If R = 2 kΩ, C= 0.1μF,then the value of inductance is Given the quality factor for the circuit is 5, compute the followings: The value of inductor, L and capacitor, C. The bandwidth, BW. Solution: Resonant frequency, f r = 1 2π = 1 2π 0.2 x 120 x 10 −6 = 32.5 ? Quality factor? State the condition for resonance to occur in a series LCR a.c. circuit and derive an expression for the resonant frequency. Leading order terms for the external quality factor and frequency shift are calculated. The quality factor relates the maximum or peak energy stored in the circuit (the reactance) to the energy dissipated (the resistance) during each cycle of oscillation meaning that it is a ratio of resonant frequency to bandwidth and the higher the circuit Q, the smaller the bandwidth, Q = ƒ r /BW. RESISTIVE, INDUCTIVE AND CAPACITIVE CIRCUITS The purpose of this reading is to understand the combination of resistive, inductive and capacitive circuits and the concepts of impedance, quality factor or 'Q', and resonant circuits. Narrower its pass band. Write the characteristics of series resonance. The quality factor is the ratio of the resonant (angular) frequency to the. O C. 1.48 kHz. 7. This is useful . 3 corresponds to a cutoff frequency of 1 / 2 π R C = 84 kHz, which matches the resonant frequency of the device at V b = 24 V. Away from the cutoff frequency, loss from the effective amplifier resistance, R E, makes a non-negligible contribution to the total quality factor, so increasing R . A "quality factor" Q, as described below, is a measure of that selectivity, and we speak of a circuit having a "high Q" if it is more narrowly selective. have the steepest magnitude response curve . Calculate, the resonant frequency, the quality factor and the bandwidth of the circuit and the circuit current at resonance. We investigate analytically the coupling of a coplanar waveguide resonator to a coplanar waveguide feedline. At resonance, the X L = X C , so Z = R. I T = V/R. = ? The quality factor can therefore be obtained as usual by multiplying 215 by 4.53 and we find Q = 972. 14.8 kHz. The Q factor of a series inductive circuit is given by the following equation: Q =. 0. = 2. The picture goes on to explain where the pole zero diagram comes from and how you can relate natural resonant frequency (\$\omega_n\$) with zeta (\$\zeta\$). 9. You have a tuned circuit with a resonant frequency of 3.7 MHz and a quality factor (Q) of 250. Question: 16. It is defined as the ratio of voltage across L or C to the applied voltage.. Q-factor = Voltage across LorC / Applied voltage The Q-factor measures the difference between a resonance that slowly ramps up during a sine sweep (a . v)The magnitude of the voltage across inductance and capacitance will be Q times the supply voltage, but they are in phase opposition. (For mathematical details about these systems and their behavior see harmonic oscillator and linear time invariant (LTI) system.). The Q factor of an RF resonant circuit is given as: \(Q=\frac{F_{0}}{F_{3dB}}\) Resonance occurs in a circuit that is connected in series when the supply frequency causes the voltage across the inductor and capacitor to be equal. While calculating the circuit Q at resonance, either reactance (X L or X C) can be used since they are equal. Hello, In the electronics world, quality factor is mostly defined as the ratio between reactive power and real (loss) power. The quality factor (Q-factor) calculator calculates the quality factor of either a bandpass filter circuit or a notch filter circuit. Consider a standard spring of force constant k, from which we hang a mass m.We let the system come to rest at an equilibrium, marked by the dashed line in the figure below. = 1 . You have a tuned circuit with a resonant frequency of 3.7 MHz and a quality factor (Q) of 250. 2. ω 0 is the resonant angular frequency in radian per second (rad/s),. C. Q will increase. In simple words, Q is the measure of the ability of a resonant circuit to select or reject a band of frequencies. The tank circuit consists of an external inductor and the MEMS drive capacitor. From this equation, we see that the largest quality factor. If the losses of the inductor are large, Q is low. . The time domain signal of the resonance is described by. Component Q is NOT the same as circuit Q! Using a conformal mapping technique we obtain an expression for the characteristic mode impedances and coupling coefficients of an asymmetric multi-conductor transmission line. A higher value for this figure of merit corresponds to a more narrow bandwidth, which is desirable in many applications. It is indeed the ratio of maximum energy stored in the circuit to the energy dissipated during each cycle of oscillation. By definition, The sharper the resonance, the quicker the resonance will resonate during a sine sweep. A quantity that is commonly used to characterize an inductor is the 'quality factor', abbreviated as 'Q'. For LCR circuits, the graph has a peak at the resonant frequency. Ratio of inductive reactance . Loaded Q. f 0 is the . X C < X L => 1/(ω C) < ω L => ω > 1/√LC So, frequency more than resonant frequency. Hence, mathematically it becomes the ratio of resonant frequency to bandwidth. Answer: a Explanation: Quality factor of a resonant network is defined as the ratio of average energy stored to the energy loss/ second . What is the correct formula for quality factor? bandwidth: Q = ω 0 B \begin {equation*} Q =\frac {\omega_0} {B} \end {equation*} Q = B ω 0 . D. All of the above. Draw a plot showing the variation of the peak current (i m) with frequency of the a.c. source used.Define the quality factor, Q of the circuit. 16. Due to the increase in current, the voltage across L and C are also increased.This magnification of voltages at series resonance is termed as Q-factor.. An example of the application of resonant circuits is the selection of AM radio stations by the radio receiver. So LCR circuits, the Q factor can be given by: \(Q={1\over{R}}\sqrt{L\over{C}}={\omega_o L\over{R}}={1\over{\omega_oRC}}\) QUESTION 23 What is the bandwidth of a series resonant circuit if its resonant frequency is 1000 Hz and quality factor (Q) is 20? Working Principle of Q meter. ω = 2πf is the angular frequency in rad/s, . (1), (1) where XL is the inductive reactance, XC is the capacitive reactance, and R is the resistance. Maximum Energy Stored Power Loss (14) With the RLC circuit calculator, you can calculate the resonant frequency and the Q-factor of any RLC circuit by providing capacitance, inductance and resistance values.. RLC circuit. 2π = 60 40.8 = 1.47 Bandwidth?? Z RLC is the RLC circuit impedance in ohms (Ω),. define a parameter called the Quality Factor Q which is related to the sharpness of the peak and it is given by maximum energy stored 22 total energy lost per cycle at resonance S D E Q E ==ππ (1.13) which represents the ratio of the energy stored to the energy dissipated in a circuit. The frequency response graph is a graph of current vs frequency, keeping all other variables a constant. Derivation of Q factor formula: The quality factor (Q) is defined as. 46. You have a tuned circuit with a resonant frequency of 3.7 MHz and a quality factor (Q) of 250. In a series circuit of an inductor/capacitor and a resistor this becomes: Q = 2*pi*f*L/R, Q = 1/ (2*pi*f*C*R) As the current in a series circuit is same for the resistor and the inductor/capacitor, this definition . One number contained as well losses in the insulator material inside a capacitor, the resistance of the metal wire and even losses caused by the dirt which the maker of the coil had left on the surface of the wire from his hands. f is the frequency in hertz (Hz),. The Q meter measures the quality factor of the circuit which shows the total energy dissipated by it. Gain in the resonant circuit C. Magnetic energy stored in the circuit D. Electric energy stored in the circuit Answer: A Clarification: Quality factor of a resonant network is defined as the ratio of average energy stored to the energy loss/ second. The Q-factor of the circuit is given by, Q=1RLC. =?? In the simple RL and RC series circuits, Q is the ratio of reactance to resistance, as in Eqs. 1,480 kHz. 15,026. O B. Quality Factor Or Q-Factor In AC Circuit objective questions (mcq) and answers. L is the inductance in henries (H),. More formally, Q is the ratio of power stored to power dissipated in the circuit reactance and resistance . 16. The amplification is maximum at resonance and equal to the quality factor (Q). The bandwidth of this circuit is approximately O A. Q-factor: The Q-factor is a widespread measure used to characterize resonators. 17. This is used to tune radios and other devices to specific radio frequency channels. The Q factor implies energy losses within a resonant device that might be anything from a mechanical pendulum, an entity in a mechanical structure, or from an electrical circuit, such as a resonant circuit.. Q factor shows the energy loss due to the quantity of energy contained in the design. A perfect inductor has no losses; therefore, there is no dissipation of energy within the inductor and Q is infinite. Current Magnification The Q factor is the energy stored per unit cycle to the energy dissipated per cycle. This is an extremely good quality factor for an inductor based resonant circuit, mainly due to the large amount of copper used in the coil. For a band pass filter, the quality factor is the ratio of the center frequency of the bandpass over the entire bandpass region from the lower to upper cutoff frequencies. =? Loss in the resonant circuit B. In order to calculate the Q, quality factor for an inductor, the formula or equation below can be used: Q = X L R. As the resistance is equal to 2 π f L, this can be substituted in the formula to give: Q = 2 π f L R. Looking at these formulas it can be seen that the overall, inductive reactance, X varies according . 9. at the resonant frequency . 25 Hz 50 Hz 75 Hz O 100 Hz QUESTION 24 Band-pass filters pass a range of frequencies between low and high cutoff frequencies. B. At the . A measure of the sharpness of the resonance peak is the quality factor. For your reference, zeta = 1/2Q. Resonance: In an electrical circuit, the condition that exists when the inductive reactance and the capacitive reactance are of equal magnitude, causing electrical energy to oscillate between the magnetic field of the inductor and the electric field of the capacitor. Ratio of displacement for oscillating and static force Another aspect of the "Q factor" can be seen if we compare the response of a system to static and oscillating forces.. Q-factor was an easy measure for the total losses in LC circuit at the operating frequency. To find the resonant frequency, substitute the values of L and C in the resonant frequency formula: f0= 12π(4H27×10-6F) f0= 15.31 Hz. View solution. 16.An RLC circuit consists of a resistance of 1000W,an inductance of 100 mH and a capacitance of 10μF.The Q factor of the circuit is. The mathematical representation is: Q = E stored /E lost per cycle. Answer: a Explanation: Current is lagging the voltage indicates inductor dominating circuit. Likewise, we know that inductive reactance may be found by the following equation: X L = 2 πf L. We also know that the resonant frequency of a series LC circuit is given by this equation: f r =. Quality factor-Q of a resonant circuit signifies: a) Loss in the resonant circuit b) Gain in the resonant circuit c) Magnetic energy stored in the circuit d) Electric energy stored in the circuit View Answer. Resonant drive uses the fact that the voltage across the capacitor of a series LC tank can be much higher than the input signal driving the tank. Then we will determine the change in Q and the BW if R is changed from 2 to 0.2 Ω. a) Q=BW*fr b) Q=BW/fr c) Q=fr/BW d) Q=fr2 View Answer Answer: c Explanation: The correct formula for quality factor is Q=fr/BW, where fr is the resonant frequency . Higher the Q factor means more energy is stored. Q factor or quality factor is a dimensionless parameter that is used to describe the underdamped resonator and characterizes the bandwidth and center frequency of the resonator. O B. Unloaded Q of a rectangular waveguide cavity resonator: a) Does not exist b) Defined as the ratio of length of the waveguide to breadth of the waveguide c) Defined as the ratio of stored energy to the power dissipated in the walls d) None of the mentioned Answer: c Explanation: Quality factor signifies the power loss in the circuit. The Q factor of the pMUT can be determined by the real part of the impedance frequency spectrum, which is defined as Q = f r /Δf, where the resonance frequency f r is the frequency at which the real part of the impedance reaches its maximum, Δf is the width of the peak at its half height, so-called 3 dB bandwidth. Abstract: The exact and corrected approximate QZE (ω) quality factors of an electrically small antenna were derived by using an equivalent circuit of the antenna. Low Q circuits are therefore damped and lossy and high Q circuits are underdamped. The total Q of this circuit is called the loaded Q or QL and is given by You have a tuned circuit with a resonant frequency of 3.7 MHz and a quality factor (Q) of 250. If the coil is represented as a series resistor, r, and reactor, X, then Wire-wound inductors with a substantial number of turns will have Q values in the range of 10 to 50. The top three pictures show you the effect of varying the Q-factor. The Q-factor of the 67.99Hz resonance was 25.4, 12.4 for the 142.1Hz resonance, and 68.5 for the 538.1Hz resonance. The bandwidth of the resonance peak is defined as the range of angular frequencies over which the average power is greater than one-half the maximum value of The sharpness of the peak is described by a dimensionless quantity known as the quality factor Q of the circuit. Answer: a Explanation: Current is lagging the voltage indicates inductor dominating circuit. 160.8k + views. Given a series circuit with R = 2 Ω, L = 2 mH, and C = 5 μF, we wish to determine the resonant frequency, the quality factor, and the bandwidth for the circuit. For a circuit with an elevated quality factor, ξ can be evaluated with Q using the perturbation method. The quality factor controls the damping of oscillations. Hint: The quality factor or 'Q' is a dimensionless quantity that describes the nature of damping in a resonating circuit. Inductor Q factor formulas. The circuit forms an Oscillator circuit which is very commonly used in Radio receivers and televisions. In a series of resonant circuit, with an increase in L. A. Resonant frequency will decrease. A higher value for this figure of merit corresponds to a more narrow bandwith, which is desirable in many applications. True False QUESTION 25 See Figure 22.1. Q-Factor. The quality of a resonant circuit is also a measure of selectivity, i.e. Question 1. Quality factor-Q of a resonant circuit signifies: A. X L. R series. Q (electricity) Often called the quality factor of a circuit, Q is defined in various ways, depending upon the particular application. It is defined as the peak energy stored in the circuit divided by the average energy dissipated in it per radian at resonance. O D. 148 kHz. Resistance, R=8.4 Ω. Series RLC Circuit - Quality Factor Quality factor, . What is the correct formula for quality factor? O C. 1.48 kHz. When a resonant circuit is connected to the outside world, its total losses (let's call them RP or GP) are combined with the source and load resistances, RS and RL. how well the tank circuit can select a specific frequency while filtering out the others. The bandwidth of this circuit is approximately O A. C. Greater its bandwidth. Quality factor or Q-factor. 4 Q factor The Quality Factor, or Q Factor, describes how under-damped a resonator is; the higher the Q factor the less damping there is. The selectivity can be measured by the quality factor Q If the angular frequency in the formula equals the angular frequency of resonance, we get the resonant quality factor There is a more general definition of the quality factor: The voltage across the inductor or capacitor can be much higher then the voltage of the total circuit. Complete step by step solution: Part 1: This concept of quality factor Q is . A RLC circuit as the name implies consist of a Resistor, Capacitor and Inductor connected in series or parallel. Figure 24.24 shows the real part of the impedance frequency spectrum of the . True False QUESTION 25 See Figure 22.1. The resonant efficiency of a circuit is expressed through the dimensionless quality factor Q. 1,480 kHz. 25 Hz 50 Hz 75 Hz O 100 Hz QUESTION 24 Band-pass filters pass a range of frequencies between low and high cutoff frequencies. The Q meter works on series resonant. Higher the Q of a series circuit. This paper reports a new methodology whereby a resonant sensor is coupled to an external electrical resonator making the system a collective coupled system to . Parallel resonant circuits • For a parallel RLC circuit, the Q factor is the inverse of the series case: • Q = R = 0 = 0 • Consider a circuit where R, L and C are all in parallel. Band width will decrease. Quality-Factor Q The most important feature of this new current-amplified resonant circuit is its ability to boost current by a factor of 2 for free in order to generate a high-frequency magnetic . The 538.1Hz resonance was the sharpest. Another important parameter related to resonant circuits is the damping factor, ξ. In electricity: Piezoelectricity …of the crystals have a quality factor Q of several hundred, and, in the case of quartz, the value can be 10 6.The result is a piezoelectric coefficient a factor Q higher than for a static electric field. - Q factor is a dimensionless parameter that indicates the energy losses within a resonant element which could be anything from a mechanical pendulum, an element in a mechanical structure, or within electronic circuit such as a resonant circuit. Typically, the Q-factor is defined as a ratio of the energy stored in an oscillating resonator to the driving energy. = . The quality factor of a resonant sensor affects its bandwidth, peak amplitude as well as sensitivity. The quality factors complying with the lower bound on the quality factor Q lb (ω) were defined by means of magnitudes of frequency derivatives of reactance of resonant and antiresonant subcircuits to provide their additivity in the . = 32.5 1.47 = 22 ? EXAMPLE 4.2: View Answer. What is Q factor? LOOP QUALITY FACTOR Q. The Q factor determines the qualitative behavior of simple damped oscillators. The energy stored in the circuit is 2 11 S 22 E =+LI CVc2 . The current in the series RLC circuit becomes maximum at resonance. X C < X L => 1/(ω C) < ω L => ω > 1/√LC So, frequency more than resonant frequency. Engineering Electrical Engineering Q&A Library A parallel RLC circuit has an admittance of 20 ms when it resonates at 10 KHz. O D. 148 kHz. 0. At resonance, inductive and capacitive reactances (magnitudes) are equal, so . A high-quality LCR resonance has a narrow graph, while a low-quality has a flatter graph - the sharpness determines the quality. The quality factor Q of an inductor is by definition= wL/R where w is the operating frequency of the inductor normally the resonance frequency of a resonance circuit. Consider a standard spring of force constant k, from which we hang a mass m.We let the system come to rest at an equilibrium, marked by the dashed line in the figure below. Quality Factor: It is the ratio of stored energy to the energy dissipated in the circuit. A. = ! Ratio of displacement for oscillating and static force Another aspect of the "Q factor" can be seen if we compare the response of a system to static and oscillating forces.. Other formula used to calculate bandwidth is:, where t he Q factor is a measure of the quality of a resonance circuit represented by the letter Q. Q factor is calculated using the formula: Think back to the radio example, when we are tuning in to a radio station what we're doing is adjusting the resonant frequency of a circuit to match the . Q is related to bandwidth; low Q circuits are wide band and Narrower its pass band. Q is the quality factor of a parallel RLC circuit (dimensionless),. When looking at the bandwidth of an RF resonant circuit this translates to the Q factor formula: Q = F 0 F 3dB. Real time control of the quality factor is highly useful for a number of sensing applications, not least dual mode ultrasound systems. R is the resistance in ohms (Ω),. View Answer. Bandwidth: B.W = f r / Q. Resonant Circuit Current: The total current through the circuit when the circuit is at resonance. More formally, Q is the ratio of reactive power to average power in the circuit reactance and resistance . For simplicity, the Q-factor of the resonant tank circuit 108 is calculated as Q=Vr/Vs, where Vr is the resonant voltage over the inductor coil L3 or the capacitor C2, and Vs is the supply voltage from the voltage supply 102. Question: 16. The quality factor relates the maximum or peak energy stored in the circuit to the energy dissipated during each cycle of oscillation. To find the Q-factor of the circuit, substitute the values of L, C, and R in the Q-factor . It also explains the properties of the coil and capacitor. The value of quality factor (Q-value) of the series resonant circuit with inductance L 2.0H, capacitance C = 32Uf and resistance R = 10 ohms, is Medium. Resonance In AC Circuit objective questions (mcq) and answers. A system with low quality factor (Q < 1 ⁄ 2) is said to be overdamped.Such a system doesn't oscillate at all, but when displaced from its equilibrium steady-state output it returns to . C is the capacitance in farads (F),. QUESTION 23 What is the bandwidth of a series resonant circuit if its resonant frequency is 1000 Hz and quality factor (Q) is 20? If . Q quality factor showing the centre and -3dB points. Within any RF or other circuit, each individual component can contribute to the Q or quality factor of the circuit network as a whole. Read More; resonant electric circuits Fano resonance has received much attention due to the interesting physics such as distinctly asymmetric shape and high quality-factor (Q-factor) 1.The interference of a discrete autoionized state . 36. A series resonant LCR circuit has a quality factor (Q-factor) 0.4. Q-factor can also be reduced to make a maximally flat pass-band (aka a butterworth filter). a) Q=BW*fr b) Q=BW/fr c) Q=fr/BW d) Q=fr2 View Answer Answer: c Explanation: The correct formula for quality factor is Q=fr/BW, where fr is the resonant frequency . Broader its resonance curve. built from the inductor L in . to resistance . Note 1: Resonance occurs because the collapsing magnetic field of the inductor generates an electric current in its windings . D. Sharper its resonance. The Q factor of a capacitor, also known as the quality factor, or simply Q, represents the efficiency of a given capacitor in terms of energy losses. Define quality factor of resonance in series LCR circuit. B. Not all 'Q's are the same! Therefore, Q = X L /R = 2πf r L/R A series resonance circuit with high quality factor provides good frequency discrimination. It is defined as: where QC is the quality factor, XC is the reactance of the capacitor, C the capacitance of the capacitor, RC is the equivalent series resistance (ESR) of the capacitor, and ω0 . Inductance, L=4 H. Capacitance, C=27 μF. Thus, the larger the Q factor, the lower the rate of energy loss, and hence the slower the oscillations. Linear time invariant ( LTI ) system. ) is it angular frequency in,! 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