Analog Electronics Lecture Notes

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48551 Analog Electronics Lecture Notes 2014 T T 1 1.5 Brick wall 1.0 T 2 T 3 0.5 T T T product 1 2 3 0 0 0.5 1.0 1.5  V T T T V i 1 2 3 o 1 1 1 1 Q 1 0 1 v o R 1 R 2 C 3 v i PMcL i Contents LECTURE 1 – SIMPLE FILTERS INTRODUCTION ...................................................................................................... 1.1 OP-AMP CIRCUITS ................................................................................................. 1.2 INVERTING AMPLIFIER ...................................................................................... 1.4 NON-INVERTING AMPLIFIER ............................................................................. 1.5 THE VOLTAGE FOLLOWER ................................................................................ 1.6 BILINEAR TRANSFER FUNCTIONS .......................................................................... 1.8 FREQUENCY RESPONSE REPRESENTATION .......................................................... 1.10 MAGNITUDE RESPONSES ..................................................................................... 1.12 PHASE RESPONSES .............................................................................................. 1.16 SUMMARY OF BILINEAR FREQUENCY RESPONSES .......................................... 1.20 BODE PLOTS ........................................................................................................ 1.21 FREQUENCY AND MAGNITUDE SCALING ............................................................. 1.22 FREQUENCY SCALING (DENORMALISING) ...................................................... 1.23 MAGNITUDE SCALING .................................................................................... 1.24 CASCADING CIRCUITS ......................................................................................... 1.25 INVERTING BILINEAR OP-AMP CIRCUIT .............................................................. 1.26 INVERTING OP-AMP CIRCUITS ............................................................................ 1.28 CASCADE DESIGN ................................................................................................ 1.29 QUIZ .................................................................................................................... 1.33 EXERCISES .......................................................................................................... 1.34 PROBLEMS ........................................................................................................... 1.36 LECTURE 2 – BUTTERWORTH LOWPASS FILTERS SECOND-ORDER PARAMETERS .............................................................................. 2.1 THE LOWPASS BIQUAD CIRCUIT ........................................................................... 2.4 FREQUENCY RESPONSE OF THE LOWPASS BIQUAD CIRCUIT ................................ 2.10 THE UNIVERSAL BIQUAD CIRCUIT ...................................................................... 2.14 APPROXIMATING THE IDEAL LOWPASS FILTER ................................................... 2.17 THE BUTTERWORTH RESPONSE ........................................................................... 2.19 BUTTERWORTH POLE LOCATIONS ....................................................................... 2.20 LOWPASS FILTER SPECIFICATIONS ...................................................................... 2.24 QUIZ .................................................................................................................... 2.30 EXERCISES .......................................................................................................... 2.31 PROBLEMS ........................................................................................................... 2.33 Analog Electronics 2014 ii LECTURE 3 - HIGHPASS AND BANDPASS FILTERS NEGATIVE FREQUENCY ......................................................................................... 3.1 PROTOTYPE RESPONSE .......................................................................................... 3.2 FREQUENCY TRANSFORMATIONS .......................................................................... 3.3 FOSTER REACTANCE FUNCTIONS ........................................................................... 3.5 HIGHPASS TRANSFORMATION ................................................................................ 3.9 BANDPASS TRANSFORMATION ............................................................................. 3.11 HIGHPASS FILTER DESIGN ................................................................................... 3.14 EXAMPLE ............................................................................................................. 3.18 BANDPASS RESPONSE .......................................................................................... 3.20 BANDPASS FILTER DESIGN .................................................................................. 3.25 BANDPASS POLE LOCATIONS ............................................................................... 3.28 FIRST-ORDER FACTOR .................................................................................... 3.29 SECOND-ORDER FACTORS .............................................................................. 3.30 FRIEND CIRCUIT .................................................................................................. 3.32 EXAMPLE ............................................................................................................. 3.34 QUIZ .................................................................................................................... 3.40 EXERCISES ........................................................................................................... 3.41 PROBLEMS ........................................................................................................... 3.43 LECTURE 4 – PASSIVE COMPONENTS INTRODUCTION ...................................................................................................... 4.1 RESISTOR CHARACTERISTICS................................................................................. 4.2 TOLERANCE ON VALUE ..................................................................................... 4.2 PREFERRED VALUES AND THE DECADE PROGRESSION ..................................... 4.2 THE ‘E’ SERIES VALUES ................................................................................... 4.4 MARKING CODES .............................................................................................. 4.6 STABILITY ......................................................................................................... 4.9 TEMPERATURE COEFFICIENT (TEMPCO) ............................................................ 4.9 VOLTAGE COEFFICIENT (VOLTCO) ................................................................. 4.11 HUMIDITY EFFECTS ........................................................................................ 4.11 POWER DISSIPATION ....................................................................................... 4.11 VOLTAGE RATING ........................................................................................... 4.13 FREQUENCY EFFECTS ...................................................................................... 4.14 NOISE .............................................................................................................. 4.16 RELIABILITY ................................................................................................... 4.17 DERATING ....................................................................................................... 4.18 RESISTOR TYPES .................................................................................................. 4.19 CARBON COMPOSITION RESISTORS ................................................................. 4.19 CARBON FILM RESISTORS ............................................................................... 4.20 METAL FILM RESISTORS ................................................................................. 4.21 WIRE WOUND RESISTORS ............................................................................... 4.22 CHIP RESISTORS .............................................................................................. 4.23 RESISTOR NETWORKS ..................................................................................... 4.25 CHOOSING RESISTORS ......................................................................................... 4.26 SUMMARY OF RESISTOR CHARACTERISTICS ACCORDING TO TYPE ................. 4.27 Analog Electronics 2014 iii CAPACITOR DEFINITIONS AND BASIC RELATIONS ............................................... 4.28 CAPACITOR CHARACTERISTICS ........................................................................... 4.30 RATED CAPACITANCE AND TOLERANCE ON VALUE ....................................... 4.30 RATED VOLTAGE ............................................................................................ 4.30 SURGE VOLTAGE ............................................................................................ 4.31 LEAKAGE CURRENT ........................................................................................ 4.31 INSULATION (LEAKAGE) RESISTANCE ............................................................ 4.31 MAXIMUM CURRENT ...................................................................................... 4.32 RATED PULSE RISE-TIME ............................................................................... 4.32 RIPPLE CURRENT ............................................................................................ 4.33 TYPES OF DIELECTRICS ....................................................................................... 4.33 NON-POLAR DIELECTRICS .............................................................................. 4.33 POLAR DIELECTRICS ....................................................................................... 4.34 CAPACITOR MODELS ........................................................................................... 4.35 QUALITY OF A CAPACITOR ............................................................................. 4.36 EQUIVALENT SERIES RESISTANCE (ESR) ....................................................... 4.37 SERIES RESONANT FREQUENCY (SRF) ........................................................... 4.38 FILM CAPACITORS ............................................................................................... 4.40 WOUND FOIL CAPACITORS ............................................................................. 4.40 METALLISED FILM CAPACITORS ..................................................................... 4.41 STACKED FILM CAPACITORS .......................................................................... 4.42 BASIC PROPERTIES OF FILM CAPACITOR DIELECTRICS ................................... 4.43 TOLERANCE .................................................................................................... 4.44 RECOMMENDED APPLICATIONS FOR FILM CAPACITORS ................................. 4.45 CERAMIC CAPACITORS ........................................................................................ 4.47 EIA TEMPERATURE COEFFICIENT CODES ........................................................ 4.48 CLASS 1 CAPACITOR CODES ............................................................................ 4.48 CLASS 2 CAPACITOR CODES ............................................................................ 4.49 CONSTRUCTION OF CERAMIC CAPACITORS .................................................... 4.50 CHARACTERISTICS OF CERAMIC CAPACITORS ................................................ 4.52 APPLICATIONS OF CERAMIC CAPACITORS ...................................................... 4.54 ELECTROLYTIC CAPACITORS ............................................................................... 4.55 ALUMINIUM ELECTROLYTIC CAPACITORS ...................................................... 4.55 APPLICATIONS OF ALUMINIUM ELECTROLYTIC CAPACITORS ......................... 4.59 TANTALUM ELECTROLYTIC CAPACITORS ....................................................... 4.60 APPLICATIONS OF TANTALUM CAPACITORS ................................................... 4.62 MICA CAPACITORS .............................................................................................. 4.63 GLASS CAPACITORS ............................................................................................ 4.64 CHOOSING CAPACITORS ...................................................................................... 4.65 DECOUPLING CAPACITORS .................................................................................. 4.67 Analog Electronics 2014 iv LECTURE 5 – SENSITIVITY, VARIOUS RESPONSES SENSITIVITY .......................................................................................................... 5.1 PROPERTIES OF THE SENSITIVITY FUNCTION ..................................................... 5.3 BODE SENSITIVITY ............................................................................................ 5.7 CHEBYSHEV RESPONSE ......................................................................................... 5.9 INVERSE CHEBYSHEV RESPONSE - OVERVIEW ..................................................... 5.16 COMPARISON OF BUTTERWORTH, CHEBYSHEV AND INVERSE CHEBYSHEV RESPONSES ..................................................................................................... 5.18 CAUER (ELLIPTIC) RESPONSE - OVERVIEW .......................................................... 5.21 PHASE RESPONSES ............................................................................................... 5.22 DELAY EQUALISATION ........................................................................................ 5.27 ALLPASS FILTERS ........................................................................................... 5.27 QUIZ .................................................................................................................... 5.31 EXERCISES ........................................................................................................... 5.32 LECTURE 6 – ELECTROMAGNETIC COMPATIBILITY PRINCIPLES OF EMC .............................................................................................. 6.1 TYPES OF SOURCES ................................................................................................ 6.2 SUPPLY LINE TRANSIENTS ................................................................................ 6.2 EMP AND RFI ................................................................................................... 6.3 ESD .................................................................................................................. 6.3 INTENTIONAL SOURCES .................................................................................... 6.3 COUPLING .............................................................................................................. 6.4 COMMON IMPEDANCE (“GROUND”) COUPLING ................................................ 6.4 CAPACITIVE COUPLING ..................................................................................... 6.5 INDUCTIVE COUPLING ....................................................................................... 6.6 RADIATED COUPLING ....................................................................................... 6.7 COMBATING EMI .................................................................................................. 6.8 COMBATING CAPACITIVE COUPLING ................................................................ 6.8 COMBATING INDUCTIVE COUPLING ................................................................ 6.12 RF SHIELDING ................................................................................................ 6.15 GROUNDS ........................................................................................................ 6.18 POWER SUPPLY DISTRIBUTION AND DECOUPLING .......................................... 6.21 REGULATORY STANDARDS .................................................................................. 6.24 REFERENCES ........................................................................................................ 6.27 Analog Electronics 2014 v LECTURE 7 – PRINTED CIRCUIT BOARDS INTRODUCTION ...................................................................................................... 7.2 GENERAL CHARACTERISTICS ................................................................................ 7.3 STACKUP ............................................................................................................... 7.5 CONDUCTORS ........................................................................................................ 7.6 POWER PLANES ..................................................................................................... 7.7 SHEET RESISTANCE ............................................................................................... 7.8 INSULATORS .......................................................................................................... 7.9 VIAS .................................................................................................................... 7.10 SPECIAL VIAS ...................................................................................................... 7.13 MANUFACTURING PROCESS ................................................................................ 7.14 PANELS ............................................................................................................... 7.24 TYPICAL ASSEMBLY PROCESS ............................................................................. 7.25 LAYOUT .............................................................................................................. 7.26 LECTURE 8 - DIRECT FILTER REALISATIONS DIRECT REALISATION ............................................................................................ 8.1 DOUBLY TERMINATED LOSSLESS LADDERS .......................................................... 8.1 FREQUENCY TRANSFORMATIONS ........................................................................ 8.10 LOWPASS TO HIGHPASS .................................................................................. 8.11 LOWPASS TO BANDPASS ................................................................................. 8.12 LADDER DESIGN WITH SIMULATED ELEMENTS ................................................... 8.15 LEAPFROG SIMULATION OF LADDERS ................................................................. 8.23 SWITCHED-CAPACITOR FILTERS ......................................................................... 8.23 IC FILTERS .......................................................................................................... 8.30 DIGITAL FILTERS ................................................................................................. 8.31 IMPLEMENTATION ISSUES OF ACTIVE FILTERS .................................................... 8.33 GAIN BANDWIDTH PRODUCT (GB) ................................................................. 8.33 SLEW RATE .................................................................................................... 8.33 SETTLING TIME ............................................................................................... 8.34 SATURATION .................................................................................................. 8.34 NOISE ............................................................................................................. 8.34 DESIGN VERIFICATION ................................................................................... 8.34 DESIGN TIPS ................................................................................................... 8.35 EXERCISES .......................................................................................................... 8.36 ANSWERS Analog Electronics 2014 1.1 Lecture 1 – Simple Filters Introduction. Op-amp circuits. Bilinear transfer functions. Transfer function representation. Magnitude responses. Phase responses. Bode plots. Magnitude and frequency scaling. Cascading circuits. Inverting op-amp circuit. Cascade design. Introduction Filters are essential to electrical engineering. They are used in all modern electronic systems. In communications, filters are essential for the generation Filters are essential to all modern and detection of analog and digital signals, whether via cable, optic fibre, air or electronic systems satellite. In instrumentation, filters are essential in “cleaning up” noisy signals, or to recover some “special” part of a complicated signal. In control, feedback through a filter is used to achieve a desired response. In power, filters are used to inject high frequency signals on the power line for control purposes, or for removing harmonic components of a current. In machines, filters are used to suppress the generation of harmonics, or for controlling switching transients. The design of filters is therefore a useful skill to possess. Filters can be of two types: analog and digital. In this subject, we will concentrate on analog filters. There are two reasons for this: analog filters are necessary components in “digital” systems, and analog filter theory serves as a precursor to digital filter design. The analog filters we will be looking at will also be of two types: passive and active. Active filters represent the most common, and use electronic components (such as op-amps) for their implementation. This is opposed to passive filters, which use the ordinary circuit elements: resistors, capacitors, inductors. Filter has the commonly accepted meaning of something retained, something rejected. There are many examples of filters in everyday life:  You’re being a filter right now. You have removed external distractions and are concentrating on reading these notes. Your brain is filtering out the unnecessary things going on around you (for a while, anyway). Analog Electronics Spring 2014 1.2  The media are information filters. They supposedly decide for us what is important information, and what is not. We rarely have time to investigate a topic for ourselves, and so we rely on them to pass us the essential points. The extreme of this is propaganda.  More tangible filters are sunglasses, tinted windows, ear muffs, air filters, flour sifters, radios, TVs, etc. For us, a filter is very simple: it is an electric circuit designed to implement a specific transfer function. Given a filter, obtaining the transfer function is just a A filter is a circuit that implements a matter of applying circuit theory. This is analysis. The choice of a transfer specific transfer function function and the choice of an implementation for a filter, however, are never unique. This is called design. To firstly analyse, and then design, active analog filters, a review of op-amps, transfer functions and frequency response is beneficial. Op-Amp Circuits A simplified model of an op-amp is: v - R o R v i o v + A( - ) v v + - Figure 1.1 For most applications, we assume the op-amp is ideal. Analog Electronics Spring 2014 1.3 An ideal op-amp has the following parameter values: A The ideal op-amp’s R  (1.1) i parameters R 0 o If there is a negative feedback path (ie a connection between the output of the amplifier and the (-) input terminal), then the op-amp will have a finite output voltage. It follows that: vAv v  o  v v oo vv  0  A (1.2) vv  The input to the op-amp looks like a short circuit for voltages, but due to the The virtual short circuit is the key to input resistance being infinite, it looks like an open circuit for currents. The analysing op-amp circuits input terminals can therefore be considered a virtual short circuit. We will use the virtual short circuit concept frequently. Analog Electronics Spring 2014 1.4 Inverting Amplifier An inverting amplifier is constructed as: The inverting amplifier R 2 R 1 v i v o Figure 1.2 We analyse the circuit using a virtual short circuit: analysed using a virtual short circuit R 2 R 1 v i i 2 v o i 1 Figure 1.3 KCL at the middle node gives: vv io  R R 12 v R o 2 (1.3)  v R i 1 Analog Electronics Spring 2014 1.5 Non-Inverting Amplifier A non-inverting amplifier and its equivalent circuit for analysis are: The non-inverting amplifier analysed R using a virtual short 2 circuit R 1 v o v i R 2 R 1 i 2 v i o 1 v i Figure 1.4 KCL at the middle node gives: v vv io i  R R 12 v R o 2 (1.4)  1 v R i 1 Analog Electronics Spring 2014 1.6 The Voltage Follower A voltage follower is a special case of the non-inverting amplifier circuit. If we set R  , then any value of R will give the gain as: 1 2 v o  1 (1.5) v i A simple value of R is 0, a short circuit. The voltage follower circuit is 2 therefore: The voltage follower circuit v o v i i = 0 v o v i Figure 1.5 The circuit differs from a piece of wire in that the input resistance for v is i acts as a buffer between two parts infinite and the controlled-source nature of the circuit provides isolation. It is of a circuit sometimes called a unity-gain buffer. The voltage follower is used to provide isolation between two parts of a circuit when it is required to join them without interaction. Analog Electronics Spring 2014 1.7 For example, to couple a high resistance source to a low resistance load, without suffering a voltage drop, we insert a buffer between source and load: A buffer is used to couple a high 1000 impedance to a low impedance v o = 0.01 V v i = 0.1 V 100 1000 i = 0 Voltage v o = 0.1 V v i = 0.1 V 0.1 V Follower 100 Figure 1.6 Analog Electronics Spring 2014 1.8 Bilinear Transfer Functions Filter design and analysis is predominantly carried out in the frequency domain. The circuits we design and analyse will be assumed to be operating with sinusoidal sources and be in the steady state. This means we can use phasors and complex numbers to describe a circuit’s response. Define the voltage ratio transfer function as: V Transfer function o T s defined (1.6) V i For example, consider a simple RC circuit: R v C v i o Figure 1.7 The transfer function is: V 1 RC o T s (1.7) V s1 RC i When a transfer function is the quotient of two linear terms like Eq. (1.7), it is said to be bilinear. Thus a bilinear transfer function is of the form: Bilinear transfer a s a 1 2 function defined T s (1.8) b s b 1 2 Analog Electronics Spring 2014 1.9 where the a and b constants are real numbers. If Eq. (1.8) is written in the form: and rewritten in a s a a s z 1 2 1 T s K terms of poles and (1.9) zeros b s b b s p 1 2 1 then -z is the zero of T s and -p is the pole of Ts. In the s plane the pole and zero are located at: (1.10) sz and s p Since z and p are real, the zero and pole of Ts are located on the real axis of the s plane. For real circuits, p will always be on the negative real axis, while z may be on either the positive or negative part of the real axis. For T s as in Eq. (1.7), the pole-zero plot in the s plane is: The pole-zero plot of a bilinear transfer function j   -1 RC Figure 1.8 Analog Electronics Spring 2014 1.10 Frequency Response Representation The sinusoidal steady state corresponds to s j . Therefore, Eq. (1.7) is, for the sinusoidal steady state, the frequency response:  1 0 T j , (1.11) 0 j RC 0 The complex function T j can also be written using a complex exponential in terms of magnitude and phase: j (1.12) T j T je which is normally written in polar coordinates: The transfer function in terms of (1.13) magnitude and T j T j phase We also normally plot the magnitude and phase of T j as a function of  or f . We use both linear and logarithmic scales. If the logarithm (base 10) of the magnitude is multiplied by 20, then we have the gain of the transfer function in decibels (dB): The magnitude of (1.14) the transfer function A 20log T j dB 10 in dB A negative gain in decibels is referred to as attenuation. For example, -3 dB gain is the same as 3 dB attenuation. The phase function is usually plotted in degrees. Analog Electronics Spring 2014 1.11 Example For the RC circuit, let  1 RC so that the frequency response can be written 0 as: 1 T j 1 j 0 The magnitude function is found directly as: 1 T j 2 1 0 The phase is:  1   tan    0 These are graphed below, using a normalised log scale for  : Analog Electronics Spring 2014 1.12 Magnitude Responses A magnitude response is the magnitude of the transfer function for a sinusoidal steady-state input, plotted against the frequency of the input. Magnitude The magnitude response is the responses can be classified according to their particular properties. To look at magnitude of the transfer function in these properties, we will use linear magnitude versus linear frequency plots. the sinusoidal steady state For the RC circuit of Figure 1.7, the magnitude function has three frequencies of special interest corresponding to these values of T j : T j0 1 1 T j 0.707 0 2 T j 0 (1.15) The frequency  is known as the half-power frequency. The plot below 0 shows the complete magnitude response of T j as a function of  , and the circuit that produces it: A simple low pass filter T 1 R 1 2 v C v i o 0 0 2 0 0 Figure 1.9 Analog Electronics Spring 2014

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