EE 215 22 September 1999

Lab Project 3

In class and in lab we have discussed the operational amplifier and in many cases, where we looked at circuits consisting of op amps and other components, we assumed that the op amp was a near ideal device. By this is meant that its characteristics that include the following:

In reality, we all know that the op amp does not have ideal characteristics. However, many circuit applications are not effected by the variations from Ideal characteristics because we scale the problem so that the limitations imposed by the actual op amp are not troublesome.

By Scale I mean that we select the range of values such as gain, frequency range, etc. such that they are all within the useful range of the device. {As an example: we select the gain of the final circuit to be in the 1 to 100 range such that the error introduced by the finite gain of the op amp, which is typically > 100,000, does not contribute more that a fraction of 1% error in our design.}

However, there are situations where the op amp is "pushed" ( i.e. used close to its useful operating limits) in a design. This is typically done to gain all that can be achieved in circuit performance. It is important

that we become aware of the limitations of the op amp and learn under what conditions the limitations become troublesome.

Because of the nature of this lab, and the number of different characteristics you will be investigating, I strongly suggest you take your time and do it correctly rather than rushing through and miss important characteristics.

The objective of this lab is to measure the magnitude of some of the non-ideal characteristics of two different op amps. In doing this we will get an appreciation for the circumstances under which we can expect to see op amp performance degrade. In addition we will compare the values we measure to the values specified in the manufacturers data sheets, allowing us to relate manufacturing specifications to actual circuit operation.

The op amps we will be using in our experiment are the uA741 and the LF411. In this experiment we will have an opportunity to observe the actual characteristics of the device, and hopefully understand why we can make some of the assumptions we do in using the device the way we do. We can also observe the performance of two op amps and make some judgement over which device we would use for specific applications.

Because of the limitations in both equipment and time, not all the characteristics can be measured to the level of detail we would like. Therefore, in some cases, we must make some approximations in the measurement technique, and for some parameters, assume the manufacturers specifications in the data sheet are correct.

In addition to the observations, where possible, circuit variations to compensate for the "non-ideal" characteristics will be demonstrated.

Data on the manufacturer's data sheet in many cases is not a specific value. Sometimes a range of values is given, and other times a typical value is given. So that the student will have some idea of what value to use in the calculations (and also values for comparison purposes), in this lab we will assume the Open Loop Gain (Aol) of both op amps is 200,000 volts/volt.

With this assumption, the object of the lab will be to measure the following characteristics:

NOTE: Power supply connections are not depicted in any of the following circuits. These connections can be found on the data sheets.

The procedures for each of the various parts of the lab are defined in each of the sections below.

Please pay attention to the instructions relative to the addition of components and magnitude of the components suggested.

Before you start - MAKE SURE THAT THE OP AMP IS GOOD. You can do this by connect up a simple inverting amp circuit with a gain of two or three and verify operation of the circuit (i.e. gain, 180° phase shift, etc.)

Before you apply power - CHECK YOUR CONNECTIONS.

Keep in mind - REMOVE POWER WHEN MAKING CIRCUIT CHANGES.

Be sure to answer all questions as you go. They are marked Qxx throughout the report.

As you proceed, remember that you have to do each part for two (2) different op amps.

The input resistance of an op amp will be discussed in detail in class. We will assume for the purpose of this lab that it is simply a resistance in the input circuit and measure it accordingly.

Connect up the circuit as shown in the figure below. From the measured values, calculate Rin. In your calculations, do not forget to take the impedance of the meter into consideration.

Q1.1) How does the input resistance compare to the manufacturers data given in the spec sheet.

Q1.2) How do the two op amps compare?

The offset voltage is an unwanted voltage that causes a voltage to appear at the output. It is a result of a few different contributors. Input bias current, Ib, and input offset voltage, Vios, are the primary contributors to the voltage that appears at the output, which we will call the output offset voltage, Voos.

Since there are two contributors, what we will do is to use the circuits that minimize the effect of one contributor, assume a value for it, and then measure the other. Although this is not exact, it will give us a good approximation for the values of the contributors.

Two important things to note are:

These two factors are the basis for the measurement of Vios that follows. The relationships describing the contributions to Voos from Ib and Vios, are described by the following expressions:

To observe these effects, connect up the following circuit:

Using the DMM, accurately measure and record Voos for the conditions given in tables 2.1 and 2.2. (Note: the values for the resistors given in the tables are approximate. Using the DMM, measure the resistors and record the actual values.)

To isolate the effects of Ib and Vios from each other, one must consider what effect each would have in the circuit and then adjust the conditions so that you are able to observe the effect of each independently, or as close to independent as you can get under the circumstances.

Since Ib is a leakage current, its effect would be greatly enhanced if the resistor were large since E=IR. For Vios, however, large resistors would have little effect. To see the effect of Vios, the closed loop gain is the important factor (i.e. Rf/Ri).

Note: Since we will be measuring Ib and Vios under DC conditions, the capacitor does not enter into the calculations. The capacitor Cc, is used to reduce the effect of noise. Also, Voos is in the mv range and a DMM should be used to measure Voos. The resolution on the scope may not be adequate.

Since gain enhances the errors due to Vios, we want to keep the gain small. In the table you can see we are using a gain of 1. Thus if Vios is very small (from the spec sheet we see that Vios is typically 1 mv), we will see the contribution due to Vios is essentially V''oos = 1 mv * 1 = 1 mv.

The bias current, Ib is a current that is flowing in the two inputs (i.e. + & - ) as a result of the non-ideal transistor characteristics at the input of the difference amplifier stage of the op amp. Since the transistors are usually matched fairly closely to provide good overall performance of the op amp, the bias currents in each input are very close in magnitude. Thus to insure that there is no voltage generated due to an imbalance in the impedance of the two inputs, a resistor is added to the non-inverting input. (i.e. the "+" input.) The magnitude of the resistor is equal to the parallel combination of the two resistors connected to the inverting input (i.e. "-" input). To observe the effect of input bias current, perform the measurements indicated in table 2.1, using the resistance values indicated. {To get a more accurate value, the contribution due to Vios could be subtracted (i.e. V''oos = Acl * Vios) from the measured Voos. Then calculate Ib as indicated.}

Q2.1) Compare the measured results to the values given in the data sheets. Comment on the differences observed (magnitudes, possible causes, etc.).

_____________________________________________________________

| R1 | R2 | Rf | Voos | V'oos | Ib = V'oos/Rf |

|_________|________|_________|________|________|________________| | 100 K | 0 | 100 K | | | |

|_________|________|_________|________|________|________________|

| 100 K | 50 K | 100 K | | | |

|_________|________|_________|________|________|________________|

| 2.7 M | 0 | 2.7 M | | | |

|_________|________|_________|________|________|________________|

| 2.7 M | 1 M | 2.7 M | | | |

|_________|________|_________|________|________|________________|

Vios, as defined in the text, is the differential input voltage that must be applied across the inputs of the op amp in order to make the output voltage go to zero. By measuring Voos and calculating the gain, we can find Vios. We will use a resistor in the non-inverting input to minimize the effects of the input bias current, as seen in part 2.1). Remember the output offset voltage, due to Voos alone is V''oos. Hence, it is described by Voos - R1*Ib. (Note: use the largest value of Ib from table 2.1).

Q2.2) Compare the measured value of Vios and compare it to the value given in the manufacturers data sheet. Comment on the possible reasons for the differences, magnitudes of differences, etc.

Q2.3) Is it apparent that Voos is gain dependent? What are your reasons for the answer you have given.

Q2.4) How do the bias currents and offset voltages of the two different op amps compare?

R1 R2 Rf Acl Voos V''oos Vios (=V''oos/Acl)

100 K 100 K 2.7 M

10 K 10 K 2.7 M

The change in an op amp's input offset voltage caused by variations in supply voltages is called the Power Supply Rejection Ratio (PSRR). A variety of terms are used by different manufactures: Supply Voltage Rejection Ratio (SVRR); Supply Voltage Sensitivity (SVS); and others. These terms are expressed either in microvolts/volt or decibels. If we denote the change in supply voltages by ∆V and the corresponding change in input offset voltage by ∆Vio, PSRR can be defined as follows:

PSRR = ∆Vio/ ∆V

Using the same circuit as was used in 2.2, with R1=R2=10K and Rf=2.7 M, carefully measure Voos when both the + and - supplies are set at 15 volts. Then reduce the supplies to 14 volts and remeasure Voos. Now using the technique indicated in TABLE 2.2, calculate:

Vios (@ 15 volt) =

Vios (@ 14 volt) =

Q3.1) From this data, calculate the PSRR and compare it to the manufacturers data. How do the data compare? Comment on your observations.

Q3.2) How do the two op amps compare?

CMRR is defined as the ratio of the differential mode gain to the common mode gain . Usually it is expressed in dB which is defined as CMRR = 20 Log [ Diff. Mode gain/Common Mode gain]. Differential mode gain is the open loop gain and Common mode gain is the gain with the inputs tied together.

4.1) The CMRR may be measured using the following circuit.

Select R11 and R22 such that E1 is about 5 volts DC. Select R1 to be about 150 ohms and R2 about 150,000 ohms. Carefully measure and record values of R1 and R2. Using the DMM, accurately measure and record E and E1.

Then calculate CMRR from the equation:

E - E1 = { [ R2/R1] +1} * {[E1/CMRR] + [E/Aol]}

Since Aol is about 50,000, then E/Aol is about 0.

Then CMRR = { E1/(E-E1)} * {[R2/R1] + 1}

Q4.1) Compare the measured value of CMRR to the manufacturer's specification sheet. If we assume the spec sheet is correct, how accurate is this technique? What assumptions are made in the formula that may account for the difference?

The actual output impedance of most general purpose op amps is generally quite large (50 ohms to 1.5 Kohms). Note from the spec sheet that the output resistance of this op amp is spec'd at 75 ohms. Yet when we assume Ro is = 0 in analytical calculations, we find our approximation is close to what we observe in actual operation. The following experiment should demonstrate how feedback appears to reduce Ro such that the effective output resistance Ro', appears very small.

5.1) To demonstrate this connect up the following circuit.

* Select R1 and R2 such that about 6 volts is applied to the + input. (i.e. Ein = 6 volts). Select a value of RL of about 5 Kohms.

* Using the DMM, measure and record in table 51 the value of RL.

* Using the DMM, measure and record the value of Eout for the conditions specified in the table 5.1. For these measurements, we can assume the DMM does not represent a significant load.

Case Ein SW1 RL Eout Ro'

Measured (Feedback

Value connection)

1 open infinite

2 open 5 Kohms

3 closed infinite

4 closed 5 Kohms

Employing the following model, the value of Ro' can be calculated for the case with and without feedback.

Q5.1) Does the value of Ro' calculated for the case without feedback compare to the manufacturers data sheet? How close is it and what are the possible reasons for the differences?

Q5.2) Describe the observed differences for the cases with and without feedback.

Q5.3) How do the two op amps compare?

In this particular case, we want to measure the frequency response and the phase of the output relative to the input for three values of gain and compare the values to the manufacturers specifications.

6.1) Begin by connecting up the following circuit.

Starting with an input that results in a 5 Vpp 100 Hz sine wave on the output, gradually increase the frequency and observe, on the scope, the input and output waveforms.

Measure and record in Table 6.1 the phase and amplitude you observe for Ein and Eo. It is important to measure the input since the signal generator is not ideal and the waveform magnitude may change as you change the frequency.

Frequency Ein Eo Phase

Hz volts p-p volts p-p Eo re. Ein

Acl = 1 10 100 Acl = 1 10 100 Acl = 1 10 100

100

300

1000

3000

10000

30000

100000

Don't be afraid to take a few other values, especially in the region of interest, i.e. where the response is down 3 dB, since this is the value you are really looking for.

Q6.1) Neatly plot gain and phase as a function of frequency.

Q6.2) What is the 3 dB point of the op amp circuit for each gain you measured? Is this what you expected?

Q6.3) How do phase and Bandwidth compare to the data sheets?

Q6.4) Does the phase ever get to 360 °? Why? Is this a problem in actual operation of the device? Why?

Q6.5) How do the two op amps compare?

The slew rate of an op amp is the maximum rate at which the output voltage can change. This is due to the internal construction of the op amp, primarily the compensation capacitor in compensated op amps. It is an inherent limitation in the amp and we must learn to live with it. As with many things in electronics, it is part of a trade-off. Reduce performance to enhance ease of application.

To measure the slew rate, connect up the circuit as shown in figure 7. Using a square wave input, set the amplitude at 5 volts peak, and set the frequency at 1000 Hz. Observe the input and output waveforms on the oscilloscope.

In the voltage range of -4 volts to +4 volts, what is the maximum rate of change [de/dt] of the output voltage waveform. This value, usually given in units of volts/microsecond, is the slew rate.

Q7.1) How closely does this compare to the manufacturer's data sheets? What are some possible reasons for the differences?

Q7.2) Is this a severe limitation in the use of the op amp? Why?

Q7.3) How do the two op amps compare?

Cross over distortion is the distortion that occurs when the output voltage goes through zero volts.

Using the same setup as in 6.1, except with a 1000 ohm resistive load from the op amp output to ground, look closely at the area where the output changes from - to + and + to - (i.e. around zero for a 1000 Hz. sine wave input.

Q7.4) Is there any distortion at or around zero observable? State or draw what you observed and indicate how accurately you were able to measure this area ( time and amplitude sensitivity of the scope).

Q7.5) How do the two op amps compare?

Using the circuit in FIGURE 7, measure and observe the following and record your observations.

The overshoot is the ringing that occurs (if any) as the output goes from on value to another. Compare the response that you measure on the oscilloscope to FIGURE 8.1 below. (Overshoot is measured in % and is the maximum and minimum values the output attains before settling to the desired value. Assume to within 1% of the final desired value).

Associated with this is the total time it takes the amplifier to settle to within some predefined value. This is called the settling time (ts). See FIGURE 8.1 below.

The rise and fall times of the output are controlled by the slew rate of the amplifier. I have however asked you to measure them so that you can relate the measurement to the inherent op amp characteristic.

Q8.1) State your observations how accurately you were able to measure the values. How do the op amps compare?

The propagation delay is the time it takes for a signal applied at the input to propagate through the op amp to the output. (It is defined as the point at which the output changes by 10%). See FIGURE 8.2 below. (tp is the propagation delay).

Q8.2) State your observations and comment on how accurately you were able to measure the values.

Q8.3) How do the two op amps compare?