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Circuit design follows the same lines for all electronic circuits. A specification is drawn up governing what the circuit is required to do, with allowable limits. A basic circuit is designed, often with the help of circuit modeling on a computer. Specific commercially available op amps and other components are then chosen that meet the design criteria within the specified tolerances at acceptable cost. If not all criteria can be met, the specification may need to be modified.

A prototype is then built and tested; changes to meet or improve the specification, alter functionality, or reduce the cost, may be made. That is, the op amp is being used as a voltage comparator. Note that a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found, since such devices can quickly recover from full on or full off "saturated" states. A voltage level detector can be obtained if a reference voltage V ref is applied to one of the op amp's inputs.

This means that the op amp is set up as a comparator to detect a positive voltage. If E i is a sine wave, triangular wave, or wave of any other shape that is symmetrical around zero, the zero-crossing detector's output will be square. Zero-crossing detection may also be useful in triggering TRIACs at the best time to reduce mains interference and current spikes.

Another typical configuration of op-amps is with positive feedback, which takes a fraction of the output signal back to the non-inverting input. An important application of it is the comparator with hysteresis, the Schmitt trigger. Some circuits may use positive feedback and negative feedback around the same amplifier, for example triangle-wave oscillators and active filters. Because of the wide slew range and lack of positive feedback, the response of all the open-loop level detectors described above will be relatively slow.

External overall positive feedback may be applied, but unlike internal positive feedback that may be applied within the latter stages of a purpose-designed comparator this markedly affects the accuracy of the zero-crossing detection point. Using a general-purpose op amp, for example, the frequency of E i for the sine to square wave converter should probably be below Hz. In a non-inverting amplifier, the output voltage changes in the same direction as the input voltage. The non-inverting input of the operational amplifier needs a path for DC to ground; if the signal source does not supply a DC path, or if that source requires a given load impedance, then the circuit will require another resistor from the non-inverting input to ground.

When the operational amplifier's input bias currents are significant, then the DC source resistances driving the inputs should be balanced. That ideal value assumes the bias currents are well matched, which may not be true for all op amps.

In an inverting amplifier, the output voltage changes in an opposite direction to the input voltage. Again, the op-amp input does not apply an appreciable load, so. A resistor is often inserted between the non-inverting input and ground so both inputs "see" similar resistances , reducing the input offset voltage due to different voltage drops due to bias current , and may reduce distortion in some op amps. A DC-blocking capacitor may be inserted in series with the input resistor when a frequency response down to DC is not needed and any DC voltage on the input is unwanted.

That is, the capacitive component of the input impedance inserts a DC zero and a low-frequency pole that gives the circuit a bandpass or high-pass characteristic. The potentials at the operational amplifier inputs remain virtually constant near ground in the inverting configuration.

The constant operating potential typically results in distortion levels that are lower than those attainable with the non-inverting topology. Most single, dual and quad op amps available have a standardized pin-out which permits one type to be substituted for another without wiring changes. A specific op amp may be chosen for its open loop gain, bandwidth, noise performance, input impedance, power consumption, or a compromise between any of these factors.

An op amp, defined as a general-purpose, DC-coupled, high gain, inverting feedback amplifier , is first found in U. Patent 2,, "Summing Amplifier" filed by Karl D. Swartzel Jr. It had a single inverting input rather than differential inverting and non-inverting inputs, as are common in today's op amps. In , the operational amplifier was first formally defined and named in a paper [18] by John R.

Ragazzini of Columbia University. In this same paper a footnote mentioned an op-amp design by a student that would turn out to be quite significant. This op amp, designed by Loebe Julie , was superior in a variety of ways.

It had two major innovations. Its input stage used a long-tailed triode pair with loads matched to reduce drift in the output and, far more importantly, it was the first op-amp design to have two inputs one inverting, the other non-inverting. The differential input made a whole range of new functionality possible, but it would not be used for a long time due to the rise of the chopper-stabilized amplifier.

In , Edwin A. Goldberg designed a chopper -stabilized op amp. This signal is then amplified, rectified, filtered and fed into the op amp's non-inverting input. This vastly improved the gain of the op amp while significantly reducing the output drift and DC offset. Unfortunately, any design that used a chopper couldn't use their non-inverting input for any other purpose.

Nevertheless, the much improved characteristics of the chopper-stabilized op amp made it the dominant way to use op amps. Techniques that used the non-inverting input regularly would not be very popular until the s when op-amp ICs started to show up in the field. In , vacuum tube op amps became commercially available with the release of the model K2-W from George A.

Philbrick Researches, Incorporated. Two nine-pin 12AX7 vacuum tubes were mounted in an octal package and had a model K2-P chopper add-on available that would effectively "use up" the non-inverting input. This op amp was based on a descendant of Loebe Julie's design and, along with its successors, would start the widespread use of op amps in industry. With the birth of the transistor in , and the silicon transistor in , the concept of ICs became a reality. The introduction of the planar process in made transistors and ICs stable enough to be commercially useful.

By , solid-state, discrete op amps were being produced. These op amps were effectively small circuit boards with packages such as edge connectors. They usually had hand-selected resistors in order to improve things such as voltage offset and drift. There have been many different directions taken in op-amp design.

Varactor bridge op amps started to be produced in the early s. By , several companies were producing modular potted packages that could be plugged into printed circuit boards. Monolithic ICs consist of a single chip as opposed to a chip and discrete parts a discrete IC or multiple chips bonded and connected on a circuit board a hybrid IC. Almost all modern op amps are monolithic ICs; however, this first IC did not meet with much success.

This simple difference has made the the canonical op amp and many modern amps base their pinout on the s. The same part is manufactured by several companies. In the s high speed, low-input current designs started to be made by using FETs.

A single sided supply op amp is one where the input and output voltages can be as low as the negative power supply voltage instead of needing to be at least two volts above it. The result is that it can operate in many applications with the negative supply pin on the op amp being connected to the signal ground, thus eliminating the need for a separate negative power supply.

The LM released in was one such op amp that came in a quad package four separate op amps in one package and became an industry standard. In addition to packaging multiple op amps in a single package, the s also saw the birth of op amps in hybrid packages. These op amps were generally improved versions of existing monolithic op amps.

As the properties of monolithic op amps improved, the more complex hybrid ICs were quickly relegated to systems that are required to have extremely long service lives or other specialty systems. Recent trends. Recently supply voltages in analog circuits have decreased as they have in digital logic and low-voltage op amps have been introduced reflecting this.

Supplies of 5 V and increasingly 3. To maximize the signal range modern op amps commonly have rail-to-rail output the output signal can range from the lowest supply voltage to the highest and sometimes rail-to-rail inputs. From Wikipedia, the free encyclopedia. High-gain voltage amplifier with a differential input. Main article: Operational amplifier applications.

An op amp connected in the non-inverting amplifier configuration. An op amp connected in the inverting amplifier configuration. Electronics portal. Philbrick Instrumentation amplifier Negative feedback amplifier Op-amp swapping Operational amplifier applications Operational transconductance amplifier Sallenâ€”Key topology.

Often these pins are left out of the diagram for clarity, and the power configuration is described or assumed from the circuit. Modern precision op amps can have internal circuits that automatically cancel this offset using choppers or other circuits that measure the offset voltage periodically and subtract it from the input voltage.

See Output stage. Maxim Application Note Archived from the original on Retrieved November 10, Archived from the original on 1 January Retrieved 8 November Microelectronics: Digital and Analog Circuits and Systems. ISBN X. Archived PDF from the original on The Art of Electronics. ISBN Handbook of Operational Amplifier Circuit Design. Texas Instruments.

Retrieved Analog Devices. Electronic Design News. The operational amplifier forces the inverting - terminal voltage to equal the input voltage, which creates a current flow through the feedback resistors. The output voltage is always in phase with the input voltage, which is why this topology is known as non-inverting.

Note that with a non-inverting amplifier, the voltage gain is always greater than 1, which is not always the case with the inverting configurations. VOUT can be calculated with Equation 4 :. An operational amplifier voltage comparator compares voltage inputs, and drives the output to the supply rail of whichever input is higher.

This configuration is considered open-loop operation because there is no feedback. Voltage comparators have the benefit of operating much faster than the closed-loop topologies discussed above see Figure 7. The section below discusses certain considerations when selecting the proper operational amplifier for your application.

Firstly, choose an op amp that can support your expected operating voltage range. A negative supply is useful if the output needs to support negative voltages. If your application needs to support higher frequencies, or requires a higher performance and reduced distortion, consider op amps with higher GBPs. One should also consider the power consumption, as certain applications may require low-power operation.

Power consumption can also be estimated from the product of the supply current and supply voltage. Generally, op amps with lower supply currents have lower GBP, and correspond with lower circuit performance. Operational amplifiers are widely used in many analog and power applications. The benefits of using an op amp are that they are generally widely understood, well-documented and supported, and are fairly easy to use and implement. Op amps are useful for many applications, such as voltage buffers, creating analog filters, and threshold detectors.

With a greater understanding of key parameters and common topologies related to operational amplifiers, you can begin implementing them in your circuits. Did you find this interesting? Get valuable resources straight to your inbox - sent out once per month! It has three built-in current-sense amplifiers. What is the range of frequency char The Input to this is the voltage acr Session popupval Session textval Session Titefor popup.

Remember me. Forgot password? Log in. Don't have an account? Sign up. Password Strength: No Password. Create Basic Account. Already have an account? Forgot Password. Please enter your email address below to receive a password reset link. Go back Go back. Log in to continue. Get early access to new products, datasheets, and free samples. Share this article. Get valuable resources straight to your inbox - sent out once per month Subscribe.

What is an Operational Amplifier? Operational Amplifier Clasifications There are four ways to classify operational amplifiers:. Latest activity 2 weeks ago. MP for Flash lighting. Latest activity a year ago. MP charge current. Average, if you look at the block diagram the amplifier GMI is a GM amp that compares the amplified voltage signal from the current sense resistor to Latest activity 12 months ago.

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Forexplaat kopen | The value for the compensation capacitor, C, was optimized to provide a maximum phase margin of about 58 degrees. You have a modified version of this example. At gains equal to 1 and 2, the phase shift between the formula 11is equal to 0. The simulation shows that with a wire providing closed-loop feedback from the output back to the inverting input, the huge open-loop gain is tamed, yielding a closed-loop gain of 1, out until the GBW limit is reached. In the s high speed, low-input current designs started to be made by using FETs. The procedure proposed Pandiev, |

How buy coinbase ipo | Tutorial MT Out of the loop compensation technique uses a simple resistor to isolate the capacitive load with the op-amp, lowering the capacitive loading of the op-amp. Next, you want to create a transfer function model of this system using Control System Toolbox. Swartzel Jr. CircuitLab, Inc. Then use 's' to construct the open-loop transfer function, a s :. |

Forex medium-term trading strategies | Solving for R2 yields:. Dallas, circuits and systems. Forgot Password. In a truly ideal op-amp, with infinite gain and bandwidth and slew rate, the process described in the intuitive model happens instantaneously. There have been many different directions taken in op-amp design. This means that the op amp is set up as a comparator to detect a positive voltage. Retrieved 28 April |

Investing amplifier circuit frequency response analysis | The section below discusses certain considerations when selecting the proper operational amplifier for your application. Get valuable resources straight to your inbox - sent out once per month Subscribe. This technique modifies b s by adding a capacitor, C, in parallel with the feedback resistor, R2. The miller compensation circuit is shown below. Enter the email address you signed up with and we'll email you a reset link. |

Sedco forex international drilling inc mumbai address | Miller compensation Another effective compensation technique is the miller compensation technique and it is an in-loop compensation technique where a simple capacitor is used with or without load isolation resistor Nulling resistor. An ideal op amp would have an infinite bandwidth BWand would be able to maintain a high gain regardless of signal frequency. Get valuable resources straight to your inbox - sent out once per month. The Phase curve is much better now. For the analysis of analogue circuits, the model of the CFOA is used. A specific op amp may be chosen for its open loop gain, bandwidth, noise performance, input impedance, power consumption, or a compromise between any of these factors. Do you want to open this example with your edits? |

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Ideally, when the dominant upper critical frequency, fcu dom , of each amplifier stage is different from the other stages, the overall dominant upper critical frequency, equals the dominant critical frequency of the stage with the lowest fcu dom. In practice, the critical frequencies interact, so these calculated values should be considered approximations that are useful for troubleshooting or estimating the response.

The bandwidth of a multistage amplifier is the difference between the overall dominant lower critical frequency and the overall dominant upper critical frequency. When each amplifier stage in a multistage arrangement has equal dominant critical frequencies, you may think that the overall dominant critical frequency is equal to the critical frequency of each stage.

This is not the case, however. With multistage amplifiers, the detailed calculation of the frequency response is greatly simplified by computer simulation. There are several interactions within each stage and other interactions between the stages that affect the overall response.

When you need more accuracy, a computer simulation is used. This is particularly useful in design work because you can change a component and see the effect immediately on the frequency response. The following example illustrates the application of computer analysis to a multistage amplifier.

Two basic methods are used to measure the frequency response of an amplifier. You will concentrate on determining the two dominant critical frequencies. From these values, you can get the bandwidth. The schematic for the circuit board is also shown. The amplifier is driven by a sinusoidal voltage source with a dual-channel oscilloscope connected to the input and to the output. The input frequency is set to a midrange value, and its amplitude is adjusted to establish an output signal reference level, as shown in FIG.

This output voltage reference level for midrange should be set at a convenient value within the linear operation of the amplifier: for example, mV, 1 V, 10 V, and so on. In this case, set the output signal to a peak value of 1 V. Next, the frequency of the input voltage is decreased until the peak value of the output drops to 0.

The amplitude of the input voltage must be kept constant as the frequency is reduced. Readjustment may be necessary because of changes in loading of the voltage source with frequency. When the output is 0. Next, the input frequency is increased back up through midrange and beyond until the peak value of the output voltage again drops to 0. Again, the amplitude of the input must be kept constant as the frequency is increased. The lower and upper critical frequencies of an amplifier can be determined using the step response method by applying a voltage step to the input of the amplifier and measuring the rise and fall times of the resulting output voltage.

The basic test setup shown in FIG. The input step is created by the rising edge of a pulse that has a long duration compared to the rise and fall times to be measured. The rise time of the input pulse must be fast compared to the rise time you measure from the amplifier. When a step input is applied, the amplifier's high frequency RC circuits internal capacitances prevent the output from responding immediately to the step input.

As a result, the output voltage has a rise time tr associated with it, as shown in FIG. In fact, the rise time is inversely related to the upper critical frequency fcu of the amplifier. As fcu becomes lower, the rise time of the output becomes greater. The scope must be set on a short time base so the relatively short interval of the rise time can be accurately observed. Once this measurement is made, fcu can be calculated with the following formula:.

The outputs are inverted. To determine the lower critical frequency fcl of the amplifier, the step input must be of sufficiently long duration to observe the full charging time of the low-frequency RC circuits coupling capacitances , which cause the "sloping" of the output and which we will refer to as the fall time tf. This is illustrated in FIG. The fall time is inversely related to the low critical frequency of the amplifier. As fcl becomes higher, the fall time of the output becomes less.

The scope must be set on a long time base so the complete interval of the fall time can be observed. Once this measurement is made, fcl can be determined with the following formula. BandwidthThe characteristic of certain types of electronic circuits that specifies the usable range of frequencies that pass from input to output. Bode plotAn idealized graph of the gain in dB versus frequency used to graphically illustrate the response of an amplifier or filter.

Critical frequencyThe frequency at which the response of an amplifier or filter is 3 dB less than at midrange. Decibel A logarithmic measure of the ratio of one power to another or one voltage to another. Midrange gain The gain that occurs for the range of frequencies between the lower and upper critical frequencies.

Roll-off The rate of decrease in the gain of an amplifier above or below the critical frequencies. Miller's theorem states that both gain and internal capacitances influence high-frequency response. The low-frequency response of an amplifier is determined in part by a the voltage gain b the type of transistor c the supply voltage d the coupling capacitors. The high-frequency response of an amplifier is determined in part by a the gain-bandwidth product b the bypass capacitor c the internal transistor capacitances d the roll-off.

The Miller input capacitance of an amplifier is dependent, in part, on a the input coupling capacitor b the voltage gain c the bypass capacitor d none of these. The decibel is used to express a power gain b voltage gain c attenuation d all of these. When the voltage gain is In an amplifier, the gain that occurs between the lower and upper critical frequencies is called the a critical gain b midrange gain c bandwidth gain d decibel gain.

A certain amplifier has a voltage gain of at midrange. If the gain decreases by 6 dB, it is equal to a 50 b The gain of a certain amplifier decreases by 6 dB when the frequency is reduced from 1 kHz to 10 Hz. The roll-off is a b c d. The gain of a particular amplifier at a given frequency decreases by 6 dB when the frequency is doubled. The roll-off is a b c d answers b and c. The lower critical frequency of a direct-coupled amplifier with no bypass capacitor is a variable b 0 Hz c dependent on the bias d none of these.

At the upper critical frequency, the peak output voltage of a certain amplifier is 10 V. The peak voltage in the midrange of the amplifier is a 7. The high-frequency response of an amplifier is determined by the a coupling capacitors b bias circuit c transistor capacitances d all of these.

The bandwidth of an amplifier is determined by a the midrange gain b the critical frequencies c the roll-off rate d the input capacitance. An amplifier has the following critical frequencies: 1. The bandwidth is a Hz b Hz c Hz d Hz. The frequency at which an amplifier's gain is 1 is called the a unity-gain frequency b midrange frequency c corner frequency d break frequency.

When the voltage gain of an amplifier is increased, the bandwidth a is not affected b increases c decreases d becomes distorted. If the fT of the transistor used in a certain amplifier is 75 MHz and the bandwidth is 10 MHz, the voltage gain must be a b 7.

In the midrange of an amplifier's bandwidth, the peak output voltage is 6 V. At the lower critical frequency, the peak output voltage is a 3 V b 3. The dominant lower critical frequency of a multistage amplifier is the a lowest fcl b highest fcl c average of all the fcl's d none of these.

When the critical frequencies of all of the stages are the same, the dominant critical frequency is a higher than any individual fcl b lower than any individual fcl c equal to the individual fcl's d the sum of all individual fcl's. In the step response of a noninverting amplifier, a longer rise time means a a narrower bandwidth b a lower fcl c a higher fcu d answers a and b.

In a capacitively coupled amplifier, the input coupling capacitor and the output coupling capacitor form two of the circuits along with the respective resistances that determine the low-frequency response. Assuming that the input and output impedances are the same and neglecting the bypass circuit, which circuit will first cause the gain to drop from its midrange value as the frequency is lowered?

Explain why the coupling capacitors do not have a significant effect on gain at sufficiently high-signal frequencies. In the amplifier of FIG. A certain amplifier exhibits an output power of 5 W with an input power of 0. What is the power gain in dB? If the output voltage of an amplifier is 1. What is the gain in dB? The midrange voltage gain of a certain amplifier is At a certain frequency beyond midrange, the gain drops to What is the gain reduction in dB? Express the midrange voltage gain of the amplifier in FIG.

Also express the voltage gain in dB for the critical frequencies. Which is the dominant critical frequency? Sketch the Bode plot. Determine the voltage gain of the amplifier in FIG. Indicate the dominant critical frequency and draw the Bode plot. Find the voltage gain of the amplifier in FIG.

Determine the critical frequencies associated with the high-frequency response of the amplifier in FIG. Identify the dominant critical frequency and sketch the Bode plot. Determine the critical frequencies associated with the high-frequency response of the amplifier, and indicate the dominant frequency. Determine the voltage gain in dB and the phase shift at each of the following multiples of the dominant critical frequency in FIG.

A particular amplifier has the following low critical frequencies: 25 Hz, 42 Hz, and Hz. It also has high critical frequencies of 8 kHz and 20 kHz. Determine the upper and lower critical frequencies. If the midrange gain is determined to be 38 and if fcl is low enough to be neglected compared to fcu, what bandwidth would you expect? What value of fcu would you expect? If the midrange gain of a given amplifier is 50 dB and therefore 47 dB at fcu, how much gain is there at 2fcu?

At 4fcu? At 10fcu? In a certain two-stage amplifier, the first stage has critical frequencies of Hz and 1. The second stage has critical frequencies of Hz and 2 MHz. What are the dominant critical frequencies? Determine the bandwidth of a two-stage amplifier in which each stage has a lower critical frequency of Hz and an upper critical frequency of kHz.

Determine the bandwidth. Determine fcl and fcu. Suppose you are measuring the frequency response of an amplifier with a signal source and an oscilloscope. Assume that the signal level and frequency are set such that the oscilloscope indicates an output voltage level of 5 V rms in the midrange of the amplifier's response. If you wish to determine the upper critical frequency, indicate what you would do and what scope indication you would look for.

Determine the approximate bandwidth of an amplifier from the indicated results of the step response test in FIG. Determine the dominant lower critical frequency for the amplifier in FIG. How does a change from 29 kOhm to kOhm in load resistance on the final output of the amplifier in FIG. Referring to the partial datasheet for a 2N in FIG. A certain amplifier uses a 2N and has a midrange voltage gain of Referring to the partial datasheet in FIG.

Determine Cgd, Cgs, and Cds. Two single-stage capacitively coupled amplifiers like the one in FIG. Determine whether or not this con figuration will operate as a linear amplifier with an input voltage of 10 mV rms. If not, modify the design to achieve maximum gain without distortion. Two stages of the amplifier in FIG. Determine the overall bandwidth. Redesign the amplifier in FIG.

Home Articles Forum Glossary Books. Phase Shift of the Input RC Circuit Because the output voltage of a high-frequency input RC circuit is across the capacitor, the output of the circuit lags the input. The phase angle is expressed as: EQN. The upper critical frequency for the input circuit is EQN. Goals: -- Analyze an amplifier for total frequency response -- Discuss bandwidth -- Define the dominant critical frequencies -- Explain gain-bandwidth product -- Define unity-gain frequency FIG.

Bandwidth An amplifier normally operates with signal frequencies between fcl dom and fcu dom. The amplifier's bandwidth is expressed in units of hertz as EQN. Goals: -- Analyze multistage amplifiers for frequency response -- Analyze the case where the stages have different critical frequencies -- Determine the overall bandwidth -- Analyze the case where the stages have equal critical frequencies -- Determine the overall bandwidth When amplifier stages are cascaded to form a multistage amplifier, the dominant frequency response is determined by the responses of the individual stages.

There are two cases to consider: 1. Different Critical Frequencies Ideally, when the dominant lower critical frequency, fcl dom , of each amplifier stage is different from the other stages, the overall dominant lower critical frequency, equals the dominant critical frequency of the stage with the highest fcl dom. When more accuracy is required, a computer simulation is the best solution. We begin this chapter by considering the frequency response of simple circuits using their transfer functions.

We then consider Bode plots which are the industry-standard way of presenting frequency response. We also consider series and parallel resonant circuits and encounter important concepts such as resonance, quality factor, cutoff frequency and bandwidth. We discuss different kinds of filters and network scaling. In the last section, we consider one practical application of resonant circuits and two applications of filters.

The transfer function is a useful analytical tool for finding the frequency response of a circuit. A transfer function is the frequency-dependent ratio of the forced function to the forcing function or of an output to an input. The idea of a transfer function was implicit when we used the concepts of impedance and admittance to relate voltage and current. In general, a linear network can be represented by the block diagram shown in [link].

Since the input and output can be either voltage or current at any place in circuit, there are four possible transfer functions:. We can obtain the frequency response of the circuit by plotting the magnitude and phase of the transfer function as the frequency varies. A computer is a real time-saver for plotting the transfer function. A zero as a root of the numerator polynomial, is a value that results in a zero value of the function. A pole, as a root of the denominator polynomial, is a value for which the function is infinite.

It is not always easy to get a quick plot of the magnitude and phase of the transfer function as we did above. A more systematic way of obtaining the frequency response is to us Bode plots. Before we begin to construct Bode plots, we should take care of two important issues: the use of logarithms and decibels in expressing gain. Since Bode plots are based on logarithms, it is important that we keep the following properties of logarithms in mind:. In communications systems, gain is measured in bels.

Historically, the bel is used to measure the ratio of two levels of power or power gain G; that is,. The decibel dB provides us with a unit of less magnitude. Alternatively, the gain G can be expressed in terms of voltage or current ratio. To do so, consider the network shown in [link]. Three things are important to note from [link] , [link] , and [link] :. With this in mind, we now apply the concepts of logarithms and decibels to construct Bode plots.

Obtaining the frequency response from the transfer function as we did in section 2 is an uphill task. The frequency range required in frequency response is often so wide that it is inconvenient to use a linear scale for the frequency axis.

Also, there is a more systematic way of locating the important features of the magnitude and phase plots of the transfer function. For these reasons, it has become standard practice to use a logarithmic scale for the frequency axis and a linear scale in each of the separate plots of magnitude and phase.

Such semilogarithmic plots of the transfer function-known as Bode plots have become the industry standard. Bode plots are semilog plots of the magnitude in decibels and phase in degrees of a transfer function versus frequency. Bode plots contain the same information as the nonlogarithmic plots discussed in the previous section, but they are much easier to construct, as we shall see shortly. Thus, the real part of ln H is a function of the magnitude while the imaginary part is the phase.

In a Bode magnitude plot, the gain. Both magnitude and phase plots are made on semilog graph paper. A transfer function in the form of [link] may be written in terms of factors that have real and imaginary parts. One such representation might be. These are:.

In constructing a Bode plot, we plot each factor separately and then combine them graphically. The factors can be considered one at time and then combined additively because of the logarithm that makes Bode plots powerful engineering tool. We will now make straight-line plots of the factors listed above. We shall find that these straight-line plots known as Bode plots approximate the actual plots to a surprising degree of accuracy.

Thus, the magnitude and phase plots of the gain are shown in [link]. We notice that. Thus, the approximate magnitude plot is shown in [link] a, where the actual plot is also shown. However, we will use the straight-line approximation for the sake of simplicity. We see again that the difference between the actual plot and the straight-line plot is due to the damping factor.

Notice that the straight-line approximations for both magnitude and phase plots for the quadratic pole are the same as those for a double pole, i. Thus, the quadratic pole can be treated as a double pole as fa as straight-line approximation is concerned. The combined graph is often drawn from left to right, changing slopes appropriately each time a corner frequency is encountered. The most prominent feature of frequency response of a circuit may be the sharp peak or resonant peak exhibited in its amplitude characteristic.

The concept of resonance applies in several areas of science and engineering. Resonance occurs in any system that has a complex conjugate pair of poles; it is the cause of oscillations of stored energy from one form to another. It is the phenomenon that allows frequency discrimination in communication networks. Resonance occurs in any circuit that has at least one inductor and one capacitor. Resonant circuits series or parallel are useful for constructing filters, as their transfer functions can be highly frequency selective.

They are used in any applications such as selecting the desired stations in radio and TV receivers. Consider the series RLC circuit shown in [link] in the frequency domain. The input impedance is. Resonance results when the imaginary part of the transfer function is zero, or.

Thus, the resonance condition is. The inductor voltage and capacitor voltage can be much more than the source voltage. Is shown in [link] ; the plot only shows the symmetry illustrated in this graph when the frequency axis is a logarithm. The average power dissipated by the RLC circuit is. We can relate the half-power frequencies with the resonant frequency. From [link] and [link] ,. Solving that the resonant frequency is the geometric mean of the half-power frequencies.

However, as will be explained shortly, symmetry of the half-power frequencies around the resonant frequency is often a reasonable approximation. Although the height of the curve in [link] is determined by R, the width of the curve depends on other factors. The width of response curve depends on the bandwidth B, which is defined as the difference between the two half-power frequencies,.

This definition of bandwidth is just one of several that are commonly used. Strickly speaking, B in [link] is a half-power bandwidth, because it is the width of the frequency band between the half-power frequencies. The quality factor relates the maximum or peak energy stored to the energy dissipated in the circuit per cycle of oscillation:. It is also regarded a measure of the energy storage property of a circuit in relation to its energy dissipation property.

Notice that the quality factor is dimentionless. The relationship between the bandwidth B and the quality factor Q is obtained by substituting [link] into [link] and utilizing [link]. The quality factor of a resonant circuit is the ratio of its resonant frequency to its bandwidth.

Keep in mind that [link] , [link] , [link] , and [link] only apply to a series RLC circuit. As illustrated in [link] , the higher the vale of Q, the more selective the circuit is but the smaller the bandwidth. The selectivity of an RLC circuit is the ability of the circuit to respond to a certain frequency and discriminate against all other frequencies.

If the band of frequencies to be selected or rejected is narrow, the quality factor of the resonant circuit must be high. If the band of frequencies is wide, the quality factor must be low. A resonant circuit is designed to operate at or near its resonant frequency. It is said to be a high-Q circuit when its quality factor is equal to or greater than So we will avoid needless repetition. The admittance is. The voltage V is sketched in [link] as a function of frequency.

Notice that at resonance, the parallel LC combination acts like an open circuit, so that the entire current flows through R. We exploit the duality between [link] and [link] by comparing [link] with [link].

Generally, the frequency response analysis of a circuit or system is shown by plotting its gain, that is the size of its output signal to its input signal. The characteristics of the frequency response plots discussed in this application note will focus on the most common operational amplifier circuits and. This video explores the frequency response of a realistic op-amp and discusses how this frequency response influences the operation of op-amp-based.