生物醫(yī)學(xué)電子學(xué)：轉(zhuǎn)換速率

1、 Outline Frequency Domain Specifications - Gain Bandwidth Product (GBP) - Open Loop Gain/Phase (AOL,PH) - Output Impedance (ZO) - Full Power Bandwidth (FPBW) Time Domain Specifications - Slew Rate (SR) - Settling Time (tS) - Overshoot Slew rate(SR) 轉(zhuǎn)換速率（有時(shí)也稱為壓擺率）轉(zhuǎn)換速率（有時(shí)也稱為壓擺率） pWe know that the outp

2、ut voltage of an amplifier circuit is limited.During any period of time when the output tries to exceed these limits, the output will saturate, and the signal will be distorted! pBut, this is not the only way in which the output signal is limited, nor is saturation the only way it can be distorted!

3、pSR in time Slew Rate q Linear RC Step Response: the slope of the step response is proportional to the final value of the output, that is, if we apply a larger input step, the output rises more rapidly. q If Vin doubles, the output signal doubles at every point, therefore a twofold increase in the s

4、lope. q But the problem in real OpAmp is that this slope can not exceed a certain limit. Slewing in Op Amp In the above case, if input is too large, output of the OpAmp can not change than the limit, causing a ramp waveform. Output resistant of OpAmp Slew rate(SR) pSlew rate is defined as the maximu

5、m rate of change of output voltage produced in response to a large input step. usually expressed in volts per microsecond . Small-Signal Operation of OpAmp Op Amp Slewing Slew rate = Iss/CL Op Amp Slewing (cont.) This is negative slewing Vp I1 G*I2 G*I1 I2 X1 CM CM In Vn Vo IZ X1 Ceq I C Vi Vo CM I

6、C Voltage FeedbackCurrent Feedback All the current for charging and discharging C comes from current source I. This is the slew rate limitation in VFA. Slew Rate The current needed for slewing the node at Z comes from current mirrors G*I1 and G*I2. Larger step inputs causes greater I1-I2 and produce

7、 larger output slew rates. pEffect of Slew Rate on a Sine Wave For a sine wave output voltage of amplitude, A, and frequency, f: ftAVOUT2sin Rate of change of the output voltage is: ftfA t VOUT 2cos2 d d To avoid slew rate limiting: SRfASRftfASR t VOUT 22cos2 d d Slew Rate Slew Rate Slew Rate Distor

8、tion desired output waveform actual output because of slew rate limitation The picture above shows exactly what happens when the slew rate limitations are not met and the output of the operational amplifier is distorted. SR = dv/dt = m (slope) Slew Rate pThere is a maximum rate of change associated

9、with the output of an op-amp. The Slew Rate. pTypical value for a 741 is 0.5 V/m ms. Input waveform Output waveform Time FULL POWER BANDWIDTH 全功率帶寬全功率帶寬 pThe Full Power Bandwidth(FPBW) of an amplifier is the maximum frequency that the output of an amplifier can swing over the full dynamic range with

10、out significant distortion. FULL POWER BANDWIDTH 全功率帶寬全功率帶寬 If the amplitude of the sine wave output is just below the saturation level, the maximum frequency that an undistorted SINE WAVE output can be obtained is often known as the full power bandwidth. E.g. 741 with saturation levels of 13.5 V: k

11、Hz 9 . 5 5 .132 105 . 0 2 6 max max A SR f Settling Time (ts) 建立時(shí)間建立時(shí)間 pSettling time, ts, is the time required for the output voltage to settle to within a specified percentage of the final value given a step input. Two reason: pIt takes a finite time for a signal to propagate through the internal

12、circuitry of an op amp. pthe output normally overshoots the target value, experiences damped oscillation, and settles to a final value. Settling Time (ts) 建立時(shí)間建立時(shí)間 等效輸入噪聲電壓等效輸入噪聲電壓EN pNoise produced internally by an op-amp is conveniently modeled as shown in Figure , by a noiseless op-amp with a noi

13、se voltage and a noise current generator at its input terminal. Input and Output Impedances pIdeal model assumes: nRIN is infinite nROUT is zero pIn real life: nRIN 1 MW nROUT 1 and that ROUT is either small or comparable with R1 and R2. 01 2 010 21 1 A A R R R A R RA RRR I V V OUT OUTOUTOUT Typical

14、ly, ROUT appears to be reduced by several orders of magnitude. Input/Output Impedance Summary pNegative feedback is very good at compensating for non-ideal properties of the amplifier. pThe effects of finite input impedance and non-zero output impedance are greatly reduced thanks to negative feedbac

15、k. nEg. Using a 741, an amplifier with a gain of 10 has ROUT of around 100W x 10/105 = 10 mW! pNB. Negative feedback will not work so well unless the open-loop gain of the op-amp is very large. nReasonable at d.c. and low frequencies. nAt higher frequencies Effects of Frequency Response Ideally, gai

16、n = 10 10 91 1 0 OUT IN OUTIN OUT V s K V s K VV s K VV s K VVAV 1/10 10 10/1 / 10 KssK sK V V s KV s KV V IN OUT INOUT OUT Frequency Response (cont) 1 10 10 1 102 2 10 10 1/10 10 56 f j fj KsV V IN OUT Constant, K, depends on the op-amp. For a 741 it is around 2106. f f j V V f V V f IN OUT IN OUT

17、6 5 5 5 10 10 10 10 1010 i.e. A first order low- pass filter, cut-off frequency of 100 kHz. Frequency Response Summary pIt is impossible to design an amplifier whose gain exceeds A0(f) at any frequency. pAt high frequencies, gain is limited by A0 which typically rolls-off at 20dB-decade. pThe cut-of

18、f frequency is nThe intersection of the low and high frequency asymptotes nThe 3dB point nThe gain-bandwidth product divided by the mid-band gain Summary pReal op-amps deviate from the ideal model in many ways. pNegative feedback automatically compensates for many of these. pMost of the time, theref

19、ore, the ideal model works pretty well pexcept under extreme conditions. p. Comparison of Op-Amp Parameters Harold Stephen Black (April 14, 1898 December 11, 1983) C.A. Desoer, In memoriam: Harold Stephen Black, IEEE Trans. Automatic Control, vol. AC-29, no. 8, pp. 673- 674, Aug. 1984. Harold Stephe

20、n Black (April 14, 1898 December 11, 1983) Harold Stephen Black (April 14, 1898 December 11, 1983) was an American electrical engineer, who revolutionized the field of applied electronics by inventing the negative feedback amplifier in 1927. To some, his invention is considered the most important br

21、eakthrough of the twentieth century in the field of electronics, since it has a wide area of application. This is because all electronic devices (vacuum tubes, bipolar transistors and MOS transistors) invented by mankind are basically nonlinear devices. Harold Stephen Black (April 14, 1898 December

22、11, 1983) pIt is the invention of negative feedback which makes highly linear amplifiers possible. Negative feedback basically works by sacrificing gain for higher linearity (or in other words, smaller distortion or smaller intermodulation). By sacrificing gain, it also has an additional effect of i

23、ncreasing the bandwidth of the amplifier. However, a negative feedback amplifier can be unstable such that it may oscillate. Once the stability problem is solved, the negative feedback amplifier is extremely useful in the field of electronics. Black published a famous paper, Stabilized feedback ampl

24、ifiers, in 1934. Work Amplifiers are non-linear, therefore every time a signal is amplified in a telecommunications network, which can happen dozens of times on a circuit, noise and distortion are added. Black first invented the feed-forward amplifier which compares the input and output signals and

25、then negatively amplifies the distortion and combines the two signals, canceling out some of the distortion. This amplifier design improved, but did not solve, the problems of transcontinental telecommunication. 2 Harold Stephen Black (April 14, 1898 December 11, 1983) Harold Stephen Black (April 14

26、, 1898 December 11, 1983) After years of work Black invented the negative feedback amplifier which uses negative feedback to reduce the gain of a high-gain, non-linear amplifier and makes it act as a low-gain, linear amplifier with much lower noise and distortion. The Negative feedback amplifier all

27、owed Bell system to reduce overcrowding of lines and extend its long-distance network by means of carrier telephony. It enabled the design of accurate fire-control systems in World War II, and it formed the basis of early operational amplifiers, as well as precise, variable-frequency audio oscillato

28、rs. 3 Harold Stephen Black (April 14, 1898 December 11, 1983) According to Black4 he got his inspiration to invent the negative feedback amplifier when he was traveling from New Jersey to New York City by taking a ferry to cross the Hudson River in August 1927. Having nothing to write on he sketched

29、 his thoughts on a misprinted page of the New York Times and then signed and dated it. 5 At that time, Bell Laboratories headquarters were located in 463 West Street, Manhattan, New York City instead of New Jersey and he lived in New Jersey such that he took the ferry every morning to go to work. Ha

30、rold Stephen Black (April 14, 1898 December 11, 1983) Harold Stephen Black (April 14, 1898 December 11, 1983) Negative feedback is one of the most useful concepts in electronics, particularly in opamp applications. Negative feedback is the process whereby a portion of the output voltage of all ampli

31、fier is returned to the input with a phase angle that opposes (or subtracts from) the input signal. Negative feedback The inverting (-) input effectively makes the feedback signal 180o out of phase with the input signal. The op-amp has extremely high gain and amplifies the difference in the signals

32、applied to the inverting and noninverting inputs. A very tiny difference in these two signals is all the op-amp needs to produce the required output. When negative feedback is preset, the noninverting and inverting inputs input nearly identical Negative feedback Hendrik Wade Bode (24 December 1905 2

33、1 June 1982 He made important contributions to the design, guidance and control of anti-aircraft systems during World War II and continuing post-WWII during the Cold War with the design and control of missiles and anti- ballistic missiles.2 an American engineer, researcher, inventor, author and scie

34、ntist, of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research. In addition, his research impacted many other engineering disciplines and laid the foundation for a diverse array of

35、modern innovations such as computers, robots and mobile phones among others. Bode was one of the great engineering philosophers of his era.3 Long respected in academic circles worldwide,45 he is also widely known to modern engineering students mainly for developing the asymptotic magnitude and phase

36、 plot that bears his name, the Bode plot. Hendrik Wade Bode (24 December 1905 21 June 1982 Non-inverting amplifier 同相放大器 Outline pConfiguration pVoltage Gain pInput Resistance pOutput Resistance pExample about Output Resistance pUnity-gain Buffer Non-inverting Amplifier: Configuration pInput signal

37、is applied to the non-inverting input terminal. pPortion of the output signal is fed back to the negative input terminal. pAnalysis is done by relating voltage at v1 to input voltage vs and output voltage vo . Non-inverting Amplifier:Voltage Gain Since i-=0and But vid =0 21 1 o v 1 v RR R 1 v id v s

38、 v 1 v s v 1 2 1 1 21 s v o v 1 21 s v o v R R R RR v A R RR Av is the closed-loop voltage gain FA A V V A OL OL in V 1 0 F A V 1 The original closed loop gain equation is: Ideally AOL = , Therefore F or is the feedback factor Non-inverting Amplifier: Input Resistance Since i+=0 i s v if r Ideally,

39、the input resistance for this configuration is infinity, but the a closer prediction of the actual input resistance can be found with the following formula: Where ri is given for the specified device. Usually ri is in the MW range. )1 (FArr OLiif Non-inverting Amplifier: Output Resistance prof is fo

40、und by applying a test current source to amplifier output and setting vs = 0 and is identical to the output resistance of inverting amplifier i.e. rof =0 pIdeally, the output resistance is zero, but the formula below gives a more accurate value: Where ro is given for the specified device. Usually ro

41、 is in the 10100s W range )1/( 0 FArr OLof Non-inverting Amplifier: Example about Output Resistance pTo see the effect of feedback on the output impedance, suppose that An op-amp with open-loop gain AOL=106 and Output resistance ro =50W, a closed-loop op-amp has F= 0.1, so that ACL=10, a closed-loop

42、 output impedance will be pAt high frequencies the open-loop gain reduces, which causes the output impedance to rise. W mFArr OLof 5 . 0 1 . 0101 50 )1/( 6 0 Unity-gain Buffer pA special case of non-inverting amplifier, also called voltage follower with infinite R1 and zero R2. Hence Av =1. pProvide

43、s excellent impedance-level transformation while maintaining signal voltage level. pIdeal voltage buffer does not require any input current and can drive any desired load resistance without loss of signal voltage. pUnity-gain buffer is used in may sensor and data acquisition systems. Inverting ampli

44、fier 反相放大器 Outline pConfiguration pVoltage Gain pInput and Output Resistances; pExample 1 and Example 2 pProblems in Inverting Amplifier; pInverter circuit using resistive T feedback network Inverting Amplifier: Configuration pPositive input is grounded. pFeedback network, resistors R1 and R2 connec

45、ted between inverting input and signal source and amplifier output node respectively. Inverting Amplifier:Voltage Gain pNegative voltage gain implies 1800 phase shift between dc/sinusoidal input and output signals. pGain greater than 1 if R2 R1 pGain less than 1 if R1 R2 pInverting input of op amp i

46、s at ground potential (not connected directly to ground) and is said to be at virtual ground. 0 o v 22 i 1 i s vRR s But is=i2 and v-=0 (since vid=v+-v-=0) 1 s v s i R and 1 2 s v o v R R v A Inverting Amplifier: Input and Output Resistances 1 s i s v R in R Rout is found by applying a test current

47、(or voltage) source to amplifier output and determining the voltage(or current) and turning off all independent sources. Hence, vs = 0 11 i 22 i x vRR But i1=i2 ) 12 ( 1 i x vRR Since v- = 0, i1=0 and vx = 0 irrespective of the value of ix . 0 out R Inverting Amplifier: Example 1 pProblem:Design an

48、inverting amplifier pGiven Data: Av=40 dB, Rin =20k, pAssumptions: Ideal op amp pAnalysis: Input resistance is controlled by R1 and voltage gain is set by R2 / R1. and Av=-100 p A minus sign is added since the amplifier is inverting. 100 dB20/dB40 10 v A Wk20 1in RR WMRR R R v A2 1 100 2 1 2 Inverti

49、ng Amplifier: Example 2 100 dB20/dB40 10 v A WM in RR1 1 pProblem:Design an inverting amplifier pGiven Data: Av=40 dB, Rin =1M, pAssumptions: Ideal op amp pAnalysis: Input resistance is controlled by R1 and voltage gain is set by R2 / R1. and Av=-100 p A minus sign is added since the amplifier is in

50、verting. WMRR R R v A100 1 100 2 1 2 pThe more gain, the less input resistance. pKept gain fixed, the more input resistance, the higher value feedback resistor ,the less BW Problems in Inverting Amplifier : Inverter circuit using resistive T feedback network Inverter circuit using resistive T feedba

51、ck network 54 5 RR R VV outTH 45 /RRRTH Break the circuit at point XY, stand on the terminals looking into R5, and calculate the Thevenin equivalent voltage and the Thevenin equivalent impedance: , 51 545242 5 54 1 45 45 2 )( RR RRRRRR R RR R RR RR R V V I o Inverter circuit using resistive T feedba

52、ck network Specifications for the circuit you are required to build are an inverting amplifier with an input resistance of 10 k (R1 = 10 k), a gain of 100, and a feedback resistance of 20 K or less. The inverting op amp circuit can not meet these specifications because RF must equal 1000 k. Insertin

53、g a T network with R2 = R5 = 10 k and R4 = 485 k approximately meets the specifications. 98 100 485010048510 I o V V Differential amplifier 差動(dòng)放大器差動(dòng)放大器 or 差分放大器差分放大器 The name differential amplifier should not be confused with the differentiator Outline pDifferential Amplifier； pOutput of Differential

54、 Amplifier； pCommon-Mode Signals； pEvaluating the CMRR of differential amplifier pInfluence of resistor matching on the CMRR of the circuit； pTotal CMRR of the circuit Historical background pThe long-tailed pair was originally implemented using a pair of vacuum tubes. The circuit works the same way

55、for all three-terminal devices with current gain. Today, its main feature is mostly vestigial, by virtue of the fact that long-tail resistor circuit bias points are largely determined by Ohms Law and less so by active component characteristics. p The long-tailed pair was developed from earlier knowl

56、edge of push-pull circuit techniques and measurement bridges.1 The earliest circuit that is truly recognizable as a long-tailed pair in its conventional form is given by Matthews (1934)2 Matthews, B. H. C. A Special Purpose Amplifier. The Jo rnal of Physiology, March 17, 1934, 81, 28P-29P. and the s

57、ame circuit form appears in a patent submitted by Alan Blumlein in 1936.3 By the end of the 1930s the topology was well established and had been described by various authors including Offner (1937),4 Schmitt (1937)5 Schmitt, O. H. Cathode Phase Inversion. Review of Scientific Instruments, 1937, p.10

58、0-101. and Toennies (1938) and It was particularly used for detection and measurement of physiological impulses.6 Historical background Single-Ended vs. Differential A signal applied between an input and ground is called a single-ended signal. A common mode signal is one where the voltages on both t

59、erminals rise and fall together. A signal applied from one input to the other input is called a differential signal. Differential Amplifier p Resistances must be symmetric for a diff-amp. p A differential amplifier circuit is commonly used to amplify or buffer differential signals while rejecting co

60、mmon mode signals. p op amp output voltage resulting from the input source VI1 Output of Differential Amplifier 1 1 2 IOI V R R V p op amp output voltage resulting from the input source VI2 2 1 21 43 4 2IO V R RR RR R V p Output of differential amplifier 21OOO VVV 2 1 21 43 4 1 1 2 II V R RR RR R V