## 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...

## 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...

## 135 Anti Aliasing Filters

Spurious effects in the receiver channel Figure 13-1 appear as high frequency noise in the baseband signal present at the ADC. The spurious signals gt 2 must be blocked from getting to the ADC sampling at Nyquist rate, s where they will cause aliasing errors in the ADC output. A suitable anti-aliasing low-pass analog filter placed immediately before the ADC can block all frequency components capable of causing aliasing from reaching the ADC. The anti-aliasing filter cutoff frequency fc is set...

## 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...

## 34 The Adder

An adder circuit can be made by connecting more inputs to the inverting op amp Figure 3-4 . The opposite end of the resistor connected to the inverting input is held at virtual ground by the feedback therefore, adding new inputs does not affect the response of the existing inputs. Superposition is used to calculate the output voltages resulting from each input, and the output voltages are added algebraically to obtain the total output voltage. Equation 3-6 is the output equation when V- and V2...

## Contents

1 The Op Amp's Place In The World 1-1 2.1 Introduction 2.2 Laws of Physics 2.3 Voltage Divider Rule 2.4 Current Divider Rule 2.5 Thevenin's Theorem 2.6 Superposition 2.7 Calculation of a Saturated Transistor 3 Development of the Ideal Op Amp Equations 3-1 3.1 Ideal Op Amp Assumptions 3-1 3.2 The Noninverting Op Amp 3-3 3.5 The Differential Amplifier 3-6 3.6 Complex Feedback Networks 3-7 3-11 4 Single Supply Op Amp Design Techniques 4-1 4.1 Single Supply versus Dual Supply 4-1 4.3.1 Case 1 VOUT...

## 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...