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Analogue Electronic 2Analogue Electronic 2EMT 212EMT 212

Chapter 2Op-Amp Applications and

Frequency ResponseByBy

En. Tulus Ikhsan NasutionEn. Tulus Ikhsan Nasution

04/20/23

IntroductionIntroduction

Op-amps are used in many different applications.

We will discuss the operation of the fundamental

op-amp applications. Keep in mind that the basic

operation and characteristics of the op-amps do not

change — the only thing that changes is how we

use them.

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1. Constant-Gain Multiplier1. Constant-Gain Multiplier

V

One of the most common op-amp circuit is an inverting constant-gain multiplier (Fig. 2-1 (a)) or a non-inverting constant-gain multiplier (Figure 2-1 (b)), which provides a precise gain or amplification.

Fig. 2-1: Fixed-gain amplifier.

(a) (b)

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Multiple-Stage GainsMultiple-Stage Gains

When a number of stages are connected in series, the overall gain is the product of the individual stage gains.

Fig. 2-2: Constant-gain connection with multiple stages.

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The first stage provides non-inverting gain and the next two stages provides an inverting gain. The overall circuit gain is then non-inverting and is calculated by

321 AAAA

where A1 = 1 + Rf/R1, A2 = -Rf/R2 and A3 = -Rf/R3.

(2-1)

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2. Voltage Subtraction2. Voltage Subtraction

Two signals can be subtracted from one another in a number of ways. Figure 2-3 shows two op-amp stages used to provide subtraction of input signals.

Fig. 2-3: Circuit for subtracting two signals.

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The resulting output is given by

1

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2

22

VRR

RV

R

RV ffo (2-2)

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Another connection to provide subtraction of two signals is shown in Figure 2-4. This connection uses only one op-amp stage to provide subtracting two input signals.

Using superposition, we can show the output to be

22

41

2

42

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3 VR

RV

R

RR

RR

RVo

Fig. 2-4: Subtraction circuit.

(2-3)

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3. Voltage Follower/Buffer3. Voltage Follower/Buffer

The input impedance to the buffer is very high and its output impedance is low.

This “buffer” is used to isolate an input signal from a load by using a stage having unity voltage gain (Av

= 1).

The output voltage is determined by

1VVo

Fig. 2-5: Unity-gain (buffer) amplifier.

(2-4)

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Figure 2-6 shows how an input signal can be provided to two separate outputs.

The advantage of this connection is:

The load connected across one output has no (or little) effect on the other output because the outputs are buffered or isolated from each other.

Fig. 2-6 : Use of buffer amplifier to provide output signals.

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4. Comparators4. Comparators The comparator is an op-amp circuit that compares two input voltages

and produces an output indicating the relationship between them. The inputs can be two signals (such as two sine waves) or a signal and a fixed dc reference voltage.

Fig. 2-7: Digital waveform characteristics.

Comparators are most commonly used in digital applications. Digital circuits respond to rectangular or square waves, rather than sine waves. These waveforms are made up of alternating (high and low) dc levels and the transitions between them.

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3.1. Zero Level Detection3.1. Zero Level Detection

Fig. 2-8: The op-amp as a zero-level detector.

An op-amp without negative feedback (or in the open-loop configuration) is essentially a comparator.

Figure 2-8 (a) shows that a zero-level detector can be built by applying the input signal voltage to the non-inverting (+) input and the inverting (-) input is grounded to produce a zero level.

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Figure 2-8 (b) shows the result of a sinusoidal input voltage applied to the non-inverting (+) input of the zero-level detector.

When the sine wave is above the zero line (V+>V-) the output reaches its maximum positive level. When the sine wave is below the zero line (V->V+), the amplifier is driven to its opposite state and the output reaches its maximum negative level. As can be seen here, the zero-level detector can produce a square wave from a sine wave.

V+

V-

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3.2. Nonzero-Level Detection3.2. Nonzero-Level Detection

The zero-level detector in Figure 2-8 (a) can be modified in three different arrangements to set the reference reference voltagevoltage, VVREFREF by connecting a reference voltage to the by connecting a reference voltage to the

inverting (-) inputinverting (-) input.

Fig. 2-9: Nonzero-level detectors.

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Fig. 2-9 (a) shows an op-amp circuit uses a fixed voltage source to set the reference voltage.

The circuit in Fig. 2-9 (b) uses a voltage-divider circuit to set the reference voltage.

The circuit in Fig. 2-9 (c) uses a zener diode to set the reference voltage.

Among them, the voltage-divider circuit is most often used to set the reference voltage for a given level detector and the reference voltage is expressed as

)(21

2 VRR

RVREF

(2-5)

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3.3. Effects of Input Noise on Comparator 3.3. Effects of Input Noise on Comparator OperationOperation

In many practical situations, noise (unwanted voltage noise (unwanted voltage fluctuations)fluctuations) appears on the input lineinput line. This noise voltage becomes superimposedsuperimposed on the input voltage, as shown in Fig. 2-10 for the case of a sine wave, and can cause a comparator to erratically switch output states.

Figure 2-10:

Sine wave with superimposed noise.

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Low-frequency sinusoidal voltage

Fig. 2-11: Effect of noise on comparator circuit.

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In order to understand the potential effects of noise voltage, consider a low-frequency sinusoidal voltage applied to the non-inverting (+) input of an op-amp comparator used as a zero-level detector as shown in Fig. 2-11 (a).

Fig. 2-11: Effects of noise on comparator circuit.

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Reducing Noise Effects with HysteresisReducing Noise Effects with Hysteresis

In order to make the comparator is less sensitive to noise, a technique incorporating positive feedback, called hysteresishysteresis, can be used.

Fig. 2-12: Comparator with positive feedback for hysteresis.

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Basically, hysteresis means that there is a Basically, hysteresis means that there is a

higher reference level when the input voltage higher reference level when the input voltage

goes from a lower to higher value than when it goes from a lower to higher value than when it

goes from a higher to a lower value.goes from a higher to a lower value.

The two reference levels are referred to as the The two reference levels are referred to as the

upper trigger point (UTP) and the lower trigger upper trigger point (UTP) and the lower trigger

point (LTP).point (LTP).

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The basic operation of the comparator with hysteresis is illustrated in Fig. 2-13 .

Fig. 2-13: Operation of a comparator with hysteresis.

(a) (b)

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(a)

When the input voltage Vin exceeds VUTP and the output is at the maximum positive voltage, the output voltage drops to its negative maximum, -Vout(max). The voltage fed back to the non-inverting input is VLTP and is expressed as .

)( (max)21

2outLTP V

RR

RV

(2-6)

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(b)

When the input goes below LTP and the output is at the maximum negative voltage, the output switches back to the maximum positive voltage. Now the voltage fed back to the non-inverting input is VUTP and is expressed as

)( (max)21

2outUTP V

RR

RV

(2-7)

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Fig. 2-14: Input and output signals for an operation of a comparator with hysteresis.

This figure shows that the device triggers only once when UTP or LTP is reached; thus, there is immunity to noise that is riding on the input signal.

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3.4. Comparator Applications3.4. Comparator Applications

Fig. 2-15: An over-temperature sensing circuit.

Thermistor is a temperature-sensing resistor with a negative temperature coefficient (its resistance decreases as temperature increases).

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Fig. 2-16: An analog-to-digital converter (ADC) using op-amp as comparators.

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4. Controlled Sources4. Controlled Sources

An input voltage can be used to control an output voltage or current, or an input current can be used to control an output voltage or current.

The types of controlled source are:

Voltage-controlled voltage source

Voltage-controlled current source

Current-controlled voltage source

Current-controlled current source

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4.1. Voltage-Controlled Voltage Source4.1. Voltage-Controlled Voltage Source

A voltage source whose output Vo is controlled by an input voltage V1 is shown in Figure 2-17.

Fig. 2-17: Ideal voltage-controlled voltage.

The output voltage is dependent on the input voltage (times a scale factor k).

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The type of circuit in Figure 2-17 can be built using an op-amp in two versions: one using the inverting input and the other the non-inverting input as shown in Figure 2-18.

Fig. 2-18: Practical voltage-controlled voltage source circuits using (a) inverting input and (b) non-inverting input.

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4.2. Voltage-Controlled Current Source4.2. Voltage-Controlled Current Source

Figure 2-19 shows an ideal circuit providing an output current Io controlled by an input voltage.

Fig. 2-19: Ideal voltage-controlled current source.

The output current is dependent on the input voltage.

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A practical circuit can be built with the output current through load resistor RL controlled by the input voltage V1.

The current through RL can be expressed as

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1 kVR

VIo

Fig. 2-20: Practical voltage-controlled current source.

(2-8)

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4.3. Current-Controlled Voltage Source4.3. Current-Controlled Voltage Source

A voltage source controlled by an input current is shown in Fig. 2-21.

The output voltage is dependent on the input current.

Fig. 2-21: Ideal current-controlled voltage source.

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A practical circuit can be built using an op-amp as shown in Figure 2-22.

Fig. 2-22: Practical current-controlled voltage source.

The output voltage is written as

11 kIRIV Lo (2-9)

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4.4. Current-Controlled Current Source4.4. Current-Controlled Current Source

Figure 2-23 shows an ideal circuit providing an output current dependent on an input current.

The output current is dependent on the input current.

Fig. 2-23: Ideal current-controlled current source.

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A practical circuit can be built using an circuit connection as follows,

The input current I1 can result in the output current Io so that

1

12

1

2

111

21

1

kII

IR

RI

R

RIII

III

o

o

o

o

Fig. 2-24: Practical current-controlled current source.

(2-10)

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5. Scaling Adder5. Scaling Adder

ini

Fig. 2-25: Summing amplifier with n inputs.

A different weight different weight can be assigned to each input of a summing amplifier by simply adjusting the values of the input resistors .

V1

V2

V3

Vn

Vo

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ini

As you have known that the output voltage is,

n

n

ffffo V

R

RV

R

RV

R

RV

R

RV ...3

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1

The weight of a input is set by the ratio of Rf to the resistance, Rx, for that input (Rx = R1, R2, R3,…Rn. For example: - if weight of Vin = 1, then Rx = Rf

- if weight of Vin = 0.5, required Rx = 2Rf

The greater the Rx, the smaller the weight and vice versa.

(2-11)

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6. Summing Amplifiers Applications6. Summing Amplifiers Applications

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Fig. 2-26: A scaling adder as four-digit digital-to-analog converter.

A four-digit four-digit digital-to-analog converter (DAC) is called a binary-weighted resistorbinary-weighted resistor DAC.

Switch symbols represent transistor switchestransistor switches for applying each of the four binary digits to the input.

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Fig. 2-26: A scaling adder as four-digit digital-to-analog converter.

Since the inverting (-) input is at virtual groundvirtual ground, the output voltage is proportional to the current through the feedback resistor Rf (sum of input current).

IT

If

I1

I2

I3

I4

Short circuit

Virtual ground

Ii=0

If = IT

= I1+I2+I3+I4

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ini

Fig. 2-26: A scaling adder as four-digit digital-to-analog converter.

The lowest-value resistor R corresponds to the highest weighted binary input (23).

All of the other resistors are multiples of R and corresponds to the binary weights 22, 21, and 20.

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ini

Fig. 2-27: An R/2R ladder DAC.

R/2R ladder is more commonly used for D/A conversion than the scaling adder.

It overcomes one of the disadvantages of the binary-weight- input DAC because it requires only two resistor values.

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The “frequency response” of any circuit is the magnitude of the gain in decibels (dB) as a function of the frequency of the input signal.

The decibel is a common unit of measurement for the relative magnitude of two power levels. The expression for such a ratio of power is

Power level in dB = 10log10(P1/P2)

(A decibel is one-tenth of a "Bel", a seldom-used unit named for Alexander Graham Bell, inventor of the telephone.)

7. Op-Amp Frequency Response & 7. Op-Amp Frequency Response & Compensation Compensation

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7.1. Frequency Versus Gain7.1. Frequency Versus Gain

Fig. 2-28: Op-amp frequency-response curve.

The relationship between the frequency and gain is as follows: Decreasing the voltage gain of an op-amp will increases its maximum operating frequency.

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The unity-gain frequency (funity-gain frequency (funityunity)) is the maximum operating frequency of an op-amp measured at ACL = 0 dB (unity).

Since bandwidth (BW = fC2 – fC1; ffCC = cutoff frequency = cutoff frequency) increases as voltage gain decreases, we can make the following statements:

The higher the gain of an op-amp, the narrower its bandwidth.

The lower the gain of an op-amp, the wider its bandwidth.

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7.2. Gain-Bandwidth Product7.2. Gain-Bandwidth Product

The gain-bandwidth product of an amplifier is a constant that always equals the unity-gain frequency of its op-amp.

The product of ACL and bandwidth is always approximately equal to this constant.

The relationship among ACL, fC, and funity for an amplifier is:

unityCCL ffA (2-12)