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1、Analog and Digital（模拟电子和数字电子）:Analog and Digital Ideal Operational Amplifiers and Practical LimitationsIn order to discuss the ideal parameters of operational amplifiers, we must first define the terms, and then go on to describe what we regard as the ideal values for those terms. At first sight, th

2、e specification sheet for an operational amplifier seems to list a large number of values, some in strange units, some interrelated, and often confusing to those unfamiliar with the subject. The approach to such a situation is to be methodical, and take the necessary time to read and understand each

3、 definition in the order that it is listed. Without a real appreciation of what each means, the designer is doomed to failure. The objective is to be able to design a circuit from the basis of the published data, and know that it will function as predicted when the prototype is constructed.1 It is a

4、ll too easy with linear circuits, which appear relatively simple when compared with todays complex logic arrangements, to ignore detailed performance parameters which can drastically reduce the expected performance.Let us take a very simple but striking example. Consider a requirement for an amplifi

5、er having a voltage gain of 10 at 50kHz driving into a 10 kW load. A common low-cost, internally frequency-compensated op amp is chosen; it has the required bandwidth at a closed-loop gain of 10, and it would seem to meet the bill. The device is connected, and it is found to have the correct gain. B

6、ut it will only produce a few volts output swing when the data clearly shows that the output should be capable of driving to within two or three volts of the supply rails. The designer has forgotten that the maximum output voltage swing is severely limited by frequency, and that the maximum low-freq

7、uency output swing becomes limited at about 10kHz. Of course, the information is in fact on the data sheet, but its relevance has not been appreciated. This sort of problem occurs regularly for the inexperienced designer. So the moral is clear: always take the necessary time to write down the full o

8、perating requirements before attempting a design. Attention to the detail of the performance specification will always be beneficial. It is suggested the following list of performance details be considered:1.Closed loop gain accuracy, stability with temperature, time and supply voltage2.Power supply

9、 requirements, source and load impedances, power dissipation3.Input error voltages and bias currents. Input and output resistance, drift with time and temperature4.Frequency response, phase shift, output swing, transient response, slew rate, frequency stability, capacitive load driving, overload rec

10、overy5.Linearity, distortion and noise6.Input, output or supply protection required. Input voltage range, common-mode rejection7.External offset trimming requirementNot all of these terms will be relevant, but it is useful to remember that it is better to consider them initially rather than to be fo

11、rced into retrospective modifications.All parameters are subject to wide variationsNever forget this fact. How many times has a circuit been designed using typical values, only to find that the circuit does not work because the device used is not typical? The above statement thus poses a tricky ques

12、tion: when should typical values and when should worst-case values be used in the design? This is where the judgment of the experienced designer must be brought to bear. Clearly, if certain performance requirements are mandatory, then worst-case values must be used. In many cases, however, the desir

13、ability of a certain defined performance will be a compromise between ease of implementation, degree of importance, and economic considerations.Do not over-specify or over-designIn the end, we are all controlled by cost, and it is really pointless taking a sledgehammer to crack a nut, Simplicity is

14、of the essence since the low parts count implementation is invariably cheaper and more reliable.As an example of this judgment about worst-case design, consider a low-gain DC transducer amplifier required to amplify 10 mV from a voltage source to produce an output of .l V with an accuracy of 1% over

15、 a temperature range of 070C. Notice that the specification calls for an accuracy of 1%. This implies that the output should be 1 V 10 mV from 0 70C. The first step is, of course, to consider our list above, and decide which of the many parameters are relevant. Two of the most important to this (ver

16、y limited) specification are offset voltage drift and gain stability with temperature. We will assume that all initial errors are negligible (rarely the case in practice). The experienced designer would know that most op amps have a very large open-loop gain, usually very much greater than 10000. A

17、closed-loop gain change of 1% implies that the loop gain (as explained later) should change by less than 100% for a closed-loop gain of 100. This is clearly so easily fulfilled that the designer knows immediately that he can use typical open-loop gain values in his calculations. However, offset volt

18、age drift is another matter. Many op amp specifications include only typical values for offset voltage drift; this may well be in the order of 5 mV/C, with an unquoted maximum for any device of 30 mV/C. If by chance we use a device which has this worst-case drift, then the amplifier error could be 3

19、070=2100 mV=2.1 mV over temperature, which is a significant proportion of our total allowable error from all sources. Here is a case, then, where one can be confident that the typical value of open-loop gain can be used, but where the maximum value of drift may well cause significant errors. This so

20、rt of judgment is essential in careful design, and great care is required in interpreting manufacturers data. This consideration must be extended to all the details listed above apart from the fact that worst-case values are often not quoted. It is often found that values given are not 100% tested.

21、Statistical testing is employed which, for example, guarantees that 90% of all devices fall within the range specified. It could be very inconvenient for the user who relies on the specified performance and then finds that he has several of the other 10% actually plugged into his circuit.Data Regist

22、ers and CountersData registerThe simplest type of register is a data register, which is used for the temporary storage of a “word” of data. In its simplest form, it consists of a set of N D flip-flops, all sharing a common clock. All of the digits in the N bit data word are connected to the data reg

23、ister by an N-line “data bus”. Figure 1.1 shows a 4 bit data register, implemented with four D flip-flops. The data register is said to be a synchronous device, because all the flip-flops change state at the same time.Shift registers Another common form of register used in computers and in many othe

24、r types of logic circuits is a shift register. It is simply a set of flip-flops (usually D latches or RS flip-flops) connected together so that the output of one becomes the input of the next, and so on in series. It is called a shift register because the data is shifted through the register by one

25、bit position on each clock pulse. Figure 1.2 shows a 4 bit shift register, implemented with D flip-flops.On the leading edge of the first clock pulse, the signal on the DATA input is latched in the first flip-flop. On the leading edge of the next clock pulse, the contents of the first flip-flop is s

26、tored in the second flip-flop, and the signal which is present at the DATA input is stored in the first flip-flop, etc. Because the data is entered one bit at a time, this called a serial-in shift register. Since there is only one output, and data leaves the shift register one bit at a time, then it

27、 is also a serial out shift register. (Shift registers are named by their method of input and output; either serial or parallel.) Parallel input can be provided through the use of the preset and clear inputs to the flip-flop. The parallel loading of the flip-flop can be synchronous (i.e., occurs wit

28、h the clock pulse) or asynchronous (independent of the clock pulse) depending on the design of the shift register. Parallel output can be obtained from the outputs of each flip-flop as shown in Figure 1.3.Communication between a computer and a peripheral device is usually done serially, while comput

29、ation in the computer itself is usually performed with parallel logic circuitry. A shift register can be used to convert information from serial form to parallel form, and vice versa. Many different kinds of shift registers are available, depending upon the degree of sophistication required. Counter

30、s weighted coding of binary numbersIn a sense, a shift register can be considered a counter based on the unary number system. Unfortunately, a unary counter would require a flip-flop for each number in the counting range. A binary weighted counter, however, requires only flip-flops to count to N. A

31、simple binary weighted counter can be made using T flip-flops. The flip-flops are attached to each other in a way so that the output of one acts as the clock for the next, and so on. In this case, the position of the flip-flop in the chain determines its weight; i.e., for a binary counter, the “powe

32、r of two” it corresponds to. A 3-bit (modulo 8) binary counter could be configured with T flip-flops as shown in Figure 1.4. A timing diagram corresponding to this circuit is shown in Figure 1.5.Note that a set of lights attached to O0, O1, O2 would display the numbers of full clock pulses which had

33、 been completed, in binary (modulo 8), from the first pulse. As many T flip-flops as required could be combined to make a counter with a large number of digits. Note that in this counter, each flip-flops changes state on the falling edge of the pulse from the previous flip-flop. Therefore there will

34、 be a slight time delay, due to the propagation delay of the flip-flops between the time one flip-flop changes state and the time the next one changes state, i.e., the change of state ripples through the counter, and these counters are therefore called ripple counters. As in the case of a ripple car

35、ry adder, the propagation delay can become significant for large counters. It is possible to make, or buy in a single chip, counters which will count up, count down, and which can be preset to any desired number. Counters can also be constructed which count in BCD and base 12 or any other number bas

36、e. A count down counter can be made by connecting the output to the clock input in the previous counter. By the use of preset and clear inputs, and by gating the output of each T flip- flop with another logic level using AND gates (say logic 0 for counting down, logic 1 for counting up), then a pres

37、etable up-down binary counter can be constructed. Figure 1.6 shows an up-down counter, without preset or clear.Synchronous countersThe counters shown previously have been “asynchronous counters”; so called because the flip-flops do not all change state at the same time, but change as a result of a p

38、revious output. The output of one flip-flop is the input to the next; the state changes consequently “ripple through” the flip-flops, requiring a time proportional to the length of the counter. It is possible to design synchronous counters, using JK flip-flops, where all flip-flops change state at t

39、he same time; i.e., the clock pulse is presented to each JK flip-flop at the same time. This can be easily done by nothing that, for a binary counter, any given digit changes its value (from 1 to 0 or from 0 to 1) whenever all the previous digits have a value of 1. A count down timer can be made by

40、connecting the output to the J and K, through the AND gates. Preset and clear could also be provided, and the counter could be made “programmable” as in the previous case. The timing diagram is similar to that shown for the asynchronous (ripple) counters, except that the ripple time is now zero; all

41、 counters clock at the same time. It is common for synchronous counters to trigger on the positive edge of the clock, rather than the trailing edge. Nature of Phase LockThe phase detector compares the phase of a periodic input signal against the phase of the VCO. Output of PD is a measure of the pha

42、se difference between its two inputs. The difference voltage is then filtered by the loop filter and applied to the VCO. Control voltage on the VCO changes the frequency in a direction that reduces the phase difference between the input signal and the local oscillator.When the loop is locked, the co

43、ntrol voltage is such that the frequency of the VCO is exactly equal to the average frequency of the input signal. For each cycle of input there is one, and only one, cycle of oscillator output. One obvious application of phase lock is in automatic frequency control (AFC). Perfect frequency control

44、can be achieved by this method, whereas conventional AFC techniques necessarily entail some frequency error.To maintain the control voltage needed for lock it is generally necessary to have a nonzero output from the phase detector. Consequently, the loop operates with some phase error present. As a

45、practical matter, however, this error tends to be small in a well-designed loop.A slightly different explanation may provide a better understanding of loop operation. Let us suppose that the incoming signal carries information in its phase or frequency; this signal is inevitably corrupted by additiv

46、e noise. The task of a phase lock receiver is to reproduce the original signal while removing as much of the noise as possible.To reproduce the signal the receiver makes use of a local oscillator whose frequency is very close to that expected in the signal. Local oscillator and incoming signal wavef

47、orms are compared with one another by a phase detector whose error output indicates instantaneous phase difference. To suppress noise the error is averaged over some length of time, and the average is used to establish frequency of the oscillator.If the original signal is well behaved (stable in fre

48、quency), the local oscillator will need very little information to be able to track, and that information can be obtained by averaging for a long period of time, thereby eliminating noise that could be very large. The input to the loop is a noisy signal, whereas the output of the VCO is a cleaned-up

49、 version of the input. It is reasonable, therefore, to consider the loop as a kind of filter that passes signals and rejects noise.Two important characteristics of the filter are that the bandwidth can be very small and that the filter automatically tracks the signal frequency. These features, automatic tracking and narrow bandwidth, account for the major uses of phase lock receivers. Narrow bandwidth is capable of rejecting large amounts of noise; it