Barrel Shifter

An n-bit q-shifter can also be implemented using a barrel-shifter scheme. This scheme is based on the fact that any shift distance s is representable as a sum of shift distances that are powers of 2. That is,

,

where r = log₂ q.

Therefore, a network of r stages such that the ith stage shifts a distance of 0 or 2ⁱ implements a q-shifter (Figure 1.60.)

The delay of the network is proportional to the number of stages. The comparison between the presented schemes for multimodule shifters is left as an exercise

Fig 1.60 - Barrel shifter.

1.12 Comparators

An operational amplifier without feedback, as in Fig. 1.61, represents the basic circuit of a comparator. Its output voltage is given by

Owing to the high gain, the circuit responds to very small voltage differences U₁ - U₂. It is thus suitable for the comparison of two voltages, and operates with high accuracy.

Fig. 1.61 - Operational amplifier as Fig. 1.62 - Transfer characteristic.

comparator.

At zero crossing of the input voltage difference, the output voltage does not immediately reach the saturation level because the transition is limited by the slew rate. For frequency-compensated standard operational amplifiers it is about 1 V/s. A rise from – 12 V to + 12 V therefore takes 24 s. An additional delay is incurred due to the recovery time needed after the amplifier has been saturated.

Fig. 1.63 - Comparator with logic output. Fig. 1.64 - Transfer characteristic.

y = 1 for U₁ >U₂

As the amplifier possesses no negative feedback, it also does not require any frequency compensation. Its omission can improve the slew rate and recovery time by a factor of about 20.

Considerably shorter response times can be attained when using special comparator amplifiers which are designed for use without feedback and have especially small recovery times. However, the gain and hence the accuracy of the threshold are somewhat lower than those of operational amplifiers. Usually, the amplifier output is directly connected to a level-shift circuit which permits compatible operation with logic circuits. Its application and characteristics are shown in Figs. 1.63 and 1.64 A number of commonly used comparators are listed in Fig. 1.65.

Fig. 1.65 - Examples of comparators.

Window comparator

A window comparator can determine whether or not the value of the input voltage lies between two reference voltage levels. Figure 1.66.shows that two comparators are used to decide whether the input voltage is above a lower and below an upper reference voltage. When this condition arises, both comparator amplifiers produce Boolean "one", the and gate providing the defined logic evaluation. The characteristics in Fig. 1.67 illustrate the operation.

Fig, 1.66 - Window comparator. Fig. 1.67 - Variables as a function of the.

input voltage

y = 1 for U₁ <U_i<U₂