Chapter 12 investigated application of operational amplifiers in six types of circuits including continuous time active filters, switched-capacitor circuits, digital-to-analog converters, analog-to-digital converters, precision rectifiers, and multivibrators. Design of these circuits is based on the characteristics of ideal operational amplifiers.

• Active RC filters including low-pass, high-pass, and band-pass circuits were introduced. These designs use RC feedback networks and operational amplifiers to replace bulky inductors that would normally be required in R LC filters designed for the audio range. Single-amplifier active filters employ a combination of negative and positive feedback to realize second-order low-pass, high-pass, and band-pass transfer functions.
• Sensitivity of filter characteristics to passive component and op amp parameter tolerances is an important design consideration. Multiple op amp filters offer low sensitivity and ease of design, compared to their single op amp counterparts.
• Magnitude and frequency scaling can be used to change the impedance level and ω_o of a filter without affecting its Q.
• Switched-capacitor (SC) circuits use a combination of capacitors and switches to replace resistors in integrated circuit filter designs. These filters represent the sampled-data or discrete-time equivalents of the continuous-time RC filters and are fully compatible with MOS IC technology. Both inverting and noninverting integrators can be implemented usingSC techniques.
• Digital-to-analog (D/A) and analog-to-digital (A/D) converters, also known as DACs and ADCs, provide the interface between the digital computer and the world of analog sig-nals. Gain, offset, linearity, and differential linearity errors are important in both types of converters.
• The resolution of A/D and D/A converters is measured in terms of the least significant bit or LSB. The LSB of an n-bit converter is equal to V_FS/2ⁿ, where V_FS is the full scale voltage range of the converter. The most significant bit or MSB of the converter is equal to V_FS/2.
• Simple MOS DACs can be formed using weighted-resistor, R-2R ladder and inverted R-2R ladder circuits, and MOS transistor switches. The inverted R-2R ladder configuration maintains a constant current within the ladder elements. Switched-capacitor techniques based on weighted-capacitor and C-2C ladder configurations are also widely used in VLSIICs. In bipolar technology, DACs are usually based on multiple current sources and cur-rent switching. BJT matching is combined with weighted resistor and/or R-2R ladders to generate binary-weighted currents. Identical currents can also be switched into an R-2Rladder.
• Good-quality DACs have monotonic input-output characteristcs.
• Basic ADC circuits compare an unknown input voltage to a known time-varying reference signal. The reference signal is provided by a D/A converter in the counting and successive approximation converters. The counting converter sequentially compares the unknown to all possible outputs of the D/A converter; a conversion may take as many as 2ⁿ clock periods to complete. The counting converter is simple but relatively slow. The successive approximation converter uses an efficient binary search algorithm to achieve a conversion in only n clock periods and is a very popular conversion technique.
• In the single- and dual-ramp ADCs, the reference voltage is an analog signal with a well- defined slope, usually generated by an integrator with a constant input voltage. The digital output of the single-ramp converter suffers from its dependence on the absolute values of the integrator time constant. The dual ramp greatly reduces this problem, and can achieve high differential and integral linearity, but with conversion rates of only a few conversions per second. The dual-ramp converter is widely used in high-precision instru-mentation systems. Rejection of sinusoidal signals with periods that are integer multiples of the integration time, called normal-mode rejection, is an important feature of integrating converters.
• The fastest A/D conversion technique is the parallel or "flash" converter, which simulta- neously compares the unknown voltage to all possible quantized values. Conversion speed is limited only by the speed of the comparators and logic network that form the converter.This high-speed is achieved at a cost of high hardware complexity.
• Good-quality ADCs exhibit linearity and differential linearity errors of less than 1/2 LSB and have no missing codes.
• A/D converters employ circuits called comparators to compare an unknown input voltage with a precision reference voltage. The comparator can be considered to be a high-gain,high-speed op amp designed to operate without feedback.
• Nonlinear circuit applications of operational amplifiers were also introduced including several precision-rectifier circuits.
• Multivibrator circuits are used to develop various forms of electronic pulses. The bistable Schmitt-trigger circuit has two stable states and is often used in place of the comparator in noisy environments. The monostable multivibrator or one shot is used to generate a single pulse of known duration, whereas the astable multivibrator has no stable state and oscillates continuously, producing a square wave output.