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# Operational Amplifier Principle and Circuit

Introduction

The operational amplifier is referred to as an op amp. It was named "Operational Amplifier" because it was used in analog computers in the early days to implement mathematical operations. Mainly used in analog circuits, such as amplifiers, comparators, analog operators, is a device that electronics engineers often use. An operational amplifier is a circuit unit with a very high amplification factor. In an actual circuit, a feedback function is usually combined with a feedback network to form a certain functional module. It is an amplifier with a special coupling circuit and feedback. The output signal can be the result of mathematical operations such as addition, subtraction or differentiation of the input signal, integration, and the like. An op amp is a functional unit named from a functional point of view and can be implemented in discrete devices or in semiconductor chips. To know How a op amp works? It is better to know its working principle and circuit.

Operational Amplifier Operation: How Does it Work?

Catalog

 Introduction Ⅰ Working Principle of Operational Amplifier1.1 Terminology1.2 Closed Loop Negative Feedback1.3 Closed Loop Positive Feedback Ⅱ Main Parameters of the Operational Amplifier2.1 Typical Parameters2.2 Important Indicators Ⅲ Common Operational Amplifier Circuit Analysis3.1 Inverter Amp3.2 Non-inverter Amp3.3 Voltage Follower3.4 Comparator Ⅳ Operational Amplifier Classification4.1 General Purpose Operational Amplifier4.2 High-impedance Operational Amplifier4.3 Low Temperature Drift Type Operational Amplifier4.4 High Speed Operational Amplifier4.5 Low Power Operational Amplifier4.6 High Voltage And High Power Operational Amplifier4.7 Programmable Control Operational Amplifier Ⅴ Ideal Operational Amplifier and Ideal Operational Amplifier Conditions

## Ⅰ Working Principle of Operational Amplifier

### 1.1 Terminology

With the development of semiconductor technology, most of the op amps exist in the form of a single chip. There are many types of op amps, which are widely used in the electronics industry. For a better use of the op amp, a thorough understanding of the operational principle of the op amp is a must.

An operational amplifier (OP, OPA, OPAMP for short) is a DC-coupled, differential-mode (differential-mode) input, usually a single-ended output (gain) voltage amplifier, because At the beginning, it was mainly used in arithmetic circuits such as addition and multiplication, hence the name. An ideal op amp must have the following characteristics: an infinite input impedance, an output impedance equal to zero, an infinite open loop gain, an infinite part of the common mode rejection ratio, and an infinite bandwidth. The most basic operational amplifier is shown in Figure 1-1. An operational amplifier module generally includes a positive input (OP_P), a negative input (OP_N), and an output (OP_O). Figure 1-1 The Most Basic Operational Amplifier

When an op amp is typically used, its output is connected to its inverting input node to form a negative feedback configuration. The reason is that the op amp's voltage gain is very large, ranging from hundreds to tens of thousands of times, using negative feedback to ensure stable operation of the circuit. However, this does not mean that the op amp cannot be connected to positive feedback. Conversely, in many systems that need to generate an oscillating signal, an operational amplifier with a positive feedback configuration is a very common component. Figure 1-2 Open Loop Operational Amplifier

Open-loop operational amplifiers are shown in Figure 1-2. When an ideal operational amplifier is operated in an open-loop manner, the relationship between its output and the input voltage is as follows:

Vout = ( V+ -V-) * Aog

Aog stands for open-loop differential gai of the operational amplifier.

Since the open-loop gain of the op amp is very high, even if the differential signal at the input is small, the output signal will still be saturated, resulting in nonlinear distortion. Therefore, op amps rarely appear in circuit systems in open-loop loops. A few exceptions are the use of op amps as comparators. The output of the comparator is typically "0" and "1" of the logic level.

### 1.2 Closed Loop Negative Feedback

Connecting the inverting input of the op amp to the output, the amplifier circuit is in a negative feedback configuration, and the circuit can often be referred to simply as a closed-loop amplifier. The closed-loop amplifier enters the end of the amplifier according to the input signal, and can be divided into two types: an inverting amplifier and a non-inverting amplifier.

The inverting closed loop amplifier is shown in Figure 1-3. Assuming that the closed-loop amplifier uses an ideal op amp, the open-loop gain is infinite, so the two inputs of the op amp are virtual ground, and the relationship between the output and the input voltage is as follows:

Vout = -(Rf / Rin) * Vin Figure 1-3 Inverted Closed-loop Amplifier

Non-inverted closed-loop amplifiers are shown in Figure 1-4 Assuming that the closed-loop amplifier uses an ideal op amp, the open-loop gain of the op amp is infinite, so the voltage difference between the two inputs of the op amp is almost zero. The relationship between the output and the input voltage is as follows:

Vout = ((R2 / R1) + 1) * Vin Figure 1-4 Non-inverting Closed-loop Amplifier

### 1.3 Closed Loop Positive Feedback

The positive input and the output of the operational amplifier are connected, and the amplifier circuit is in the state of positive feedback. Since the positive feedback configuration works in a very unstable state, it is mostly used in applications that need to generate the oscillation signal.

## Ⅱ Main Parameters of the Operational Amplifier

### 2.1 Typical Parameters

• Common Mode Input Resistance (RINCM)

This parameter indicates the ratio of the input common-mode voltage range to the amount of change in the bias current over the range when the op amp is operating in the linear region.

• DC Common Mode Rejection (CMRDC)

This parameter is used to measure the op amp's ability to reject the same DC signal applied to both inputs.

• AC common mode rejection (CMRAC)

CMRAC is a measure of the op amp's ability to reject the same AC signal acting on both inputs, as a function of the differential mode open-loop gain divided by the common-mode open-loop gain.

• Gain Bandwidth Product (GBW)

The gain-bandwidth product AOL * ƒ is a constant defined in the region where the open-loop gain varies with frequency and -20dB/decade tumbling.

• Input Bias Current (IB)

This parameter refers to the average current flowing into the input when the op amp is operating in the linear region.

• Input Bias Current Temperature Drift (TCIB)

This parameter represents the amount of change in the input bias current as the temperature changes. TCIB is usually expressed in units of pA/°C.

• Input Offset Current (IOS)

This parameter refers to the difference in current flowing into the two inputs.

• Input Offset Current Temperature Drift (TCIOS)

This parameter represents the amount of change in the input offset current as the temperature changes. TCIOS is usually expressed in units of pA/°C.

• Differential Mode Input Resistance (RIN)

This parameter indicates the ratio of the amount of change in the input voltage to the amount of change in the corresponding input current. The change in voltage causes a change in current. When measuring at one input, the other input is connected to a fixed common-mode voltage.

• Output Impedance (ZO)

This parameter refers to the internal equivalent small signal impedance at the output of the op amp when operating in the linear region.

• Output Voltage Swing (VO)

This parameter refers to the peak-to-peak value of the maximum voltage swing that can be achieved without the output signal being clamped. VO is generally defined at a specific load resistance and supply voltage.

• Power Consumption (Pd)

Indicates the static power consumed by the device at a given supply voltage. Pd is usually defined under no-load conditions.

• Power Supply Rejection Ratio (PSRR)

This parameter is used to measure the ability of the op amp to maintain its output as the supply voltage changes. The PSRR is typically expressed as the amount of change in the input offset voltage caused by the supply voltage change.

• Conversion Rate / Slew Rate (SR)

This parameter refers to the maximum value of the ratio of the amount of change in the output voltage to the time required for this change to occur. SR is usually expressed in units of V/µs, and is sometimes expressed as a positive change and a negative change, respectively.

• Power Supply Current (ICC, IDD)

This parameter is the quiescent current consumed by the device at the specified supply voltage. These parameters are usually defined under no-load conditions.

• Unity Gain Bandwidth (BW)

This parameter refers to the maximum operating frequency of the op amp when the open loop gain is greater than one.

• Input Offset Voltage (VOS)

This parameter indicates the voltage difference that needs to be applied at the input when the output voltage is zero.

• Input Offset Voltage Drift (TCVOS)

This parameter refers to the change in input offset voltage caused by temperature changes, usually expressed in units of µV/°C.

• Input Capacitor (CIN)

CIN represents the equivalent capacitance of any input when the op amp is operating in the linear region (the other input is grounded).

• Input Voltage Range (VIN)

This parameter refers to the range of input voltages allowed when the op amp is operating normally (the expected result is obtained), and VIN is typically defined at the specified supply voltage.

• Input Voltage Noise Density (eN)

For op amps, the input voltage noise can be thought of as a series noise voltage source connected to any of the inputs, and eN is usually expressed in nV / Hz, defined at the specified frequency.

• Input Current Noise Density (iN)

For op amps, the input current noise can be thought of as two sources of noise current, connected to each input and common, usually expressed in pA / root Hz, defined at the specified frequency.

### 2.2 Important Indicators

• Input Offset Voltage UIO

An ideal integrated op amp, when the input voltage is zero, the output voltage should also be zero (no zeroing device). However, in practice, the differential input stage of the integrated op amp is difficult to achieve complete symmetry. Usually, when the input voltage is zero, there is a certain output voltage. The input offset voltage is the compensation voltage applied to the input to make the output voltage zero. In fact, when the input voltage is zero, the output voltage is divided by the voltage amplification factor, and the value converted to the input terminal is called the input offset voltage, that is,

The size of the UIO reflects the degree of symmetry and potential matching of the op amp. The smaller the UIO, the better the magnitude is between 2mV and 20mV. The UIO of the ultra-low offset and low drift op amps is generally between 1μV and 20μV.

• Input Offset Current IIO

When the output voltage is zero, the difference between the quiescent current of the differential pair and the base of the differential input stage is called the input offset current IIO, that is: due to the internal resistance of the signal source, the change of IIO will cause the input voltage to change, making the op amp The output voltage is not zero. The smaller the IIO, the better the symmetry of the input stage differential pair tube, which is generally about 1nA~0.1μA.

• Input Bias Current IIB

When the output voltage of the integrated op amp is zero, the average value of the static bias current of the two inputs of the op amp is defined as the input bias current: From the point of view of use, the bias current is small, and the output voltage change due to the change of the internal resistance of the signal source is smaller, so the input bias current is an important technical indicator. Generally, IIB is about 1 nA to 0.1 μA.

• Input Offset Voltage Temperature Drift △UIO/△T

Input Offset Voltage Temperature drift is the ratio of the amount of change in input offset voltage with temperature to the amount of temperature change over the specified operating temperature range. It is an important indicator to measure the temperature drift of the circuit, and it cannot be compensated by the method of external zero adjustment device. The input offset voltage temperature drift is as small as possible. The input offset voltage of a general op amp drifts between ±1mV/°C and ±20mV/°C.

• Input Offset Current Temperature Drift △IIO/△T

In the specified operating temperature range, the ratio of the amount of change in the input offset current with temperature to the amount of temperature change is called the input offset current temperature drift. The input offset current temperature drift is a measure of the current drift of the amplifier circuit and cannot be compensated by an external zero adjustment device. High quality op amps are several pA per degree.

• Maximum Differential Mode Input Voltage Uidmax

The maximum differential mode input voltage Uidmax is the maximum differential mode input voltage that the op amp's two inputs can withstand. Beyond this voltage, the op amp input stage will enter the non-linear region, causing the op amp's performance to deteriorate significantly or even cause damage. Uidmax is about ±5V~±30V depending on the process.

• Maximum Common Mode Input Voltage Uicmax

The maximum common mode input voltage Uicmax refers to the maximum common mode input voltage that the op amp can withstand under the normal operating conditions of the op amp. When the common mode voltage exceeds this value, the operating point of the input differential pair tube enters the nonlinear region, the amplifier loses the common mode rejection capability, and the common mode rejection ratio drops significantly.

The maximum common mode input voltage Uicmax is defined as the common mode input voltage value that causes the output voltage to produce a 1% following error when the op amp is connected to the voltage follower at the nominal supply voltage; or is defined as the common mode added when the amplifier is dropped by 6 dB. Enter the voltage value.

The open-loop differential mode voltage amplification factor Aud refers to the ratio of the variation of the output voltage to the change of the input voltage at the input port of the op amp when the integrated op amp operates in the linear region, accesses the specified load. The Aud of the op amp is between 60 and 120 dB. Different functions of the op amp, Aud is very different.

The differential mode input resistance Rid is the input resistance of the op amp when the differential mode signal is input. The larger the Rid, the smaller the influence on the signal source, and the input resistance Rid of the op amp is generally several hundred kilo ohms or more.

The definition of the op amp common mode rejection ratio KCMR is the same as that defined in the differential amplifier circuit. It is the ratio of the differential mode voltage amplification factor to the common mode voltage amplification factor, which is usually expressed in decibels. Different functions of the op amp, KCMR is also different, some between 60 ~ 70dB, and some as high as 180dB. The larger the KCMR, the stronger the suppression of common mode interference.

• Open Loop Bandwidth BW

The open-loop bandwidth, also known as -3dB bandwidth, refers to the frequency fH of the op amp's differential-mode voltage amplification factor Aud that drops by 3dB in the high-band.

The unity gain bandwidth BWG refers to the frequency fT corresponding to the increase of the signal frequency and the decrease of Aud to 1, that is, the signal frequency fT when Aud is 0 dB. It is an important parameter for integrated op amps. The fT=7Hz of the 741 op amp is relatively low.

• Slew Rate SR (swing rate)

The slew rate SR is the maximum rate of change of the output voltage of the amplifying circuit with respect to time when a large signal (such as a step signal) is input under the condition that the voltage amplification factor is equal to 1, as shown in Figure 7-1-1. It reflects the op amp's ability to respond to rapidly changing input signals. The expression of the conversion rate SR is: The slew rate SR is an important indicator when working with large signals and high-frequency signals. At present, the general-purpose op amp slew rate is about 1~10V/μs.  The op amp above has two inputs a, b and one output o. Also known as a reverse input (inverting input), a non-inverting input (in-phase input) and an output. When the voltage is added - added between the a terminal and the common terminal (the common terminal is the zero of the voltage, which is equivalent to the reference node in the circuit), and the actual direction of the output voltage U is from the a terminal to the common terminal. The common end points to the o end, that is, the direction of the two is opposite. When the input voltage U+ is added between the b end and the common end, the actual direction of U and U+ is exactly the same as the common end. For the sake of distinction, the a end and the b The terminals are marked with "-" and "+" respectively, but do not mistake them for positive and negative polarity of the voltage reference direction. The positive and negative polarities of the voltage should be marked or indicated by arrows. Inverting amplifiers and non-reverse The turn amplifier is shown below: The op amp can generally be viewed simply as a high-gain direct-coupled voltage amplifying unit with one signal output port (Out) and two in-phase, inverting, high-impedance inputs, so op amps can be used to make in-phase, inverting, and differential amplifiers. .

The power supply mode of the op amp is divided into dual power supply and single power supply. For dual-supply op amps, the output can be varied across zero voltage and the output can be set to zero when the differential input voltage is zero. With a single-supply op amp, the output varies over a range of power and ground.

The input potential of the op amp is usually required to be higher than a certain value of the negative power supply and lower than a certain value of the positive power supply. A specially designed op amp allows the input potential to vary from the negative supply to the positive supply, even slightly above the positive supply or slightly below the negative supply. This type of op amp is called a rail-to-rail input operational amplifier.

The output signal of the operational amplifier is proportional to the difference between the signal voltages of the two inputs. In the audio segment: output voltage = A0 (E1-E2), where A0 is the low-frequency open-loop gain of the op amp (eg 100dB, ie 100000 times) , E1 is the input signal voltage of the non-inverting terminal, and E2 is the input signal voltage of the inverting terminal.

## Ⅲ Common Operational Amplifier Circuit Analysis

### 3.1 Inverter Amp The magnification is Av = R2 / R1 but the Gain-Bandwidth value of the specification needs to be considered.

R3 = R4 provides 1 / 2 power bias

C3 is the power supply decoupling filter

C1, C2 input and output are separated by DC

At this point, the output signal phase is opposite to the input.

### 3.2 Non-inverter Amp Magnification is Av=R2 / R1

R3 = R4 provides 1 / 2 power supply bias

C1, C2, C3 are DC-blocking

At this point, the output signal phase is the same as the input.

### 3.3 Voltage Follower The potential of the O/P output is the same as the potential of the I/P input. Both single and dual power supplies are available.

### 3.4 Comparator O/P output is Logic low when I/P voltage is higher than Ref.

O/P output is Logic high when I/P voltage is lower than Ref.

R2 = 100 * R1 is used to eliminate the Hysteresis state, which is to strengthen the O/P output, Logic high and low potential difference to improve the sensitivity of the comparator.

(R1=10 K, R2=1 M), both single and dual power supplies are available.

• Virtual Short And Imaginary Meanings In Operational Amplifiers

Two important conclusions can be drawn when the ideal op amp works in the linear region:

• Virtual Short

Because the voltage amplification factor of the ideal op amp is very large, and the op amp works in the linear region, it is a linear amplifying circuit, and the output voltage does not exceed the linear range (ie, finite value). Therefore, the potential of the non-inverting input terminal and the inverting input terminal of the operational amplifier Very close to equal. When the op amp supply voltage is ±15V, the maximum output is generally 10~13V. Therefore, the voltage difference between the two input terminals of the op amp is below 1 mV, and the two input terminals are short-circuited. This feature is called a virtual short. Obviously this is not a true short circuit, but a reasonable approximation within the allowable error range when analyzing the circuit.

• Virtual Break

Since the input resistance of the op amp is generally several hundred kilo ohms or more, the current flowing into the non-inverting input and the inverting input of the operational amplifier is very small, several orders of magnitude smaller than the current in the external circuit, and the current flowing into the operational amplifier can often Ignore, this is quite an open circuit at the input of the op amp. This feature is called virtual break. Obviously, the input of the op amp can't really open the way.

Using the two concepts of “virtual short” and “virtual break”, the analysis process of the application circuit can be simplified when analyzing the linear application circuit of the operational amplifier. The operational circuits formed by the operational amplifiers all require a certain functional relationship between the input and the output, so both conclusions can be applied. If the op amp does not work in the linear region, there is no "virtual short" or "virtual break" feature. If the potential of the two inputs of the op amp is measured and reaches a few millivolts or more, the op amp often does not work in the linear region or is damaged.

## Ⅳ Operational Amplifier Classification

According to the parameters of the integrated operational amplifier, the integrated operational amplifier can be divided into the following categories.

### 4.1 General Purpose Operational Amplifier

General purpose operational amplifiers are designed for general purpose use. The main features of this type of device are low price, wide product range, and its performance indicators can be suitable for general use. Examples of μA741 (single op amp), LM358 (dual op amp), LM324 (four op amps) and LF356 with FET as the input stage fall into this category. They are currently the most widely used integrated operational amplifiers.

### 4.2 High-impedance Operational Amplifier

The characteristics of this type of integrated operational amplifier are that the differential mode input impedance is very high, and the input bias current is very small. Generally, rid>1GΩ~1TΩ, IB is several picoamperes to several tens of picoamperes. The main measure to achieve these indicators is to use the high input impedance of the FET, and use the FET to form the differential input stage of the operational amplifier. Using the FET as the input stage, not only the input impedance is high, the input bias current is low, but also has the advantages of high speed, wide bandwidth and low noise, but the input offset voltage is large. Common integrated devices are LF355, LF347 (four op amps) and CA3130, CA3140 with higher input impedance.

### 4.3 Low Temperature Drift Type Operational Amplifier

In automatic control instruments such as precision instruments and weak signal detection, it is always desirable that the offset voltage of the operational amplifier is small and does not change with temperature. Low temperature drift op amps are designed for this purpose. At present, the commonly used high-precision, low-temperature drift operational amplifiers include OP07, OP27, AD508, and chopper-stabilized low-drift device ICL7650 composed of MOSFETs.

### 4.4 High Speed Operational Amplifier

In fast A/D and D/A converters and video amplifiers, the conversion rate SR of the integrated operational amplifier is required to be high, and the unity gain bandwidth BWG must be large enough, like a general-purpose integrated operational amplifier is not suitable for high-speed applications. Occasionally. The main features of high speed op amps are high slew rate and wide frequency response. Common operational amplifiers include LM318, μA715, etc., SR=50~70V/us, BWG>20MHz.

### 4.5 Low Power Operational Amplifier

Since the biggest advantage of electronic circuit integration is that it can make complex circuits small and light, with the expansion of the scope of portable instruments, it is necessary to use an operational amplifier with low power supply voltage and low power consumption. Commonly used operational amplifiers are TL-022C, TL-060C, etc., and their operating voltage is ±2V~±18V, and the current consumption is 50~250μA. At present, some products have reached the power consumption level of μW. For example, the power supply of the ICL7600 is 1.5V, and the power consumption is 10mW. It can be powered by a single battery.

### 4.6 High Voltage And High Power Operational Amplifier

The output voltage of an op amp is primarily limited by the power supply. In a conventional operational amplifier, the maximum value of the output voltage is generally only a few tens of volts, and the output current is only a few tens of milliamps. To increase the output voltage or increase the output current, an auxiliary circuit must be added to the outside of the integrated op amp. High-voltage, high-current integrated op amps can output high voltages and large currents without any additional circuitry. For example, the D41 integrated op amp has a supply voltage of ±150V, and the μA791 integrated op amp has an output current of 1A.

### 4.7 Programmable Control Operational Amplifier

In the process of using the instrument, the range is involved. In order to get the output of the fixed voltage, the amplifier must be changed in magnification. For example, if the operational amplifier has a magnification of 10 times and the input signal is 1mv, the output voltage. For 10mv, when the input voltage is 0.1mv, the output is only 1mv. In order to get 10mv, the magnification must be changed to 100. The programmable op amp is generated to solve this problem. For example, PGA103A, by controlling the 1 and 2 feet Level to change the multiple of amplification.

## Ⅴ Ideal Operational Amplifier and Ideal Operational Amplifier Conditions

Ideal op amp parameters: differential mode amplification, differential mode input resistance, common mode rejection ratio, upper limit frequency are infinite; input offset voltage and its temperature drift, input offset current and its temperature drift, and noise are zero.

When analyzing and integrating op amp application circuits, the integrated op amp can be considered an ideal op amp in most cases. Ideally, the ideal operational amplifier is ideal for the technical indicators of the integrated operational amplifier. Since the technical specifications of the actual operational amplifier are closer to the ideal operational amplifier, the error caused by idealization is very small and can be ignored in general engineering calculations.

The technical indicators of the ideal op amp are as follows:

1. Open-loop differential mode voltage amplification factor Aod = ∞;

2. Input resistance Routput resistance Rod =0

3. Input bias current IB1 = IB2 = 0;

4. Offset voltage UIO, offset current IIO, offset voltage drift, offset current drift are zero;

5. Common mode rejection ratio CMRR = ∞;;

6. -3dB bandwidth fH = ∞;

7. No internal interference and noise.

The actual op amp's parameters can be treated as ideal with the following levels:

The voltage amplification factor is 104-105 times; the input resistance reaches 105Ω; the output resistance is less than several hundred ohms; the current in the external circuit is much larger than the bias current; the offset voltage, the offset current and its temperature drift are small, causing the circuit drift to allow Within the scope, the stability of the circuit can meet the requirements; when inputting the minimum signal, there is a certain signal-to-noise ratio, and the common mode rejection ratio is greater than or equal to 60 dB; the bandwidth can meet the circuit bandwidth requirement.