# Sophomore Physics Laboratory (PH005/105)

Size: px
Start display at page:

Transcription

1 CALIFORNIA INSTITUTE OF TECHNOLOGY PHYSICS MATHEMATICS AND ASTRONOMY DIVISION Sophomore Physics Laboratory (PH5/15) Analog Electronics Active Filters Copyright c Virgínio de Oliveira Sannibale, 23 (Revision December 212)

2 Chapter 6 Active Filters Introduction An electronic circuit that modifies the frequency spectrum of an arbitrary signal is called filter A filter that modifies the spectrum producing amplification is said to be an active filter Vis à vis its definition, it is convenient to study the filter characteristics in terms of the frequency response of its associated two port network H(ω) = (ω) (ω), where and are respectively the input voltage and the output voltage of the network, and ω the angular frequency Depending on the design, active filters have some important advantages: they can provide gain, they can provide isolation because of the typical characteristic impedances of amplifiers, they can be cascaded because of the typical characteristic impedances of amplifiers, they can avoid the use of inductors greatly simplifying the design of the filters Here some disadvantages: 127

3 128 CHAPTER 6 ACTIVE FILTERS they are limited by the amplifiers band-with, and noise, they need power supplies, they dissipate more heat than a passive circuit Let s make some simple definitions useful to classify different types of filters 61 Classification of Ideal Filters Based on their magnitude response H(ω), Some basic ideal filters can be classified as follows: H(ω) H(ω) 1 1 ω Low-pass ω ω High-pass ω H(ω) 1 H(ω) 1 H(ω) 1 ω ω 1 ω ω ω 1 ω Band-pass Stop-band/band-reject ω ω Notch Practical filters approximate more or less the ideal definitions

4 62 FILTERS AS RATIONAL FUNCTIONS 129 A 1 DA 1 DA 3 A 3 DA 2 A 2 ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 ω 7ω 8 ω Figure 61: Graphical definition of the filter performance specifications, and hypothetical filter response (red curve) that satisfy the specification Usually, the filter requirements are specified defining the band frequencies with their gains (attenuation or amplification) gain ripples, and slope transitions in terms of power of the frequency Figure 61 shows a quite general graphical definition of the design parameters of a filter with an hypothetical design For a complete specification one should also define the requirement for phase response 62 Filters as Rational Functions Let s consider filters whose transfer function can be expressed as rational function or standard form H(ω) = α α 1 jωα 2 (jω) 2 α N (jω) N β β 1 jωβ 2 (jω) 2 β M (jω) M For the filter not to diverge M N H(ω) < for any value of ω Writing the transfer function as a polynomial factorization we obtain H(ω) = k (ω z 1) n 1 (ωz 2 ) n 2 (ω z N ) n N (ω p 1 ) m 1 (ω p 2 ) m 2 (ω p M ) m M

5 13 CHAPTER 6 ACTIVE FILTERS Denominator roots p 1, p 2,, p n are called poles, and numerator roots z 1, z 2,, z m are called zeros The integers n 1, n 2,, n N, and m 1, m 2,, m N are therefore the multiplicity of poles and zeros Poles and zeros values determine the shape of the filter, and apart from zero frequency, one could say that poles provide attenuation and zeros amplification The transition from transmission to attenuation, and vice versa, in the filter magnitude H(ω) is characterized by an asymptote slope which determine the so called filter order For example, considering the RC low pass filter with ω = 1/RC, we have one pole p 1 = jω H(ω) = ω ω jω first oder low pass filter with cut-off freq ω For the RC high pass filter with ω = 1/RC, we have one pole p 1 = jω and one zero z 1 = H(ω) = ω ω jω first oder high pass filter with cut-off freq ω In the next sub-sections, we will analyze into more details filters with the following transfer function H(ω) = H ω 2 jω ω 1 Q 1 ω 2 1 ω 2 jω ω Q ω2

6 62 FILTERS AS RATIONAL FUNCTIONS Second Order Low-Pass Filter Figure below shows the second order low pass filter bode plot, with resonant frequency ω res, and characteristic frequency ω Magnitude [db] H max Filter ω res ω ω res ω Phase [Deg] 5 φ res ω res ω Frequency [rad/s] The second order low-pass filter written in standard form Transfer Function Resonance Maximum DC High Freq Gain Gain H ω 2 ω 2 jω ω Q ω2 ω 1 1 Q 2Q 2 H 1 1 4Q 2 H

7 132 CHAPTER 6 ACTIVE FILTERS 622 Second Order High-Pass Filter Magnitude [db] H max Filter ω res ω ω 1 3 ω res Phase [Deg] 1 9 φ res ω 1 3 ω res 1 4 Frequency [rad/s] The second order high-pass filter written in standard form Transfer Function Resonance Maximum DC High Freq Gain Gain H ω 2 ω 2 jω ω Q ω2 ω 1 1 2Q 2 H Q 1 1 4Q H

8 62 FILTERS AS RATIONAL FUNCTIONS Band-Pass Filter Magnitude [db] H 5 max Filter ω res ω ω ω res Phase [Deg] φ res ω 1 3 ω res 1 4 Frequency [rad/s] The band-pass filter written in standard form is Transfer Function Resonance Maximum DC Gain High Freq Gain H jω ω Q ω 2 jω ω Q ω2 ω H

9 134 CHAPTER 6 ACTIVE FILTERS For example, depending on the output we consider, the already studied LRC series circuit is a low-pass, a band-pass, or a high-pass filter with the transfer function described above When we will study difference filters topologies we will reduce their transfer function into one of the standard form above 63 Common Circuit Filters Topologies This is a brief and not exhaustive at all list of filter topologies that use resistors, capacitors, and operational amplifiers to implement the filters types described above: Infinite gain, multiple feedback (IGMF) Generalized Sallen-Key (GSK) State Variable (SV) Switched Capacitor Filters (SC) Cascading these implementation allows to increase the filter order

10 64 INFINITE GAIN MULTIPLE FEEDBACK CONFIGURATION (IGMF) Infinite Gain Multiple Feedback Configuration (IGMF) I 1 Y 1 I 4 Y 4 Y 5 I3 A B V A Y 3 V I 2 Y 2 V Figure 62: Infinite Gain Multiple Feedback Filter Let s consider the circuit in Figure 62 with generic admittances Y 1, Y 2, Y 3, Y 4, and Y 5 Applying the KCL to node A and considering the circuit virtual ground (V = ), we have V A Y 3 ( V A ) Y 4 ( V A ) Y 1 V A Y 2 = (61) Again, applying KCL to node B and for the virtual ground we have Y 5 V A Y 3 = V A = Y 5 Y 3 Replacing the last expression into eq 61 and after some algebra we obtain the generic transfer function for the circuit Y = 1 Y 3 Y 5 (Y 1 Y 2 Y 3 Y 4 ) Y 3 Y 4 Choosing the proper type of admittances we can construct different types of active filters, low-pass band-pass, and high-pass It is worthwhile noticing that IGMF configuration allows to implement low-pass, bandpass, and high-pass filter with capacitors, resistor and no inductors This simplifies considerably the design of the filters

11 136 CHAPTER 6 ACTIVE FILTERS 641 Low-pass Filter R 4 C 5 R R V 1 3 i C 2 G Figure 63: Low-pass filter configuration of the infinite gain multiple feedback filter A possible choice to implement a low-pass filter as shown in Figure 63 is Y 1 = 1 R 1, Y 2 = jωc 2, Y 3 = 1 R 3, Y 4 = 1 R 4, Y 5 = jωc 5, and the transfer function of the circuit becomes 1/R 1 R 3 = jωc 5 (1/R 1 jωc 2 1/R 3 1/R 4 )1/R 3 R 4 Rearranging the expression to obtain a rational fraction in ω we finally obtain = 1 R 1 R 3 C 2 C 5 ω 2 jω 1 1 (1/R 1 1/R 3 1/R 4 ) C 2 R 3 R 4 C 2 C 5 Comparing the denominator of the previous equation with the denominator of the transfer function in section 621 we find that the frequency ω, the quality factor Q, and the DC gain H are respectively ω = 1 R 3 R 4 C 2 C 5, Q = ω C 2 (1/R 1 1/R 3 1/R 4 ), H = R 4 R 1

12 64 INFINITE GAIN MULTIPLE FEEDBACK CONFIGURATION (IGMF) High-pass Filter C 4 R 5 C 1 C 3 R 2 G Figure 64: High-pass filter configuration of the infinite gain multiple feedback filter A possible choice to implement a high-pass filter as shown in Figure 64is Y 1 = jωc 1, Y 2 = 1 R 2, Y 3 = jωc 3, Y 4 = jωc 4, Y 5 = 1, R 5 and the transfer function of the circuit becomes jωc = 1 jωc 3 1/R 5 (jωc 1 1/R 2 jωc 3 jωc 4 ) jωc 3 jωc 4 Rearranging the expression to obtain a rational fraction in ω we obtain = ω 2 (C 1/C 4 ) ω jω(c 1 C 3 C 4 ) R 5 C 3 C 4 R 2 R 5 C 3 C 4 Comparing the denominator of the previous equation with the denominator of the transfer function in section 622 we find that the frequency ω, the quality factor Q, High frequency gain H are respectively ω = 1 R 2 R 5 C 3 C 4, Q = ω R 5 C 3 C 4 (C 1 C 3 C 4 ), H = C 1 C 4

13 138 CHAPTER 6 ACTIVE FILTERS 643 Band-pass Filter C 4 R 5 R 1 C 3 R 2 Figure 65: Band-pass filter configuration of the infinite gain multiple feedback filter A possible choice to implement a Band-pass filter is shown in Figure 65 The admittances are Y 1 = 1 R 1, Y 2 = 1 R 2, Y 3 = jωc 3, Y 4 = jωc 4, Y 5 = 1 R 5, and the transfer function of the circuit becomes jωc = 3 /R 1 1/R 5 (1/R 1 1/R 2 jωc 3 jωc 4 ) jωc 3 jωc 4 Rearranging the expression to get a rational fraction in ω we finally obtain ( ) C3 C = R jω 4 5 R 5 C 3 C 4 R 1 ω 2 jω C 3 C 4 R 1R 2 C 3 C 4 R 5 R 1 R 2 R 5 C 3 C 4 Comparing the denominator of the previous equation with the denominator of the transfer function in section 623 we find that the resonance frequency, and the quality factor are respectively R ω = 1 R 2 R, Q = 5 C 3 C ω 4, H R 1 R 2 R 5 C 3 C 4 C 3 = R 5 C 4 R 1

14 65 GENERALIZED SALLEN-KEY FILTER TOPOLOGY (GSK) Generalized Sallen-Key Filter Topology (GSK) I 4 Y 4 I 1 I 3 Y 1 A V A Y 2 B V I 3 Y 3 V C Y 6 I 5 Y 5 I 6 Figure 66: Generalized Sallen-Key Topology Let s consider the circuit in Figure 66 with generic admittances Y 1, Y 2, Y 3, Y 4, Y 5, and Y 6 Applying the KCL to node A, we have ( V A ) Y 1 ( V A ) Y 4 (V V A ) Y 2 = (62) Applying KCL to node B (V V A ) Y 2 V Y 3 = V A = Y 2 Y 3 Y 2 V Applying KCL to node C (V V ) Y 6 V Y 5 = V = V = Y 6 Y 6 Y 5 V Replacing the expression found for V A, and V into eq (62) and after quite some boring algebra, we obtain ( = 1 Y 5 Y 6 ) Y 1 Y 2 Y 6 Y 1 Y 6 (Y 2 Y 3 )Y 3 Y 6 (Y 2 Y 4 )Y 2 Y 4 Y 5 Let s analyze some admittances configuration of the this filter topology

15 14 CHAPTER 6 ACTIVE FILTERS 651 GSK Second Order Low-pass Filter C 4 R 1 R 2 C 3 R 6 R 5 Figure 67: Low-pass filter configuration of the Generalized Sallen-Key filter A possible choice to implement a low-pass filter as shown in Figure 67 is Y 1 = 1 R 1, Y 2 = 1 R 2, Y 3 = jωc 3, Y 4 = jωc 4, Y 5 = 1 R 5, Y 6 = 1 R 6, and the transfer function of the circuit becomes 1 ( = 1 R ) 6 R 1 R 2 C 3 C ( 4 R 5 1 ω 2 jω 1 1 ) R 6 1 R 1 C 4 R 2 C 4 R 2 C 3 R 5 R 1 R 2 C 3 C 4 Comparing the denominator of the previous equation with the denominator of the transfer function in section 621we find that the frequency square ω 2, the quality factor Q, and the DC gain H are respectively ( ω 2 = 1 R, Q = 1 R 2 R 5 C 3 C 4 ω, H = R 1 C 4 R 2 C 3 R 5 (R 1 R 2 ) C 3 R 1 R 6 C 4 1 R 6 R 5 )

16 65 GENERALIZED SALLEN-KEY FILTER TOPOLOGY (GSK) Simple Case If R 1 = R 2 = R, C 3 = C 4 = C, and R 5 = R 6 =, then = ω 2 ω 2 jωω ω 2, ω 2 = 1 R 2 C 2,, Q = 1, which is the transfer function of a second order low-pass filter with low quality factor 653 GSK Second Order High-pass Filter R 4 C 2 C 1 R 3 R 6 R 5 Figure 68: High-pass filter configuration of the Generalized Sallen-Key filter To implement a low-pass filter as shown in Figure 68 one needs to choose the admittances as follows Y 1 = jωc 1, Y 2 = jωc 2, Y 3 = 1 R 3, Y 4 = 1 R 4, Y 5 = 1 R 5, Y 6 = 1 R 6, and the transfer function of the circuit becomes

17 142 CHAPTER 6 ACTIVE FILTERS ( = 1 R ) 6 R 5 ω ( 2 1 ω² jω 1 1 ) R 6 R 3 C 2 R 3 C 1 R 4 C 1 R 5 1 R 3 R 4 C 1 C 2 Comparing the denominator of the previous equation with the denominator of the transfer function in section 622 we find that the frequency square ω 2, the quality factor Q, and the DC gain H are respectively ω 2 = 1 R 3 C 1 R 4 C 2, Q = ω R 3 R 4 R 5 C 1 C 2 R 5 (C 1 C 2 ) R 3 C 1 R 6 R 4, H = 654 Simple Case If R 1 = R 2 = R, C 3 = C 4 = C, and R 5 = R 6 =, then = ω 2 ω 2 jωω ω 2, ω 2 = 1 R 2 C 2,, Q = 1, which is the transfer function of a second order high-pass filter with low quality factor 655 GSK Band-pass Filter ( 1 R ) 6 R 5 R 4 C 2 V R 1 i R 3 C 3 R6 R 5 Figure 69: Band-pass filter configuration of the Generalized Sallen-Key filter

18 65 GENERALIZED SALLEN-KEY FILTER TOPOLOGY (GSK) 143 To implement a band-pass filter as shown in Figure 69 one needs to choose the admittances as follows Y 1 = 1 R 1, Y 2 = jωc 2, Y 3 = 1 R 3 jωc 3, Y 4 = 1 R 4, Y 5 = 1 R 5, Y 6 = 1 R 6, and the transfer function of the circuit becomes ( = 1 R ) 6 R 5 R 1 C ( 3 C2 ω 2 C 3 jω ) R 6 C 2 C 3 R 1 C 3 R 3 C 2 R 4 C 3 R 4 R 5 Comparing the denominator of the previous equation with the denominator of the transfer function in section 623 we find that the frequency square ω 2, the quality factor Q, and the DC gain H are respectively jω R 1R 4 C 2 C 3 R 1 R 3 R 4 Q = ω C 2 C 3 R 1 R 3 R 4 R 5 (C 2 C 3 ) R 3 R 4 R 5 C 2 R 1 R 4 R 5 C 3 R 1 R 3 R 5 C 2 R 1 R 3 R 6, 656 Simple Case ω 2 = R 1R 4,H = 1 ( C 2 C 3 R 1 R 3 R 4 R 1 C 3 1 R 6 R 5 ) Q ω If R 1 = R 3 = R 4 = R, C 2 = C 3 = C, and R 5 = R 6 =, then = jω ω Q ω 2 jω ω Q ω2 2 2, ω = RC,, Q = 3, which is the transfer function of a second order high-pass filter with low quality factor

19 144 CHAPTER 6 ACTIVE FILTERS 66 State Variable Filter Topology (SV) The state variable filter provides a low pass, a band pass, and a high pass filter outputs At the same time, it allows to change the gain, the cut-off frequencies, and the quality factor independently, but it requires 4 Op- Amps R 1 R 2 R3 R 4 R 5 C 1 C 2 G V HP G V BP G V LP R 7 R 6 Figure 61: State variable filter circuit TBF 67 Practical Considerations 671 Component Values How do we select the values of capacitance and resistance? Here are some considerations that should help the filter design: reducing the resistance values reduces the thermal noise and therefore the filter noise, reducing resistance values minimizes the op-amp voltage offsets,

20 67 PRACTICAL CONSIDERATIONS 145 increasing the resistance reduce the current load on the op-amps, increasing the resistances usually allows to decrease the capacitance and therefore it make easier to find capacitors because of the small capacitance values needed, reducing the capacitance minimizes the capacitance fluctuations due to temperature, increasing the capacitance allows to reduce resistance values and therefore the thermal noise As we can clearly see, some of the consideration cannot be used at the same time Based on the design requirements one can decide which of the consideration above are more important to finally meet the design requirements Rules of Thumb Particularly critical design often overrule these following rules: Capacitor with capacitance less of ~1 pf should be avoided, Try to use resistor with resistance between few kilo-ohms to few hundreds of kilo-ohms 672 Components technology Capacitors The use of low loss dielectric is very important to obtain good results If possible one should use plastic film capacitors or CG/NPO ceramic capacitors, 1% tolerance for temperature stability Resistor Low thermal noise resistors such as metal film resistors 1% tolerance for temperature stability should be used

21 146 CHAPTER 6 ACTIVE FILTERS

22 Bibliography [1] Hank Zumbahlen, State Variable Filters, Mini Tutorial MT-223, Analog Devices 147

23 148 BIBLIOGRAPHY

### 2.161 Signal Processing: Continuous and Discrete Fall 2008

MT OpenCourseWare http://ocw.mit.edu.6 Signal Processing: Continuous and Discrete Fall 00 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS

### Frequency Response of Filters

School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 2 Frequency Response of Filters 1 Introduction Objectives To

### Application Report SLOA024B

Application Report July 999 Revised September 2002 Mixed Signal Products SLOA024B IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications,

### S-DOMAIN ANALYSIS: POLES, ZEROS, AND BODE PLOTS

S-DOMAIN ANAYSIS: POES, ZEROS, AND BODE POTS The main objectiveis to find amplifier voltage gain as a transfer function of the complex frequency s. In this s-domain analysis a capacitance С is replaced

### LAB 12: ACTIVE FILTERS

A. INTRODUCTION LAB 12: ACTIVE FILTERS After last week s encounter with op- amps we will use them to build active filters. B. ABOUT FILTERS An electric filter is a frequency-selecting circuit designed

### SECTION 5-5: FREQUENCY TRANSFORMATIONS

ANALOG FILTERS FREQUENCY TRANSFORMATIONS SECTION 55: FREQUENCY TRANSFORMATIONS Until now, only filters using the lowpass configuration have been examined. In this section, transforming the lowpass prototype

### Positive Feedback and Oscillators

Physics 3330 Experiment #6 Fall 1999 Positive Feedback and Oscillators Purpose In this experiment we will study how spontaneous oscillations may be caused by positive feedback. You will construct an active

### 30. Bode Plots. Introduction

0. Bode Plots Introduction Each of the circuits in this problem set is represented by a magnitude Bode plot. The network function provides a connection between the Bode plot and the circuit. To solve these

### Chapter 12: The Operational Amplifier

Chapter 12: The Operational Amplifier 12.1: Introduction to Operational Amplifier (Op-Amp) Operational amplifiers (op-amps) are very high gain dc coupled amplifiers with differential inputs; they are used

### More Filter Design on a Budget

Application Report SLOA096 December 2001 More Filter Design on a Budget Bruce Carter High Performance Linear Products ABSTRACT This document describes filter design from the standpoint of cost. Filter

### How to Design 10 khz filter. (Using Butterworth filter design) Application notes. By Vadim Kim

How to Design 10 khz filter. (Using Butterworth filter design) Application notes. By Vadim Kim This application note describes how to build a 5 th order low pass, high pass Butterworth filter for 10 khz

### Laboratory #5: RF Filter Design

EEE 194 RF Laboratory Exercise 5 1 Laboratory #5: RF Filter Design I. OBJECTIVES A. Design a third order low-pass Chebyshev filter with a cutoff frequency of 330 MHz and 3 db ripple with equal terminations

### Analog Filters. A common instrumentation filter application is the attenuation of high frequencies to avoid frequency aliasing in the sampled data.

Analog Filters Filters can be used to attenuate unwanted signals such as interference or noise or to isolate desired signals from unwanted. They use the frequency response of a measuring system to alter

### Programmable-Gain Transimpedance Amplifiers Maximize Dynamic Range in Spectroscopy Systems

Programmable-Gain Transimpedance Amplifiers Maximize Dynamic Range in Spectroscopy Systems PHOTODIODE VOLTAGE SHORT-CIRCUIT PHOTODIODE SHORT- CIRCUIT VOLTAGE 0mV DARK ark By Luis Orozco Introduction Precision

### Analog and Digital Filters Anthony Garvert November 13, 2015

Analog and Digital Filters Anthony Garvert November 13, 2015 Abstract In circuit analysis and performance, a signal transmits some form of information, such as a voltage or current. However, over a range

### Lab #9: AC Steady State Analysis

Theory & Introduction Lab #9: AC Steady State Analysis Goals for Lab #9 The main goal for lab 9 is to make the students familar with AC steady state analysis, db scale and the NI ELVIS frequency analyzer.

### Lecture 24. Inductance and Switching Power Supplies (how your solar charger voltage converter works)

Lecture 24 Inductance and Switching Power Supplies (how your solar charger voltage converter works) Copyright 2014 by Mark Horowitz 1 Roadmap: How Does This Work? 2 Processor Board 3 More Detailed Roadmap

### RLC Resonant Circuits

C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document

### Design of op amp sine wave oscillators

Design of op amp sine wave oscillators By on Mancini Senior Application Specialist, Operational Amplifiers riteria for oscillation The canonical form of a feedback system is shown in Figure, and Equation

### Frequency response: Resonance, Bandwidth, Q factor

Frequency response: esonance, Bandwidth, Q factor esonance. Let s continue the exploration of the frequency response of circuits by investigating the series circuit shown on Figure. C + V - Figure The

### Analog signals are those which are naturally occurring. Any analog signal can be converted to a digital signal.

3.3 Analog to Digital Conversion (ADC) Analog signals are those which are naturally occurring. Any analog signal can be converted to a digital signal. 1 3.3 Analog to Digital Conversion (ADC) WCB/McGraw-Hill

### ES250: Electrical Science. HW7: Energy Storage Elements

ES250: Electrical Science HW7: Energy Storage Elements Introduction This chapter introduces two more circuit elements, the capacitor and the inductor whose elements laws involve integration or differentiation;

### Laboratory 4: Feedback and Compensation

Laboratory 4: Feedback and Compensation To be performed during Week 9 (Oct. 20-24) and Week 10 (Oct. 27-31) Due Week 11 (Nov. 3-7) 1 Pre-Lab This Pre-Lab should be completed before attending your regular

### Understanding Power Impedance Supply for Optimum Decoupling

Introduction Noise in power supplies is not only caused by the power supply itself, but also the load s interaction with the power supply (i.e. dynamic loads, switching, etc.). To lower load induced noise,

### Chapter 16. Active Filter Design Techniques. Excerpted from Op Amps for Everyone. Literature Number SLOA088. Literature Number: SLOD006A

hapter 16 Active Filter Design Techniques Literature Number SLOA088 Excerpted from Op Amps for Everyone Literature Number: SLOD006A hapter 16 Active Filter Design Techniques Thomas Kugelstadt 16.1 Introduction

### NAPIER University School of Engineering. Electronic Systems Module : SE32102 Analogue Filters Design And Simulation. 4 th order Butterworth response

NAPIER University School of Engineering Electronic Systems Module : SE32102 Analogue Filters Design And Simulation. 4 th order Butterworth response In R1 R2 C2 C1 + Opamp A - R1 R2 C2 C1 + Opamp B - Out

### 2.996/6.971 Biomedical Devices Design Laboratory Lecture 2: Fundamentals and PCB Layout

2.996/6.971 Biomedical Devices Design Laboratory Lecture 2: Fundamentals and PCB Layout Instructor: Hong Ma Sept. 12, 2007 Fundamental Elements Resistor (R) Capacitor (C) Inductor (L) Voltage Source Current

### Chapter 4: Passive Analog Signal Processing

hapter 4: Passive Analog Signal Processing In this chapter we introduce filters and signal transmission theory. Filters are essential components of most analog circuits and are used to remove unwanted

### Analog Signal Conditioning

Analog Signal Conditioning Analog and Digital Electronics Electronics Digital Electronics Analog Electronics 2 Analog Electronics Analog Electronics Operational Amplifiers Transistors TRIAC 741 LF351 TL084

### Using the Impedance Method

Using the Impedance Method The impedance method allows us to completely eliminate the differential equation approach for the determination of the response of circuits. In fact the impedance method even

### 11: AUDIO AMPLIFIER I. INTRODUCTION

11: AUDIO AMPLIFIER I. INTRODUCTION The properties of an amplifying circuit using an op-amp depend primarily on the characteristics of the feedback network rather than on those of the op-amp itself. A

### BJT Amplifier Circuits

JT Amplifier ircuits As we have developed different models for D signals (simple large-signal model) and A signals (small-signal model), analysis of JT circuits follows these steps: D biasing analysis:

### MAS.836 HOW TO BIAS AN OP-AMP

MAS.836 HOW TO BIAS AN OP-AMP Op-Amp Circuits: Bias, in an electronic circuit, describes the steady state operating characteristics with no signal being applied. In an op-amp circuit, the operating characteristic

### Electronics for Analog Signal Processing - II Prof. K. Radhakrishna Rao Department of Electrical Engineering Indian Institute of Technology Madras

Electronics for Analog Signal Processing - II Prof. K. Radhakrishna Rao Department of Electrical Engineering Indian Institute of Technology Madras Lecture - 18 Wideband (Video) Amplifiers In the last class,

### CIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis

CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis 3.1 Introduction The steady-state behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the

### Selected Filter Circuits Dr. Lynn Fuller

ROCHESTER INSTITUTE OF TECHNOLOGY MICROELECTRONIC ENGINEERING Selected Filter Circuits Dr. Lynn Fuller Webpage: http://people.rit.edu/lffeee 82 Lomb Memorial Drive Rochester, NY 146235604 Tel (585) 4752035

### Fig. 1 :Block diagram symbol of the operational amplifier. Characteristics ideal op-amp real op-amp

Experiment: General Description An operational amplifier (op-amp) is defined to be a high gain differential amplifier. When using the op-amp with other mainly passive elements, op-amp circuits with various

### Design of a TL431-Based Controller for a Flyback Converter

Design of a TL431-Based Controller for a Flyback Converter Dr. John Schönberger Plexim GmbH Technoparkstrasse 1 8005 Zürich 1 Introduction The TL431 is a reference voltage source that is commonly used

ECSE 4440 Control System Engineering Fall 2001 Project 3 Controller Design in Frequency Domain TA 1. Abstract 2. Introduction 3. Controller design in Frequency domain 4. Experiment 5. Colclusion 1. Abstract

### Designing Stable Compensation Networks for Single Phase Voltage Mode Buck Regulators

Designing Stable Compensation Networks for Single Phase Voltage Mode Buck Regulators Technical Brief December 3 TB47. Author: Doug Mattingly Assumptions This Technical Brief makes the following assumptions:.

### BJT Amplifier Circuits

JT Amplifier ircuits As we have developed different models for D signals (simple large-signal model) and A signals (small-signal model), analysis of JT circuits follows these steps: D biasing analysis:

### LM833,LMF100,MF10. Application Note 779 A Basic Introduction to Filters - Active, Passive,and. Switched Capacitor. Literature Number: SNOA224A

LM833,LMF100,MF10 Application Note 779 A Basic Introduction to Filters - Active, Passive,and Switched Capacitor Literature Number: SNOA224A A Basic Introduction to Filters Active, Passive, and Switched-Capacitor

### Bode Diagrams of Transfer Functions and Impedances ECEN 2260 Supplementary Notes R. W. Erickson

Bode Diagrams of Transfer Functions and Impedances ECEN 2260 Supplementary Notes. W. Erickson In the design of a signal processing network, control system, or other analog system, it is usually necessary

### University of Rochester Department of Electrical and Computer Engineering ECE113 Lab. #7 Higher-order filter & amplifier designs March, 2012

University of Rochester Department of Electrical and Computer Engineering ECE113 Lab. #7 Higherorder filter & amplifier designs March, 2012 Writeups, due one week after the lab is performed, should provide

### Lock - in Amplifier and Applications

Lock - in Amplifier and Applications What is a Lock in Amplifier? In a nut shell, what a lock-in amplifier does is measure the amplitude V o of a sinusoidal voltage, V in (t) = V o cos(ω o t) where ω o

### Since any real component also has loss due to the resistive component, the average power dissipated is 2 2R

Quality factor, Q Reactive components such as capacitors and inductors are often described with a figure of merit called Q. While it can be defined in many ways, it s most fundamental description is: Q

### A Single-Supply Op-Amp Circuit Collection

Application Report SLOA058 November 2000 A SingleSupply OpAmp Circuit Collection Bruce Carter OpAmp Applications, High Performance Linear Products One of the biggest problems for designers of opamp circuitry

### CHAPTER 8 ANALOG FILTERS

ANALOG FILTERS CHAPTER 8 ANALOG FILTERS SECTION 8.: INTRODUCTION 8. SECTION 8.2: THE TRANSFER FUNCTION 8.5 THE SPLANE 8.5 F O and Q 8.7 HIGHPASS FILTER 8.8 BANDPASS FILTER 8.9 BANDREJECT (NOTCH) FILTER

### Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor)

Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor) Concept: circuits Time: 30 m SW Interface: 750 Windows file: RLC.SWS EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage

### ε: Voltage output of Signal Generator (also called the Source voltage or Applied

Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and

### CTCSS REJECT HIGH PASS FILTERS IN FM RADIO COMMUNICATIONS AN EVALUATION. Virgil Leenerts WØINK 8 June 2008

CTCSS REJECT HIGH PASS FILTERS IN FM RADIO COMMUNICATIONS AN EVALUATION Virgil Leenerts WØINK 8 June 28 The response of the audio voice band high pass filter is evaluated in conjunction with the rejection

### Homework Assignment 03

Question 1 (2 points each unless noted otherwise) Homework Assignment 03 1. A 9-V dc power supply generates 10 W in a resistor. What peak-to-peak amplitude should an ac source have to generate the same

### APPLICATION BULLETIN

APPLICATION BULLETIN Mailing Address: PO Box 11400, Tucson, AZ 85734 Street Address: 6730 S. Tucson Blvd., Tucson, AZ 85706 Tel: (520) 746-1111 Telex: 066-6491 FAX (520) 889-1510 Product Info: (800) 548-6132

### TDA2040. 20W Hi-Fi AUDIO POWER AMPLIFIER

20W Hi-Fi AUDIO POWER AMPLIFIER DESCRIPTION The TDA2040 is a monolithic integrated circuit in Pentawatt package, intended for use as an audio class AB amplifier. Typically it provides 22W output power

### Digital Signal Processing IIR Filter Design via Impulse Invariance

Digital Signal Processing IIR Filter Design via Impulse Invariance D. Richard Brown III D. Richard Brown III 1 / 11 Basic Procedure We assume here that we ve already decided to use an IIR filter. The basic

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT 4 Understand single-phase alternating current (ac) theory Single phase AC

### Chapter 10. RC Circuits ISU EE. C.Y. Lee

Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine

### Op-Amp Simulation EE/CS 5720/6720. Read Chapter 5 in Johns & Martin before you begin this assignment.

Op-Amp Simulation EE/CS 5720/6720 Read Chapter 5 in Johns & Martin before you begin this assignment. This assignment will take you through the simulation and basic characterization of a simple operational

### The D.C Power Supply

The D.C Power Supply Voltage Step Down Electrical Isolation Converts Bipolar signal to Unipolar Half or Full wave Smoothes the voltage variation Still has some ripples Reduce ripples Stabilize the output

### UNIVERSITY OF CALIFORNIA AT BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences. EE105 Lab Experiments

UNIVERSITY OF CALIFORNIA AT BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences EE15 Lab Experiments Bode Plot Tutorial Contents 1 Introduction 1 2 Bode Plots Basics

### AN48. Application Note DESIGNNOTESFORA2-POLEFILTERWITH DIFFERENTIAL INPUT. by Steven Green. 1. Introduction AIN- AIN+ C2

Application Note DESIGNNOTESFORA2-POLEFILTERWITH DIFFERENTIAL INPUT by Steven Green C5 AIN- R3 C2 AIN C2 R3 C5 Figure 1. 2-Pole Low-Pass Filter with Differential Input 1. Introduction Many of today s Digital-to-Analog

### School of Engineering Department of Electrical and Computer Engineering

1 School of Engineering Department of Electrical and Computer Engineering 332:223 Principles of Electrical Engineering I Laboratory Experiment #4 Title: Operational Amplifiers 1 Introduction Objectives

### LR Phono Preamps. Pete Millett ETF.13. pmillett@hotmail.com

LR Phono Preamps Pete Millett ETF.13 pmillett@hotmail.com Agenda A bit about me Part 1: What is, and why use, RIAA? Grooves on records The RIAA standard Implementations of RIAA EQ networks and preamps

### Series and Parallel Resistive Circuits

Series and Parallel Resistive Circuits The configuration of circuit elements clearly affects the behaviour of a circuit. Resistors connected in series or in parallel are very common in a circuit and act

### Impedance 50 (75 connectors via adapters)

VECTOR NETWORK ANALYZER PLANAR TR1300/1 DATA SHEET Frequency range: 300 khz to 1.3 GHz Measured parameters: S11, S21 Dynamic range of transmission measurement magnitude: 130 db Measurement time per point:

### Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49

Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large

### Using the Texas Instruments Filter Design Database

Application Report SLOA062 July, 2001 Bruce Carter Using the Texas Instruments Filter Design Database High Performance Linear Products ABSTRACT Texas Instruments applications personnel have decades of

### Basic Op Amp Circuits

Basic Op Amp ircuits Manuel Toledo INEL 5205 Instrumentation August 3, 2008 Introduction The operational amplifier (op amp or OA for short) is perhaps the most important building block for the design of

### Technical Note #3. Error Amplifier Design and Applications. Introduction

Technical Note #3 Error Amplifier Design and Applications Introduction All regulating power supplies require some sort of closed-loop control to force the output to match the desired value. Both digital

### Lecture 7 Circuit analysis via Laplace transform

S. Boyd EE12 Lecture 7 Circuit analysis via Laplace transform analysis of general LRC circuits impedance and admittance descriptions natural and forced response circuit analysis with impedances natural

### Mutual Inductance and Transformers F3 3. r L = ω o

utual Inductance and Transformers F3 1 utual Inductance & Transformers If a current, i 1, flows in a coil or circuit then it produces a magnetic field. Some of the magnetic flux may link a second coil

### The front end of the receiver performs the frequency translation, channel selection and amplification of the signal.

Many receivers must be capable of handling a very wide range of signal powers at the input while still producing the correct output. This must be done in the presence of noise and interference which occasionally

### First, we show how to use known design specifications to determine filter order and 3dB cut-off

Butterworth Low-Pass Filters In this article, we describe the commonly-used, n th -order Butterworth low-pass filter. First, we show how to use known design specifications to determine filter order and

### Digital Systems Ribbon Cables I CMPE 650. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip.

Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip. Each dielectric configuration has different high-frequency characteristics. All configurations

### LM118/LM218/LM318 Operational Amplifiers

LM118/LM218/LM318 Operational Amplifiers General Description The LM118 series are precision high speed operational amplifiers designed for applications requiring wide bandwidth and high slew rate. They

### CHAPTER 6 Frequency Response, Bode Plots, and Resonance

ELECTRICAL CHAPTER 6 Frequency Response, Bode Plots, and Resonance 1. State the fundamental concepts of Fourier analysis. 2. Determine the output of a filter for a given input consisting of sinusoidal

### Ver 3537 E1.1 Analysis of Circuits (2014) E1.1 Circuit Analysis. Problem Sheet 1 (Lectures 1 & 2)

Ver 3537 E. Analysis of Circuits () Key: [A]= easy... [E]=hard E. Circuit Analysis Problem Sheet (Lectures & ). [A] One of the following circuits is a series circuit and the other is a parallel circuit.

### How To Calculate The Power Gain Of An Opamp

A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 8 p. 1/23 EE 42/100 Lecture 8: Op-Amps ELECTRONICS Rev C 2/8/2012 (9:54 AM) Prof. Ali M. Niknejad University of California, Berkeley

### Reading: HH Sections 4.11 4.13, 4.19 4.20 (pgs. 189-212, 222 224)

6 OP AMPS II 6 Op Amps II In the previous lab, you explored several applications of op amps. In this exercise, you will look at some of their limitations. You will also examine the op amp integrator and

### SUMMARY. Additional Digital/Software filters are included in Chart and filter the data after it has been sampled and recorded by the PowerLab.

This technique note was compiled by ADInstruments Pty Ltd. It includes figures and tables from S.S. Young (2001): Computerized data acquisition and analysis for the life sciences. For further information

### Digital to Analog Converter. Raghu Tumati

Digital to Analog Converter Raghu Tumati May 11, 2006 Contents 1) Introduction............................... 3 2) DAC types................................... 4 3) DAC Presented.............................

### www.jameco.com 1-800-831-4242

Distributed by: www.jameco.com 1-800-831-4242 The content and copyrights of the attached material are the property of its owner. LF411 Low Offset, Low Drift JFET Input Operational Amplifier General Description

### Op amp DC error characteristics and the effect on high-precision applications

Op amp DC error characteristics and the effect on high-precision applications Srudeep Patil, Member of Technical Staff, Maxim Integrated - January 01, 2014 This article discusses the DC limitations of

### Design Considerations for an LLC Resonant Converter

Design Considerations for an LLC Resonant Converter Hangseok Choi Power Conversion Team www.fairchildsemi.com 1. Introduction Growing demand for higher power density and low profile in power converter

### BJT AC Analysis. by Kenneth A. Kuhn Oct. 20, 2001, rev Aug. 31, 2008

by Kenneth A. Kuhn Oct. 20, 2001, rev Aug. 31, 2008 Introduction This note will discuss AC analysis using the beta, re transistor model shown in Figure 1 for the three types of amplifiers: common-emitter,

### SIMULATIONS OF PARALLEL RESONANT CIRCUIT POWER ELECTRONICS COLORADO STATE UNIVERSITY

SIMULATIONS OF PARALLEL RESONANT CIRCUIT POWER ELECTRONICS COLORADO STATE UNIVERSITY Page 1 of 25 PURPOSE: The purpose of this lab is to simulate the LCC circuit using MATLAB and ORCAD Capture CIS to better

### Frequency response. Chapter 1. 1.1 Introduction

Chapter Frequency response. Introduction The frequency response of a system is a frequency dependent function which expresses how a sinusoidal signal of a given frequency on the system input is transferred

### Electronic filters design tutorial -2

In the first part of this tutorial we explored the bandpass filters designed with lumped elements, namely inductors and capacitors. In this second part we will design filters with distributed components

### Lecture 23: Common Emitter Amplifier Frequency Response. Miller s Theorem.

Whites, EE 320 ecture 23 Page 1 of 17 ecture 23: Common Emitter mplifier Frequency Response. Miller s Theorem. We ll use the high frequency model for the BJT we developed the previous lecture and compute

### AN1991. Audio decibel level detector with meter driver

Rev. 2.1 20 March 2015 Application note Document information Info Keywords Abstract Content SA604A, LM358, RSSI, cellular radio The SA604A can provide a logarithmic response proportional to the input signal

### Impedance Matching and Matching Networks. Valentin Todorow, December, 2009

Impedance Matching and Matching Networks Valentin Todorow, December, 2009 RF for Plasma Processing - Definition of RF What is RF? The IEEE Standard Dictionary of Electrical and Electronics Terms defines

### Making Accurate Voltage Noise and Current Noise Measurements on Operational Amplifiers Down to 0.1Hz

Author: Don LaFontaine Making Accurate Voltage Noise and Current Noise Measurements on Operational Amplifiers Down to 0.1Hz Abstract Making accurate voltage and current noise measurements on op amps in

### PHYSICS 360 - LAB #2 Passive Low-pass and High-pass Filter Circuits and Integrator and Differentiator Circuits

PHYSICS 360 - LAB #2 Passie Low-pass and High-pass Filter Circuits and Integrator and Differentiator Circuits Objectie: Study the behaior of low-pass and high-pass filters. Study the differentiator and

### A Basic Introduction to Filters Active Passive and Switched-Capacitor

A Basic Introduction to Filters Active Passive and Switched-Capacitor 1 0 INTRODUCTION Filters of some sort are essential to the operation of most electronic circuits It is therefore in the interest of

### OPERATIONAL AMPLIFIERS. o/p

OPERATIONAL AMPLIFIERS 1. If the input to the circuit of figure is a sine wave the output will be i/p o/p a. A half wave rectified sine wave b. A fullwave rectified sine wave c. A triangular wave d. A

### LM 358 Op Amp. If you have small signals and need a more useful reading we could amplify it using the op amp, this is commonly used in sensors.

LM 358 Op Amp S k i l l L e v e l : I n t e r m e d i a t e OVERVIEW The LM 358 is a duel single supply operational amplifier. As it is a single supply it eliminates the need for a duel power supply, thus

### AVX EMI SOLUTIONS Ron Demcko, Fellow of AVX Corporation Chris Mello, Principal Engineer, AVX Corporation Brian Ward, Business Manager, AVX Corporation

AVX EMI SOLUTIONS Ron Demcko, Fellow of AVX Corporation Chris Mello, Principal Engineer, AVX Corporation Brian Ward, Business Manager, AVX Corporation Abstract EMC compatibility is becoming a key design

### Switch Mode Power Supply Topologies

Switch Mode Power Supply Topologies The Buck Converter 2008 Microchip Technology Incorporated. All Rights Reserved. WebSeminar Title Slide 1 Welcome to this Web seminar on Switch Mode Power Supply Topologies.