Operating Modes and Characteristics of Operational Amplifiers - Essay Example

Electronic Devices Abstract The word ‘operational’ in the term operational amplifiers is because of the fact that early operational amplifiers were used primarily to perform addition, subtraction, integration and differentiation. They have variety of applications in the present era. Modern electronic systems and communications are largely relying on operational amplifiers as some difficult operations like analog to digital conversion and digital to analog conversion, scaling, high frequency signal generation and so on has been made simple and flexible by these devices. This report is a detailed study of operational amplifiers, their operating modes, characteristics and a few of their applications. First these devices are introduced and their symbols are presented. Then a historical paragraph is written which throws light on the evolution of modern Op-amplifiers. In the subsequent sections operating modes and two applications, i.e., over temperature sensing circuit and analog to digital convertor are presented. The report is concluded with the references used and a paragraph of conclusions drawn from this study. 1. Introduction: - 1.1- Introduction to operational amplifiers An operational amplifier (op amp) is a high gain differential amplifier with nearly ideal external characteristics. Internally the op amp is constructed using many transistors. An 'ideal' amplifier has Infinite voltage gain Infinite bandwidth Infinite input impedance (open) so that it does not load the driving source Zero output impedance Bandwidth--infinite Current entering the amp at either terminal--extremely small However, practical amplifiers fall short of these ideal properties. The characteristics of the practical operational amplifier are good enough, however, to allow us to treat it as ideal. Terminology: V+ = non-inverting input voltage V- = inverting input voltage Vo = output voltage Io = output current I+ = non-inverting input current I- = inverting input current ±VDC = positive and negative DC supply voltages used to power the op amp (typically ±5V to ±30V) ΔV = V+ -V-= difference voltage 1.2- History The term operational amplifier goes all the way back to about 1943 where this name was mentioned in a paper written by john R. Ragazzinni with the title “Analysis of problems inverting dynamics” and also covered the work of technical aid George A. it was 1947 that the operational amplifier concepts was originally advanced. The vary first series of modular solid state operational amplifier were introduce by Burr-Brown Research corporation and G.A Philbrick Researches Inc. in 1962. The op-amp has been a workhorse of linear systems ever since. A developmental background of the op amp begins early in the twentieth century, starting with certain fundamental beginnings. Of these, there were two key inventions very early in the century. The first was not an amplifier, but a two-element vacuum-tube-based rectifier. 1.3- Block diagram representation Block diagram of an operational amplifier. The input stage is a differential amplifier. The differential amplifier used as an input stage provides differential inputs and a frequency response down to d.c. Special techniques are used to provide the high input impedance necessary for the operational amplifier. The second stage is a high-gain voltage amplifier. This stage may be made from several transistors to provide high gain. A typical operational amplifier could have a voltage gain of 200,000. Most of this gain comes from the voltage amplifier stage. The final stage of the OP AMP is an output amplifier. The output amplifier provides low output impedance. The actual circuit used could be an emitter follower. The output stage should allow the operational amplifier to deliver several milli-amperes to a load. Notice that the operational amplifier has a positive power supply (+V CC) and a negative power supply (-V EE). This arrangement enables the operational amplifier to produce either a positive or a negative output. The two input terminals are labeled "inverting input" (-) and "non-inverting input" (+). The operational amplifier can be used with three different input conditions (modes). With differential inputs (first mode), both input terminals are used and two input signals which are 180 degrees out of phase with each other are used. This produces an output signal that is in phase with the signal on the non-inverting input. If the non-inverting input is grounded and a signal is applied to the inverting input (second mode), the output signal will be 180 degrees out of phase with the input signal (and one-half the amplitude of the first mode output). If the inverting input is grounded and a signal is applied to the non-inverting input (third mode), the output signal will be in phase with the input signal (and one-half the amplitude of the first mode output) 2. Circuit and operation 2.1- Operational amplifier circuit model Above is shown an ideal amplifier. The practical amplifier is the one which has following characteristics, Gain = very large, Input impedance = very large, Output impedance = very small, Bandwidth = very large, And current entering the amplifier at either terminal is extremely small. 2.2- Operating modes Normally an operational amplifier will operate in one of the two modes i.e., either inverting or non-inverting. Both are explained below. 2.2.1. Inverting amplifier: - Circuit diagram of inverting amplifier is shown below. An inverting amplifier works on the principal of negative feedback. Two resistor Rf is used in the feedback path which allows some of the output signal to be fed back to the input. Since for the negative feedback the output is 180° out of phase with the input, this amount of output effectively subtracted from the input, thereby reducing the input into the operational amplifier. This reduces the overall gain of the amplifier and is called negative feedback. Considering that input resistance is very high the output voltage will be, Zin = Rin The gain of the amplifier is determined by the ratio of Rf to Rin. That is: The presence of the negative sign is a convention indicating that the output is inverted. For example, if Rf is 10 000 Ω and Rin is 1 000 Ω, then the gain would be -10 000Ω/1 000Ω, which is -10. Theory of operation: An Ideal Operational Amplifier has 2 characteristics that imply the operation of the inverting amplifier: Infinite input impedance, and infinite differential gain. Infinite input impedance implies that there is no current in either of the input pins because current cannot flow through infinite impedance. Infinite differential gain implies that both the (+) and (-) input pins are at the same voltage because the output is equal to infinity times (V+ - V-). As the output approaches any arbitrary finite voltage, then the term (V+ - V-) approaches 0, thus the two input pins are at the same voltage for any finite output. To begin analysis, first it is noted that with the (+) pin grounded, the (-) must also be at 0 volts potential due to implication 2. with the (-) at 0 volts, the current through Rin (from left to right) is given by I = Vin/Rin by Ohm's law. Second, since no current is flowing into the op amp through the (-) pin due to implication 1, all the current through Rin must also be flowing through Rf (see Kirchhoff’s Current Law). Therefore, with V- = 0 volts and I(Rf) = Vin/Rin the output voltage given by Ohm's law is -Vin*Rf/Rin. Real op amps have both finite input impedance and differential gain; however both are high enough as to induce error that is considered negligible in most applications. 2.2.2. Non-inverting Amplifier: - An operational amplifier connected in closed loop configuration is a non- inverting amplifier. The basic circuit for the non-inverting amplifier is shown below. In this circuit the signal is applied to the non-inverting input of the op-amp. However, feedback is taken from the output of the op-amp through a resistor to the inverting input of the operational amplifier. Another resistor R2 is connected to the ground and this assembly of R1 and R2 makes a voltage divider configuration. These two resistors are used to set the gain of the operational amplifier. Gain of non-inverting amplifier is given by (A)……….. Feed back voltage is (B)…………… If the open loop voltage gain of the operational amplifier is Aol then output voltage is (C)…………………Vout = Aol(Vin - Vf) In the equation (B) letting equal to B then equation (C) will become Vout = Aol(Vin - BVout) Then applying simple algebra we can show that Vout(1+ AolB) = Aol(Vin) The overall voltage gain of the amplifier is given by Vout /Vin . the above equation can be re-arranged as Which gives Using the value of B from equation (B) we get the final close loop gain. Acl(NI) = 1+ Rf/Rin Notice that the close loop gain is not dependent on the open loop gain of the operational amplifier. Close loop gain can be set by selecting suitable values of Rf and Rin. 3. Applications There is wide variety of applications of operational amplifiers in today’s modern electronics and communication systems. It is impossible to cover all these applications in these report therefore only two fundamental applications of op-amps are presented in this report. These are: 3.1- Over temperature sensing circuit The circuit below is configured as a comparator. A fixed reference voltage at the non inverting input is provided by R1 and R2. The inverting input voltage is set by the other two resistors. The output goes to minus 12 volts and the buzzer is energized if the voltage at the inverting input rises above the reference voltage. By swapping the preset and temperature dependent resistors, we can change the behavior of the circuit. The temperature dependent one can be replaced by light dependent resistors. The circuit consists of a Wheatstone bridge with an Op-amp used to detect when the bridge is balanced. One leg of the bridge contains temperature dependent resistor or a Thermister. It has negative temperature co-efficient. Other leg has potentiometer which is set at a value equal to resistance of thermistor at the critical temperature. At normal temperature (below critical) thermistor resistance is greater than potentiometer resistance thus creating an unbalanced condition that drives the op-amp to its low saturated output level. As the temperature increases, the resistance of the thermistor decreases. When the temperature reaches the critical value, the two resistances (thermistor resistance and potentiometer resistance) become equal and the bridge becomes balanced. At this point the op-amp switches to its high saturated output level. This energizes the buzzer and an alarm is produced. 3.2- Digital to Analog convertor Given below is the circuit schematic diagram of Digital to Analog convertor using operational amplifiers. Typically the inputs are driven by CMOS gates, which have low but equal resistance for both logic ‘0’ and logic ‘1’. Also, if we use the same logic levels, CMOS gates really do provide +5 and 0 volts for their logic levels. The input circuit is a remarkable design, known as an R-2R ladder network. It has several advantages over the basic summer circuit we saw first: Only two resistance values are used anywhere in the entire circuit. This means that only two values of precision resistance are needed, in a resistance ratio of 2:1. This requirement is easy to meet, and not especially expensive.  The input resistance seen by each digital input is the same as for every other input. The actual impedance seen by each digital source gate is 3R. With a CMOS gate resistance of 200 ohms, we can use the very standard values of 10k and 20k for our resistors.  The circuit is indefinitely extensible for binary numbers. Thus, if we use binary inputs instead of BCD, we can simply double the length of the ladder network for an 8-bit number (0 to 255) or double it again for a 16-bit number (0 to 65535). We only need to add two resistors for each additional binary input.  The circuit lends itself to a non-inverting circuit configuration. Therefore we need not be concerned about intermediate inverters along the way. However, an inverting version can easily be configured if that is appropriate.  One detail about this circuit: Even if the input ladder is extended, the output will remain within the same output voltage limits. Additional input bits will simply allow the output to be subdivided into smaller increments for finer resolution. This is equivalent to adding inputs with ever-larger resistance values (doubling the resistance value for each bit), but still using the same two resistance values in the extended ladder. The basic theory of the R-2R ladder network is actually quite simple. Current flowing through any input resistor (2R) encounters two possible paths at the far end. The effective resistances of both paths are the same (also 2R), so the incoming current splits equally along both paths. The half-current that flows back towards lower orders of magnitude does not reach the op amp, and therefore has no effect on the output voltage. The half that takes the path towards the op amp along the ladder can affect the output. The most significant bit (marked "8" in the figure) sends half of its current toward the op amp, so that half of the input current flows through that final 2R resistance and generates a voltage drop across it. This voltage drop (from bit "8" only) will be one-third of the logic 1 voltage level, or 5/3 = 1.667 volts. This is amplified by the op amp, as controlled by the feedback and input resistors connected to the "-" input. For the components shown, this gain will be 3. With a gain of 3, the amplifier output voltage for the "8" input will be 5/3 × 3 = 5 volts. The current from the "4" input will split in half in the same way. Then, the half going towards the op amp will encounter the junction from the "8" input. Again, this current "sees" two equal-resistance paths of 2R each, so it will split in half again. Thus, only a quarter of the current from the "4" will reach the op amp. Similarly, only 1/8 of the current from the "2" input will reach the op amp and be counted. This continues backwards for as many inputs as there are on the R-2R ladder structure. The maximum output voltage from this circuit will be one step of the least significant bit below 10 volts. Thus, an 8-bit ladder can produce output voltages up to 9.961 volts (255/256 × 10 volts). This is fine for many applications. If you have an application that requires a 0-9 volt output from a BCD input, you can easily scale the output upwards using an amplifier with a gain of 1.6. 4. Design and simulation 5. References : Following references have been used in the preparation of this report: [1] T. L. Floyd, “Electronic Devices” Pearson Education, 2006, pp.580-95 [2] T. L. Floyd, “Electronic Devices” Pearson Education, 2006, pp.653-62 [3] “www.simplecircuitdiagram.com/2010/12/05/temperature-alarm-with-op-amp-comparator/” Read More