Measurement Noise & Signal Processing 5.3 Introduction to signal processing This Signal processing aims at improving the quality of the reading or signal at the output of a measurement system. It also aims to attenuate any noise in the measurement signal that has not been eliminated (due to design limitation) of the measurement system. However, signal processing performs many other functions apart from dealing with noise. The exact procedures that are applied depend on the nature of the raw output signal from a measurement transducer. Procedures of signal filtering, signal amplification, signal attenuation, signal linearization and bias removal are applied according to the form of correction required in the raw signal. 1 Measurement Noise & Signal Processing 5.3 Introduction to signal processing. … Traditionally, signal processing has been carried out by analogue techniques in the past, using various types of electronic circuit. Recent trend is to go for digital signal processing, using software modules to condition the input measurement data. Digital signal processing is inherently more accurate than analogue techniques, but this advantage is greatly reduced in the case of measurements coming from analogue sensors and transducers. Because an analogue-to-digital conversion stage is necessary before the digital processing can be applied, thereby introducing conversion errors. Analogue processing remains the faster of the two, in spite of recent advances in the speed of digital signal processing. Some preliminary analogue processing is often carried out even when the major part of the processing is carried out digitally. 2 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Early operational amplifiers were used primarily to perform mathematical operations such as addition, subtraction, integration and differentiation- hence the term operational. Early operational amplifiers were constructed with vacuum tubes and worked with high voltages. Today’s op-amps are linear integrated circuits (IC’s) that use relatively low dc voltages and are reliable and inexpensive. Symbol and terminals 3 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … The Ideal Op-Amp -It has infinite voltage gain. -It has infinite input impedance (open), so that it does not load the driving source. -It has zero output impedance. -The input voltage Vin appears between the two input terminals and the output voltage is Av Vin. 4 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … The Practical Op-Amp Although modern integrated circuit op-amps approach parameter values that can be treated as ideal in many cases, the ideal device can never be made. Op amps have both voltage and current limitations -It has very high voltage gain. -It has very high input impedance. -It has very low output impedance. 5 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … The Differential Amplifier The op-amp in its basic form typically consists of two or more differential amplifiers stages. Because the differential amplifier (diff-amp) is fundamental to the op-amp’s internal operation, it is useful to have a basic understanding of this type of circuit. A basic differential amplifier circuit and its symbol are shown in the figure below 6 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … The Differential Amplifier The diff amp stages that make up part of the op-amp provide high voltage gain and common mode rejection. 7 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Basic Operation An op-amp typically has more than one differential amplifier stage, we will use a single diff-amp stage to illustrate the basic operation. First, when both inpts are grounded (0 V), the emitters are at -0.7 V 8 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Basic Operation It is assumed that the transistors are identically matched by careful process control during manufacturing so that their dc emitter currents are at the same level, when there is no input signal. IE1 = IE2 Since both the emitter currents combine through RE, IE1 = IE2 = IRe/2 Where IRe = VE- VEE/RE 9 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Basic Operation Based on the approximation that IC~= IE , it can be stated that IC1= IC2 ~= IRe/2 Since both the collector currents and both collector resistors are equal (when the input voltage is zero). VC1 = VC2 = VCC - ICRC 10 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Basic Operation Next, input 2 is left grounded and a positive bias voltage is applied to input 1 as shown in the fig. The positive voltage on the base Q1 increases IC1 and raises the emitter voltage to VE = VB – 0.7 This action reduces the forward bias (VBE) of Q2 because its base is held at 0 V (ground), thus causing IC2 to decrease as indicated in part(b) of the diagram. 11 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Basic Operation The net result is that IC1 causes a decrease in VC1 and decrease in IC2 causes an increase in VC2. 12 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Basic Operation Finally, input 1 is grounded and a positive bias voltage is applied to input 2. The positive bias voltage causes Q2 to conduct more, thus increasing IC2. Coincidently, the rise in emitter voltage causes forward bias of Q1 to decrease and causes IC1 to decrease. VC1 And conversely, decrease VC2 and to increase. 13 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation Single-Ended Input When a diff-amp is operated in this mode. one input is grounded and the signal voltage is applied only to the other input as shown in Figure. In the case where the voltage is applied to input 1 part, an inverted, amplified voltage appears at output shown. signal as in signal 1 as Also, a signal voltage appears in phase at the emitter of Q1 Since the emitters of Q1 and Q2 are common. 14 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation The emitter signal becomes an input to Q2 which functions as a common-base amplifier. The signal is amplified by Q2 and appears, non-inverted, at output 2. . 15 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation Differential Input In this mode, two oppositepolarity (out-of-phase) signals are applied to the inputs, as shown in Figure. This type of operation is also referred to as double-ended. Figure (b) shows the output signals due to the signal on input I acting alone as a single-ended input. 16 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation Figure (c) shows the output signals due to the signal on input 2 acting alone as a single-ended input. Notice in parts (b) and (c) that the signals on output I are of the same polarity. The same is also true for output 2. By superimposing both output 1 signals and both output 2 signals. we get the total differential operation. as pictured in (d) 17 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation Figure (c) shows the output signals due to the signal on input 2 acting alone as a single-ended input. Notice in parts (b) and (c) that the signals on output I are of the same polarity. The same is also true for output 2. By superimposing both output 1 signals and both output 2 signals. we get the total differential operation. as pictured in (d) 18 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation Common mode input One of the most important aspects of the operation of a diff-amp can be seen by considering the common-mode condition where two signal voltages of the same phase, frequency, and amplitude are applied to the two inputs, as shown in Figure (a). Again, by considering each input signal as acting alone, the basic operation can be understood. 19 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation Figure(b) shows the output signals due to the signal on only input 1, Figure(c) shows the output signals due to the signal on only input 2. Notice that the corresponding signals on output I are of the opposite polarity and so are the ones on output 2. 20 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation When the input signals are applied to both inputs. the outputs are superimposed and they cancel, resulting in a zero output voltage, as shown in Figure (d). This action is called commonmode rejection. Its importance lies in the situation where an unwanted signal appears commonly on both diff-amp inputs. 21 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Modes of Signal Operation Common-mode rejection means that this unwanted signal will not appear on the outputs and distort the desired signal. Common-mode signals (noise) generally are the result of the pick-up of radiated energy on the input lines from adjacent lines, the 60 Hz power line, or other sources. 22 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Common Mode Rejection Ratio Un-wanted signals (noise) appearing with the same polarity on both input lines are essentially cancelled by the diff-amp and do not appear on the outputs. The measure of an amplifier's ability to reject commonmode signals is a parameter called the common-mode rejection ratio (CMRR). Ideally, a diff-amp provides a very high gain for desired signals (single-ended or differential) and zero gain for common-mode signals. Practical diff-amps has a very small common-mode gain (usually much less than 1), while providing a high differential voltage gain (usually several thousand). 23 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Common Mode Rejection Ratio The higher the differential gain with respect to the common-mode gain, the better the performance of the diff-amp in terms of rejection of common-mode signals. This suggests that a good measure of the diff-amp's performance in rejecting unwanted common-mode signals is the ratio of the differential voltage gain Av(d) to the common-mode gain, Acm. This ratio is the common-mode rejection ratio, CMRR. 24 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Common Mode Rejection Ratio A very high value of CMRR means that the differential gain Av(d) is high and the common-mode gain Acm is low. The CMRR is often expressed in decibels (dB) as 25 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … A Simple Op-Amp Arrangement The figure shows two differential amplifier stages and an emitter follower connected to form a simple op-amp. The first stage can be used with a single ended or a differential input. The differential outputs of the first stage are directly coupled into the differential inputs of the second stage. The output of the second stage is single ended to drive an emitter follower to achieve a low output impedance. Both diff. stages provide a high voltage gain and a high CMRR. 26 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Emitter Follower In order to fully appreciate an omamp. We have to have a clear understanding of an emitter follower. When the output is taken from the emitter terminal of the transistor. The configuration is known as emitter follower configuration as shown in the figure. The output voltage is always slightly less than 1 due to the drop from base to emitter. The gain Av ~=1 27 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Emitter Follower Unlike the collector voltage, the emitter voltage is in phase with the signal V i. The fact that Vo “follows” the magnitude of Vi with an in-phase relationship accounts for the terminology emitter-follower. The figure shows the most common emitter-follower configuration. This is also known as common collector configuration. Substituting the re equivalent circuit into the network will result in the network. 28 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Emitter Follower Substituting the re equivalent circuit into the network will result in the network. Zi, the input impedance will result in With or 29 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Emitter Follower And Zo: The output impedance is best described by first writing the equation for the current Ib: And then multiplying with (β+1) o establish Ie. That is, 30 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Emitter Follower Substituting for Zb gives Constructing the network for the equation, will result in 31 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Emitter Follower Since RE is typically much greater than re, the following approx. is often applied Av, voltage gain can be determined using the voltage divider rule 32 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Emitter Follower 33 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp parameters Input offset voltage Ideal op-amp produces zero volts out for zero volts in. Practical op-amp has a small dc voltage, VOUT(error) when no differential input voltage is applied. Its primary cause is a slight mismatch of the base-emitter voltages of the differential input stage of an op-amp. the output voltage of the differential input stage is expressed as VOUT = IC2RC – IC1RC In data sheet, the input offset voltage, VOS, is the differential dc voltage required between the inputs to force the differential output to zero. Typical values are in the range of 2 mV or less. 34 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp parameters Input offset voltage drift with temperature The input offset voltage drift is a parameter related to VOS that specifies how much change occurs in the input offset voltage for each degree change in temperature. Typical values range from 5μV per ⁰C to about 50μV per ⁰C. Usually an op-amp with a higher nominal value of input offset voltage exhibits a higher drift. 35 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp parameters Input Bias Current The input terminals of a bipolar differential amplifier are the transistor bases, therefore, the input currents are the base currents. The input bias current is the dc current required by the inputs of the amplifier to properly operate the first stage. 36 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp parameters Input Impedance There are two basic ways of specifying the input impedance of an op-amp. They are the differential and the common mode. The differential input impedance is the total resistance between the inverting and non-inverting inputs. 37 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp parameters Input Impedance There are two basic ways of specifying the input impedance of an op-amp. They are the differential and the common mode. The common mode input impedance is the resistance between each input and ground. 38 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp parameters Input Offset current Ideally the two input bias currents are equal, and thus their difference is zero. In a practical op-amp, however, the bias currents are not exactly equal. The input offset current is the difference of the input bias currents, expressed as an absolute value. IOS = |I1-I2| 39 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp parameters Input Offset current Actual magnitudes of offset are usually atleast ten times less than the bias current. High-gain, high input impedance amplifiers should as little IOS as possible, the difference in currents through large input resistances develops a substantial offset voltage. 40 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp parameters Input Offset current The offset voltage developed by the input offset Current is Vos = I1Rin - I2Rin = (I1 – I2)Rin Vos = IosRin The error created by los is amplified by the gain Av of the op-amp and appears in the output as VOUT(error) = AvIos Rin A change in offset current with temperature affects the error voltage. Values of temperature coefficient for the offset current in the range of 0.5 nA per degree centigrade are common. 41 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Negative Feedback Negative feedback is one of the most useful concepts in electronics, particularly in op-amp applications. Negative feedback is the process whereby a portion of the output voltage of an amplifier is returned to the input with a phase angle that opposes (or subtracts from) the input signal. 42 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Why use Negative Feedback? ◼ The open loop gain of a typical op-amp is very high (greater than 100,000), therefore, an extremely small input voltage drives the opamp into its saturated output states. Even the input offset voltage of the op-amp can drive it into saturation. For example, assume VIN = 1 mV and Aol = 100,000. Then, VinAol = (l mV)(100,000) = lOO V Since the output level of an op-amp can never reach 100V, it is driven into saturation and the output is limited to its max output levels. 43 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Why use Negative Feedback? ◼ The usefulness of an op-amp is severely restricted if it is without negative feedback. ◼ With negative feedback, the closed loop voltage gain (Acl) can be reduced and controlled so that op-amp can function as a linear amplifier. 44 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Closed loop gain, Acl The closed-loop voltage gain is the voltage gain of an op-amp with external feedback. The amplifier configuration consists of the op-amp and an external negative feedback circuit that connects the output to the inverting input. The closed-loop voltage gain is determined by the external component values and can be precisely controlled by them. 45 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Non-inverting amplifier An op-amp connected in a closed loop configuration is a noninverting amplifier with a controlled amount of voltage gain 46 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Non-inverting amplifier Ri and Rf form a voltage divider circuit which reduces Vout and connects the reduced voltage Vf to the inverting input 47 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Non-inverting amplifier Therefore, 48 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Non-inverting amplifier Therefore, 49 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Non-inverting amplifier 50 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Voltage Follower The voltage-follower configuration is a special case of the noninverting amplifier where all of the output voltage is fed back to the inverting (-) input by a straight connection, as shown in Figure 51 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Voltage Follower As you can see, the straight feedback connection has a voltage gain of 1 (which means there is no gain). The closed-loop voltage gain of a noninverting amplifier is 1/B as previously derived. Since B = 1 for a voltage-follower, the closed-loop voltage gain of the voltage-follower is Acl(VF) = I It has very high input impedance and very low output impedance making it an ideal buffer for interfacing high impedance sources and low impedance loads. 52 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Comparator A comparator is a type of op-amp circuit that compares two input voltages and produces an output in either of two states indicating the greater than or less than relationship of the inputs. One application of an op-amp used as a comparator is to determine when an input voltage exceeds a certain level. The Figure shows a zero-level detector. 53 Measurement Noise & Signal Processing 5.3 Introduction to Operational Amplifier. … Op-Amp Comparator Notice that the inverting ( - ) input is grounded to produce a zero level and that the input signal voltage is applied to the non-inverting (+) input. Because of the high open-loop voltage gain, a very small difference voltage between the two inputs drives the amplifier into saturation, causing the output voltage to go to its limit. 54
