LC Resonant Circuits Dr. Roger King June Introduction

Size: px
Start display at page:

Download "LC Resonant Circuits Dr. Roger King June Introduction"

Transcription

1 LC Resonant Circuits Dr. Roger King June 01 Introduction Second-order systems are important in a wide range of applications including transformerless impedance-matching networks, frequency-selective networks, and control system models. Second-order systems occur whenever two independent energy-storing elements are present. The study of first- and second-order networks is important because of their useful properties, and because they are frequently used as approximations to the main features of even more complex networks. Resonance is usually defined to occur when the imaginary part of the impedance or admittance of a network zeros at a specific resonant frequency, and is usually accompanied by a very large increase in voltage and/or current in some part of the network. Strongly resonant behavior will occur in a network composed of a low-loss inductor and a low-loss capacitor. It can also occur in a two-capacitor or two-inductor system, but only if a controlled source is also present. The purpose of this paper is the review of resonant behavior in a one-capacitor one-inductor system. The primary interest here is the resonance phenomenon, although some note is made of the overdamped condition where the resonance is no longer obvious, but the system behavior remains distinctly second order. Series vs. Parallel LC Resonance Fig. 1 displays two series-resonant LC circuits. Fig. 1(a) shows the classic textbook form of the circuit, including a series-connected inductor, capacitor, and a resistor representing the sum of all internal energy losses in the circuit elements along with any added damping. An independent voltage source is also included. The circuit response may be considered either the inductor current i or the capacitor voltage v. Fig. 1(b) is the same circuit, except that the voltage source and damping resistor are replaced with their Norton equivalent. The key feature of both circuits in Fig. 1 is that with their sources zeroed, the capacitor, inductor and damping resistor are all in series. Fig. displays two parallel-resonant LC circuits. Fig. (a) is the classic form of the circuit. Here the inductor, capacitor and damping resistance are all in parallel, along with an independent current source. Fig. (b) is a Thevenin equivalent to Fig. (a). The key feature of both circuits in Fig. is that with their sources zeroed, the capacitor, inductor and damping resistor are all in parallel. Again, the circuit response may be considered either the inductor current i or the capacitor voltage v. 1 of 14

2 Fig. 1 (a) Series-resonant LC network with voltage source. (b) Series-resonant LC network with current source. Fig. (a) Parallel-resonant LC network with current source. (b) Parallel-resonant LC network with voltage source. The series-resonant configuration arises naturally in a circuit having a voltage source in which the resistive losses in the inductor windings give the predominant damping effect. It is typically found that in LC resonant circuits the losses in the capacitor are much smaller than those in the inductor. The parallel-resonant configuration arises when the circuit has a current source and the predominant damping effect is the inductor core loss, which is modeled by an equivalent resistance in parallel with the inductor. An LC resonant circuit having some damping resistance in series with the inductor as well as additional damping resistance in parallel with the inductor will also be considered in a later section of this paper. This arrangement is neither series nor parallel resonant, but a reasonable approximate series- or parallel-equivalent may be made. of 14

3 Table 1 Parameters of an LC Resonant Network Symbol O Q Parameter Name (units) Resonant Frequency (radians/sec) Characteristic Resistance (ohms) Quality Factor (unit less) Damping Ratio (unit less) Damping Factor (radians/sec) o Z o Equation 1 LC L C Q 1 1 Q o Q o Q Zo R s Q Rp Z o Comments series res. parallel res. d Damped Resonant Frequency (radians/sec) d o 1 d o for a lightly damped network Characterization of a Resonant Network Any of the networks in Figs. 1 and can be described by listing the values of L, C and R S (or R P ), although this does not give immediate insight into how the network will behave. A more intuitive description is given by stating three equivalent parameters of the network: the resonant frequency, the characteristic resistance, and the quality factor ( O,, Q). Definitions of these three parameters are given in Table 1. As will be seen, O,, and Q give an immediate sense of what the natural response will be like, and how the network will interact with its independent source. The definitions of O and are the same for both the series- and parallel-resonant networks. The resonant frequency O is the radian frequency at which the circuit will ring if it has no energy dissipation and is excited by some initial stored energy. The characteristic resistance is the expected ratio of voltage amplitude to current amplitude in the ringing response. Resistors represent energy-dissipative elements which tend to damp the ringing of the network. There are three different measures of this same thing: quality factor (Q), damping factor ( ) and damping ratio ( ). As Table 1 indicates, these are mutually interrelated. However, the relationship of damping to the circuit element values is different for series- and parallel-resonant networks. The equations for the Q factor are given in Table 1; the expressions for damping factor and damping ratio are easily derived from these. It will also be seen that a damped network will ring at a frequency lower than O, given by the damped resonant frequency d. 3 of 14

4 Table. Three Different Damping Conditions Damping Type Undamped (lossless system) Underdamped Critically Damped Overdamped Quality Factor - Q Q Q > 0.5 Q = 0.5 Q < 0.5 Damping Ratio - Damping Factor - O O O The network equations for Figs. 1 and will be solved in the time-domain and the frequency-domain. The form of the solutions will change depending upon the amount of damping. The three cases to be distinguished are under-damping, critical-damping, and over-damping. Applications of the resonant LC network as a narrow-band filter or impedance transformer often prefer light or zero damping, in which case equations are usually written in terms of Q. In control system applications, the expected damping levels often range from just below to just above critical damping, and the expressions are written in terms of. Overdamping will be considered only briefly for the sake of completeness. The damping conditions for each of these three cases are described in Table. Time-Domain Equations for the Resonant Network For the series-resonant network of Fig. 1(a), write the loop equation in inductor current i. The substitution i = C dv/ may be used to get an equivalent equation in v. These equations are: d i Q d v Q di dv o i Z o dv s o v o v s (1) Note that the series-resonant definition for Q has been used. Fig. 1(b) is best analyzed by converting the Norton form of the independent source into its Thevenin equivalent. For the parallel-resonant network of Fig. (a), write the node equation in capacitor voltage v. The substitution v = -L di/ may be used to get an equivalent equation in i. These equations are: d i d v Q Q di dv o i o i s o v o Z o di s () Note the parallel-resonant definition for Q has been used. Fig. (b) is best analyzed by converting the Thevenin form of the independent source into its Norton equivalent. 4 of 14

5 It may be noted that (1) and () are essentially the same, except for their specific independent source terms. The method for solving (1) or () for any specific driving term and initial conditions is the following. With the driving term (right hand side of equation (1) or ()) set to zero, find the solution of the resulting homogeneous equation. This is the natural response. Then the particular solution to the specific driving term is found. This is known as the forced response. These two solutions are added together to form the general solution. The initial conditions for the network are applied to the general solution to determine the specific values of any unknown constants. The natural response is instructive: It shows what the resonant network will do by itself, given as a starting point the stored energy implied by the initial capacitor voltage and inductor current. These initial conditions are defined as follows: V o I o v(0) i(0) (3) The homogeneous equations in (1) and () are all the same, as shown below using the generic variable x. d x d x Q dx o x 0 or o dx o x 0 (4) The natural solution is given by: x t e ot [A 1 sin d t A cos d t] for 0 <1 x t A 3 e ot A 4 ( o t) e ot for =1 x t A 5 e 1 ot A 6 e 1 ot for >1 where d o 1 (5) The solutions in (5) separate into the three cases of underdamped, critically damped, and overdamped. The underdamped case ( < 1) is the interesting one. 5 of 14

6 For the series-resonant circuit of Fig. 1(a), and assuming initial conditions V O and I O, (5) is rewritten to give the natural behaviors of the capacitor voltage and inductor current. In each case, constant A is determined by applying the initial condition (I O or V O ). A 1 is determined by applying the initial rate-of-change of current or voltage. This can be calculated by finding the initial inductor voltage and initial capacitor current from the given initial conditions and the circuit in Fig. 1(a). The results are, for the underdamped case ( < 1): i t e ot v t e ot 1 1 V O I O 1 and I O V O 1 sin d t I O cos d t sin d t V O cos d t for 0 1 and damped series resonance (6) These results can be reasonably approximated in the case of light damping ( < 0.1 or Q>5): i t e ot V O I O sin o t I O cos o t and v t e ot [I O V O ] sin o t V O cos o t for 0.1 and damped series resonance (7) For the case of zero damping ( =0 or Q i t V O sin o t I O cos o t and v t I O sin o t V O cos o t for 0, undamped resonance (8) For the parallel-resonant circuit of Fig. (a) the result is similar to (6), but not identical. i t e ot v t e ot 1 1 V O I O 1 and I O V O 1 sin d t I O cos d t sin d t V O cos d t for 0 1 and damped parallel resonance (9) These results can be reasonably approximated in the case of light damping ( < 0.1 or Q>5): 6 of 14

7 i t e ot V O I O sin o t I O cos o t and v t e ot [I O V O ] sin o t V O cos o t for 0.1 and damped parallel resonance (10) For the case of zero damping ( =0 or Q the behaviors of the parallel-resonant and series-resonant circuits become the same. Both are given by (8). Careful comparison of (6)-(10) shows that both underdamped series- and parallel-resonance produce decaying sinusoidal oscillations in current and voltage if started with some stored energy. However, there are subtle differences in the two ringing behaviors. The less the damping (higher Q), the less these differences. If the two cases are both considered undamped altogether, the difference disappears entirely. This is explored further by PSpice simulation of three resonant circuits, each having an initial stored energy of 1 J, a natural resonant frequency of 1 rad/s, and an impedance of 1. See Fig. 3. One is series resonant with Q=5, another parallel resonant with Q=5, and the third has very little damping (Q=1000). The capacitor voltage and inductor current for each is plotted in Fig. 3, lower waveforms. The voltage/current waveforms for the series- and parallel-resonant circuits with Q=5 are seen to be close, but slightly different. Fig. 3. Three resonant circuits with initial energy of 1 J and resonant frequency of 1 rad/s. One is series resonant with Q=5, one is parallel resonant with Q=5, and the third has Q= of 14

8 The upper waveforms in Fig. 3 plot the energy stored in each circuit as it rings down. These suggest that the reason for the small differences in the voltage and current waveforms for the parallel- and series-resonant circuits with same Q factor is that the energy losses occur at different times in the ringing cycles, but that as one would expect for two circuits with the same Q, the total energy loss over a complete cycle is the same for both. The high-q circuit is provided as a reference, and has very little energy loss over the time span shown. Some references will note that Q may be defined as times peak energy stored in the circuit divided by energy dissipated over one cycle. This is true if the energy dissipated over one cycle is calculated based on the voltage/current levels remaining the same throughout the cycle. This statement is not true for Fig. 3 with Q = 5 because the voltage/current amplitudes are rapidly decaying. Series-Parallel Equivalents for High-Q Resonant Circuits Sometimes a resonant network includes both series and parallel damping, as illustrated in Fig. 4, left side. In this case, the network is strictly neither series- nor parallel-resonant. However, if the Q factor accounting for all of the damping is higher than about 5, two approximate equivalents are possible. These are shown in Fig. 4 center (series equivalent) and left side (parallel equivalent). The approximate equivalents are given as follows: R P R S R P Q R S Z O P R P (series equivalent) or R P R S Q S R P R S (parallel equivalent) where R S Q P Q S Q eff R P R S 1 1 Q 1 S Q P for Q eff 5 (11) Fig. 4. Resonant network with both series- and parallel-damping, along with an approximate series equivalent, and an approximate parallel equivalent. 8 of 14

9 Fig. 5. Parallel-resonant network, with two approximately equivalent options for placement of the damping (or load) resistance. Converting all of the damping resistances to either a series or a parallel equivalent is a useful approximation when analyzing a lossy inductor, which may show both ohmic losses in its windings (series damping resistance) and core loss related to its magnetic core material (parallel damping resistance). Fig. 5 shows additional options for placement of the damping resistance in a parallel-resonant network. These approximate equivalents are derived by comparing the impedances (or admittances) between the two nodes indicated. Given a high effective Q in each case, the following approximate equivalents may be found. R C1 1 R R for Q 5 C C 1 C L 1 L 1 L (1) The equivalents in Fig. 5 are particularly useful when the resonant network is used as a signal processing circuit. In this application, an input may be applied as a voltage or current source, and the damping resistance may actually represent a resistive load device. Fig. 5 suggests that splitting the capacitor or inductor into two series-connected parts and extracting the output in parallel with one of those two parts would be useful if the load resistance is too small to get a high Q when connected across the whole network. Other useful tapping schemes may be found for a series-resonant network. In using Fig. 5 and (1), the inductor is assumed to be split into two parts having zero mutual coupling. Resonant Networks as Filters Signal-processing filters may be described by their steady-state sinusoidal responses. For this purpose, refer to Fig. 1(a) and calculate its phasor impedance, or to Fig. (a) for its phasor admittance. These results are the following: 9 of 14

10 Z j R S j L 1 j C 1 Q j ( O O ) for series resonant network (impedance) Y j 1 R P j C 1 j L Y O 1 Q j ( O O ) for parallel resonant network (admittance) (13) Note that Y O is () -1. The input signal to a series-resonant circuit may be applied as a voltage source, with the output signal extracted as the voltage drop on R S, C, L, or the series combination of C and L. The damping resistance R S is the composite value which includes losses in the inductor and capacitor, as well as any inserted load resistance. The input signal to a parallel-resonant circuit may be applied as a current source, with the outputs extracted as similar choices of element currents. In addition, a load resistance may be inserted into either of these resonant circuits through the technique of tapping-down the capacitor or inductor. This leads to a wide variety of possibilities. A sample set will be illustrated, but many others are used in practice. Fig. 6 shows four filters derived from the series resonant network. In each of these, the single resistor represents the composite of the external load resistance and internal inductor losses, converted into their series equivalent values. Each of the filters in Fig. 6 has the same loop impedance, given by (13) for a series resonant network. Therefore, each of the four transfer functions can be derived by dividing the impedance of the element(s) across which the output voltage is extracted by the loop impedance. A Spice simulation was used to plot the transfer function magnitude for each of the four filters. These are shown in Fig. 7. For these Spice Fig. 6 Four filters derived from the series-resonant network. 10 of 14

11 Fig. 7 Frequency response for the four filters of Fig. 6, all with f O = 1 Hz, Q = 0.5, 5, and 50. Upper left: bandpass filter. Lower left: bandstop filter. Upper right: lowpass filter. Lower right: highpass filter. simulations, o = (1 Hz), Z o = 1, and Q values of 0.5, 5, and 50 were used. The transfer functions plotted in Fig. 7 are V o /V s in db notation. The frequency response plots for the lowpass and highpass filters suggest that Q values ranging from critical damping to slight underdamping (Q = 0.5 to 1) should be chosen for these types. It can be noted that the peaking in these frequency responses is 0 log(q) above the passband value for values of Q exceeding 5 or so. This is generally undesirable for most applications. There are a number of practical cases where the lowpass filter appears on a dc power bus, either deliberately or created through the interaction of wiring inductance with bus bypass capacitors. In these cases, there is often insufficient damping (excessive Q) of the filter, and it becomes a design problem to add damping by some means to lower the Q to a reasonable value. The bandpass and bandstop filters are intended to act upon a narrow range around the center frequency o. In this type of filter, a high Q is generally desired. It may be seen that the wih of the band of frequencies passed by the bandpass filter, or rejected by the bandstop filter, is inversely proportional to the filter s Q. If this bandwih is defined as the range of frequency for which the bandpass filter transfer function is above -3 db, or the bandstop filter is 11 of 14

12 below -3 db, it may be calculated as follows. First, 3 db was chosen somewhat arbitrarily because it is the equivalent of, or ( ) 1, a round number, but is an industry standard choice. The lower cutoff frequency 1, and upper cutoff frequency, are then calculated for the loop impedance (13): Z j Z o 1 Q j o 1 Q j ( o ) 1 o 1 1 4Q o 1 1 4Q BW 1 Q Q Q 1 or o Q o Q (14) The approximations given for and are valid for high Q. Bandpass and bandstop filters are used to select, or eliminate, a relatively narrow range of signal components centered on. In these filters, Q is selected in accordance with the desired bandwih. Resonant Networks as Impedance Transformers Resonant networks are often used as impedance transformers. In this application, an external load is attached to the resonant network, which presents a transformed equivalent input resistance to the signal source. This is useful when the signal has a narrow bandwih, and allows the resonant network to combine impedance transformation with filtering. Two possible L-networks are shown in Fig. 8. There are at least six others in which the two arms of the L may be composed of L and C, or two series-connected inductors or capacitors. In Fig. 8, the signal sources are shown as idealized voltage or current sources: If the source s internal impedance is significant, it also becomes part of the network. The two networks in Fig. 8 will contribute both resonant filtering and load resistance transformation. The analysis of Fig. 8, network A, may be done by writing an expression for its input impedance Z eq. See equation (15), first line. Network A is parallel-resonant, with the load resistance providing the damping. The approximation in (15) is introduced by assuming that Fig. 8 Two impedance-transforming L-networks. Network A: Real part of input impedance <. Network B: Real part of input impedance >. 1 of 14

13 Q is high. The second line of (15) shows that the approximate input impedance of the network is the same as that of a series-resonant network damped by the transformed load resistance. Note that operation in the vicinity of o is assumed. Z eq j L 1 j C j L j j L j 1 ( C) ( C) C Z eq j L 1 j C Z o for Q o C 5 near o the input resistance is R eq Z o Q for Network A C (15) The effective input resistance is seen to be a fraction of the load resistance. Equation (15) also shows that the transformation turns-ratio is equivalently 1:Q. For frequencies off-resonance, the input impedance also includes significant reactive components, indicated by the terms in brackets in (15), second line. A similar analysis of network B in Fig. 8 produces similar results. In this case, the load resistance provides series-resonant damping. The effective input admittance is found to be: Y eq j C 1 j L j C j L R L ( L) Y eq j C 1 j L Z o for Q L 5 near o the input resistance is R eq Z o Q for Network B j C j L ( L) (16) As before, the approximation in the first line of (16) is introduced by assuming that the Q is high. The effective input admittance, second line, is that of a parallel-connected LC network, together with a reflected input conductance. The resistance equivalent of the input conductance is given in line five of (16). Again, the network reflects the load resistance in a manner of a transformer with a turns ratio of Q:1. A straightforward design procedure can be seen from (15) and (16). The resonant frequency of the network is its operating frequency, with a narrow working bandwih. The characteristic resistance ( ) needs to be set equal to the geometric mean of the intended load and reflected equivalent resistances ( Z o R eq ). However, the Q factor is constrained by the ratio of the load and reflected resistances. Q cannot be independently chosen to achieve bandwih objectives, or to ensure a realizable system. Although the L-network is widely used, it is too inflexible to achieve many required results. It should be noticed that the L-network matching criteria can be used to find the series- and parallel-resonant equivalents to networks with several damping resistances, given in (11) and Fig of 14

14 Fig. 9 Pi-type resonant matching network, along with two approximately equivalent load resistor placements. Finally, the pi-network will be considered. There are numerous 3-element pi- and tee-networks that can be used to get a more flexible resonant matching network, but one example of the pi-network will be sufficient. Fig. 9 (left side) shows a resonant pi-network for load resistance matching, along with two approximately equivalent load resistor placements. The network shown is assumed to be lightly damped (Q>5), and resonance is expected at the frequency corresponding to L and the series equivalent of C 1 and C. It can be seen that the load is tapped down the series combination of C 1 and C, so the equivalents shown in Fig. 5 may be used to generate the two alternate placements of equivalent damping resistance (middle of Fig. 9) and (right of Fig. 9). Using (1), the equivalent damping resistance values are: C R 1 C L C 1 and C R C L C 1 C RL C 1 (17) The equivalent input admittance of Fig. 9, left side, is then calculated using (17). Y eq 1 C 1 C j C1 j C LC 1 (18) C R L C 1 It can be seen from (18) that the reflected value of the load resistance is. The second term in (18) represents the equivalent susceptance. This term nulls at the resonant frequency determined by L and the series equivalent of C 1 and C. Design of the pi-network is flexible because the resonant frequency is determined by the signal frequency, and the C 1 -C ratio is determined by the desired reflected value of the load resistance, but the characteristic resistance of the resonant network is left undetermined. This may be set to achieve a bandwih objective. When bandwih is not critical, it is common to set Q to the range of 5-10 to keep the losses in the inductor manageable. 14 of 14

CHAPTER 9. Sinusoidal Steady-State Analysis

CHAPTER 9. Sinusoidal Steady-State Analysis CHAPTER 9 Sinusoidal Steady-State Analysis 9.1 The Sinusoidal Source A sinusoidal voltage source (independent or dependent) produces a voltage that varies sinusoidally with time. A sinusoidal current source

More information

EXPERIMENT 8: LRC CIRCUITS

EXPERIMENT 8: LRC CIRCUITS EXPERIMENT 8: LRC CIRCUITS Equipment List S 1 BK Precision 4011 or 4011A 5 MHz Function Generator OS BK 2120B Dual Channel Oscilloscope V 1 BK 388B Multimeter L 1 Leeds & Northrup #1532 100 mh Inductor

More information

UNIT 1 CIRCUIT ANALYSIS 1 What is a graph of a network? When all the elements in a network is replaced by lines with circles or dots at both ends.

UNIT 1 CIRCUIT ANALYSIS 1 What is a graph of a network? When all the elements in a network is replaced by lines with circles or dots at both ends. UNIT 1 CIRCUIT ANALYSIS 1 What is a graph of a network? When all the elements in a network is replaced by lines with circles or dots at both ends. 2 What is tree of a network? It is an interconnected open

More information

Study of Inductive and Capacitive Reactance and RLC Resonance

Study of Inductive and Capacitive Reactance and RLC Resonance Objective Study of Inductive and Capacitive Reactance and RLC Resonance To understand how the reactance of inductors and capacitors change with frequency, and how the two can cancel each other to leave

More information

10. Introduction and Chapter Objectives

10. Introduction and Chapter Objectives Real Analog - Circuits Chapter 0: Steady-state Sinusoidal Analysis 0. Introduction and Chapter Objectives We will now study dynamic systems which are subjected to sinusoidal forcing functions. Previously,

More information

Resonance. Resonance curve.

Resonance. Resonance curve. Resonance This chapter will introduce the very important resonant (or tuned) circuit, which is fundamental to the operation of a wide variety of electrical and electronic systems in use today. The resonant

More information

EECS40 RLC Lab guide

EECS40 RLC Lab guide EECS40 RLC Lab guide Introduction Second-Order Circuits Second order circuits have both inductor and capacitor components, which produce one or more resonant frequencies, ω0. In general, a differential

More information

EE 42/100: Lecture 8. 1 st -Order RC Transient Example, Introduction to 2 nd -Order Transients. EE 42/100 Summer 2012, UC Berkeley T.

EE 42/100: Lecture 8. 1 st -Order RC Transient Example, Introduction to 2 nd -Order Transients. EE 42/100 Summer 2012, UC Berkeley T. EE 42/100: Lecture 8 1 st -Order RC Transient Example, Introduction to 2 nd -Order Transients Circuits with non-dc Sources Recall that the solution to our ODEs is Particular solution is constant for DC

More information

Physics 132 Quiz # 23

Physics 132 Quiz # 23 Name (please (please print) print) Physics 132 Quiz # 23 I. I. The The current in in an an ac ac circuit is is represented by by a phasor.the value of of the the current at at some time time t t is is

More information

AC Circuits. "Look for knowledge not in books but in things themselves." W. Gilbert ( )

AC Circuits. Look for knowledge not in books but in things themselves. W. Gilbert ( ) AC Circuits "Look for knowledge not in books but in things themselves." W. Gilbert (1540-1603) OBJECTIVES To study some circuit elements and a simple AC circuit. THEORY All useful circuits use varying

More information

PHYS225 Lecture 15. Electronic Circuits

PHYS225 Lecture 15. Electronic Circuits PHYS225 Lecture 15 Electronic Circuits Last lecture Difference amplifier Differential input; single output Good CMRR, accurate gain, moderate input impedance Instrumentation amplifier Differential input;

More information

UNIVERSITY OF BABYLON BASIC OF ELECTRICAL ENGINEERING LECTURE NOTES. Resonance

UNIVERSITY OF BABYLON BASIC OF ELECTRICAL ENGINEERING LECTURE NOTES. Resonance Resonance The resonant(or tuned) circuit, in one of its many forms, allows us to select a desired radio or television signal from the vast number of signals that are around us at any time. Resonant electronic

More information

FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY

FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY In this experiment we will analytically determine and measure the frequency response of networks containing resistors, AC source/sources, and energy storage

More information

EE233 Autumn 2016 Electrical Engineering University of Washington. EE233 HW7 Solution. Nov. 16 th. Due Date: Nov. 23 rd

EE233 Autumn 2016 Electrical Engineering University of Washington. EE233 HW7 Solution. Nov. 16 th. Due Date: Nov. 23 rd EE233 HW7 Solution Nov. 16 th Due Date: Nov. 23 rd 1. Use a 500nF capacitor to design a low pass passive filter with a cutoff frequency of 50 krad/s. (a) Specify the cutoff frequency in hertz. fc c 50000

More information

Experiment 1 LRC Transients

Experiment 1 LRC Transients Physics 263 Experiment 1 LRC Transients 1 Introduction In this experiment we will study the damped oscillations and other transient waveforms produced in a circuit containing an inductor, a capacitor,

More information

ELECTRIC CIRCUITS. Third Edition JOSEPH EDMINISTER MAHMOOD NAHVI

ELECTRIC CIRCUITS. Third Edition JOSEPH EDMINISTER MAHMOOD NAHVI ELECTRIC CIRCUITS Third Edition JOSEPH EDMINISTER MAHMOOD NAHVI Includes 364 solved problems --fully explained Complete coverage of the fundamental, core concepts of electric circuits All-new chapters

More information

Circuit Systems with MATLAB and PSpice

Circuit Systems with MATLAB and PSpice Circuit Systems with MATLAB and PSpice Won Y. Yang and Seung C. Lee Chung-Ang University, South Korea BICENTENNIAL 9 I CE NTE NNIAL John Wiley & Sons(Asia) Pte Ltd Contents Preface Limits of Liability

More information

#8A RLC Circuits: Free Oscillations

#8A RLC Circuits: Free Oscillations #8A RL ircuits: Free Oscillations Goals In this lab we investigate the properties of a series RL circuit. Such circuits are interesting, not only for there widespread application in electrical devices,

More information

Design of a Regenerative Receiver for the Short-Wave Bands A Tutorial and Design Guide for Experimental Work. Part I

Design of a Regenerative Receiver for the Short-Wave Bands A Tutorial and Design Guide for Experimental Work. Part I Design of a Regenerative Receiver for the Short-Wave Bands A Tutorial and Design Guide for Experimental Work Part I Ramón Vargas Patrón rvargas@inictel-uni.edu.pe INICTEL-UNI Regenerative Receivers remain

More information

INTRODUCTION TO FILTER CIRCUITS

INTRODUCTION TO FILTER CIRCUITS INTRODUCTION TO FILTER CIRCUITS 1 2 Background: Filters may be classified as either digital or analog. Digital filters are implemented using a digital computer or special purpose digital hardware. Analog

More information

Chapter 8. Natural and Step Responses of RLC Circuits

Chapter 8. Natural and Step Responses of RLC Circuits Chapter 8. Natural and Step Responses of RLC Circuits By: FARHAD FARADJI, Ph.D. Assistant Professor, Electrical Engineering, K.N. Toosi University of Technology http://wp.kntu.ac.ir/faradji/electriccircuits1.htm

More information

Experiment VI: The LRC Circuit and Resonance

Experiment VI: The LRC Circuit and Resonance Experiment VI: The ircuit and esonance I. eferences Halliday, esnick and Krane, Physics, Vol., 4th Ed., hapters 38,39 Purcell, Electricity and Magnetism, hapter 7,8 II. Equipment Digital Oscilloscope Digital

More information

Numerical Oscillations in EMTP-Like Programs

Numerical Oscillations in EMTP-Like Programs Session 19; Page 1/13 Spring 18 Numerical Oscillations in EMTP-Like Programs 1 Causes of Numerical Oscillations The Electromagnetic transients program and its variants all use the the trapezoidal rule

More information

Electronics and Instrumentation ENGR-4300 Spring 2004 Section Experiment 5 Introduction to AC Steady State

Electronics and Instrumentation ENGR-4300 Spring 2004 Section Experiment 5 Introduction to AC Steady State Experiment 5 Introduction to C Steady State Purpose: This experiment addresses combinations of resistors, capacitors and inductors driven by sinusoidal voltage sources. In addition to the usual simulation

More information

STUDY OF RC AND RL CIRCUITS Venue: Microelectronics Laboratory in E2 L2

STUDY OF RC AND RL CIRCUITS Venue: Microelectronics Laboratory in E2 L2 EXPERIMENT #1 STUDY OF RC AND RL CIRCUITS Venue: Microelectronics Laboratory in E2 L2 I. INTRODUCTION This laboratory is about verifying the transient behavior of RC and RL circuits. You need to revise

More information

ELEN 140 ELECTRICAL CIRCUITS II Winter 2013

ELEN 140 ELECTRICAL CIRCUITS II Winter 2013 ELEN 140 ELECTRICAL CIRCUITS II Winter 2013 Professor: Stephen O Loughlin Prerequisite: ELEN 130 Office: C234B Co-requisite: none Office Ph: (250) 762-5445 ext 4376 Lecture: 3.0 hrs/week Email: soloughlin@okanagan.bc.ca

More information

CHAPTER 14. Introduction to Frequency Selective Circuits

CHAPTER 14. Introduction to Frequency Selective Circuits CHAPTER 14 Introduction to Frequency Selective Circuits Frequency-selective circuits Varying source frequency on circuit voltages and currents. The result of this analysis is the frequency response of

More information

Figure 1: Closed Loop System

Figure 1: Closed Loop System SIGNAL GENERATORS 3. Introduction Signal sources have a variety of applications including checking stage gain, frequency response, and alignment in receivers and in a wide range of other electronics equipment.

More information

ET1210: Module 5 Inductance and Resonance

ET1210: Module 5 Inductance and Resonance Part 1 Inductors Theory: When current flows through a coil of wire, a magnetic field is created around the wire. This electromagnetic field accompanies any moving electric charge and is proportional to

More information

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK UNIT I BASIC CIRCUITS ANALYSIS PART A (2-MARKS)

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK UNIT I BASIC CIRCUITS ANALYSIS PART A (2-MARKS) KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK YEAR / SEM : I / II SUBJECT CODE & NAME : EE 1151 CIRCUIT THEORY UNIT I BASIC CIRCUITS ANALYSIS PART A (2-MARKS)

More information

Lecture 5: RC Filters. Series Resonance and Quality Factor. Matching. Soldering.

Lecture 5: RC Filters. Series Resonance and Quality Factor. Matching. Soldering. Whites, EE 322 Lecture 5 Page of 2 Lecture 5: C Filters. Series esonance and Quality Factor. Matching. Soldering. eview the following sections in your text:. Section 3. Complex Numbers. 2. Section 3.2

More information

University of Jordan School of Engineering Electrical Engineering Department. EE 219 Electrical Circuits Lab

University of Jordan School of Engineering Electrical Engineering Department. EE 219 Electrical Circuits Lab University of Jordan School of Engineering Electrical Engineering Department EE 219 Electrical Circuits Lab EXPERIMENT 7 RESONANCE Prepared by: Dr. Mohammed Hawa EXPERIMENT 7 RESONANCE OBJECTIVE This experiment

More information

Chapter 33. Alternating Current Circuits

Chapter 33. Alternating Current Circuits Chapter 33 Alternating Current Circuits Alternating Current Circuits Electrical appliances in the house use alternating current (AC) circuits. If an AC source applies an alternating voltage to a series

More information

Module 1. Introduction. Version 2 EE IIT, Kharagpur

Module 1. Introduction. Version 2 EE IIT, Kharagpur Module 1 Introduction Lesson 1 Introducing the Course on Basic Electrical Contents 1 Introducing the course (Lesson-1) 4 Introduction... 4 Module-1 Introduction... 4 Module-2 D.C. circuits.. 4 Module-3

More information

UEENEEG048B Solve problems in complex multi-path power circuits SAMPLE. Version 4. Training and Education Support Industry Skills Unit Meadowbank

UEENEEG048B Solve problems in complex multi-path power circuits SAMPLE. Version 4. Training and Education Support Industry Skills Unit Meadowbank UEE07 Electrotechnology Training Package UEENEEG048B Solve problems in complex multi-path power circuits Learner guide Version 4 Training and Education Support Industry Skills Unit Meadowbank Product Code:

More information

Exercise 9: inductor-resistor-capacitor (LRC) circuits

Exercise 9: inductor-resistor-capacitor (LRC) circuits Exercise 9: inductor-resistor-capacitor (LRC) circuits Purpose: to study the relationship of the phase and resonance on capacitor and inductor reactance in a circuit driven by an AC signal. Introduction

More information

Minimizing Input Filter Requirements In Military Power Supply Designs

Minimizing Input Filter Requirements In Military Power Supply Designs Keywords Venable, frequency response analyzer, MIL-STD-461, input filter design, open loop gain, voltage feedback loop, AC-DC, transfer function, feedback control loop, maximize attenuation output, impedance,

More information

Simple Oscillators. OBJECTIVES To observe some general properties of oscillatory systems. To demonstrate the use of an RLC circuit as a filter.

Simple Oscillators. OBJECTIVES To observe some general properties of oscillatory systems. To demonstrate the use of an RLC circuit as a filter. Simple Oscillators Some day the program director will attain the intelligent skill of the engineers who erected his towers and built the marvel he now so ineptly uses. Lee De Forest (1873-1961) OBJETIVES

More information

Experiment 9 AC Circuits

Experiment 9 AC Circuits Experiment 9 AC Circuits "Look for knowledge not in books but in things themselves." W. Gilbert (1540-1603) OBJECTIVES To study some circuit elements and a simple AC circuit. THEORY All useful circuits

More information

Question Paper Profile

Question Paper Profile I Scheme Question Paper Profile Program Name : Electrical Engineering Program Group Program Code : EE/EP/EU Semester : Third Course Title : Electrical Circuits Max. Marks : 70 Time: 3 Hrs. Instructions:

More information

RLC Frequency Response

RLC Frequency Response 1. Introduction RLC Frequency Response The student will analyze the frequency response of an RLC circuit excited by a sinusoid. Amplitude and phase shift of circuit components will be analyzed at different

More information

EE42: Running Checklist of Electronics Terms Dick White

EE42: Running Checklist of Electronics Terms Dick White EE42: Running Checklist of Electronics Terms 14.02.05 Dick White Terms are listed roughly in order of their introduction. Most definitions can be found in your text. Terms2 TERM Charge, current, voltage,

More information

Hours / 100 Marks Seat No.

Hours / 100 Marks Seat No. 17323 14115 3 Hours / 100 Seat No. Instructions (1) All Questions are Compulsory. (2) Illustrate your answers with neat sketches wherever necessary. (3) Figures to the right indicate full marks. (4) Assume

More information

AC : A CIRCUITS COURSE FOR MECHATRONICS ENGINEERING

AC : A CIRCUITS COURSE FOR MECHATRONICS ENGINEERING AC 2010-2256: A CIRCUITS COURSE FOR MECHATRONICS ENGINEERING L. Brent Jenkins, Southern Polytechnic State University American Society for Engineering Education, 2010 Page 15.14.1 A Circuits Course for

More information

Chapter 11. Alternating Current

Chapter 11. Alternating Current Unit-2 ECE131 BEEE Chapter 11 Alternating Current Objectives After completing this chapter, you will be able to: Describe how an AC voltage is produced with an AC generator (alternator) Define alternation,

More information

Microwave Circuits Design. Microwave Filters. high pass

Microwave Circuits Design. Microwave Filters. high pass Used to control the frequency response at a certain point in a microwave system by providing transmission at frequencies within the passband of the filter and attenuation in the stopband of the filter.

More information

An induced emf is the negative of a changing magnetic field. Similarly, a self-induced emf would be found by

An induced emf is the negative of a changing magnetic field. Similarly, a self-induced emf would be found by This is a study guide for Exam 4. You are expected to understand and be able to answer mathematical questions on the following topics. Chapter 32 Self-Induction and Induction While a battery creates an

More information

BAKISS HIYANA BT ABU BAKAR JKE,POLISAS

BAKISS HIYANA BT ABU BAKAR JKE,POLISAS BAKISS HIYANA BT ABU BAKAR JKE,POLISAS 1 1. Explain AC circuit concept and their analysis using AC circuit law. 2. Apply the knowledge of AC circuit in solving problem related to AC electrical circuit.

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chapter 7. Response of First-Order RL and RC Circuits By: FARHAD FARADJI, Ph.D. Assistant Professor, Electrical Engineering, K.N. Toosi University of Technology http://wp.kntu.ac.ir/faradji/electriccircuits1.htm

More information

Lab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters

Lab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters Lab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters Goal: In circuits with a time-varying voltage, the relationship between current and voltage is more complicated

More information

Filter Considerations for the IBC

Filter Considerations for the IBC APPLICATION NOTE AN:202 Filter Considerations for the IBC Mike DeGaetano Application Engineering Contents Page Introduction 1 IBC Attributes 1 Input Filtering Considerations 2 Damping and Converter Bandwidth

More information

Laboratory Project 4: Frequency Response and Filters

Laboratory Project 4: Frequency Response and Filters 2240 Laboratory Project 4: Frequency Response and Filters K. Durney and N. E. Cotter Electrical and Computer Engineering Department University of Utah Salt Lake City, UT 84112 Abstract-You will build a

More information

EE 340 Power Transformers

EE 340 Power Transformers EE 340 Power Transformers Preliminary considerations A transformer is a device that converts one AC voltage to another AC voltage at the same frequency. It consists of one or more coil(s) of wire wrapped

More information

Oscillations II: Damped and/or Driven Oscillations

Oscillations II: Damped and/or Driven Oscillations Oscillations II: Damped and/or Driven Oscillations Michael Fowler 3/4/9 Introducing Damping We ll assume the damping force is proportional to the velocity, and, of course, in the opposite direction. Then

More information

Chapter 19. Basic Filters

Chapter 19. Basic Filters Chapter 19 Basic Filters Objectives Analyze the operation of RC and RL lowpass filters Analyze the operation of RC and RL highpass filters Analyze the operation of band-pass filters Analyze the operation

More information

Today s topic: frequency response. Chapter 4

Today s topic: frequency response. Chapter 4 Today s topic: frequency response Chapter 4 1 Small-signal analysis applies when transistors can be adequately characterized by their operating points and small linear changes about the points. The use

More information

Analog Filters D R. T A R E K T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N

Analog Filters D R. T A R E K T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N Analog Filters D. T A E K T U T U N J I P H I L A D E L P H I A U N I V E S I T Y, J O D A N 2 0 4 Introduction Electrical filters are deigned to eliminate unwanted frequencies Filters can be classified

More information

Chapter 33. Alternating Current Circuits

Chapter 33. Alternating Current Circuits Chapter 33 Alternating Current Circuits C HAP T E O UTLI N E 33 1 AC Sources 33 2 esistors in an AC Circuit 33 3 Inductors in an AC Circuit 33 4 Capacitors in an AC Circuit 33 5 The L Series Circuit 33

More information

Lowpass and Bandpass Filters

Lowpass and Bandpass Filters Microstrip Filters for RF/Microwave Applications. Jia-Sheng Hong, M. J. Lancaster Copyright 2001 John Wiley & Sons, Inc. ISBNs: 0-471-38877-7 (Hardback); 0-471-22161-9 (Electronic) CHAPTER 5 Lowpass and

More information

QUESTION BANK ETE (17331) CM/IF. Chapter1: DC Circuits

QUESTION BANK ETE (17331) CM/IF. Chapter1: DC Circuits QUESTION BANK ETE (17331) CM/IF Chapter1: DC Circuits Q1. State & explain Ohms law. Also explain concept of series & parallel circuit with the help of diagram. 3M Q2. Find the value of resistor in fig.

More information

Chapter 2. The Fundamentals of Electronics: A Review

Chapter 2. The Fundamentals of Electronics: A Review Chapter 2 The Fundamentals of Electronics: A Review Topics Covered 2-1: Gain, Attenuation, and Decibels 2-2: Tuned Circuits 2-3: Filters 2-4: Fourier Theory 2-1: Gain, Attenuation, and Decibels Most circuits

More information

Lab 1: Basic RL and RC DC Circuits

Lab 1: Basic RL and RC DC Circuits Name- Surname: ID: Department: Lab 1: Basic RL and RC DC Circuits Objective In this exercise, the DC steady state response of simple RL and RC circuits is examined. The transient behavior of RC circuits

More information

Department of Electronics &Electrical Engineering

Department of Electronics &Electrical Engineering Department of Electronics &Electrical Engineering Question Bank- 3rd Semester, (Network Analysis & Synthesis) EE-201 Electronics & Communication Engineering TWO MARKS OUSTIONS: 1. Differentiate between

More information

Department of Electrical and Computer Engineering Lab 6: Transformers

Department of Electrical and Computer Engineering Lab 6: Transformers ESE Electronics Laboratory A Department of Electrical and Computer Engineering 0 Lab 6: Transformers. Objectives ) Measure the frequency response of the transformer. ) Determine the input impedance of

More information

Input Filter Design for Switching Power Supplies: Written by Michele Sclocchi Application Engineer, National Semiconductor

Input Filter Design for Switching Power Supplies: Written by Michele Sclocchi Application Engineer, National Semiconductor Input Filter Design for Switching Power Supplies: Written by Michele Sclocchi Michele.Sclocchi@nsc.com Application Engineer, National Semiconductor The design of a switching power supply has always been

More information

Lecture # 3 Circuit Configurations

Lecture # 3 Circuit Configurations CPEN 206 Linear Circuits Lecture # 3 Circuit Configurations Dr. Godfrey A. Mills Email: gmills@ug.edu.gh Phone: 0269073163 February 15, 2016 Course TA David S. Tamakloe CPEN 206 Lecture 3 2015_2016 1 Circuit

More information

LINEAR MODELING OF A SELF-OSCILLATING PWM CONTROL LOOP

LINEAR MODELING OF A SELF-OSCILLATING PWM CONTROL LOOP Carl Sawtell June 2012 LINEAR MODELING OF A SELF-OSCILLATING PWM CONTROL LOOP There are well established methods of creating linearized versions of PWM control loops to analyze stability and to create

More information

Tapped Inductor Bandpass Filter Design. High Speed Signal Path Applications 7/21/2009 v1.6

Tapped Inductor Bandpass Filter Design. High Speed Signal Path Applications 7/21/2009 v1.6 Tapped Inductor Bandpass Filter Design High Speed Signal Path Applications 7/1/009 v1.6 Tapped Inductor BP Filter 1 st order (6 db/oct) LOW frequency roll-off Shunt LT 4 th order (4 db/oct) HIGH frequency

More information

Transformer. V1 is 1.0 Vp-p at 10 Khz. William R. Robinson Jr. p1of All rights Reserved

Transformer. V1 is 1.0 Vp-p at 10 Khz. William R. Robinson Jr. p1of All rights Reserved V1 is 1.0 Vp-p at 10 Khz Step Down Direction Step Up Direction William R. Robinson Jr. p1of 24 Purpose To main purpose is to understand the limitations of the B2Spice simulator transformer model that I

More information

EC Transmission Lines And Waveguides

EC Transmission Lines And Waveguides EC6503 - Transmission Lines And Waveguides UNIT I - TRANSMISSION LINE THEORY A line of cascaded T sections & Transmission lines - General Solution, Physical Significance of the Equations 1. Define Characteristic

More information

Deconstructing the Step Load Response Reveals a Wealth of Information

Deconstructing the Step Load Response Reveals a Wealth of Information Reveals a Wealth of Information Paul Ho, Senior Engineering Specialist, AEi Systems Steven M. Sandler, Chief Engineer, AEi Systems Charles E. Hymowitz, Managing Director, AEi Systems When analyzing power

More information

Design and Simulation of Passive Filter

Design and Simulation of Passive Filter Chapter 3 Design and Simulation of Passive Filter 3.1 Introduction Passive LC filters are conventionally used to suppress the harmonic distortion in power system. In general they consist of various shunt

More information

Chapter 31 Alternating Current

Chapter 31 Alternating Current Chapter 31 Alternating Current In this chapter we will learn how resistors, inductors, and capacitors behave in circuits with sinusoidally vary voltages and currents. We will define the relationship between

More information

Frequency Selective Circuits

Frequency Selective Circuits Lab 15 Frequency Selective Circuits Names Objectives in this lab you will Measure the frequency response of a circuit Determine the Q of a resonant circuit Build a filter and apply it to an audio signal

More information

Input Filter Design for Switching Power Supplies Michele Sclocchi Application Engineer National Semiconductor

Input Filter Design for Switching Power Supplies Michele Sclocchi Application Engineer National Semiconductor Input Filter Design for Switching Power Supplies Michele Sclocchi Application Engineer National Semiconductor The design of a switching power supply has always been considered a kind of magic and art,

More information

Oscillators. An oscillator may be described as a source of alternating voltage. It is different than amplifier.

Oscillators. An oscillator may be described as a source of alternating voltage. It is different than amplifier. Oscillators An oscillator may be described as a source of alternating voltage. It is different than amplifier. An amplifier delivers an output signal whose waveform corresponds to the input signal but

More information

Source Transformation

Source Transformation HW Chapter 0: 4, 20, 26, 44, 52, 64, 74, 92. Source Transformation Source transformation in frequency domain involves transforming a voltage source in series with an impedance to a current source in parallel

More information

Transmission Lines. Ranga Rodrigo. January 13, Antennas and Propagation: Transmission Lines 1/46

Transmission Lines. Ranga Rodrigo. January 13, Antennas and Propagation: Transmission Lines 1/46 Transmission Lines Ranga Rodrigo January 13, 2009 Antennas and Propagation: Transmission Lines 1/46 1 Basic Transmission Line Properties 2 Standing Waves Antennas and Propagation: Transmission Lines Outline

More information

Continuous- Time Active Filter Design

Continuous- Time Active Filter Design Continuous- Time Active Filter Design T. Deliyannis Yichuang Sun J.K. Fidler CRC Press Boca Raton London New York Washington, D.C. Contents Chapter 1 Filter Fundamentals 1.1 Introduction 1 1.2 Filter Characterization

More information

ENGINEERING CIRCUIT ANALYSIS

ENGINEERING CIRCUIT ANALYSIS ENGINEERING CIRCUIT ANALYSIS EIGHTH EDITION William H. Hayt, Jr. (deceased) Purdue University Jack E. Kemmerly (deceased) California State University Steven M. Durbin University at Buffalo The State University

More information

I. Introduction to Simple Circuits of Resistors

I. Introduction to Simple Circuits of Resistors 2 Problem Set for Dr. Todd Huffman Michaelmas Term I. Introduction to Simple ircuits of esistors 1. For the following circuit calculate the currents through and voltage drops across all resistors. The

More information

Sample Question Paper

Sample Question Paper Scheme G Sample Question Paper Course Name : Electrical Engineering Group Course Code : EE/EP Semester : Third Subject Title : Electrical Circuit and Network 17323 Marks : 100 Time: 3 hrs Instructions:

More information

VALLIAMMAI ENGINEERING COLLEGE

VALLIAMMAI ENGINEERING COLLEGE P a g e 2 Question Bank Programme Subject Semester / Branch : BE : EE6201-CIRCUIT THEORY : II/EEE,ECE &EIE UNIT-I PART-A 1. Define Ohm s Law (B.L.T- 1) 2. List and define Kirchoff s Laws for electric circuits.

More information

ECE 2100 Experiment VI AC Circuits and Filters

ECE 2100 Experiment VI AC Circuits and Filters ECE 200 Experiment VI AC Circuits and Filters November 207 Introduction What happens when we put a sinusoidal signal through a typical linear circuit? We will get a sinusoidal output of the same frequency,

More information

An Interactive Tool for Teaching Transmission Line Concepts. by Keaton Scheible A THESIS. submitted to. Oregon State University.

An Interactive Tool for Teaching Transmission Line Concepts. by Keaton Scheible A THESIS. submitted to. Oregon State University. An Interactive Tool for Teaching Transmission Line Concepts by Keaton Scheible A THESIS submitted to Oregon State University Honors College in partial fulfillment of the requirements for the degree of

More information

Kerwin, W.J. Passive Signal Processing The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

Kerwin, W.J. Passive Signal Processing The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 Kerwin, W.J. Passive Signal Processing The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 000 4 Passive Signal Processing William J. Kerwin University of Arizona 4. Introduction

More information

Transformer Waveforms

Transformer Waveforms OBJECTIVE EXPERIMENT Transformer Waveforms Steady-State Testing and Performance of Single-Phase Transformers Waveforms The voltage regulation and efficiency of a distribution system are affected by the

More information

13. Magnetically Coupled Circuits

13. Magnetically Coupled Circuits 13. Magnetically Coupled Circuits The change in the current flowing through an inductor induces (creates) a voltage in the conductor itself (self-inductance) and in any nearby conductors (mutual inductance)

More information

Department of Electrical & Computer Engineering Technology. EET 3086C Circuit Analysis Laboratory Experiments. Masood Ejaz

Department of Electrical & Computer Engineering Technology. EET 3086C Circuit Analysis Laboratory Experiments. Masood Ejaz Department of Electrical & Computer Engineering Technology EET 3086C Circuit Analysis Laboratory Experiments Masood Ejaz Experiment # 1 DC Measurements of a Resistive Circuit and Proof of Thevenin Theorem

More information

EXPERIMENT 4: RC, RL and RD CIRCUITs

EXPERIMENT 4: RC, RL and RD CIRCUITs EXPERIMENT 4: RC, RL and RD CIRCUITs Equipment List An assortment of resistor, one each of (330, 1k,1.5k, 10k,100k,1000k) Function Generator Oscilloscope 0.F Ceramic Capacitor 100H Inductor LED and 1N4001

More information

Module 2 : Current and Voltage Transformers. Lecture 8 : Introduction to VT. Objectives. 8.1 Voltage Transformers 8.1.1Role of Tuning Reactor

Module 2 : Current and Voltage Transformers. Lecture 8 : Introduction to VT. Objectives. 8.1 Voltage Transformers 8.1.1Role of Tuning Reactor Module 2 : Current and Voltage Transformers Lecture 8 : Introduction to VT Objectives In this lecture we will learn the following: Derive the equivalent circuit of a CCVT. Application of CCVT in power

More information

Thursday, 1/23/19 Automatic Gain Control As previously shown, 1 0 is a nonlinear system that produces a limit cycle with a distorted sinusoid for

Thursday, 1/23/19 Automatic Gain Control As previously shown, 1 0 is a nonlinear system that produces a limit cycle with a distorted sinusoid for Thursday, 1/23/19 Automatic Gain Control As previously shown, 1 0 is a nonlinear system that produces a limit cycle with a distorted sinusoid for x(t), which is not a very good sinusoidal oscillator. A

More information

Electric Circuit Fall 2017 Lab10. LABORATORY 10 RLC Circuits. Guide. Figure 1: Voltage and current in an AC circuit.

Electric Circuit Fall 2017 Lab10. LABORATORY 10 RLC Circuits. Guide. Figure 1: Voltage and current in an AC circuit. LABORATORY 10 RLC Circuits Guide Introduction RLC circuit When an AC signal is input to a RLC circuit, voltage across each element varies as a function of time. The voltage will oscillate with a frequency

More information

AC Power Instructor Notes

AC Power Instructor Notes Chapter 7: AC Power Instructor Notes Chapter 7 surveys important aspects of electric power. Coverage of Chapter 7 can take place immediately following Chapter 4, or as part of a later course on energy

More information

EXPERIMENT 4: RC, RL and RD CIRCUITs

EXPERIMENT 4: RC, RL and RD CIRCUITs EXPERIMENT 4: RC, RL and RD CIRCUITs Equipment List Resistor, one each of o 330 o 1k o 1.5k o 10k o 100k o 1000k 0.F Ceramic Capacitor 4700H Inductor LED and 1N4004 Diode. Introduction We have studied

More information

CHAPTER 7. Response of First-Order RL and RC Circuits

CHAPTER 7. Response of First-Order RL and RC Circuits CHAPTER 7 Response of First-Order RL and RC Circuits RL and RC Circuits RL (resistor inductor) and RC (resistor-capacitor) circuits. Figure 7.1 The two forms of the circuits for natural response. (a) RL

More information

Experiment 1: Amplifier Characterization Spring 2019

Experiment 1: Amplifier Characterization Spring 2019 Experiment 1: Amplifier Characterization Spring 2019 Objective: The objective of this experiment is to develop methods for characterizing key properties of operational amplifiers Note: We will be using

More information

Outcomes: Core Competencies for ECE145A/218A

Outcomes: Core Competencies for ECE145A/218A Outcomes: Core Competencies for ECE145A/18A 1. Transmission Lines and Lumped Components 1. Use S parameters and the Smith Chart for design of lumped element and distributed L matching networks. Able to

More information

EE-2302 Passive Filters and Frequency Response

EE-2302 Passive Filters and Frequency Response EE2302 Passive Filters and Frequency esponse Objective he student should become acquainted with simple passive filters for performing highpass, lowpass, and bandpass operations. he experimental tasks also

More information

Lab 4: Transmission Line

Lab 4: Transmission Line 1 Introduction Lab 4: Transmission Line In this experiment we will study the properties of a wave propagating in a periodic medium. Usually this takes the form of an array of masses and springs of the

More information