## 1 001111 2

Select R2 0.82 kQ and R1 equals 72.98 kQ. Since 72.98 kQ is not a standard 5 resistor value, R1 is selected as 75 kQ. The difference between the selected and calculated value of R1 has about a 3 effect on b, and this error shows up in the transfer function as an intercept rather than a slope error. The parallel resistance of R1 and R2 is approximately 0.82 kQ and this is much less than RG, which is 20 kQ, thus the earlier assumption that RG > > R1 R2 is justified. R2 could have been...

## 1021 rms versus PP Noise

Instantaneous noise voltage amplitudes are as likely to be positive as negative. When plotted, they form a random pattern centered on zero. Since noise sources have amplitudes that vary randomly with time, they can only be specified by a probability density function. The most common probability density function is Gaussian. In a Gaussian probability function, there is a mean value of amplitude, which is most likely to occur. The probability that a noise amplitude will be higher or lower than...

## 1032 Thermal Noise

Thermal noise is sometimes referred to as Johnson noise after its discoverer. It is generated by thermal agitation of electrons in a conductor. Simply put, as a conductor is heated, it will become noisy. Electrons are never at rest they are always in motion. Heat disrupts the electrons' response to an applied potential. It adds a random component to their motion (Figure 10-3). Thermal noise only stops at absolute zero. Like shot noise, thermal noise is spectrally flat or has a uniform power...

## 1033 Flicker Noise

Flicker noise is also called 1 f noise. Its origin is one of the oldest unsolved problems in physics. It is pervasive in nature and in many human endeavors. It is present in all active and many passive devices. It may be related to imperfections in crystalline structure of semiconductors, as better processing can reduce it. Some characteristics of flicker noise It increases as the frequency decreases, hence the name 1 f It is associated with a dc current in electronic devices It has the same...

## 1034 Burst Noise

Burst noise, also called popcorn noise, is related to imperfections in semiconductor material and heavy ion implants. It is characterized by discrete high-frequency pulses. The pulse rates may vary, but the amplitudes remain constant at several times the thermal noise amplitude. Burst noise makes a popping sound at rates below 100 Hz when played through a speaker it sounds like popcorn popping, hence the name. Low burst noise is achieved by using clean device processing, and therefore is beyond...

## 1035 Avalanche Noise

Avalanche noise is created when a pn junction is operated in the reverse breakdown mode. Under the influence of a strong reverse electric field within the junction's depletion region, electrons have enough kinetic energy that, when they collide with the atoms of the crystal lattice, additional electron-hole pairs are formed (Figure 10-4). These collisions are purely random and produce random current pulses similar to shot noise, but much more intense. (InplBticri Rnijcri Da telKiii R Qttir...

## 104 Noise Colors

While the noise types are interesting, real op amp noise will appear as the summation of some or all of them. The various noise types themselves will be difficult to separate. Fortunately, there is an alternative way to describe noise, which is called color. The colors of noise come from rough analogies to light, and refer to the frequency content. Many colors are used to describe noise, some of them having a relationship to the real world, and some of them more attuned to the field of...

## 1055 Noninverting Op Amp Circuit Noise

Taking the simplified equivalent op amp circuit from Paragraph 10.5.2 as the base, the noise equivalent of a noninverting op amp circuit is shown in Figure 10-11 Figure 10-11. Noninverting Equivalent Op Amp Circuit Noise Model Figure 10-11. Noninverting Equivalent Op Amp Circuit Noise Model

## 111 Introduction

This chapter is about op amp data sheet parameters. The designer must have a clear understanding of what op amp parameters mean and their impact on circuit design. The chapter is arranged for speedy access to parameter information. Their definitions, typical abbreviations, and units appear in Section 11.2. Section 11.3 digs deeper into important parameters for the designer needing more in-depth information. While these parameters are the ones most commonly used at Texas Instruments, the same...

## 1131 Input Offset Voltage

All op amps require a small voltage between their inverting and noninverting inputs to balance mismatches due to unavoidable process variations. The required voltage is known as the input offset voltage and is abbreviated VIO. VIO is normally modeled as a voltage source driving the noninverting input. Figure 11-1 shows two typical methods for measuring input offset voltage DUT stands for device under test. Test circuit (a) is simple, but since Vout is not at zero volts, it does not really meet...

## 11310Supply Voltage Rejection Ratio

Supply voltage rejection ratio, kSVR (AKA power supply rejection ratio, PSRR), is the ratio of power supply voltage change to output voltage change. The power voltage affects the bias point of the input differential pair. Because of the inherent mismatches in the input circuitry, changing the bias point changes the offset voltage, which, in turn, changes the output voltage. For a dual supply op amp, KSVR or KSVR 7 . The term AVCC means that the plus and minus power supplies are changed...

## 11311 Supply Current

Supply current, IDD, is the quiescent current draw of the op amp(s) with no load. In a Texas Instruments data sheet, this parameter is usually the total quiescent current draw for the whole package. There are exceptions, however, such as data sheets that cover single and multiple packaged op amps of the same type. In these cases, IDD is the quiescent current draw for each amplifier. In op amps, power consumption is traded for noise and speed. Slew rate, SR, is the rate of change in the output...

## 11313 Equivalent Input Noise

Noise is covered in more detail in Chapter 10. All op amps have parasitic internal noise sources. Noise is measured at the output of an op amp, and referenced back to the input. Therefore, it is called equivalent input noise. Equivalent input noise parameters are usually specified as voltage, Vn, (or current, In) per root Hertz. For audio frequency op amps, a graph is usually included to show the noise over the audio band. The spectral density of noise in op amps has a pink and a white noise...

## 1132 Input Current

The input circuitry of all op amps requires a certain amount of bias current for proper operation. The input bias current, I B, is computed as the average of the two inputs CMOS and JFET inputs offer much lower input current than standard bipolar inputs. Figure 11-3 shows a typical test circuit for measuring input bias currents. The difference between the bias currents at the inverting and noninverting inputs is called the input offset current, IIO IN-IP. Offset current is typically an order of...

## 1137 Input Parasitic Elements

Both inputs have parasitic impedance associated with them. Figure 11-5 shows a model of the resistance and capacitance between each input terminal and ground and between the two terminals. There is also parasitic inductance, but the effects are negligible at low frequency. Input impedance is a design issue when the source impedance is high. The input loads the source. Figure 11-5. Input Parasitic Elements Input capacitance, Ci, is measured between the input terminals with either input grounded....

## 1138 Output Impedance

Different data sheets list the output impedance under two different conditions. Some data sheets list closed-loop output impedance while others list open-loop output impedance, both designated by Zo. Zo is defined as the small signal impedance between the output terminal and ground. Data sheet values run from 50 Q to 200 Q. Common emitter (bipolar) and common source (CMOS) output stages used in rail-to-rail output op amps have higher output impedance than emitter follower output stages. Output...

## 1139Common Mode Rejection Ratio

Common-mode rejection ratio, CMRR, is defined as the ratio of the differential voltage amplification to the common-mode voltage amplification, ADIF ACoM. Ideally this ratio would be infinite with common mode voltages being totally rejected. The common-mode input voltage affects the bias point of the input differential pair. Because of the inherent mismatches in the input circuitry, changing the bias point changes the offset voltage, which, in turn, changes the output voltage. The real mechanism...

## 121 Introduction

The typical transducer measurement system block diagram is shown in Figure 12-1. The transducer is the electronic system's interface with the real world, and it issues data about a variable. The transducer converts the data into an electrical signal adequate for processing by the circuitry that follows the transducer. Bias and excitation circuitry does the care and feeding of the transducer, thus this circuitry provides offset voltages, bias currents, excitation signals, external components,...

## 1210 Test

The final circuit is ready to build and test. The testing must include every possible combination of transducer input and ADC output to determine that the AIA functions in all manufacturing situations. The span of the adjustments, op amp output voltage range, and ADC input range must be checked for conformance to the design criteria. After the design has been tested for the specification limits it should be tested for user abuse. What happens when the power supply is ramped up, turned on...

## 124Review of the System Specifications

The power supply has only one voltage available, and that voltage is 5V 5 5 V 250 mV. The power supply is connected with the negative terminal at ground and the positive terminal at VCC. This is not a portable application, thus the allowed current drain, 50 mA, is adequate for the job. No noise specifications are given, but the proposed power, ground, and signal traces are being done on high-quality circuit board material with planes and good size copper. A system of this quality should...

## 125Reference Voltage Characterization

A reference voltage is required to bias the transducer and act as a reference voltage for the analog interface amplifier (AIA). Selecting a reference with a total accuracy better than the accuracy specification (11 bits) does not guarantee meeting the system accuracy specification because other error sources exist in the design. Resistor tolerances, amplifier tolerances, and transducer tolerances all contribute to the inaccuracy, and the reference can't diminish these errors. The quandary here...

## 126 Transducer Characterization

The temperature transducer is a special silicon diode that is characterized for temperature measurement work. When this diode is forward biased at 2.0 mA 0.1 mA its forward voltage drop is 0.55 V 50 mV, and its temperature coefficient is -2 mV C. The wide acceptable variation in bias current makes this an easy device to work with. The circuit for the bias calculations is shown in Figure 12-12. Figure 12-12. Reference and Transducer Bias Circuit The current through RB1 is calculated in Equation...

## 127 ADC Characterization

This particular ADC was selected because it has a multiplexer and it enables different modes of operation. The temperature measurement is done in the single-shot mode because this mode allows the user to set the charge time at the input to the converter. During charging, the ADC's input resistance is low, but after the ADC input is charged the input resistance rises to 20 kfl. This high input resistance does not load the AIA output circuit, thus the AIA achieves full rail-to-rail output voltage...

## 128 Op Amp Selection

It is time to select the op amp, and the easiest way to do this is to list the known specifications or requirements, list a candidate op amp's specifications, and calculated the projected error that the candidate op amp yields. There should be almost no error from RIN because the transducer output impedance is very low. The high side of the op amp's output voltage swing (4.85 V) is much higher than the ADC input voltage (4 V). The low side of the op amp's output voltage swing (0.185 V) is less...

## 132 Wireless Systems

This chapter focuses on the requirements for the op amp and a number of techniques used in wireless communication systems to interface high-speed op amps to analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). This section provides several examples of different op amp usage. Figure 13-1 shows an example of a dual-IF receiver. In this application, several stages with different IF frequencies are used to get the desired performance. The receiver converts the received radio...

## 137 External Vref Circuits for ADCsDACs

Figure 13-8 shows an op amp voltage follower circuit that is often used to interface the external precision voltage reference supplying the ADC DAC external reference voltage (see for example, Miller and Moore, 5 , 6 ,1999, 2000 for a more detailed discussion on voltage reference circuits used in ADC an DAC systems). Vin is the output from a precision voltage reference, such as the Thaler Corp. VRE3050. The low-pass filter (formed by C1R1) filters noise from the reference and op amp buffer. The...

## 1435 The Sigma Delta DA Converter

The sigma delta D A converter takes advantage of the speed of advanced IC processes to do a conversion as a series of approximations summed together. A phase-locked loop-derived (PLL) sample clock operates at many times the overall conversion frequency in the case shown in Figure 14-5, it is 128X. The PLL is used to drive an interpolation filter, a digital modulator, and a 1-bit D A converter. The conversion is done by using the density ratio of the voltage out of the 1-bit D A as the analog...

## 21 Introduction

Although this book minimizes math, some algebra is germane to the understanding of analog electronics. Math and physics are presented here in the manner in which they are used later, so no practice exercises are given. For example, after the voltage divider rule is explained, it is used several times in the development of other concepts, and this usage constitutes practice. Circuits are a mix of passive and active components. The components are arranged in a manner that enables them to perform...

## 23 Voltage Divider Rule

When the output of a circuit is not loaded, the voltage divider rule can be used to calculate the circuit's output voltage. Assume that the same current flows through all circuit elements (Figure 2-5). Equation 2-6 is written using Ohm's law as V I (R- + R2). Equation 2-7 is written as Ohm's law across the output resistor. Substituting Equation 2-6 into Equation 2-7, and using algebraic manipulation yields Equation 2-8. A simple way to remember the voltage divider rule is that the output...

## 28 Transistor Amplifier

The amplifier is an analog circuit (Figure 2-15), and the calculations, plus the points that must be considered during the design, are more complicated than for a saturated circuit. This extra complication leads people to say that analog design is harder than digital design (the saturated transistor is digital i.e. on or off). Analog design is harder than digital design because the designer must account for all states in analog, whereas in digital only two states must be accounted for. The...

## 36 Complex Feedback Networks

T Network in Feedback Loop Break the circuit at point X-Y, stand on the terminals looking into R4, and calculate the Thevenin equivalent voltage as shown in Equation 3-15. The Thevenin equivalent impedance is calculated in Equation 3-16. Replace the output circuit with the Thevenin equivalent circuit as shown in Figure 5-8, and calculate the gain with the aid of the inverting gain equation as shown in Equation 3-17. Figure 3-8. Thevenin's Theorem Applied to T Network Substituting...

## 37 Video Amplifiers

Video signals contain high frequencies, and they use coaxial cable to transmit and receive signals. The cable connecting these circuits has a characteristic impedance of 75 Q. To prevent reflections, which cause distortion and ghosting, the input and output circuit impedances must match the 75 Q cable. Matching the input impedance is simple for a noninverting amplifier because its input impedance is very high just make R N 75 Q. RF and RG can be selected as high values, in the hundreds of Ohms...

## 38 Capacitors

At very low frequencies XC so RF dominates the parallel combination in Equation 20, and the capacitor has no effect. The gain at low frequencies is -RF RG. At very high frequencies XC 0, so the feedback resistor is shorted out, thus reducing the circuit gain to zero. At the frequency where XC RF the gain is reduced by V2 because complex impedances in parallel equal half the vector sum of both impedances. Connecting the capacitor in parallel with RG where it has the opposite effect makes a high...

## 41 Single Supply versus Dual Supply

The previous chapter assumed that all op amps were powered from dual or split supplies, and this is not the case in today's world of portable, battery-powered equipment. When op amps are powered from dual supplies (see Figure 4-1), the supplies are normally equal in magnitude, opposing in polarity, and the center tap of the supplies is connected to ground. Any input sources connected to ground are automatically referenced to the center of the supply voltage, so the output voltage is...

## 44 Summary

Single-supply op amp design is more complicated than split-supply op amp design, but with a logical design approach excellent results are achieved. Single-supply design used to be considered technically limiting because older op amps had limited capability. The new op amps, such as the TLC247X, TLC07X, and TLC08X have excellent single-supply parameters thus when used in the correct applications these op amps yield rail-to-rail performance equal to their split-supply counterparts. Single-supply...

## 57 References

DiStefano, Stubberud, and Williams, Theory and Problems of Feedback and Control Systems, Schaum's Outline Series, Mc Graw Hill Book Company, 1967 2. Bode, H. W., Network Analysis And Feedback Amplifier Design, D. Van Nostrand, Inc., 1945 3. Frederickson, Thomas, Intuitive Operational Amplifiers, McGraw Hill Book Company, 1988 4. Bower, J. L. and Schultheis, P. M., Introduction To The Design Of Servomechanisms, Wiley, 1961 5. Van Valkenberg, M. E., Network Analysis, Prentice-Hall, 1964 6. Del...

## 65 Differential Op Amps

The differential amplifier circuit is shown in Figure 6-7. The dummy variable, VE, is inserted to make the calculations easier, and a is the open loop gain. Figure 6-7. Differential Amplifier Circuit Equation 6-20 is the circuit transfer equation. VGUT aVE v+- V- The positive input voltage, V+, is written in Equation 6-21 with the aid of superposition and the voltage divider rule. The negative input voltage, V-, is written in Equation 6-22 with the aid of superposition and the voltage divider...

## 79 Comparison of Compensation Schemes

Internally compensated op amps can, and often do, oscillate under some circuit conditions. Internally compensated op amps need an external pole to get the oscillation or ringing started, and circuit stray capacitances often supply the phase shift required for instability. Loads, such as cables, often cause internally compensated op amps to ring severely. Dominant pole compensation is often used in IC design because it is easy to implement. It rolls off the closed-loop gain early thus, it is...

## 82 CFA Model

The CFA model is shown in Figure 8-1. The noninverting input of a CFA connects to the input of the input buffer, so it has very high impedance similar to that of a bipolar transistor noninverting VFA input. The inverting input connects to the input buffer's output, so the inverting input impedance is equivalent to a buffer's output impedance, which is very low. ZB models the input buffer's output impedance, and it is usually less than 50 Q. The input buffer gain, GB, is as close to one as IC...

## 86 Stability Analysis

The stability equation is repeated as Equation 8-18. Comparing Equations 8-9 and 8-15 to Equation 8-18 reveals that the inverting and non-inverting CFA op amps have identical stability equations. This is the expected result because stability of any feedback circuit is a function of the loop gain, and the input signals have no affect on stability. The two op amp parameters affecting stability are the transimpedance, Z, and the input buffer's output impedance, ZB. The external components...

## 87 Selection of the Feedback Resistor

Equation 8-27 leads one to believe that a new value for ZF can easily be chosen for each new gain. This is not the case in the real world the assumptions don't hold up well enough to rely on them. When you change to a new gain not specified on the data sheet, Equation 8-27, at best, supplies a starting point for Rf, but you must test to determine the final value of Rf. When the Rf value recommended on the data sheet can't be used, an alternate method of selecting a starting value for Rf is to...

## 89 Stability and Feedback Capacitance

When a stray capacitor is formed across the feedback resistor, the feedback impedance is given by Equation 8-31. Equation 8-32 gives the loop gain when a feedback capacitor has been added to the circuit. This loop gain transfer function contains a pole and zero, thus, depending on the pole zero placement, oscillation can result. The Bode plot for this case is shown in Figure 8-9. The original and composite curves cross the 0-dB axis with a slope of -40 dB decade, so either curve can indicate...

## 91 Introduction

The name, operational amplifier, was given to voltage-feedback amplifiers (VFA) when they were the only op amps in existence. These new (they were new in the late '40s) amplifiers could be programmed with external components to perform various math operations on a signal thus, they were nicknamed op amps. Current-feedback amplifiers (CFA) have been around approximately twenty years, but their popularity has only increased in the last several years. Two factors limiting the popularity of CFAs is...

## 92 Precision

The long-tailed pair input structure gives the VFA its precision the long-tailed pair is shown in Figure 9-1 The transistors, Q1 and Q2, are very carefully matched for initial and drift tolerances. Careful attention is paid to detail in the transistor design to insure that parameters like current gain, (3, and base-emitter voltage, VBE, are matched between the input transistors, Q1 and Q2. When VB1 VB2, the current, I, splits equally between the transistors, and VO1 VO2. As long as the...

## 93 Bandwidth

The bandwidth of a circuit is defined by high frequency errors. When the gain falls off at high frequencies unequal frequency amplification causes the signal to become distorted. The signal loses its high frequency components an example of high frequency signal degradation is a square wave with sharp corners that is amplified and turned into slump cornered semi sine wave. The error equation for any feedback circuit is repeated in Equation 9-1. This equation is valid for any feedback circuit, so...

## As

Comparing the variables of Equation 16-22 with Equation 16-20 provides the equations that determine the filter parameters To calculate the individual component values, establish the following design procedure 1) Define fm and C and calculate R with 1 2) Specify Q and determine a via 3) Specify Aq and determine p via 4) Define R2 and calculate R3 and R4 with In comparison to the twin-T circuit, the Wien-Robinson filter allows modification of the passband gain, Aq, without affecting the quality...

## Design Reference

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## Examples

16-1 First-Order Unity-Gain Low-Pass 16-2 Second-Order Unity-Gain Tschebyscheff Low-Pass 16-3 Fifth-Order Filter 16-4 Third-Order High-Pass Filter with fC 1 16-5 Second-Order MFB Band-Pass Filter with fm 1 kHz 16-6 Fourth-Order Butterworth Band-Pass 16-7 2-ms Delay All-Pass

## Jr

First-Order Noninverting Low-Pass Filter with Unity Gain There are two topologies for a second-order low-pass filter, the Sallen-Key and the Multiple Feedback (MFB) topology. The general Sallen-Key topology in Figure 16-15 allows for separate gain setting via A0 1+R4 R3. However, the unity-gain topology in Figure 16-16 is usually applied in filter designs with high gain accuracy, unity gain, and low Qs (Q < 3). Figure 16-15. General Sallen-Key Low-Pass Filter Figure 16-16....

## M1 rrr

When the input buffer output resistance approaches zero, Equation 9-5 reduces to Equation 9-6. Equation 9-6 shows that the closed-loop gain has no effect on the loop gain when RB 0, so under ideal conditions one would expect the transimpedance to fall off with a zero slope. Figure 9-4 shows that there is a finite slope, but much less than that of a VFA, and the slope is caused by RB not being equal to zero. For example, RB is usually 50 Q when Rf 1000 Q at Acl 1. If we let RF RG, then RF RG 500...

## Note

Two parallel vertical bars ( ) are used to indicate parallel components as shown in Equation 2-14. The final step is to calculate the output voltage. Notice the voltage divider rule is used again. Equation 2-15 describes the output voltage, and it comes out naturally in the form of a series of voltage dividers, which makes sense. That's another advantage of the voltage divider rule the answers normally come out in a recognizable form rather than a jumble of coefficients and parameters. The...

## Q At

With Am being the gain at mid frequency, fm, of the overall filter. Example 16-6. Fourth-Order Butterworth Band-Pass Filter The task is to design a fourth-order Butterworth band-pass with the following parameters From Table 16-2 the following values are obtained In accordance with Equations 16-14 and 16-15, the mid frequencies for the partial filters are The overall Q is defined as Q fm B , and for this example results in Q 10. Using Equation 16-16, the Qi of both filters is (1 + 1.0362)-1 With...

## R2

The Sallen-Key circuit has the advantage that the quality factor (Q) can be varied via the inner gain (G) without modifying the mid frequency (fm). A drawback is, however, that Q and Am cannot be adjusted independently. Care must be taken when G approaches the value of 3, because then Am becomes infinite and causes the circuit to oscillate. To set the mid frequency of the band-pass, specify fm and C and then solve for R 1 Because of the dependency between Q and Am, there are two options to...

## Tables

3-1 Basic Ideal Op Amp Assumptions 3-2 8-1 Data Set for Curves in Figure 8-7 8-11 9-1 Tabulation of Pertinent VFA and CFA 9-9 11 -1 Op Amp Parameter GLossary 11-2 11 -2 Cross-Reference of Op Amp 11-6 12-1 Transducer Output Voltage 12-14 12-5 Offset and Gain Error 12-19 13-1 GSM Receiver Block System Budget 13-3 13-2 High-Speed Op Amp Requirements 13-11 14-1 DC Step Size for D A converters 14-7 14-2 Converter Bits, THD, and Dynamic 14-10 16-1 Second-Order FIlter Coefficients 16-17 16-2 Values of...

## Vw

The transfer function of the active twin-T filter is Comparing the variables of Equation 16-21 with Equation 16-20 provides the equations that determine the filter parameters The twin-T circuit has the advantage that the quality factor (Q) can be varied via the inner gain (G) without modifying the mid frequency (fm). However, Q and Am cannot be adjusted independently. To set the mid frequency of the band-pass, specify fm and C, and then solve for R Because of the dependency between Q and Am,...

## Zi f

000 001 010 011 100 101 Digital Input Code Figure 14-10. Integral Nonlinearity Error Both the INL and DNL errors affect ac applications as distortion and spectral harmonics (spurs). In dc applications, they will result in an error in the dc output voltage. The mechanical steps of a positioning table, for instance, may not be exact increments. 14.5.1.5 Power Supply Rejection Ratio The power supply rejection ratio is sometimes called the power supply sensitivity. It is the ability of the...

## 129 Amplifier Circuit Design

Enough information exists for the AIA to be designed. The TLV247X op amp is selected because it meets all the system requirements. The first step in the design is to determine the AIA input and output voltages, and this has already been done. These voltages are taken from Tables 12-1 and 12-2, and repeated here as Table 12-4. Table 12-4. AIA Input and Output Voltages Table 12-4. AIA Input and Output Voltages The equation of an op amp is the equation of a straight line as given in Equation...

## 11314 Total Harmonic Distortion Plus Noise

Total harmonic distortion plus noise, THD + N, compares the frequency content of the output signal to the frequency content of the input. Ideally, if the input signal is a pure sine wave, the output signal is a pure sine wave. Due to nonlinearity and noise sources within the op amp, the output is never pure. THD + N is the ratio of all other frequency components to the fundamental and is usually specified as a percentage (2 Harmonic voltages + Noise Voltages) Fundamental Figure 11-10 shows a...

## Active Filter Design Techniques

A filter is a device that passes electric signals at certain frequencies or frequency ranges while preventing the passage of others. Webster. Filter circuits are used in a wide variety of applications. In the field of telecommunication, band-pass filters are used in the audio frequency range (0 kHz to 20 kHz) for modems and speech processing. High-frequency band-pass filters (several hundred MHz) are used for channel selection in telephone central offices. Data acquisition systems usually...

## 106 Putting It All Together

This example is provided for analysis only actual results depend on a number of other factors. Expanding on the techniques of Paragraph 10.2.5 A low-noise op amp is needed over an audio frequency range of 20 Hz to 20 kHz, with a gain of 40 dB. The output voltage is 0 dBV (1V). The schematic is shown in Figure 10-13 Figure 10-13. Split Supply Op Amp Circuit It would be nice to use a TLE2027 with a noise figure of 2.5 nV vHz . The data sheet, however, reveals that this is a 15-V part, and that...

## 134 Factors Influencing the Choice of Op Amps

IF amplifiers and filters can be built from discrete components, though most modern applications use integrated circuits. High-speed wideband op amps are employed as buffer amplifiers in the LO circuit, at the front end of ADCs, at the output of the DAC, in the external voltage reference circuits for ADCs and DACs, and in the AGC amplifier and anti-aliasing stage. Op amps operating at IF frequencies, such as the AGC amplifier in Figure 13-1, must attain a large gain control range. How well the...

## 122 Transducer Types

This is not a treatise on transducers, but an appreciation for the many different types of transducers gives a feel for the extent and complexity of the transducer characterization problem following section . The variety of electrical output that transducers offer loosely groups transducers. Various types of transducer outputs are resistive, optical, ac-excited, junction voltage, and magnetic, and each of these outputs must be converted to an electrical signal that can be amplified to fit the...

## 53 Feedback Equation and Stability

Figure 5-7 shows the canonical form of a feedback loop with control system and electronic system terms. The terms make no difference except that they have meaning to the system engineers, but the math does have meaning, and it is identical for both types of terms. The electronic terms and negative feedback sign are used in this analysis, because subsequent chapters deal with electronic applications. The output equation is written in Equation 5-1. Figure 5-7 shows the canonical form of a...

## 139 References

B., Theory and Application of Digital signal Processing, Prentice Hall, Englewood Cliffs, New Jersey, 1975 2 Parks, T.W., and Burrus, C.S., Digital Filter Design, Wiley, New York, NY, 1987 3 Miller, P., Aspects of Data Acquisition System Design, Analog Application Journal, Texas Instruments, August 1999 4 Proakis, J.G., Digital Communications, McGraw-Hill Book Company, New York, 1983 5 Miller, P., and Moore, D., Precision Voltage References, Analog Application...

## 11315 Unity Gain Bandwidth and Phase Margin

There are five parameters relating to the frequency characteristics of the op amp that are likely to be encountered in Texas Instruments data sheets. These are unity-gain bandwidth B- , gain bandwidth product GBW , phase margin at unity gain m , gain margin Am , and maximum output-swing bandwidth BOM . Unity-gain bandwidth Bi and gain bandwidth product GBW are very similar. Bi specifies the frequency at which AVD of the op amp is 1 GBW specifies the gain-bandwidth product of the op amp in an...

## 72 Internal Compensation

Miller Effect Compensation Figure 7-2 shows the gain phase diagram for an older op amp TL03X . When the gain crosses the 0-dB axis gain equal to one the phase shift is approximately 108 , thus the op amp must be modeled as a second-order system because the phase shift is more than 90 . LARGE-SIGNAL DIFFERENTIAL VOLTAGE AMPLIFICATION AND PHASE SHIFT vs LARGE-SIGNAL DIFFERENTIAL VOLTAGE AMPLIFICATION AND PHASE SHIFT vs 10 100 1 k 10 k 100 k 1 M 10 M f - Frequency - Hz 10 100 1 k 10 k...

## VN R l 1 RCs 1 xs58

The magnitude of this transfer function is VOUT VIN 1 tm 2 . This magnitude, Vout V N 1 when ra 0.1 t, it equals 0.707 when ra 1 t, and it is approximately 0.1 when ra 10 t. These points are plotted in Figure 5-9 using straight line approximations. The negative slope is -20 dB decade or -6 dB octave. The magnitude curve is plotted as a horizontal line until it intersects the breakpoint where ra 1 t. The negative slope begins at the breakpoint because the magnitude starts decreasing at that...

## R

Second-Order MFB Low-Pass Filter The transfer function of the circuit in Figure 16-19 is 1 cC1 2 R3 -Rt3 s c2 C1 C2R2R3s2 Through coefficient comparison with Equation 16-2 one obtains the relation Given C1 and C2, and solving for the resistors R1-R3 In order to obtain real values for R2, C2 must satisfy the following condition 16.3.3 Higher-Order Low-Pass Filters Higher-order low-pass filters are required to sharpen a desired filter characteristic. For that purpose, first-order...

## 138 High Speed Analog Input Drive Circuits

Communication ADCs, for the most part, have differential inputs and require differential input signals to properly drive the device. Drive circuits are implemented with either RF transformers or high-speed differential amplifiers with large bandwidth, fast settling time, low output impedance, good output drive capabilities, and a slew rate of the order of 1500 V S. The differential amplifier is usually configured for a gain of 1 or 2 and is used primarily for buffering and converting the...

## 43 Simultaneous Equations

Taking an orderly path to developing a circuit that works the first time starts here follow these steps until the equation of the op amp is determined. Use the specifications given for the circuit coupled with simultaneous equations to determine what form the op amp equation must have. Go to the section that illustrates that equation form called a case , solve the equation to determine the resistor values, and you have a working solution. A linear op amp transfer function is limited to the...

## 85 The Inverting CFA

The current equation for the input node is written as Equation 8-12. Equation 8-13 defines the dummy variable, VA, and Equation 8-14 is the transfer equation for the CFA. These equations are combined and simplified leading to Equation 8-15, which is the closed-loop gain equation for the inverting CFA. When ZB approaches zero, Equation 8-15 reduces to Equation 8-16. When Z is very large, Equation 8-16 becomes Equation 8-17, which is the ideal closed-loop gain equation for the inverting CFA. The...

## 75 Gain Compensation

When the closed-loop gain of an op amp circuit is related to the loop gain, as it is in voltage-feedback op amps, the closed-loop gain can be used to stabilize the circuit. This type of compensation can not be used in current-feedback op amps because the mathematical relationship between the loop gain and ideal closed-loop gain does not exist. The loop gain equation is repeated as Equation 7-11. Notice that the closed-loop gain parameters ZG and ZF are contained in Equation 7-11, hence the...

## 1053 Op Amp Circuit Noise Model

Texas Instruments measures the noise characteristics of a large sampling of devices. This information is compiled and used to determine the typical noise performance of the device. These noise specifications refer the input noise of the op amp. Some noise portions can be represented better by a voltage source, and some by a current source. Input voltage noise is always represented by a voltage source in series with the noninverting input. Input current noise is always represented by current...

## 1443 AC Application Error Budget

The error budget for an ac application will most likely be specified as total harmonic distortion, dynamic range, or signal-to-noise ratio. Assuming no internal noise, and no noise in the buffer op amp circuitry, the inverse of the dynamic range is the signal-to-noise ratio of the converter D A. Of course, noise is always present, and is measured with all input data set to zero. Noise will make the S N ratio decrease. The number of converter bits, however, is the overwhelming factor determining...

## 1433 The Weighted Resistor DA Converter

This type of converter is very similar to the Resistor Ladder D A converter. In this case, however, each resistor in the string is given a value proportional to the binary value of the bit it represents. Currents are then summed from each active bit to achieve the output Figure 14-2 . Figure 14 2. Binary Weighted D A Converter Figure 14 2. Binary Weighted D A Converter The number of resistors and switches reduced to one per bit, but the range of the resistors is extremely wide for...

## 76 Lead Compensation

Lead-Compensation Circuit transfer function The equation for the inverting op amp closed-loop gain is repeated below. Figure 7-14. Lead-Compensation Bode Plot When a approaches infinity, Equation 7-13 reduces to Equation 7-14. Substituting RF C for ZF and RG for ZG in Equation 7-14 yields Equation 7-15, which is the ideal closed-loop gain equation for the lead compensation circuit. The forward gain for the inverting amplifier is given by Equation 7-16. Compare Equation 7-13 with...

## Er

Fourth-Order Passive RC Low-Pass with Decoupling Amplifiers The resulting transfer function is In the case that all filters have the same cut-off frequency, fC, the coefficients become a a2 an a v2 - 1, and fC of each partial filter is 1 a times higher than fC of the overall filter. Figure 16-4 shows the results of a fourth-order RC low-pass filter. The rolloff of each partial filter Curve 1 is -20 dB decade, increasing the roll-off of the overall filter Curve 2 to 80 dB decade....

## 31 Ideal Op Amp Assumptions

The name Ideal Op Amp is applied to this and similar analysis because the salient parameters of the op amp are assumed to be perfect. There is no such thing as an ideal op amp, but present day op amps come so close to ideal that Ideal Op Amp analysis approaches actual analysis. Op amps depart from the ideal in two ways. First, dc parameters such as input offset voltage are large enough to cause departure from the ideal. The ideal assumes that input offset voltage is zero. Second, ac parameters...

## 112 Operational Amplifier Parameter Glossary

There are usually three main sections of electrical tables in op amp data sheets. The absolute maximum ratings table and the recommended operating conditions table list constraints placed upon the circuit in which the part will be installed. Electrical characteristics tables detail device performance. Absolute maximum ratings are those limits beyond which the life of individual devices may be impaired and are never to be exceeded in service or testing. Limits, by definition, are maximum...

## 1434 The R2R DA Converter

An R R2 network can be used to make a D A converter Figure 14-3 . For a given reference voltage VREF, a current I flows through resistor R. If two resistors, each the same value 2R are connected from VREF to ground, a current I 2 flows through each leg of the circuit. But the same current will flow if one leg is made up of two resistors, each with the value of R. If two resistors in parallel whose value is 2R replace the bottom resistor, the parallel combination is still R. I 4 flows through...

## Sine Wave Oscillators

15.1 What is a Sine Wave Oscillator Op amp oscillators are circuits that are unstable not the type that are sometimes unintentionally designed or created in the lab but circuits intentionally designed to remain in an unstable state. Oscillators are useful for creating uniform signals that are used as a reference in applications such as audio, function generators, digital systems, and communication systems. Two general classes of oscillators exist sinusoidal and relaxation. Sinusoidal...

## 77 Compensated Attenuator Applied to Op

Stray capacitance on op amp inputs is a problem that circuit designers are always trying to get away from because it decreases stability and causes peaking. The circuit shown in Figure 7-17 has some stray capacitance Cq, connected from the inverting input to ground. Equation 7-18 is the loop gain equation for the circuit with input capacitance. Figure 7-17. Op Amp With Stray Capacitance on the Inverting Input Op amps having high input and feedback resistors are subject to instability caused by...

## 74 Dominant Pole Compensation

We saw that capacitive loading caused potential instabilities, thus an op amp loaded with an output capacitor is a circuit configuration that must be analyzed. This circuit is called dominant pole compensation because if the pole formed by the op amp output impedance and the loading capacitor is located close to the zero frequency axis, it becomes dominant. The op amp circuit is shown in Figure 7-8, and the open loop circuit used to calculate the loop gain AP is shown in Figure 7-9. Figure 7-8....

## 24 Current Divider Rule

When the output of a circuit is not loaded, the current divider rule can be used to calculate the current flow in the output branch circuit R2 . The currents I and I2 in Figure 2-6 are assumed to be flowing in the branch circuits. Equation 2-9 is written with the aid of Kirch-off's current law. The circuit voltage is written in Equation 2-10 with the aid of Ohm's law. Combining Equations 2-9 and 2-10 yields Equation 2-11. Rearranging the terms in Equation 2-11 yields Equation 2-12. The total...

## 56 The Second Order Equation and Ringing Overshoot Predictions

The second order equation is a common approximation used for feedback system analysis because it describes a two-pole circuit, which is the most common approximation used. All real circuits are more complex than two poles, but except for a small fraction, they can be represented by a two-pole equivalent. The second order equation is extensively described in electronic and control literature tel. After algebraic manipulation Equation 5-16 is presented in the form of Equation 5-17. Equation 5-17...

## 78 Lead Lag Compensation

Lead-lag compensation stabilizes the circuit without sacrificing the closed-loop gain performance. It is often used with uncompensated op amps. This type of compensation provides excellent high-frequency performance. The circuit schematic is shown in Figure 7-20, and the loop gain is given by Equation 7-23. Figure 7-20. Lead-Lag Compensated Op Amp Ap t1s l t2s 1 RG Rf RRg RRf RgRf 7-23 Referring to Figure 7-21, a pole is introduced at ra 1 RC, and this pole reduces the gain 3 dB at the...

## The Op Amps Place In The World

In 1934 Harry Black 1 commuted from his home in New York City to work at Bell Labs in New Jersey by way of a railroad ferry. The ferry ride relaxed Harry enabling him to do some conceptual thinking. Harry had a tough problem to solve when phone lines were extended long distances, they needed amplifiers, and undependable amplifiers limited phone service. First, initial tolerances on the gain were poor, but that problem was quickly solved with an adjustment. Second, even when an amplifier was...

## Figures

2-1 Ohm's Law Applied to the Total Circuit 2-2 Ohm's Law Applied to a 2-3 Kirchoff's Voltage Law 2-4 Kirchoff's Current Law 2-5 Voltage Divider Rule 2-6 Current Divider Rule 2-7 Original Circuit 2-8 Thevenin's Equivalent Circuit for Figure 2-7 2-9 Example of Thevenin's Equivalent Circuit 2-10 Analysis Done the Hard Way 2-11 Superposition Example 2-12 When V1 is Grounded 2-13 When V2 is Grounded 2-14 Saturated Transistor 2-16 Thevenin Equivalent of the Base 2-11 3-1 The Ideal Op Amp 3-2 The...