DOCSLIB.ORG

Chapter 15: Active Filter Circuits

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chapter 15: Active Filter Circuits CHAPTER 15: ACTIVE FILTER CIRCUITS 1 Contents 15.1 First-Order Low-Pass and High-Pass Filters 15.2 Scaling 15.3 Op Amp Bandpass and Bandreject Filters 15.4 High Order Op Amp Filters 15.5 Narrowband Bandpass and Bandreject Filters Electronic Circuits, Tenth Edition J ames W. Nilsson | Susan A. Riedel 2 15.1 1st-Order Low-Pass and High-Pass Filters • Active filters consist of op amps, resistors, and capacitors. • They overcome many of the disadvantages associated with passive filters. A first-order low-pass filter. A first-order low-pass filter. A general op amp circuit. • At very low frequencies, the capacitor acts like an open circuit, and the op amp circuit acts like an amplifier with a gain. • At very high frequencies, the capacitor acts like a short circuit, thereby connecting the output of the op amp circuit to ground. Electronic Circuits, Tenth Edition J ames W. Nilsson | Susan A. Riedel 3 15.1 1st-Order Low-Pass and High-Pass Filters Transfer function for the circuit 1 ‖ Where and = The gain in the passband, K, is set by the ratio R2/R1. The op amp low-pass filter thus permits the passband gain and the cutoff frequency to be specified independently. Electronic Circuits, Tenth Edition J ames W. Nilsson | Susan A. Riedel 4 15.1 1st-Order Low-Pass and High-Pass Filters • Bode plot (1) uses a logarithmic axis, instead of using a linear axis for the frequency values (2) plotted in decibels (dB), instead of plo tting the absolute magnitude of the tra nsfer function vs. frequency 2010 1 20 3 2 15.1 1st-Order Low-Pass and High-Pass Filters • A prototype low-pass filter : component values of 1 2 1Ω and 1, : a unity passband gain and a cutoff frequency of 1 /. : Providing a useful starting point for the design of filters by using more realistic component values to achieve a desired frequency response Electronic Circuits, Tenth Edition J 6 ames W. Nilsson | Susan A. Riedel 15.1 1st-Order Low-Pass and High-Pass Filters A first-order high-pass filter. Transfer function Equation for passive high-pass filters. 1 ‐K Where , and = 15.2 Scaling Scaling : transforming the convenient values into realistic values 1. Magnitude scaling altering component values without changing the frequency response of a circuit. •For a magnitude scale factor of , Let primed variables represent the scaled values of the variables , , / 2. Frequency scaling shifting the frequency response of a circuit to another frequency region without changing the overall shape of the frequency response. • For a frequency scale factor of kf , , /, / Electronic Circuits, Tenth Edition J 8 ames W. Nilsson | Susan A. Riedel 15.2 Scaling • Components can be scaled in both magnitude and frequency, with the scaled (primed) component values given by , , • The design of active low-pass and high-pass filters 1. an a prototype filter circuit. : component values of 1 2 1Ω and 1, : a unity passband gain and a cutoff frequency of 1 /. 2. Scaling can then be applied to shift the frequency response to the desired cutoff frequency, using component values that are commercially available. Electronic Circuits, Tenth Edition J 9 ames W. Nilsson | Susan A. Riedel 15.2 Scaling The Use of Scaling in the Design of Op Amp Filters 1. Selecting the cutoff frequency , to be 1 rad/s (if you are designing low- or highpass filters), or selecting the center frequency 0, to be 1 rad/s (if you are designing bandpass or bandreject filters). 2. Selecting a 1 capacitor and calculating the values of the resistors needed to give the desired passband gain and the 1 rad/s cutoff or center frequency. 3. Using scaling to compute more realistic component values that give the desired cutoff or center frequency. 15.3 Op Amp Bandpass and Bandreject Filters Bandpass filters Three separate components consisting of the bandpass filter 1. A unity-gain low-pass filter whose cutoff frequ ency is 2, the larger of the two cutoff freque ncies 2. A unity-gain high-pass filter whose cutoff fr equency is ωc1. the smaller of the two cuto ff frequencies 3. A gain component to provide the desired l evel of gain in the passband These three components are cascaded in series (combine multiplicatively in the s domain) The formal definition of a broadband filter Constructing the Bode magni tude plot of a bandpass filter. 2 Electronic Circuits, Tenth Edition J 11 ames W. Nilsson | Susan A. Riedel 15.3 Op Amp Bandpass and Bandreject Filters A cascaded op amp bandpass filter. (a) The block diagram. (b) The circuit. *Establishing the relationship between and that will permit each 1 2 subcircuit to be designed independently, without concern for the other subcircuits in the cascade. Electronic Circuits, Tenth Edition J 12 ames W. Nilsson | Susan A. Riedel 15.3 Op Amp Bandpass and Bandreject Filters • The transfer function of the cascaded bandpass filter is the product of the transfer functions of the three cascaded components: • Standard form for the transfer function of a bandpass filter 2 15.3 Op Amp Bandpass and Bandreject Filters Converting into the form of the standard transfer function for a bandpass filter, Assumption ≫ Transfer function for the cascaded bandpass filter Upper cutoff frequency, ωc2 1 lower cutoff frequency, ωc1 1 15.3 Op Amp Bandpass and Bandreject Filters Computing the values of Ri and Rf in the inverting amplifier to provide the desired passband gain. the magnitude of the bandpass filter’s transfer function, evaluated at the center frequency, ω0 K. Gain of the inverting amplifier is Rf / Ri 15.3 Op Amp Bandpass and Bandreject Filters Bandreject filters Bandreject filter configuration 1. A unity-gain low-pass filter whose cutoff frequency is 1, the smaller of the two cutoff frequencies 2. A unity-gain high-pass filter whose cutoff frequency is 2. the larger of the two cutoff frequencies 3. A gain component to provide the desired level of gain in the passband : these three components cannot be cascaded in series (we use a parallel connection and a summing amplifier) Constructing the Bode magnitude plot of a bandreject filter. Electronic Circuits, Tenth Edition J 16 ames W. Nilsson | Susan A. Riedel 15.3 Op Amp Bandpass and Bandreject Filters The transfer function of the resulting circuit : the sum of the low-pass and high-pass filter transfer functions. = ( ) = ( ) A parallel op amp bandreject filter. (a) The block diagram. (b) The circuit. Electronic Circuits, Tenth Edition J 17 ames W. Nilsson | Susan A. Riedel 15.3 Op Amp Bandpass and Bandreject Filters 1 Cutoff frequencies 1 In the two passbands (as s 0 ands ), the gain of the transfer function is Rf / Ri Note the magnitude of the transfer function , at the center frequency 2 If ≫, then ≪2/(as / ≪1) the magnitude at the center frequency is much smaller than the passband magnitude. 15.4 Higher Order Op Amp Filters •An ideal filter has a discontinuity at the point of cutoff, which sharply divides the passband and the stopband. • Higher order active filters have multiple poles in their transfer functions, resulting in a sharper transition from the passband to the stopband and thus a more nearly ideal frequency response. The Bode magnitude plot of a cascade of identical prototype first-order filters. •With one filter, the transition generally occurs with an asymptotic slope of 20 (dB/ dec). •With two filters, a transition with an asymptotic slope of 20 + 20 = 40 dB/ dec. Electronic Circuits, Tenth Edition J 19 ames W. Nilsson | Susan A. Riedel 15.4 Higher Order Op Amp Filters • The transfer function for a cascade of n prototype low-pass filters—we just multiply the individual transfer functions: A cascade of identical unity-gain low-pass filters. (a) The block diagram. (b) The circuit. Electronic Circuits, Tenth Edition J 20 ames W. Nilsson | Susan A. Riedel 15.4 Higher Order Op Amp Filters ⋯ = *A cascade of n first-order filters produces an nth-order filter, having n poles in its transfer function and a final slope of 20n dB>dec in the transition band. • As the order of the low-pass filter is increased by adding prototype low- pass filters to the cascade, the cutoff frequency also changes. frequency scaling = , ⁄ = 2 1, 2 1. 15.4 Higher Order Op Amp Filters For example, Let’s compute the cutoff frequency of a fourth-order unity-gain low- pass filter constructed from a cascade of four prototype low-pass filters: 2 1 0.435⁄ . scaling by k f = ωc / 0.435 to place the cutoff frequency. Electronic Circuits, Tenth Edition J 22 ames W. Nilsson | Susan A. Riedel 15.4 Higher Order Op Amp Filters • A serious shortcoming of cascading identical low-pass filters The gain of the filter is not constant between zero and the cutoff frequency ωc. An ideal low-pass filter, the passband magnitude is 1 for all frequencies below the cutoff frequency. But, the magnitude is less than 1 (0 dB) for frequencies much less than the cutoff frequency. Magnitude of the transfer function for a unity-gain low-pass nth-order cascade As the denominator Magnitude = , becomes larger than 1, so the magnitude becomes smaller = than 1 ⁄ Electronic Circuits, Tenth Edition J 23 ames W. Nilsson | Susan A. Riedel 15.4 Higher Order Op Amp Filters • shortcoming: The gain of the filter is not constant between zero and the cutoff frequency. • Unity-gain Butterworth low-pass filter has a transfer function whose magnitude = ⁄ Properties 1. The cutoff frequency is ωc rad/s for all values of n. 2.
Load more

Recommended publications
  • Experiment 5 Resonant Circuits and Active Filters
    Introductory Electronics Laboratory Experiment 5 Resonant circuits and active filters Now we return to the realm of linear analog circuit design to consider the final op-amp circuit topic of the term: resonant circuits and active filters. Two-port networks in this category have transfer functions which are described by linear, second-order differential equations. First we investigate how a bit of positive feedback may be added to our repertory of linear op-amp circuit design techniques. We consider a negative impedance circuit which employs positive feedback in conjunction with negative feedback. This sort of circuit is found in a wide variety of linear op-amp applications including amplifiers, gyrators (inductance emulators), current sources, and, in particular, resonant circuits and sinusoidal oscillators. Next we switch topics to consider the archetypal resonant circuit: the LC resonator (inductor + capacitor). We use this circuit to define the resonant frequency and quality factor for a second-order system, and we investigate the frequency and transient responses of a high-Q, tuned circuit. We then introduce the general topic of second-order filters: resonant circuits with quality factors of around 1. We describe the behavior of second-order low-pass, high- pass, and band-pass filters. Finally, we implement such filters using linear op-amp circuits containing only RC combinations in their feedback networks, eliminating the need for costly and hard-to-find inductors. The filters’ circuitry will employ positive as well as negative feedback to accomplish this feat. We discuss some of the tradeoffs when selecting the Q to use in a second-order filter, and look at Bessel and Butterworth designs in particular.
    [Show full text]
  • 6 Ghz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection
    Wright State University CORE Scholar Browse all Theses and Dissertations Theses and Dissertations 2014 6 GHz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection Shuo Li Wright State University Follow this and additional works at: https://corescholar.libraries.wright.edu/etd_all Part of the Electrical and Computer Engineering Commons Repository Citation Li, Shuo, "6 GHz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection" (2014). Browse all Theses and Dissertations. 1386. https://corescholar.libraries.wright.edu/etd_all/1386 This Thesis is brought to you for free and open access by the Theses and Dissertations at CORE Scholar. It has been accepted for inclusion in Browse all Theses and Dissertations by an authorized administrator of CORE Scholar. For more information, please contact library-corescholar@wright.edu. 6 GHz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering By SHUO LI B.S., Dalian Jiaotong University, China, 2012 2014 WRIGHT STATE UNIVERSITY WRIGHT STATE UNIVERSITY GRADUATE SCHOOL July 1, 2013 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Shuo Li ENTITLED “6 GHz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection” BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Engineering ___________________________ Saiyu Ren, Ph.D. Thesis Director ___________________________ Brian D. Rigling, Ph.D. Chair, Department of Electrical Engineering Committee on Final Examination ___________________________ Saiyu Ren, Ph.D. ___________________________ Raymond Siferd, Ph.D.
    [Show full text]
  • Active Damping of Oscillations in LC-Filter for Line Connected, Current Controlled, PWM Voltage Source Converters HERNES Magnar
    Active damping of oscillations in LC-filter for line connected, current controlled, PWM voltage source converters HERNES Magnar Active damping of oscillations in LC-filter for line connected, current controlled, PWM voltage source converters Olve Mo, Magnar Hernes, Kjell Ljøkelsøy SINTEF ENERGY RESEARCH Sem Sælands vei 11 7465 Trondheim, Norway Phone: +47 73 59 72 00 Olve.Mo@sintef.no Magnar.Hernes@sintef.no Kjell.Ljokelsoy@sintef.no http://www.energy.sintef.no/ Keywords Converter control, Power Quality Abstract Presented is a method for active damping of oscillations between line reactance and filter capacitors in LC-filter for line connected current controlled pulse width modulated (PWM) voltage source converters. The idea is to include closed loop feedback control that controls the capacitor voltage oscillations to zero by adding damping components to the current references. The voltage oscillations are calculated from manipulated measured filter capacitor voltages (using phase locked loop (PLL), Park- and inverse Park-transformation, low pass filtering and summation). The advantage of such an approach is that the higher oscillation frequency components can be controlled independently of remaining converter control. It is only the higher frequency components that are controlled by this additional closed loop voltage control. Further, additional measurements and increased converter rating are not required. Simulations and measurements presented in this paper show that the method works as intended. If active damping is implemented, then the voltage quality at the point of converter connection is maintained also in cases were filter oscillations is to be expected when the LC-filter is introduced. Introduction The basis for the discussion is a current controlled, line connected, PWM voltage source converter as shown in Figure 1 (used for instance as active rectifier / inverter, STATCOM or active filter).
    [Show full text]
  • Analog Vs. Digital Filtering of Data
    ECE Senior Capstone Project 2020 Tech Notes Maximum Blue Green Analog vs. Digital Filtering of Data By Sabrina Miller, ECE ‘20 _____________________________________________________ Introduction peaks of the data. However, the surrounding data is My senior design project, Smartbell, requires data noisy. Noise is characterized by meaningless data collection from an accelerometer. The data is points – the only data that are useful are the peaks intended to eventually be classified into type of above a certain threshold, as those represent sharp movement and number of reps via a machine learning fluctuations in acceleration. In order to properly algorithm. In order for proper classification, much of count the number of deadlifts performed, the smaller the noisiness must be eliminated, otherwise it may be amplitude fluctuations must be minimized. hard for the machine learning algorithm to differentiate between movements and characterize Dealing with Noise: Filters number of reps. This report aims to explore the When dealing with noisy data, there are various ways difference between analog and digital filtering of of going about filtering that data. The two data, to establish their pros and cons, and to decide on overarching categories in which one can filter data the method that best suits Smartbell. are analog filtering and digital filtering. Analog filtering involves physical hardware that alters analog The Fundamentals of Raw Data signals before they are passed off to other components to be processed. Digital filtering What is Noise? involves passing analog data to a processor that then runs code to digitally filter the data. Digital Filtering Advantages The advantages to digital filtering are numerous.
    [Show full text]
  • Redacted for Privacy Leland C../Jensen
    AN ABSTRACT OF THE THESIS OF CHUN-PANG CHIU for the MASTER OF SCIENCE (Name) (Degree) Electrical and in Electronics Engineering presented on /2 G (Major) (Date) Title:ACTIVE NETWORK SYNTHESIS USING GYRATORS Abstract approved:Redacted for Privacy Leland C../Jensen The. paper is a study of(i) the realization of the gyrator, (ii) active filter synthesis using gyrator. Several realization methods of the gyrator are summararized. A practical gyrator composed of two operational amplifiers was built and tested.The experimental results are shown.Two RC-gyrator synthesis techniques are derived and discussed.One method is to replace the inductors in a conventional LC filter with gyrators and capacitors.The other method is the application of Calahan's opti- mum polynomial decomposition to the synthesis procedure.The sensitivity of the two synthesis techniques are compared and dis- cussed. A practical active filter was synthesized by the second method.The experimental results are shown. Active Network Synthesis Using Gyrators by Chung-Pang Chiu A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science June 1970 APPROVED: Redacted for Privacy X-4ociate Profess,,e-of Electrical and Electronics Engineering in charge of major Redacted for Privacy HO.d of Department of Electrical and Electronics Eigineering Redacted for Privacy Dead of trS.duate School Date thesis is presented Typed by Clover Redfern for Chung-Pang Chiu ACKNOWLEDGMENT The author wishes to thank Professor Leland C. Jensen who suggested the topics of this thesis and gave much assistance, instruction and encouragement during the course of this study.
    [Show full text]
  • "Handbook of Operational Amplifier Active RC Networks"
    Application Report SBOA093A – October 2001 Handbook Of Operational Amplifier Active RC Networks Bruce Carter and L.P. Huelsman ABSTRACT While in the process of reviewing Texas Instruments applications notes, including those from the recently acquired Burr-Brown – I uncovered a couple of treasures, this handbook on active RC networks and one on op amp applications. These old publications, from 1966 and 1963, respectively, are some of the finest works on op amp theory that I have ever seen. Nevertheless, they contain some material that is hopelessly outdated. This includes everything from the state of the art of amplifier technology, to the parts referenced in the document – even to the symbol used for the op amp itself: These numbers in the circles referred to pin numbers of old op amps, which were potted modules instead of integrated circuits. Many references to these numbers were made in the text, and these have been changed, of course. In revising this document, I chose to take a minimal approach to the material out of respect for the original author - L.P. Huelsman, leaving as much of the original material in tact as possible while making the document relevant to present day designers. I did clean up grammatical and spelling mistakes in the original. I even elected to leave the original RC stick figure illustrations, which have minimal technical content – but added to the readability of the document. 1 SBOA093A Contents CHAPTER 1..........................................................................................................................................
    [Show full text]
  • How to Compare Your Circuit Requirements to Active-Filter Approximations by Bonnie C
    Analog Applications Journal Industrial How to compare your circuit requirements to active-filter approximations By Bonnie C. Baker WEBENCH® Senior Applications Engineer Figure 1. Example of a low-pass Butterworth filter R1 V+ C2_S1 16 kΩ U3 R2_S1 15 nF V+ C2_S2 OPA342 ++ 14 kΩ U1 R2_S2 15 nF V+ + OPA342 5.17 k U2 + C1 + Ω V – R1_S1 + OPA342 OUT 10 nF C1_S1 + 11.7 kΩ – R1_S2 10 nF C1_S1 Vsignal V– 4.7 kΩ 10 nF – V– V– R4_S1 R3_S1 5.36 kΩ R4_S2 2.49 kΩ R3_S2 5.36 kΩ 2.49 kΩ Introduction Figure 2. Generic frequency response Numerous filter approximations, such as Butterworth, of a low-pass filter Bessel, and Chebyshev, are available in popular filter soft- ware applications; however, it can be time consuming to Transition select the right option for your system. So how do you Passband Region Region focus in on what type of filter you need in your circuit? This article defines the differences between Bessel, Butterworth, Chebyshev, Linear Phase, and traditional RP Gaussian low-pass filters. A typical Butterworth low-pass A filter is shown in Figure 1. 3 dB Generic low-pass filter frequency and time response Figure 2 illustrates the frequency response of a generic A low-pass filter. In this diagram, the x-axis shows the SB frequency in hertz (Hz) and the y-axis shows the circuit gain in volts/volts (V/V) or decibels (dB). Magnitude The low-pass filter has two frequency areas of operation: the passband region and the transition region. In the pass- band region, the input signal passes through with minimum modifications.
    [Show full text]
  • Active Filter Techniques for Reducing EMI Filter Capacitance
    Active Filter Techniques for Reducing EMI Filter Capacitance by Albert C. Chow B.S., Columbia University (1999) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements of the degree of BARKER Master of Science MASSACHUSETTS INSTI V at the OF TECHNOLOGY Massachusettes Institute of Technology JUL 3 1 2002 June 2002 LIBRAR IES © Massachusetts Institute of Technology. All Rights Reserved. Author Department of Electrical Engineering and Computer Science February 24, 2002 Certified by. 7 ,David J. Perreault Assistant Professor, Department of Electrical Engineering and Computer Science Thesis Supervisor 7< Accepted by Arthur Smith Chairman, Department Committee on Graduate Students Active Filter Techniques for Reducing EMI Filter Capacitance by Albert C. Chow Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements of the degree of Master of Science Abstract Switching power converters are widely used due to their excellent efficiency, but they inherently generate ripple. Passive low-pass LC filters have been traditionally employed to meet ripple and EMI specifications [1]. These passive filters can contribute considerably to the volume and weight of a power converter. In particular, capacitors can become relatively large in order to meet strict ripple specifications. This is detrimental to cost and reliability of these passive EMI filters. For these reasons, capacitors in EMI filters can pose a considerable design challenge. Active circuit techniques can substantially reduce passive EMI filter capacitor requirements. This thesis investigates using active circuitry to mitigate the challenges of designing with large capacitors on three fronts: reducing capacitance in EMI filters, reducing damping capacitance, and reducing capacitance cost.
    [Show full text]
  • OA-26 Designing Active High Speed Filters
    Application Report SNOA387C–September 1997–Revised May 2013 OA-26 Designing Active High Speed Filters ABSTRACT This application report provides a recipe to realize active filters using low cost, high speed operational amplifiers. Contents 1 Introduction .................................................................................................................. 2 2 Filter Types .................................................................................................................. 2 3 Introduction to the Second Order, Low Pass Sallen-Key Filter ....................................................... 3 4 Transform a Low Pass Filter into a High Pass Filter ................................................................... 5 5 Cascading Filter Sections .................................................................................................. 6 6 Component Value Sensitivities ............................................................................................ 7 7 Selecting an Op Amp for Use in an Active Filter ........................................................................ 7 8 Bandwidth .................................................................................................................... 7 9 Recommended Gain Range ............................................................................................... 7 10 Noise .......................................................................................................................... 8 11 Dynamic Range ............................................................................................................
    [Show full text]
  • Active Filter Circuits Active Filter Circuits
    ECE307-10 Active Filter Circuits Z. Aliyazicioglu Electrical and Computer Engineering Department Cal Poly Pomona Active Filter Circuits Introduction Filter circuits with RLC are passive filter circuit Use op amp to have active filter circuit Active filter can produce band-pass and band-reject filter without using inductor. Passive filter incapable of amplification. Max gain is 1 Active filter capable of amplification The cutoff frequency and band-pass magnitude of passive filter can change with additional load resistance This is not a case for active filters We look at few active filter with op amps. We look at that basic op amp filter circuits can be combined to active specific frequency response and to attain close to ideal filter response ECE 307-10 2 1 Active Filter= Circuits First-Order Low-pass Filters C Zf R2 R1 Zi - - Vi OUT Vo Vi OUT + + Vo + + −Zf 1 R2 Transfer function of the circuit Hs()= −R || − Z 2 sR C + 1 i Hs()==SC 2 RR −R ω 11 Hs()= 2 Hs()=− K c RsRC12(1)+ ()s + ωc Transfer function in jω The Gain Cutoff frequency 1 R2 1 Hj()ω =− K K = ω = ω R c RC (1+ j ) 1 2 ω ECE 307-10c 3 Active Filter Circuits Example • Find R2 and C values in the following active Low-pass filter for gain of 1 C and cutoff frequency of 1 rad/s. 1F R12 1 R1 From the gain R2 - K = = 1 RR21= =Ω1 1 R Vi OUT 1 + Vo + From the cutoff frequency 1 1 ωc = = 1 CF==1 RC2 R2 1 Hj()ω = ω (1+ j ) 1 ECE 307-10 4 2 Active Filter Circuits Example >> w=0.1:.1:10; >> h=20*log10(abs(1./(1+j*w))) ; >> semilogx(w,h) >> grid on >> xlabel('\omega(rad/s)') >> ylabel('|H(j\omega)|
    [Show full text]
  • Low-Current Design of Gaas Active Inductor for Active Filters Applications
    electronics Article Low-Current Design of GaAs Active Inductor for Active Filters Applications Leonardo Pantoli 1 , Vincenzo Stornelli 1,* , Giorgio Leuzzi 1, Hongjun Li 2 and Zhifu Hu 2 1 Department of Industrial and Information Engineering and Economics, University of L’Aquila, 67100 L’Aquila AQ, Italy; leonardo.pantoli@univaq.it (L.P.); giorgio.leuzzi@univaq.it (G.L.) 2 Hebei Semiconductor Research Institute, Shijiazhuang 050000, China; mmc-lhj@hbmmc.com (H.L.) * Correspondence: vincenzo.stornelli@univaq.it Received: 30 May 2020; Accepted: 23 July 2020; Published: 31 July 2020 Abstract: Active inductors are suitable for MMIC integration, especially for filters applications, and the definition of strategies for an efficient design of these circuits is becoming mandatory. In this work we present design considerations for the reduction of DC current in the case of an active filter design based on the use of active inductors and for high-power handling. As an example of applications, the approach is demonstrated on a two-cell, integrated active filter realized with p-HEMT technology. The filter design is based on high-Q active inductors, whose equivalent inductance and resistance can be tuned by means of varactors. The prototype was realized and tested. It operates between 1800 and 2100 MHz with a 3 dB bandwidth of 30 MHz and a rejection ratio of 30 dB at 30 MHz from the center frequency. This solution allows to obtain a P1 dB compression point of about 8 dBm and a dynamic − range of 75 dB considering a bias current of 15 mA per stage. Keywords: active filters; active inductor; MMIC; tunable filters 1.
    [Show full text]
  • A Study of Gyrator Circuits
    NPS ARCHIVE 1969 KULESZ, J. A STUDY OF GYRATOR CIRCUITS James John Kulesz DUDLEY KNOX LIBRARY NAVAL POSTGRADUATE SCHOOL MONTEREY. CA 93943-5101 United States Naval Postgraduate School THESIS A STUDY OF GYRATOR CIRCUITS by James John Kules2 , Jr. December 1969 Tkl& document kcu> been appiovzd ^o>i pubtic. *.&- Iza&e. and tale.; lt& dUVu.bwtion u> untmLte.d. I ioo 110 DUDLEY KNOX LIBRARY NAVAL POSTGRADUATE SCHOOL MONTEREY, CA 93943-5101 A Study of Gyrator Circuits by James John Kulesz, Jr. Lieutenant, United States Navy B.S., United States Naval Academy, 1961 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL December 1969 >S HOT ^7 V4JL6S-Z/T. ABSTRACT Since the introduction of the gyrator in 1948, numerous papers have been written concerning the implementation and application of these network devices. Gyrators have been realized utilizing vacuum tubes, transistors, and operational amplifiers to obtain their non- reciprocal property. It is the purpose of this thesis to consolidate the current findings. A section has been written on each of the active devices mentioned above. The individual sections consist of summaries of published gyrator realizations. The method used to obtain the gyrator properties, along with appropriate equations, is that of the original circuit designer. Some relations and equations have been modified to standard- ize notation, or to express them in a more convenient form. Where available, experimental test circuits have been included to support the synthesis method. LIBRARY NAVAL POSTGRADUATE SCHOOL "REV. CALIF. 93940 TABLE OF CONTENTS I.
    [Show full text]