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OKANAGAN COLLEGE ELEN 236 Operational Amplifiers Amplifier Introduction An amplifier is simply any device that increases (and sometimes decreases) an output magnitude by adding energy. In electronics, examples of amplifiers include devices that amplify voltage, current, and/or power. Important Amplifier Characteristics: 1. Gain: (Output Magnitude)/(Input Magnitude). For example, voltage gain (designated A v ) is in out V V , current gain (designated A i ) is in out I I , and power gain (designated A p ) is in out P P . 2. Bandwidth: The range of frequencies over which the gain is valid. Outside of this bandwidth, the gain decreases. 3. Efficiency: (The amount of power output)/(the amount of power put into the system) 4. Linearity: A measure of distortion. If an amplifier is linear, that means there is no distortion. For example, ideally for voltage: in v out V A V × = . Sometimes however, as the input voltage increases, the output voltage cannot continue increasing according to the above formula…this is distortion. The main cause of non-linearity is saturation, which occurs when the maximum V out level is reached; any further increase in V in will not increase V out . 5. Noise: Any undesirable signal added by an amplifier. It is impossible to get rid of all sources of noise because one main source of noise is random electron movement, and electron movement cannot be suppressed. Introduction to Operational Amplifiers An operational amplifier, or op amp is a special type of integrated circuit designed to amplify signals. It has two major configurations, open loop and closed loop. Open Loop Configuration

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Page 1: Introduction to Operational Amplifiers - Okanagan Collegepeople.okanagan.bc.ca/dwilliams/courses/elen236/Notes/ELEN236... · Introduction to Operational Amplifiers An operational

OKANAGAN COLLEGE ELEN 236

Operational Amplifiers

Amplifier Introduction An amplifier is simply any device that increases (and sometimes decreases) an output magnitude by adding energy. In electronics, examples of amplifiers include devices that amplify voltage, current, and/or power.

Important Amplifier Characteristics:

1. Gain: (Output Magnitude)/(Input Magnitude). For example, voltage gain (designated Av) is

in

outV

V , current gain (designated Ai) is in

outI

I , and power gain (designated Ap) is in

outP

P .

2. Bandwidth: The range of frequencies over which the gain is valid. Outside of this bandwidth, the gain decreases.

3. Efficiency: (The amount of power output)/(the amount of power put into the system)

4. Linearity: A measure of distortion. If an amplifier is linear, that means there is no distortion. For example, ideally for voltage: invout VAV ×= . Sometimes however, as the input voltage increases, the output voltage cannot continue increasing according to the above formula…this is distortion. The main cause of non-linearity is saturation, which occurs when the maximum Vout level is reached; any further increase in Vin will not increase Vout.

5. Noise: Any undesirable signal added by an amplifier. It is impossible to get rid of all sources of noise because one main source of noise is random electron movement, and electron movement cannot be suppressed.

Introduction to Operational Amplifiers

An operational amplifier, or op amp is a special type of integrated circuit designed to amplify signals. It has two major configurations, open loop and closed loop.

Open Loop Configuration

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ELEN236 – Semiconductor Theory

In the open loop configuration, two inputs are driven into the device; one at the non-inverting terminal (labeled ‘+’), and one at the inverting terminal (labeled ‘-‘). The output signal is taken at Vout. The Vs+ and Vs- signals are the power supplies to the op amp. Vs+ is the positive source, and Vs- is the negative source. While it may seem that Vs+ must have the same magnitude but opposite sign as Vs-, that is not always the case.

The behaviour of the op amp in the open loop configuration is as follows:

• )( −+ −= VVAV volout . Avol is the open loop voltage gain, and is a property of each op amp.

• For op amps, Avol is designed to be as big as possible, in fact if we model an ideal op amp, Avol is assumed to be infinite.

• The op amp Vout is limited at the positive end to Vs+ and at the negative end to Vs-, if the output (according to the above Vout) equation is calculated to be beyond these limits, the actual output is equal to the limits

o i.e., if +−+ >− Svol VVVA )( then Vout = Vs+

o if −−+ <− Svol VVVA )( then Vout = Vs-

Having such a large Avol may not seem to be very useful, but it allows us to use op amps as comparators, which basically tell us which of two inputs is bigger.

We’ll come back to op amps later, first we’ll look at how negative feedback can limit the amount of gain that we have in a circuit

Negative Feedback By using negative feedback, the gain of op amps can be controlled. The output of the op amp is fed back to the inverting terminal in a manner that limits the output to a specifically designed value. To see how negative feedback works, we will go through a derivation (it is not necessary to be able to do all of these steps, this is to give background on how negative feedback works):

1. += VVin

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ELEN236 – Semiconductor Theory

2. 21

1

RRRVV out +

=− , it’s a voltage divider

3. substitute 1. and 2. into the open loop op amp equation

21

1

21

1 )(RR

RVAVARR

RVVAV outvolinvoloutinvolout +−=

+−= ,.

4. Rearrange equation:

invols

volout VARR

RAV =+

+ )1(1

1

5. Rearrange equation to get AVclosedloop = Vout/Vin

21

1_

1RR

RA

AAVV

vol

volclosedloopv

in

out

++

==

6. If Avol is very big:

1

2

1

21

21

1

21

1_ 11

RR

RRR

RRR

RRRA

AAVV

vol

volclosedloopv

in

out +=+

=

+

=

+

≅=

We don’t have to go through this analysis everytime because we can make two assumptions about every op amp circuit with negative feedback:

1. The inverting and non-invertting terminals have infinite input impedance

2. Avol is infinite

This leads us to the two golden rules for op amps with negative feedback (and we can solve any op amp circuit with negative feedback by starting with these two rules if we don’t already know how it behaves).

1. No current will flow into the inverting or non-inverting terminal

2. The voltage at the inverting terminal will equal the voltage at the non-inverting terminal.

Example 1. Non-Inverting Op Amp

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ELEN236 – Semiconductor Theory

1. += VVin

2. 21

1

RRRVVV out +

== +−

3. 21

1

RRRVV outin +

=

4. 1

2

1

21 1RR

RRR

VV

in

out +=+

=

Example 2. Inverting Op Amp

1. −+ == VGNDV

2. 11

1 RV

RVVI inin

R =−

= +

3. 22

2 RV

RVVI outout

R =−

= +

4. IR1 = IR2 therefore: 21 R

VRV outin −

=

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ELEN236 – Semiconductor Theory

5. Rearrange equation: 1

2_ R

RAVV

closedloopvin

out −==

Example 3. Summing Amplifier

1. −+ == VGNDV

2. Calculate currents through each resistor:

111 RVI inR = 222 RVI inR = 333 RVI inR =

3. Sum currents together since they join at one node:

332

2

1

1 RVRV

RVI in

inint ++=

4. This current is the same current as flows through R4: 44 RVI outR −=

5. Therefore: 43

3

2

2

1

1 RVRV

RV

RV

outininin −=++

6. If all the resistors are equal:

outininin VVVV −=++ 321

Example 4. Voltage Buffer

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ELEN236 – Semiconductor Theory

This one’s simple, just go back to the golden rules and you get…Vout = Vin.

Example 5. Difference Amplifier

This is certainly the toughest amplifier to analyze, but start with the golden rules for op amps, through in Ohm’s Law, and it’s not so bad.

1. The voltage at the non-inverting terminal is simply a voltage divider between R3 and R4

43

42 RR

RVV+

=+

2. The voltage at the inverting terminal must be at the same voltage as the non-inverting terminal:

43

42 RR

RVVV+

== +−

3. The currents through R1 and R2 are the same and can be calculated because we know the voltages on either side of each resistor.

2

43

42

21

43

421

1

)()(

R

VRR

RVI

RRR

RVVI

out

RR

−+

==+

−=

4. Solve the above equation for Vout:

1

21

1

2

43

42 )1)((

RRV

RR

RRRVVout −++

=

5. If all of the resistors are the same value:

12 VVVout −=

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ELEN236 – Semiconductor Theory

Comparators

There is not much to a comparator. It basically takes in two input values, and the output is determined by which of the two inputs is larger (in terms of sine and magnitude). It uses the open loop gain of op amps to greatly magnify the difference in voltage between two values. Assuming the voltage gain approaches infinity, then

• If V+ > V- then Vout = +Vsupply.

• If V+ < V-, then Vout = -Vsupply.

Applications

• Zero Voltage Level Detector

• Non-Zero Voltage level Detector

• Sound Activated LED Array

• Smoke Detector

Schmitt Trigger If a comparator has a noisy input, any noise around the threshold level could cause large output swings as the input moves back and forth around the threshold. For example, the following circuit shows a basic comparator, and the waveform below that shows the input with a small amount of noise on it causing large swings in the output voltage.

A Schmitt Trigger is a special type of comparator with two different thresholds and it looks like this:

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ELEN236 – Semiconductor Theory

It looks a bit like the non-inverting amplifier, but this time the feedback is going to the non-inverting terminal. This type of feedback is called positive feedback not negative feedback. The golden rule that says V+ = V- no longer holds true and this circuit is still a comparator. i.e.:

1. If V+ > V- then Vout = +Vsupply.

2. If V+ < V-, then Vout = -Vsupply.

The difference here is that the value of V+ changes.

21

2

RRRVV out +

=+ but Vout can be equal to +Vsupply or –Vsupply.

So we have an upper trigger point (UTP): 21

2sup RR

RVV plyutp ++=

And a lower trigger point (LTP): 21

2sup RR

RVV plyltp +−=

The following diagram shows the behaviour of a Schmitt trigger:

The input is noise, but the output does not switch back and forth due to noise around one threshold because once input crosses a threshold, the threshold switches to a value farther away from the current value.

Note that Vcc is simply the supply voltage.