[Notes] 110l 1 Experiment Vii

Experiment VII

Operational Amplifier

One of the greatest achievements of electrical engineering has been the development of the

operational amplifier (op-amp). In a negative feedback configuration the op-amp is able to

provide linear, distortion free signal amplification. With various feedback networks, this high

gain, open loop circuit has been used to perform many analog mathematical operations such as

differentiation and integration.

In 1966 The Fairchild Company introduced The µA71 that became the standard for op-amp in

the electronic world. Many later manufactured op-amps have followed the conventions Fairchild

used in their 741, specially the arrangement of the pins. µA741 op-amp has the following

characteristics:

• Open -Loop Gain ≥ 300,000

• Input Impedance ≥ 2MΩ

• Output Impedance ≤ 50Ω

Theory:

The op-amp is a voltage controlled voltage source (amplifier) with a very high gain. It has a very

large input impedance and very small output impedance. Figure1 shows the symbol for an op-

amp and its equivalent circuit. When a voltage is applied across the input (Ri), that voltage is

multiplied by the gain (A) of the op-amp and the resulting voltage is sent to the output (pin 6).

The gain of an ideal op-amp is infinite. The gain of a 741 is at least 300,000. This means that if

an input voltage of 33 micro-Volts is applied across pins 2 and 3, then 10V will be produced at

point 6.

The full open-loop gain of op-amp is rarely used in real life for several reasons. First, the actual

gains of op-amps are not constant. For example, one 741 may have a gain of 300,000, while

another one may have a gain of 300,000. Second, the useful bandwidth where the gain is

constant is very narrow (about 4 Hz).

3

4

6

+7

2

Figure 1: Op-amp Symbol and Equivalent Circuit.

Definition of 741-pin functions:

Pin 1 (Offset Null): Offset nulling. Since the op-amp is the differential type, input offset

voltage must be controlled so as to minimize offset. Offset voltage is nulled by application of a

voltage of opposite polarity to the offset. An offset null-adjustment potentiometer may be used to

compensate for offset voltage. The null-offset potentiometer also compensates for irregularities

in the operational amplifier manufacturing process which may cause an offset. Consequently, the

null potentiometer is recommended for critical applications.

Offset Voltage: Build any op-amp circuit, apply 0V to its input, and what do you expect at the

output? Although you'd be tempted to say 0 V, there's actually an error voltage present at its

output. What causes this error? You can trace the error back to a number of unbalances in the

op amp's internal transistors and resistors. To account for this in a circuit design, the net error

is modeled as an offset voltage, Voff, in series with op amp's input terminals. How will it affect

your circuit? That depends on the op amp itself and your circuit design.

Pin 2 (Inverted Input): All input signals at this pin will be inverted at output pin 6. Pins 2 and

3 are very important (obviously) to get the correct input signals or the op amp can not do its

work.

Pin 3 (Non-Inverted Input): All input signals at this pin will be processed normally without

inversion. The rest is the same as pin 2.

Pin 4 (-V): The V- pin (also referred to as Vss) is the negative supply voltage terminal. Supply-

voltage operating range for the 741 is -4.5 volts (minimum) to -18 volts (max), and it is specified

for operation between -5 and -15 V DC. The device will operate essentially the same over this

range of voltages without change in timing period. Sensitivity of time interval to supply voltage

change is low, typically 0.1% per volt. (Note: Do not confuse the -V with ground).

Pin 5 (Offset Null): See pin 1.

Pin 6 (Output): Output signal's polarity will be the opposite of the input's when this signal is

applied to the op-amp's inverting input.

1

1- Null offset

2- Inverting input

3- Non Inverting Input

4- Negative DC -3→-18

8- Not connected

7- Positive DC +3→+18

6- Output

5- Null offset

Pin 7 (posV): The V+ pin (also referred to as Vcc) is the positive supply voltage terminal of the

741 op-amp. Supply-voltage operating range for the 741 is +4.5 volts (minimum) to +18 volts

(maximum), and it is specified for operation between +5 and +15 V

essentially the same over this range of voltages without change in timing period. Actuall

most significant operational difference is the output drive capability, which increases for both

current and voltage range as the supply voltage is increased. Sensitivity of time interval to supply

voltage change is low, typically 0.1% per volt.

Pin 8 (N/C): The 'N/C' stands for 'Not Connected'. There is no other explanation. There is

nothing connected to this pin, it is just there to make it a standard 8

Negative Feedback:

If we connect the output of an op

inverting input, we find that the output voltage of the

As Vin increases, Vout will increase in accordance with the differential gain. However, as V

increases, that output voltage is fed back to the inverting input, thereby acting to decrease the

voltage differential between inputs, which acts to bring the output down. What will happen for

any given voltage input is that the

low enough so that there's enough voltage difference left between V

amplified to generate the output voltage.

The circuit will quickly reach a point of stability (known as

output voltage is just the right amount to maintain the right amount of differential, which in turn

produces the right amount of output voltage. Taking the

to the inverting input is a technique kno

self-stabilizing system (this is true not only of

This stability gives the op-amp the capacity to work in its linear (active) mode, as opposed to

merely being saturated fully "on" or "off" as it was when used as a

feedback at all.

Comparator Circuit: A comparator circuit compares two voltage signals and determines which

one is greater. The result of this comparison is indicated by the output voltage: if the

output is saturated in the positive direction, the non

positive, voltage than the inverting input (

op-amp's voltage is near the negative supply voltage (in this case, 0 volts, or ground potential), it

means the inverting input (-) has a greater

The V+ pin (also referred to as Vcc) is the positive supply voltage terminal of the

voltage operating range for the 741 is +4.5 volts (minimum) to +18 volts

(maximum), and it is specified for operation between +5 and +15 V DC. The device will operate

essentially the same over this range of voltages without change in timing period. Actuall



voltage change is low, typically 0.1% per volt.

The 'N/C' stands for 'Not Connected'. There is no other explanation. There is

nothing connected to this pin, it is just there to make it a standard 8-pin package.

op-amp to its inverting input and apply a voltage signal to the non

inverting input, we find that the output voltage of the op-amp closely follows that input voltage.

will increase in accordance with the differential gain. However, as V



any given voltage input is that the op-amp will output a voltage very nearly equal to V

low enough so that there's enough voltage difference left between Vin and the (-) input to be

amplified to generate the output voltage.

The circuit will quickly reach a point of stability (known as equilibrium in physics), where the


produces the right amount of output voltage. Taking the op-amp's output voltage and coupling it

to the inverting input is a technique known as negative feedback, and it is the key to having a

stabilizing system (this is true not only of op-amps, but of any dynamic system in general).

the capacity to work in its linear (active) mode, as opposed to

being saturated fully "on" or "off" as it was when used as a comparator, with no

A comparator circuit compares two voltage signals and determines which

one is greater. The result of this comparison is indicated by the output voltage: if the

output is saturated in the positive direction, the non-inverting input (+) is a greater

positive, voltage than the inverting input (-), all voltages measured with respect to ground. If the

's voltage is near the negative supply voltage (in this case, 0 volts, or ground potential), it

) has a greater voltage applied to it than the non-inverting input (+).

The V+ pin (also referred to as Vcc) is the positive supply voltage terminal of the

voltage operating range for the 741 is +4.5 volts (minimum) to +18 volts

. The device will operate

essentially the same over this range of voltages without change in timing period. Actually, the



The 'N/C' stands for 'Not Connected'. There is no other explanation. There is

pin package.

to its inverting input and apply a voltage signal to the non-

sely follows that input voltage.

will increase in accordance with the differential gain. However, as Vout



ltage very nearly equal to Vin, but just

) input to be

hysics), where the


's output voltage and coupling it

and it is the key to having a

s, but of any dynamic system in general).

the capacity to work in its linear (active) mode, as opposed to

, with no

A comparator circuit compares two voltage signals and determines which

one is greater. The result of this comparison is indicated by the output voltage: if the op-amp's

inverting input (+) is a greater, or more

), all voltages measured with respect to ground. If the

's voltage is near the negative supply voltage (in this case, 0 volts, or ground potential), it

inverting input (+).

Because the op-amp's gain is so high, the voltage on the inverting input can be maintained almost

equal to Vin. Let's say that our op

volts, the output voltage will be 5.999970000149999 volts. This creates just enough differential

voltage (6 volts - 5.999970000149999 volts = 29.99985 µV) to cause 5.999970000149999 volts

to be manifested at the output terminal, and the system ho

29.99985 µV is not a lot of differential, so for practical calculations, we can assume that the

differential voltage between the two input wires is held by

One great advantage to using an op

the op-amp doesn't matter, so long as it's very large. If the

250,000 instead of 200,000, all it would mean is that the output voltage would hold

closer to Vin (less differential voltage needed between inputs to generate the required output). In

the circuit just illustrated, the output voltage would still be (for all practical purposes) equal to

's gain is so high, the voltage on the inverting input can be maintained almost

op-amp has a differential voltage gain of 200,000. If V


5.999970000149999 volts = 29.99985 µV) to cause 5.999970000149999 volts

to be manifested at the output terminal, and the system holds there in balance. As you can see,


differential voltage between the two input wires is held by negative feedback exactly at 0 volts.

op-amp with negative feedback is that the actual voltage gain of

doesn't matter, so long as it's very large. If the op-amp's differential gain were

250,000 instead of 200,000, all it would mean is that the output voltage would hold

(less differential voltage needed between inputs to generate the required output). In


's gain is so high, the voltage on the inverting input can be maintained almost

has a differential voltage gain of 200,000. If Vin equals 6


5.999970000149999 volts = 29.99985 µV) to cause 5.999970000149999 volts

lds there in balance. As you can see,


exactly at 0 volts.

is that the actual voltage gain of

's differential gain were

250,000 instead of 200,000, all it would mean is that the output voltage would hold just a little

(less differential voltage needed between inputs to generate the required output). In


the non-inverting input voltage. op-amp gains, therefore, do not have to be precisely set by the

factory in order for the circuit designer to build an amplifier circuit with precise gain. Negative

feedback makes the system self-correcting. The above circuit as a whole will simply follow the

input voltage with a stable gain of 1.

Figure 2 shows an example of the open-loop gain of an op-amp. In particular, negative feedback

is commonly used to cut back the gain of the op-amp, while increasing its useful frequency

range. In employing negative feedback, we adjust the gain to a desired value ( some horizontal

line under the curve in Figure 2). Which makes the overall circuit more stable and independent

of power supply‘s voltage fluctuations. When we use negative feedback, the two terminals of the

input will be approximately at he same potential. Consequently, the input current is practically

zero.

The op-amp, with negative resistive feed back, can be used for inverting and non-inverting

amplifiers. With a negative reactive feedback circuits, the op-amp can be used to implement

integrating and differentiating circuits. By placing filters in the negative feedback element

position, the inverse transfer function of those filters will appear in the output. A positive

feedback can be employed for oscillators and Schmitt trigger circuits.

Positive feedback:

Another type of feedback, namely positive feedback, also finds application in op-amp circuits.

Unlike negative feedback, where the output voltage is "fed back" to the inverting (-) input, with

positive feedback the output voltage is somehow routed back to the non-inverting (+) input. In its

simplest form, we could connect a straight piece of wire from output to non-inverting input and

see what happens:

Figure2: Gain and Bandwidth of the 741 op-amp

protos

Highlight

The inverting input remains disconnected from the feedback loop, and is free to receive an

external voltage. Let's see what happens if we ground

With the inverting input grounded (maintained at zero volts), the output voltage will be dictated

by the magnitude and polarity of the voltage at the non

be positive, the op-amp will drive its output positive as well, feeding that positive voltage back to

the non-inverting input, which will result in full positive output saturation. On the other hand, if

the voltage on the non-inverting input happens to start out negative, the

drive in the negative direction, feeding back to the non

negative saturation.

What we have here is a circuit whose output is

positive or saturated negative). Once it has reached one of those saturated states, it will tend to

remain in that state, unchanging. What is necessary to get it to switch states is a voltage placed

upon the inverting (-) input of the same polarity, but of a slightly greater mag

example, if our circuit is saturated at an output voltage of +12 volts, it will take an input voltage

at the inverting input of at least +12 volts to get the output to change. When it changes, it will

saturate fully negative.

So, an op-amp with positive feedback tends to stay in whatever output state it's already in. It

"latches" between one of two states, saturated positive or saturated negative. Technically, this is

known as hysteresis.

Hysteresis can be a useful property for a comparator ci

produce a square wave from any sort of ramping waveform (sine wave, triangle wave, saw

wave, etc.) input. If the incoming AC waveform is noise

simple comparator will work just fine.


external voltage. Let's see what happens if we ground the inverting input:


by the magnitude and polarity of the voltage at the non-inverting input. If that voltage happens to

will drive its output positive as well, feeding that positive voltage back to

inverting input, which will result in full positive output saturation. On the other hand, if

inverting input happens to start out negative, the op-amp's output will

drive in the negative direction, feeding back to the non-inverting input and resulting in full

What we have here is a circuit whose output is bi-stable: stable in one of two states (saturated

egative). Once it has reached one of those saturated states, it will tend to


) input of the same polarity, but of a slightly greater magnitude. For



h positive feedback tends to stay in whatever output state it's already in. It


Hysteresis can be a useful property for a comparator circuit to have. Comparators can be used to

produce a square wave from any sort of ramping waveform (sine wave, triangle wave, saw

wave, etc.) input. If the incoming AC waveform is noise-free (that is, a "pure" waveform), a

just fine.



inverting input. If that voltage happens to

will drive its output positive as well, feeding that positive voltage back to

inverting input, which will result in full positive output saturation. On the other hand, if

's output will

inverting input and resulting in full

stable in one of two states (saturated

egative). Once it has reached one of those saturated states, it will tend to


nitude. For



h positive feedback tends to stay in whatever output state it's already in. It


omparators can be used to

produce a square wave from any sort of ramping waveform (sine wave, triangle wave, saw-tooth

free (that is, a "pure" waveform), a

However, if there exist any anomalies in the waveform such as harmonics or "spikes" which

cause the voltage to rise and fall significantly within the timespan of a single cycle, a

comparator's output might switch states unexpectedly:

Any time there is a transition through the reference voltage level, no matter how tiny that

transition may be, the output of the comparator will switch states, producing a square wave with

"glitches."

If we add a little positive feedback to the comparato

output. This hysteresis will cause the output to remain in its current state unless the AC input

voltage undergoes a major change in magnitude.

What this feedback resistor creates is a dual

applied to the non-inverting (+) input as a reference which to compare with the incoming AC

voltage changes depending on the value of the

is saturated positive, the reference voltage at the

before. Conversely, when the op-

non-inverting input will be more negative than before. The result is easier to understand on a

graph:

When the op-amp output is saturated positive, the upper reference voltage is in effect, and the

output won't drop to a negative saturation level unless the AC input rises

reference level. Conversely, when the

voltage is in effect, and the output won't rise to a positive saturation level unless the AC input

drops below that lower reference level. The result is a clean square

significant amounts of distortion in the AC input signal. In order for a "glitch" to cause the

comparator to switch from one state to another, it would have to be at least as big (tall) as the

difference between the upper and lower reference voltage levels, and at the right point

cross both those levels.

If we add a little positive feedback to the comparator circuit, we will introduce hysteresis into the


change in magnitude.

What this feedback resistor creates is a dual-reference for the comparator circuit. The voltage

(+) input as a reference which to compare with the incoming AC

voltage changes depending on the value of the op-amp's output voltage. When the

ce voltage at the non-inverting input will be more positive than

-amp output is saturated negative, the reference voltage at the

input will be more negative than before. The result is easier to understand on a

output is saturated positive, the upper reference voltage is in effect, and the

output won't drop to a negative saturation level unless the AC input rises above that upper

reference level. Conversely, when the op-amp output is saturated negative, the lower reference


that lower reference level. The result is a clean square-wave output again, despite

stortion in the AC input signal. In order for a "glitch" to cause the


difference between the upper and lower reference voltage levels, and at the right point

r circuit, we will introduce hysteresis into the


the comparator circuit. The voltage

(+) input as a reference which to compare with the incoming AC

's output voltage. When the op-amp output

input will be more positive than

output is saturated negative, the reference voltage at the

input will be more negative than before. The result is easier to understand on a

output is saturated positive, the upper reference voltage is in effect, and the

that upper

rated negative, the lower reference


wave output again, despite

stortion in the AC input signal. In order for a "glitch" to cause the


difference between the upper and lower reference voltage levels, and at the right point in time to

protos

Highlight

protos

Highlight

protos

Highlight

protos

Highlight

protos

Highlight

protos

Highlight

Another application of positive feedback in op-amp circuits is in the construction of oscillator

circuits. An oscillator is a device that produces an alternating (AC), or at least pulsing, output

voltage. Technically, it is known as an astable device: having no stable output state (no

equilibrium whatsoever). Oscillators are very useful devices, and they are easily made with just

an op-amp and a few external components.

When the output is saturated positive, the Vref will be positive, and the capacitor will charge up

in a positive direction. When Vramp exceeds Vref by the tiniest margin, the output will saturate

negative, and the capacitor will charge in the opposite direction (polarity). Oscillation occurs

because the positive feedback is instantaneous and the negative feedback is delayed (by means of

an RC time constant). The frequency of this oscillator may be adjusted by varying the size of any

component.

Inverting Amplifier Circuits:

This Circuit (Figure 3) utilizes negative feedback to amplify the negative of the input signal.

Applying Kirchhoff’s rules at node, we have

This equation for gain is independent of the open-loop gain A of the op-amp.

Non-Inverting Amplifier Circuits:

This circuit (Figure 4) utilizes negative feedback to amplify the input signal.

Applying Kirchhoff’s rule at the node,

This equation for the gain is independent of the open-loop gain A of the op-amp.

Figure 3: Inverting Amplifier

+

-

Vi

R1

-V

+V

Vo

Rf

+

+

-

Vi

R1

-V

+V

Vo

Rf

+

Figure 4: Non-Inverting Amplifier

Circuit with Positive Feedback (Oscillator Circuit):

Figure 5 illustrate an op-amp circuit using both positive and negative feedbacks. This circuit is

an oscillator. This is its output has two stable levels, very positive and very negative.

To analyze this circuit, first, we predict the voltage of one of the nodes. Since there is a positive

feedback, it would be a safe assumption to consider output voltage is at its saturation point.

When Vo is high, the voltage at the non-inverting input can be determined by voltage divider law

with R2 and R3. At this time the output voltage starts to charge the capacitor C. This charging

continues until the voltage across the capacitor exceeds the voltage at the non-inverting input. At

this time, the output voltage drops to its lowest point(negative saturation) and capacitor starts to

charge in opposite direction.

With the output in its negative saturation, the voltage at the non-inverting input can be calculated

by the voltage divider law. The voltage at the inverting input is the same as potential difference

across the capacitor. When the capacitor is sufficiently discharged ( its potential difference is

smaller ( more negative) than the non-inverting input), the output voltage jumps again to its

positive saturation.

The potential difference across the capacitor can be expressed by the exponential equation with

two constant parameters.

τ

VoC

-V

+V

+

R1

R2

R3

Figure 5: Oscillator Circuit

Where

And

!

Where τ = R1C. The capacitor reaches its maximum possible potential difference at " # where

T is the period of the oscillation. At this time:

$ ! % !&

#'()

At " #, . After this time, changes sign and the output voltage goes to the

negative saturation point. The period of this oscillation is

$ *+ !

Pre-lab:

1. Design an inverting amplifier circuit with again near-10. Use resistors between 100Ω and

1MΩ. Choose values which are available with 5% tolerance.

Rf =________Ω, R1= _________Ω

2. Design a non-inverting amplifier with a gain of 11, using the same resistors.

Rf =________Ω, R1= _________Ω

3. Using inverting and non-inverting amplifiers, it is possible to design an amplifier with

almost any gain. What gains are not possible to achieve?

Experiments:

1. Construct the inverting op-amp circuit you designed in step 1 of the. Use a signal about

1Vp-p as your input. Measure and plot the gain of the circuit as function of frequency (use

log scale for frequency.

f Vo/Vin GdB

Extrapolate roll-off part of your graph to find gain at 4Hz.

Vo/Vin|f=4Hz =____________

At f= 1 kHz, increase your voltage until sine-wave gets distorted. Sketch the output signal. Label

all key voltages and times.

Vary your power supply voltage and

observe what happens to your output

signal. How does the saturation

voltage depend on the power supply

rail voltage? Do not exceed 18 volts

on your power supply.

Relation between VDC and Vsat is

_________________________________

_________________________________

_________________________________

2. Real op-amp has a small internal DC Offset voltage that might cause unexpected results

for small input signals, especially when no feedback is employed. Experimentally

measure this “input offset voltage”. Find what DC input voltage is necessary to apply

between the inverting and non-inverting inputs of the op-amp such that the output voltage

reduces exactly to zero. Do not use any feedback.

How does this compare to the expected of the input offset voltage? (±30mV)

3. Another undesirable feature of the op-amp is that they have common mode gain. That is,

if two identical nonzero signals are applied to both inputs, then the output signal (with no

feedback) should be ideally zero. But actually it will be a small fraction of the input

voltage. This fraction is known as the Common Mode Gain (Gcm).

Measure the common mode gain of your op-amp by applying a sinusoidal input signal of

20Vp-p to both the inverting and non-inverting inputs. Do not apply any feedback to the

op-amp. Measure the ratio of the output to the input voltage magnitude using the

oscilloscope. This ratio is your Common Mode Gain.

Gcm = ___________

Common Mode Rejection Ratio (CMRR) is the ratio of the open loop gain of your

amplifier (at 4 Hz) to the Common Mode Gain. It is regularly reported in dB. CMRR is a

measure of how well an op-amp will amplify differential signals and not Common Mode

Signals. What is the CMMR of your op-amp? How does this compare to the expected

value? (≅90dB)

CMMR _______, % difference ________

How large a CMRR will cause an error of 10% when amplifying a 0.1 Vp-p signal by a

factor of 10?

Voltage across Capacitor and Output Voltage

4. Construct the non-inverting op-amp circuit that you designed in step 2 of the Pre-lab. Use

a sin-wave signal of about 1Vp-p amplitude and 1 kHz frequency as your input. Measure

the output voltage and then the frequency and plot the gain vs. Frequency (log scale).

Then extrapolate your roll-off part of the graph to find gain at 4 Hz.

f Vo/Vin GdB

1 kHz

Construct the circuit in Figure 5 with R1 = 100kΩ, R2 =1kΩ, R3 = 9kΩ, and C = 0.01µF. This

circuit uses positive feedback. Observe and record the voltage across capacitor and out put

voltage of this circuit. Explain how this output signal is generated.

Date post:	11-Dec-2015
Category:	Documents
Upload:	keyboard2014
View:	225 times
Download:	2 times

[Notes] 110l 1 Experiment Vii

Documents