rms measurements.  Sketch or print and describe the relationship between input and output waveforms.  Compare the experimental A.C. gain with the gain formula for the actual resistor values and with the gain found in step 2 from the slope of the transfer function.

5. Repeat the A.C. voltage measurements from step 4 after replacing the feedback resistor with resistors calculated to give each of the following amplifier gains: -1 and -0.56.  A larger input signal may be used to get a cleaner waveform as long as the peaks of the output waveform are well away from the saturation voltage levels.

6. With R_F = 10 k, add a second  input resistor, R_{in 2}, to the summing or the, v_-, node creating a summing amplifier (Fig. 3.). Use a 1.5 k resistor for this second input.  Connect an A.C. source to the original input, V_IN1, with an A.C. input of about 0.1 V_rms. The second input, V_IN2, should be connected to ground to give V_IN2 = 0 volts for the first observation. With the oscilloscope mode set to DC coupling on both channels, observe and print the output waveform along with the a.c. input. Use the oscilloscope measure mode and  Wavestar to measure and print the peak to peak value and the average( or mean) value of each waveform.   Also carefully determine and record the max and min values of each waveform.  Remember the output of this circuit is the sum of a DC voltage and an AC voltage.  How can you verify that the output follows the prediction of the gain formula for this circuit?  What is the result of adding a DC component to an AC voltage waveform?  Compare the measured output with the prediction of the summing amplifier formula. Then repeat with V_IN2 = 0.25 volts DC and again with V_IN2 = 0.5 volts DC.

7. Remove the second input resistor.  Place a 1k resistor, R, between the signal generator and the original input of the inverting amplifier circuit. Where the signal generator was originally connected.  This is at end of resistor, R_a, where the source has been connected not the end connected to the summing point.  Set the source voltage at about 1V_rms. Reduce this voltage if any sign of saturation is seen in the output waveform.  Then measure both the input voltage, V_in, to the amplifier and the voltage across the extra series resistor, V_R,  (or you could measure the source voltage, V_S, and the input voltage and subtract to get the voltage across the extra series resistor). Using the measured value of this extra resistor and the voltage across it calculate the amplifier input current, I_in. Then using, V_in , and this current calculate the amplifier input impedance.  I_in = ( V_S - V_in)/R, then R_in = V_in /I_in.

Procedure 2: Non-inverting Amplifier configuration

1. Build a noninverting amplifier with a gain of 11 (see Fig. 4 and the accompanying gain formula).

2. With an oscilloscope connected to both the input and output, apply a small A.C. voltage of about 500 mV_RMS at a frequency of 1 kHz to the input and measure v_in and v_out. making sure the output level is well below the saturation level. Print the waveform and describe the relationship between input and output waveforms. Compare the A.C. gain with the gain formula.

3. Change the circuit to the unity gain buffer form (R_f = 0, and R_A = infinity ).

4. With an input voltage of about 1.5 V_rms compare the input and output waveforms as closely as possible on the oscilloscope. Then measure, V_in , and, V_o , as accurately as possible with the Multi-meter (at least four significant figures).  The BK meters can give five significant figures, if you press and hold for one second small round button on the left side of the meter.

CALCULATIONS / GRAPHS:

1. Determine the accuracy of the ideal op-amp gain formulas from your experimental data.  

2. Does the accuracy depend on the gain of the amplifier?   If so, in what way does it depend on the gain?   

3. Since the summing amp has two inputs, one constant and one a time changing ac value while the output is a weighted sum of the two, how do you compare the results with the mathematical formula?  

a) Divide the output into components?

b) Pick a set of specific points in time?

c) Calculate the total effective or rms value of the components and measure the total true rms value of the output?

d) All of the above?

SUMMARY/CONCLUSIONS:

What can you say about Op-Amps and their circuits based on your experimental observations?

This page last updated 02/06/2006