University of Basrah College of Engineering Department of Electrical Engineering

Analogue Electronics

CS307

Third Year Class

Lecturer Mr. Abdul-Basset A. AL-Hussein

1 Analogue Electronics

 Analogue electronics (American English:  It differs from a digital signal, in which analog electronics) are electronic systems the continuous quantity is a with a continuously variable signal. representation of a sequence of discrete  An analog signal is any continuous signal values which can only take on one of a for which the time-varying feature finite number of values. (variable) of the signal is a representation  The term analog signal usually refers to of some other time varying quantity, i.e., electrical signals; however, mechanical, analogous to another time varying signal. pneumatic, hydraulic, human speech, For example, in an analog audio signal, and other systems may also convey or be the instantaneous voltage of the signal considered analog signals. varies continuously with the pressure of  The word analogue is derived from the the sound waves. Greek word ανάλογος (analogos) meaning "proportional"

Electrical Engineering Department/ University of Basrah 2 Analogue Electronics

 Syllabus:

1. Operational Amplifiers. 2. Active Filters . 3. Oscillators. 4. Voltage and Current Regulators. 5. Analogue Multipliers and PLL.

 References:

1. Microelectronics Circuits: By Adel S. Sedra, 7Th Edition. 2. Electronics Device: By Thomas l. Floyd, 7th Edition.

Electrical Engineering Department/ University of Basrah 3 Chapter One Operational Amplifiers

Introduction  Early operational amplifiers (op-amps) were  The operational amplifier concept used primarily to perform mathematical originated around 1947. It was proposed operations such as addition, subtraction, that such a device would form an integration, and differentiation—thus the extremely useful analog building block. term operational. These early devices were In 1964, the first integrated circuit op- constructed with vacuum tubes and amp, designated the 702, was developed worked with high voltages. Today’s op- by Fairchild Semiconductor. This was amps are linear integrated circuits (ICs) that later followed by the 709 and use relatively low dc supply voltages and eventually the 741, which has become an are reliable and inexpensive. industry standard.

Electrical Engineering Department/ University of Basrah 4 The standard operational amplifier (op-amp) symbol is shown in Figure 1–1(a). It has two input terminals, the inverting (-) input and the noninverting (+) input, and one output terminal. Most op-amps operate with two dc supply voltages, one positive and the other negative, as shown in Figure 1–1(b), although some have a single dc supply. Some typical op-amp IC packages are shown in Figure 1–1(c).

Electrical Engineering Department/ University of Basrah 5 Op amp is combination of many transistors, GETs, Resisters in a pin head space. Find application in: 1. Audio amplifier. 2. Signal generator. 3. Signal filters. 4. Biomedical Instrumentation. First patent for Vacuum Tube Op-Amp (1946) 5. And numerous other applications. Advantages of OP-Amp over transistor amplifier: 1. Less power consumption. 2. Costs less. 3. More compact. 4. More reliable. 5. Higher gain can be obtained. First commercially successfully Monolithic 6. Easy design Op-Amp (1965)

Electrical Engineering Department/ University of Basrah 6 The Ideal Op-Amp First, the ideal op-amp has infinite voltage gain and infinite bandwidth. Also, it has an infinite input impedance (open) so that it does not load the driving source. Finally, it has a zero output impedance. Op-amp characteristics are illustrated in Figure 1–2(a). The input voltage, Vin, appears between the two input terminals, and the output voltage is AvVin, as indicated by the internal voltage source symbol.

Figure 1-2 Basics Op Amp representation

Electrical Engineering Department/ University of Basrah 7 The Practical Op-Amp Characteristics of a practical op-amp are very high voltage gain, very high input impedance, and very low output impedance. These are labelled in Figure 1–2(b). Internal Block Diagram of an Op-Amp A typical op-amp is made up of three types of amplifier circuits: a differential amplifier, a voltage amplifier, and a push-pull amplifier, as shown in Figure 1–3. The differential amplifier is the input stage for the op-amp. It provides amplification of the difference voltage between the two inputs. The second stage is usually a class A amplifier that provides additional gain. Some op-amps may have more than one voltage amplifier stage. A push-pull class B amplifier is typically used for the output stage.

Figure 1-3 Basic Internal arrangement of Op Amp.

Electrical Engineering Department/ University of Basrah 8 Input Signal Modes Recall that the input signal modes are determined by the differential amplifier input stage of the op-amp. Differential Mode: In the differential mode, either one signal is applied to an input with the other input grounded or two opposite-polarity signals are applied to the inputs. When an op-amp is operated in the single-ended differential mode, one input is grounded and a signal voltage is applied to the other input, as shown in Figure 1–4. In the case where the signal voltage is applied to the inverting input as in part (a), an inverted, amplified signal voltage appears at the output. In the case where the signal is applied to the noninverting input with the inverting input grounded, as in Figure 1–4(b), a non-inverted, amplified signal voltage appears at the output.

Figure 1-4 Single-ended differential mode

Electrical Engineering Department/ University of Basrah 9 In the double-ended differential mode, two opposite-polarity (out-of-phase) signals are applied to the inputs, as shown in Figure 1–5(a). The amplified difference between the two inputs appears on the output. Equivalently, the double-ended differential mode can be represented by a single source connected between the two inputs, as shown in Figure 1–5(b).

Figure 1-5 Double-ended differential mode.

Electrical Engineering Department/ University of Basrah 10 Common Mode: In the common mode, two signal voltages of the same phase, frequency, and amplitude are applied to the two inputs, as shown in Figure 1–6. When equal input signals are applied to both inputs, they tend to cancel, resulting in a zero output voltage.

This action is called common-mode rejection. Its importance lies in the situation where an unwanted signal appears commonly on both op- amp inputs. Common-mode rejection means that this unwanted signal will not appear on the output and distort the desired signal. Common-mode signals (noise) generally are the result of the pick-up of radiated energy on Figure 1-6 Common mode operation the input lines, from adjacent lines, the 50 Hz power line, or other sources.

Electrical Engineering Department/ University of Basrah 11 Op-Amp Parameters Common-Mode Rejection Ratio: Desired signals can appear on only one input or with opposite polarities on both input lines. These desired signals are amplified and appear on the output as previously discussed. Unwanted signals (noise) appearing with the same polarity on both input lines are essentially cancelled by the op-amp and do not appear on the output. The measure of an amplifier’s ability to reject common-mode signals is a parameter called the CMRR (common-mode rejection ratio).  Ideally, an op-amp provides a very high gain for differential-mode signals and zero gain for common-mode signals.

The higher the CMRR, the better. A very high value of CMRR means that the open-loop gain, Aol, is high and the common-mode gain, Acm, is low. The CMRR is often expressed in decibels (dB) as

Electrical Engineering Department/ University of Basrah 12 The open-loop voltage gain, Aol, of an op-amp is the internal voltage gain of the device and represents the ratio of output voltage to input voltage when there are no external components. The open-loop voltage gain is set entirely by the internal design. Open-loop voltage gain can range up to 200,000 (106 dB) and is not a well-controlled parameter. Datasheets often refer to the open-loop voltage gain as the large-signal voltage gain. A CMRR of 100,000, for example, means that the desired input signal (differential) is amplified 100,000 times more than the unwanted noise (common-mode). If the amplitudes of the differential input signal and the common-mode noise are equal, the desired signal will appear on the output 100,000 times greater in amplitude than the noise. Thus, the noise or interference has been essentially eliminated.

Maximum Output Voltage Swing (VO(p-p)) With no input signal, the output of an op-amp is ideally 0 V. This is called the quiescent output voltage. When an input signal is applied, the ideal limits of the peak-to-peak output signal are . In practice, however, this ideal can be approached but never reached. varies with the load connected to the op-amp and increases directly with load resistance. For example, the Fairchild KA741 datasheet shows a typical increases to

Input Offset Voltage The ideal op-amp produces zero volts out for zero volts in. In a practical op-amp, however, a small dc voltage, VOUT(error), appears at the output when no differential input voltage is applied. Its primary cause is a slight mismatch of the base emitter voltages of the differential amplifier input stage of an op-amp.

Electrical Engineering Department/ University of Basrah 13 Input Bias Current You have seen that the input terminals of a bipolar differential amplifier are the transistor bases and, therefore, the input currents are the base currents. The input bias current is the dc current required by the inputs of the amplifier to properly operate the first stage. By definition, the input bias current is the average of both input currents and is calculated as follows:

The concept of input bias current is illustrated in Figure 1–7.

Figure 1-7 Input bias current is the average of the two op-amp input currents.

Electrical Engineering Department/ University of Basrah 14 Input Impedance Two basic ways of specifying the input impedance of an op-amp are the differential and the common mode. The differential input impedance is the total resistance between the inverting and the noninverting inputs, as illustrated in Figure 1–8(a). Differential impedance is measured by determining the change in bias current for a given change in differential input voltage. The common-mode input impedance is the resistance between each input and ground and is measured by determining the change in bias current for a given change in common-mode input voltage. It is depicted in Figure 1–8(b).

Figure 1-8 Op-amp input impedance

Electrical Engineering Department/ University of Basrah 15 Input Offset Current Ideally, the two input bias currents are equal, and thus their difference is zero. In a practical op-amp, however, the bias currents are not exactly equal. The input offset current, IOS, is the difference of the input bias currents, expressed as an absolute value.

Actual magnitudes of offset current are usually at least an order of magnitude (ten times) less than the bias current. In many applications, the offset current can be neglected. However, high-gain, high-input impedance amplifiers should have as little IOS as possible because the difference in currents through large input resistances develops a substantial offset voltage, as shown in Figure 1–9. The offset voltage developed by the input offset current is

The error created by IOS is amplified by the gain Av of the op-amp and appears in the output as Figure 1-9 Effect of input offset current.

Electrical Engineering Department/ University of Basrah 16 Slew Rate The maximum rate of change of the output voltage in response to a step input voltage is the slew rate of an op-amp. The slew rate is dependent upon the high-frequency response of the amplifier stages within the op-amp. Slew rate is measured with an op-amp connected as shown in Figure 1–10(a). This particular op-amp connection is a unity- gain, noninverting configuration that will be discussed later. It gives a worst-case (slowest) slew rate. Recall that the high frequency components of a voltage step are contained in the rising edge and that the upper critical frequency of an amplifier limits its response to a step input. For a step input, the slope on the output is inversely proportional to the upper critical frequency. Slope increases as upper critical frequency decreases.

Figure 1-10 Slew rate measurement Electrical Engineering Department/ University of Basrah 17 A pulse is applied to the input and the resulting ideal output voltage is indicated in Figure 1–10(b). The width of the input pulse must be sufficient to allow the output to “slew” from its lower limit to its upper limit. A certain time interval, is required for the output voltage to go from its lower limit to its upper limit once the input step is applied. The slew rate is expressed as

Electrical Engineering Department/ University of Basrah 18 Op Amps with Negative Feedback An op-amp can be connected using negative feedback to stabilize the gain and increase frequency response. Negative feedback takes a portion of the output and applies it back out of phase with the input, creating an effective reduction in gain. This closed loop gain is usually much less than the open-loop gain and independent of it. Closed-Loop Voltage Gain, Acl The closed-loop voltage gain is the voltage gain of an op-amp with external feedback. The amplifier configuration consists of the op-amp and an external negative feedback circuit that connects the output to the inverting input. The closed-loop voltage gain is determined by the external component values and can be precisely controlled by them. Noninverting Amplifier An op-amp connected in a closed-loop configuration as a noninverting amplifier with a controlled amount of voltage gain is shown in Figure 1–11. The input signal is applied to the noninverting (+) input. The output is applied back to the inverting input through the feedback circuit (closed loop) formed by the input resistor Ri and the feedback resistor Rf. The feedback voltage is expressed as Electrical Engineering Department/ University of Basrah 19 Figure 1-11 Noninverting configuration

Electrical Engineering Department/ University of Basrah 20 Electrical Engineering Department/ University of Basrah 21 Voltage-Follower The voltage-follower configuration is a special case of the noninverting amplifier where all of the output voltage is fed back to the inverting (-) input by a straight connection, as shown in Figure 1–12. As you can see, the straight feedback connection has a voltage gain of 1 (which means there is no gain). The closed-loop voltage gain of a noninverting amplifier is as previously derived. Since B =1 for a voltage-follower, the closed-loop voltage gain of the voltage-follower is Note that the most important features of the voltage-follower configuration are its very high input impedance and its very low output impedance. These features make it a nearly ideal buffer amplifier for interfacing high- impedance sources and low-impedance loads. Figure 1-12 Op Amp Voltage Follower

Electrical Engineering Department/ University of Basrah 22 Inverting Amplifier An op-amp connected as an inverting amplifier with a controlled amount of voltage gain is shown in Figure 1–13. The input signal is applied through a series input resistor Ri to the inverting input. Also, the output is fed back through Rf to the same input. The noninverting input is grounded. In particular, the concept of infinite input impedance is of great value. An infinite input impedance implies zero current at the inverting input. If there is zero current through the input impedance, then there must be no voltage drop between the inverting and noninverting inputs. This means that the voltage at the inverting input is zero because the noninverting input is grounded. This zero voltage at the inverting input terminal is referred to as virtual ground. This condition is illustrated in Figure 1–14(a). Since there is no current at the inverting input, Figure 1-13 Inverting Configuration the current through Ri and the current through Rf are equal, as shown in Figure 1–14(b). Electrical Engineering Department/ University of Basrah 23 Figure 1-14 Virtual ground and closed loop gain Electrical Engineering Department/ University of Basrah 24 Note that the closed-loop voltage gain of the inverting amplifier (Acl(I)) is the ratio of the feedback resistance (Rf) to the input resistance (Ri). The closed loop gain is independent of the op-amp’s internal open-loop gain. Thus, the negative feedback stabilizes the voltage gain. The negative sign indicates inversion.

Electrical Engineering Department/ University of Basrah 25 Effect of Negative Feedback on Op Amp Impedances Negative feedback affects the input and output impedances of an op-amp. The effects on both inverting and noninverting amplifiers are examined in this section.

Impedances of the Noninverting Amplifier Input Impedance: The input impedance of a noninverting amplifier can be developed with the aid of Figure 1–15. For this analysis, assume a small differential voltage, Vd, exists between the two inputs, as indicated. This means that you cannot assume the op-amp’s input impedance to be infinite or the input current to be zero. Express the input voltage as

Electrical Engineering Department/ University of Basrah 26 Figure 1-15

Electrical Engineering Department/ University of Basrah 27 Output Impedance: An expression for output impedance of a noninverting amplifier can be developed with the aid of Figure 1–16.

Figure 1-16

Electrical Engineering Department/ University of Basrah 28 This equation shows that the output impedance of the noninverting amplifier configuration with negative feedback is much less than the internal output impedance, , of the op-amp itself (without feedback) because is divided by the factor 1 + . 𝑍𝑍𝑜𝑜𝑜𝑜𝑜𝑜 𝑍𝑍𝑜𝑜𝑜𝑜𝑜𝑜 Electrical Engineering𝐴𝐴 Department/𝑜𝑜𝑙𝑙 𝐵𝐵 University of Basrah 29 Impedances of the Inverting Amplifier The input and output impedances of an inverting op-amp configuration are developed with the aid of Figure 1–17. Both the input signal and the negative feedback are applied, through resistors, to the inverting terminal as shown.

Figure 1-17

Output Impedance As with a noninverting amplifier, the output impedance of an inverting amplifier is decreased by the negative feedback. In fact, the expression is the same as for the noninverting case.

The output impedance of both the noninverting and the inverting amplifier configurations is very low; in fact, it is almost zero in practical cases. Because of this near zero output impedance, any load impedance within limits can be connected to the op-amp output and not change the output voltage. The limits for the load impedance are determined by the maximum peak-to-peak swing of the output and the current limit of the op-amp.

Electrical Engineering Department/ University of Basrah 30 Basic Op Amp Circuits Op-amps are used in such a wide variety of circuits and applications: A comparator is a specialized op-amp circuit that compares two input voltages and produces an output that is always at either one of two states, indicating the greater or less than relationship between the inputs. Zero-Level Detection One application of an op-amp used as a comparator is to determine when an input voltage exceeds a certain level. Figure 1–18(a) shows a zero-level detector. Notice that the inverting input is grounded to produce a zero level and that the input signal voltage is applied to the noninverting input. Because of the high open-loop voltage gain, a very small difference voltage between the two inputs drives the amplifier into saturation, causing the output voltage to go to its limit.

Figure 1-18 The op amp as a zero level detector.

Electrical Engineering Department/ University of Basrah 31 Nonzero-Level Detection The zero-level detector in Figure 1–18 can be modified to detect positive and negative voltages by connecting a fixed reference voltage source to the inverting input, as shown in Figure 1–19(a). A more practical arrangement is shown in Figure 1–19(b) using a voltage divider to set the reference voltage, , as follows:

Electrical Engineering Department/ University of Basrah 32 Figure 1-19 None zero level detectors

Electrical Engineering Department/ University of Basrah 33 Summing Amplifier A summing amplifier has two or more inputs, and its output voltage is proportional to the negative of the algebraic sum of its input voltages as shown in Figure 1-20.

Figure 1-20 Summing amplifier with n inputs

Electrical Engineering Department/ University of Basrah 34 Difference Amplifier: Consider the Op-Amp circuit connected as difference amplifier in Figure 1-21.

Figure 1-21

Electrical Engineering Department/ University of Basrah 35 Figure 1-22

Electrical Engineering Department/ University of Basrah 36 Integrators and Differentiators An op-amp integrator simulates mathematical integration, which is basically a summing process that determines the total area under the curve of a function. An op-amp differentiator simulates mathematical differentiation, which is a process of determining the instantaneous rate of change of a function. It is not necessary for you to understand mathematical integration or differentiation, at this point, in order to learn how an integrator and differentiator work. Ideal integrators and differentiators are used to show basic principles. Practical integrators often have an additional resistor in parallel with the feedback capacitor to prevent saturation. Practical differentiators may include a resistor in series with the comparator to reduce high frequency noise.

The Op-Amp Integrator The Ideal Integrator: An ideal integrator is shown in Figure 1–23. Notice that the feedback element is a capacitor that forms an RC circuit with the input resistor.

Figure 1-23 The Op Amp Integrator Electrical Engineering Department/ University of Basrah 37 How a Capacitor Charges To understand how an integrator works, it is important to review how a capacitor charges. Recall that the charge Q on a capacitor is proportional to the charging current (IC) and the time (t).

From Figure 1–23, the inverting input of the op-amp is at virtual ground (0 V), so the voltage across Ri equals Vin. Therefore, the input current is and

Electrical Engineering Department/ University of Basrah 38 Example 1-1 (a) Determine the rate of change of the output voltage in response to the input square wave, as shown for the ideal integrator in Figure 1–24(a). The output voltage is initially zero. The pulse width is 100 us. (b) Describe the output and draw the waveform.

Figure 1-24

Electrical Engineering Department/ University of Basrah 39 During the time the input is at +2.5 V, the output will go from 0 to -5V. During the time the input is at -2.5 V, the output will go from -5 V to 0V. Therefore, the output is a triangular wave with peaks at 0V and -5V as shown in Figure 1– 24(b).

Electrical Engineering Department/ University of Basrah 40 The Op-Amp Differentiator The Ideal Differentiator: An ideal differentiator is shown in Figure 1–25. Notice how the placement of the capacitor and resistor differ from the integrator. The capacitor is now the input element, and the resistor is the feedback element. A differentiator produces an output that is proportional to the rate of change of the input voltage.

Since the current at the inverting input is negligible, . Both currents are constant because the slope of the capacitor voltage (VC/t) is constant. The output voltage is also constant and equal to the voltage across because one side of the feedback resistor is always 0 V (virtual ground).

Figure 1-25 Electrical Engineering Department/ University of Basrah 41 Example 1-2 Determine the output voltage of the ideal op-amp differentiator in Figure 1–26 for the triangular-wave input shown.

Figure 1-26

Electrical Engineering Department/ University of Basrah 42 Electrical Engineering Department/ University of Basrah 43  Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance  Frequency dependence of the open loop gain:

Electrical Engineering Department/ University of Basrah 44  Frequency Response of Closed loop Amplifiers The inverting amplifier transfer function

Electrical Engineering Department/ University of Basrah 45 Electrical Engineering Department/ University of Basrah 46 Gain Bandwidth Product: The gain–bandwidth product (designated as GBWP, GBW, GBP, or GB) for an amplifier is the product of the amplifier's bandwidth and the gain at which the bandwidth is measured

For devices such as operational amplifiers that are designed to have a simple one-pole frequency response, the gain–bandwidth product is nearly independent of the gain at which it is measured; in such devices the gain–bandwidth product will also be equal to the unity-gain bandwidth of the amplifier (the bandwidth within which the amplifier gain is at least 1).

For Example: If the GBWP of an operational amplifier is 1 MHz, it means that the gain of the device falls to unity at 1 MHz. Hence, when the device is wired for unity gain, it will work up to 1 MHz (GBWP = gain × bandwidth, therefore if BW = 1 MHz, then gain = 1) without excessively distorting the signal. The same device when wired for a gain of 10 will work only up to 100 kHz, in accordance with the GBW product formula. Further, if the minimum frequency of operation is 1 Hz, then the maximum gain that can be extracted from the device is 1×10 . 6

Electrical Engineering Department/ University of Basrah 47 Special Purpose Op-Amp Circuits:

 A general-purpose op-amp, such as the 741, is a versatile and widely used device.  However, some specialized IC amplifiers are available that have certain features or characteristics oriented to special applications. Most of these devices are actually derived from the basic op-amp. These special circuits include: 1. The instrumentation amplifier that is used in high noise environments, 2. The logarithmic amplifiers that are used for linearizing certain types of inputs and for mathematical operations. Log amplifiers are also used in communication systems, including fiber optics.

Electrical Engineering Department/ University of Basrah 48 Instrumentation Amplifier

 An instrumentation amplifier is a differential voltage-gain device that amplifies the difference between the voltages existing at its two input terminals.  The main purpose of an instrumentation amplifier is to amplify small signals that may be riding on large common mode voltages.  The key characteristics are high input impedance, high common-mode rejection, low output offset, and low output impedance.  The basic instrumentation amplifier is an integrated circuit that internally has three operational amplifiers and several resistors.  The voltage gain is usually set with an external resistor.

A basic instrumentation amplifier is shown in Figure1–27. Op-amps A1 and A2 are noninverting configurations that provide high input impedance and voltage gain. Op-amp A3 is used as a unity-gain differential amplifier with high-precision resistors that are all equal in value (R3=R4=R5=R6).

Electrical Engineering Department/ University of Basrah 49 Electrical Engineering Department/ University of Basrah 50 Electrical Engineering Department/ University of Basrah 51 Electrical Engineering Department/ University of Basrah 52 Electrical Engineering Department/ University of Basrah 53 Electrical Engineering Department/ University of Basrah 54 Electrical Engineering Department/ University of Basrah 55 Applications The instrumentation amplifier is normally used to measure small differential signal voltages that are super imposed on a common-mode voltage often much larger than the signal voltage. Applications include situations where a quantity is sensed by a remote device, such as a temperature-or pressure- sensitive transducer, and the resulting small electrical signal is sent over a long line subject to electrical noise that produces common-mode voltages in the line. The instrumentation amplifier at the end of the line must amplify the small signal from the remote sensor and reject the large common-mode voltage. The Figure below illustrates this.

Electrical Engineering Department/ University of Basrah 56 Constant-Current Source  A constant-current source delivers a load current that remains constant when the load resistance changes.  Figure below shows a basic circuit in which a stable voltage source (VIN) provides a constant current ( ) through the input resistor ( ). Since the inverting input of the op- amp is at virtual ground (0 V), the value of is determined as 𝐼𝐼𝑖𝑖 𝑅𝑅𝑖𝑖 𝐼𝐼𝑖𝑖

 If changes, remains constant as long as and are held constant. 𝑅𝑅𝐿𝐿 𝐼𝐼𝐿𝐿 𝑉𝑉𝐼𝐼𝐼𝐼 𝑅𝑅𝑖𝑖

Electrical Engineering Department/ University of Basrah 57 Current-to-Voltage Converter  A current-to-voltage converter converts a variable input current to a proportional output voltage.  A basic circuit that accomplishes this is shown in Figure (a). Since practically all of is through the feedback path, the voltage dropped across is . Because the left side of 𝑖𝑖 is at virtual ground (0 V), the output voltage equals the voltage across which𝐼𝐼 is 𝑓𝑓 𝑖𝑖 𝑓𝑓 proportional to 𝑅𝑅 𝐼𝐼 𝑅𝑅 𝑅𝑅𝑓𝑓 𝑅𝑅𝑓𝑓 𝐼𝐼𝑖𝑖  A specific application of this circuit is illustrated in Figure (b), where a photoconductive cell is used to sense changes in light level. As the amount of light changes, the current through the photoconductive cell varies because of the cell’s change in resistance.  This change in resistance produces a proportional change in the output voltage ( = ).

𝑑𝑑𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 𝑑𝑑𝐼𝐼𝑖𝑖 𝑅𝑅𝑓𝑓Electrical Engineering Department/ University of Basrah 58 Voltage-to-Current Converter  A basic voltage-to-current converter is shown in Figure below. This circuit is used in applications where it is necessary to have an output (load) current that is controlled by an input voltage.  Neglecting the input offset voltage, both inverting and noninverting input terminals of the op-amp are at the same voltage . Therefore, the voltage across equals . Since there is negligible current at the inverting input, the current through is the same 𝒊𝒊𝒊𝒊 𝟏𝟏 𝒊𝒊𝒊𝒊 as the current through ; thus 𝑽𝑽 𝑹𝑹 𝑽𝑽 𝑹𝑹𝟏𝟏 𝑹𝑹𝑳𝑳

Electrical Engineering Department/ University of Basrah 59 Peak Detector  An interesting application of the op-amp is in a peak detector circuit such as the one shown in Figure below. In this case the op-amp is used as a comparator. This circuit is used to detect the peak of the input voltage and store that peak voltage on a capacitor. For example,  this circuit can be used to detect and store the maximum value of a voltage surge; this value can then be measured at the output with a voltmeter or recording device.  The basic operation is as follows. When a positive voltage is applied to the noninverting input of the op-amp, the high-level output voltage of the op-amp forward-biases the diode and charges the capacitor. The capacitor continues to charge until its voltage reaches a value equal to the input voltage and thus both op-amp inputs are at the same voltage.  At this point, the op-amp comparator switches, and its output goes to the low level. The diode is now reverse biased, and the capacitor stops charging. It has reached a voltage equal to the peak of Vin and will hold this voltage until the charge eventually leaks off or until it is reset with a switch as indicated. If a greater input peak occurs, the capacitor charges to the new peak.

Electrical Engineering Department/ University of Basrah 60 Precision Half-Wave Rectifier: The “Superdiode” The circuit works as follows: If goes positive, the output voltage of the op amp will go positive and the diode will 𝐼𝐼 conduct, thus establishing a closed 𝑣𝑣feedback path between the op 𝐴𝐴 amp’s output𝑣𝑣 terminal and the negative input terminal.

This negative-feedback path will cause a virtual short circuit to appear between the two input terminals of the op amp. Thus the voltage at the negative input terminal, which is also the output voltage , will equal (to within a few millivolts) that at the positive input terminal, which is the input voltage , 𝑣𝑣𝑂𝑂 = 𝑣𝑣𝐼𝐼 Note that the offset voltage ( 0.5 ) exhibited in the simple half-wave- 𝒗𝒗𝑶𝑶 𝒗𝒗𝑰𝑰 𝒗𝒗𝑰𝑰 ≥ 𝟎𝟎 rectifier circuit is no longer present. For the op-amp circuit to start operation, has to exceed only a negligibly≈ small𝑉𝑉 voltage equal to the diode drop divided by 𝐼𝐼 the op amp’s open-loop gain. This makes 𝑣𝑣 this circuit suitable for applications involving very small signals. Electrical Engineering Department/ University of Basrah 61 Industrial op-amp

A741 LM741 TL741

μ − −

Electrical Engineering Department/ University of Basrah 62 741 Amplifier BJT Transistor Level Schematic

Electrical Engineering Department/ University of Basrah 63