# How to measure phase margin

how to measure phase margin It is basically a measure of how close the second pole of the system is to causing instability. Knowing your system gain margin and phase margin gives you the certainty that your system will be stable even under changed circumstances. Phase Margin for LoopGainEnv 2 port only PhMrgnEnv. Answer c. It minimizes the effect of the phase drop due to this pole and as a result the phase margin is higher. Another way to measure the phase is to use the results of the Fourier Transform FFT of a system s step response. The design team will make adjustments during the design phase for optimal performance. . Sinusoidal waveforms of the same frequency can have a phase difference. 8 1 Phase Margin To measure the phase margin of a linear regulator IC or switching regulator IC you can use existing measuring instruments such as oscilloscopes and network analyzers. Use the Adjust knob to move the cursors and set the phase margin as shown in Figure 12. This gives a better phase margin at the crossover frequency. frequency of 180 degree phase shift Open Loop Gain Open Loop Phase 0 dB w odB 180o w 180 b odB Phase Margin 180 b 0dB Gain Margin m 180 Determining Phase and Gain Margins lesson22et438a. It is one of the most com mon design verification measure ments made in power systems. Enter the Display menu and then enter the Cursors menu to turn on the cursors. A phase margin of 90 degrees is unconditionally stable but the op amp circuit has very poor dynamic characteristics. However the circuit for injecting a signal into the feedback loop needs its signal source to be floated using a transformer. measuring the additional gain would be needed in order to reach the point of instability. How to find it Find the frequency at which the amplitude gain plot of the Bode plot crosses 1 0dB . variable. Dear Sir I am new user for octave GNU. phase assuming there are no differ of servo components can result in at the frequency for which the entiators or integrators in the loop . Measure the period T between repeats. This way plant gain measurements can be performed. The phase margin and damping ratio are very closely related as shown in Fig. Click in the Results Display area of the Panel to display the context sensitive menu then select Measure Preference gt gt All Values. Explanation The concepts used to measure relative stability are phase margin and gain margin. Gain and phase margins are open loop characteristics. at the gain crossover frequency i. It is usually expressed as a phase in degrees. It depends on a variety of factors including expected price movements type of asset and market conditions. the phase of the system needs to be greater than 180 degrees at the gain crossover frequency 10 i there is exactly one gain crossover frequency ii the system is open loop stable May 16 2012 The cursor is set to the peak of the group delay so the software can measure the resulting bandwidth Q and phase margin of 19 kHz 2. Oct 11 2020 The greater the Phase Margin PM the greater will be the stability of the system. Open loop experimental testing has the Gain margin The loop gain should be 20dB or lower when the loop phase delay reaches 360 . This is the equivalent of changing the y axis on the magnitude plot. Find the frequency where the PHASE becomes 180 degrees. you have 120 degrees . Image credit Motion Engineering. Care must be taken when measuring over a wide frequency bandwidth since the nbsp Phase margin is a critical figure of merit which serves to indicate the stability of a closed loop control system. As phase margin approaches zero the loop phase shift approaches 180 and the op amp circuit approaches instability. com Many articles and application notes describe the extraction of phase margin using a non invasive technique that extracts the phase margin from an output impedance measurement. A comparison of the gain phase margins of some well known PID tuning methods has been reported in 26 . Phase Margin P 180 degrees Now to check your understanding let 39 s solve for the Gain and Phase Margin for both the blue and red transfer functions plotted above. This video also covers some common techniques on how to improve the phase margin of a design and build your circuit intuition. Phase margin is the phase differ . Use dB Phase Probe to measure the Phase across the AC injection source Nov 25 2015 Your operating profit margin is a great measure of how profitable your business is overall. Long term stability measurement zDirect digital test sets Measures phase like a TIC but with SDR like process gain zCan often measure phase noise as well State of the art resolution is in the 1 fs 1E 15 second range z1000x better than the best counters You can measure the phase margin if you compare each phase difference of signals between the applied reference signal and the output signal. I don 39 t know how to calculate phase margin using extrapolation for a bode plot with if or for loop. Dec 13 2015 Higher phase margin indicates lower loop gain at the frequency corresponding to 180 phase shift so the circuits with higher phase margin suppress these oscillations more quickly. meas statement. The and phase margin. For a non minimum phase to be stable it must have positive phase and gain margins. There are some advantages of Nichols plot in control system engineering. The results shown in Figure 5 indicate a phase margin of 36 degrees and a bandwidth of approximately 16kHz confirming the mathematical result. Feb 10 2014 This open loop phase at the cross over will determine your phase margin at least for resistive feedback. In this measurement we measure the open loop gain nbsp 22 Jun 2018 Gain Margin. B 4. The gain needed to raise the magnitude plot so that the gain crossover frequency occurs at 10 rad sec appears to be approximately 40 dB. Breaking the loop To measure loop gain and its phase we must break the loop. The first appli cation section B describes phase margin measurements whereas the second application section C explains how to measure bath tub May 29 2019 The phase five initial margin IM calculation period in the US is June August 2019 and not March May 2020 as in other jurisdictions. Recently a measurement device called a frequency response analyzer FRA has come into quite widespread use and can be used to measure phase margins and Sep 15 2010 Phase Margin angle by which the system phase di ers from 180 when the loop gain is 1. Measurement Showing 0dB Crossover Typically the two sine waves are phase shifted to each other. Sep 26 2006 measure the amplitude and phase shift. Figure 2 shows the FRA 5097 adapter for loop gain measurement. a True b False. We do have S Parameters available from which you can calculate K Factor Rollett 39 s nbsp In this article we demonstrate how to determine the phase margin of a voltage for the non invasive phase margin measurement based on output impedance. 6 a bit larger than our original system with 63 margin. Questions are typically answered within 1 hour. section 4. Figure 5 phase margin measurement spice the reason i failed is that I typed ugain_freq as ugain freq so when it is being refered in other . 4 0. the oscillation wave figure and tina ti schem file are attached. The Bode diagram represents the open loop frequency response of the system in two plots a magnitude vs. Ali Shirsavar from Biricha Digital Power Ltd describes how to measure the loop of a power supply defining the injection points and measurement points in order to determine the crossover frequency phase margin and gain margin. Jan 05 2012 For this reason the automated phase margin measurement built into the Bode analyzer block described below defines phase margin as 360 minus the greatest phase shift encountered while the loop gain is greater than unity. The common section A describes the basic steps until the whole setup is prepared for the application sections. The crossover point is Phase Margin and Peak Overshoot Relationship It can be shown Appendix C that Phase Margin Degrees 57. Long term stability measurement zDirect digital test sets Measures phase like a TIC but with SDR like process gain zCan often measure phase noise as well State of the art resolution is in the 1 fs 1E 15 second range z1000x better than the best counters in the growth phase start thinking more about longer term viability. The phase of the nodal voltage at node 5 is plotted with the VP output variable. Consider the following statements associated with phase and gain margins 1. It stands for the 5 distinct phases it goes through Define the problem Measure aspects of the problem Analyze the information flow Improve and Control the process . Traditionally a The phase margin is a qualitative measure about how far away the system is from being unstable. WHY if I remove Cout and change values of m of both M12 and M16 to m 8 then it gives good phase margin phase plot starts at 180 degree negative feedback and decreases monotonously. signs the phase margin at very low fre quencies is usually enough to yield a stable circuit. If there is any reactance in the feedback you 39 ll need to add its corresponding phase. Even as they primarily focus on top line performance they increase attention to retention rates margins and cash flows. Phase margin is the phase differ ence between the input and output LDO the phase margin cannot be measured because of its closed loop circuit. The gain margin is 35dB measured from 0dB to the point where the phase crosses 360 Comparing these gain and phase margins to the target values of 20dB gain margin and 60 phase margin room is available for change without approaching areas of instability. The magnitude and phase together help determine the stability of the system. Stability can be explored by investigating if the signal The magnitude and phase together help determine the stability of the system. The test circuit is very similar to the one used to measure open loop output impedance. 4 If the phase angle at gain crossover frequency is estimated to be 105 what will be the value of phase margin of the system Sep 01 2008 Typically the two sine waves will be phase shifted relative to each other. In Figure 3 the phase margin is about 50 degrees and the gain margin above the crossover frequency is about 15 dB. 28 May 2016 To determine the gain margin find the point where the phase response crosses 180 degrees and at that frequency also known as the phase nbsp quasi polynomials unstable plants and plants described by measured data ii the sensors The gain and phase margin conditions the typical measures. Polarity reversal pol rev is never phase shift on the time axis t. 5 Gain and Phase Margin for stable system in a polar plot Oct 13 2020 Whether the system is stable The gain margin And the phase margin. Dec 26 2017 Phase margin can be easily measured using a Frequency Analyzer FRA made by NF Corporation as shown in Figure 1. At the beginning having no link to frequency can disturb the user but it is a straightforward measurement as stability is concern. 2 0. Important points in performing evaluations were described above the phase margin and crossover frequency can always be inferred from an observed waveform but this is fairly troublesome. 360 360 278 . Please take a look at our phase at 11kHz. Even at small phase margin values problems can occur such as peaking in the frequency response or ringing in a step response. CMFB circuit is in nature an amplifier in close loop which means it must also be stable to ensure the design valid and this is also interpreted as good phase margin gt 50 . Even though measuring the phase margin directly is not possible a non invasive stability method shows the phase margin of the recommended circuit to be about 12 degrees in the typical case. So both are possible. If the total phase shift exceeds 360 at some Jan 04 2018 Can the E5071C measure phase margin and gain margin of DCDC converter circuit Question asked by swilli66 on Jan 4 2018 Latest reply on Feb 5 2018 by DavidVW. the practical way i used to measure delay was with a dual channel scope and i would show the sinusoid applied to the input of the system along with the sinusoid coming out. occurs. 0 10 20 30 40 50 60 70 80 Phase Margin Degrees 1. II. It explains how to break the feedback loop in an op amp circuit while maintaining the correct operating point so that the plot the open loop transfer function of the circuit can be obtained and the phase margin measured. A polar plot intersects the unit circle at a point making 45 to the negative real axis then the phase margin of the system is a 45 b 45 c 180 45 d 180 45 Answer b. Comparing these gain and phase margins to the target values of 20 dB gain margin and 60 phase margin confirms that the transient response and regulation of the power supply tested would be overdamped and unacceptable. We can have MATLAB calculate and display the gain and phase margins using the margin G nbsp Phase margin is a measure of the relative stability of our power supply. It is an important measure of robustness nbsp 24 Aug 2006 measuring system robustness secondly high gain can improve robustness if it is Equation 12 is used to calculate the phase margin. 4Hz. One nice thing about the phase margin is that you don 39 t need to re plot the Bode in order to find the new phase margin when changing the gains. If there is a phase shift phase difference or phase delay of the phase angle Greek letter Phi in degrees it has to be specified between which pure signals The open loop phase margin measurement shown in the previous video was used to directly measure the phase margin of this circuit. The phase margin is infinite because the gain is always less than one so no matter how much the phase changes the 1 j0 point will never be encircled. First order solution by hand of inverter figures of path phase margin gt 50 . Answered Yogananda Jeppu on 13 Nov 2017 Jan 21 2020 The phase margin therefore measures the safety margin for the phase. These two measures may be read from Nyquist plots or Bode plots both of which nbsp The experimentally measured Bode plot of the loop for this design is shown in Figure 8. Scale the time base by a May 29 2020 Once the meter is in place you should see a number on the digital display immediately. frequency plot. 0 10 0 0. Conclusion We have covered quite a wide variety of topics related to the theory and practical implementation of negative feedback in the context of amplifier circuits. Some power supplies need to be able to respond very quickly to step changes in load such as the Voltage Regulator Modules for PC processors. In order for a feedback loop to oscillate the phase lag has to be 360 at the frequency where the gain is unity. The gain and phase margin are two metrics to tell you how close the system is to instability. Phase Margin Phase of loop gain 180 . A phase margin of 60 degrees is also a magic number because it allows for the fastest settling time when attempting to follow a voltage step input a Butterworth design . 180o 0 PM 180 Lead Compensator Design using Frequency response The Transfer Function Km z p z p m m The Maximum Gain and phase margins measure how much gain or phase variation at the gain crossover frequency will cause a loss of stability. However you don 39 t want to provide feedback in such a way that the system will oscillate. Use Hspice to plot the closed loop transient response of an amplifier and be able to plot and measure both the large signal e. Let c be the frequency at which L j c 1 and L j c typically less than zero then PM 180 Typical stable system needs both GM gt 0 and PM gt 0 Fig. Concept of load line graphical technique to visualize transfer characteristics of inverter. The term non invasive comes from the fact that this type of measurement can be made in the system without breaking the control loop and in parallel with any and all There are two measures of stability phase margin and gain margin. 05 radians sec while the gain crossover frequency is at 1. phase shift phase margin 180 . Reply nbsp In the last lecture we found that the phase margin test is a way to determine the stability of the closed loop transfer functions based on the loop gain T and its nbsp stability determined via frequency methods Gain Margin and Phase Margin. Thanks. It is one of the most com mon design verification measure ments made in power systems. Period jitter is used to calculate the system timing margin. Apr 29 2016 Measuring Phase Lag with a Bode Plot. Find out how to measure phase margin and gain margin using a 5 or 6 Series MSO with automated power supply measurement software and their built in function generators. This allows us to verify the accuracy of our results from the indirect phase margin measurements. The phase margin determined from the gain crossover frequency is 33 degrees. The proposed approach is based on Middlebrook 39 s loop gain measurement nbsp 7 May 2020 Hi How to capture Gain Margin amp Phase margin for DC DC regulator Currently i am trying to run AC analysis but not seeing any plot in nbsp 22 Apr 2006 Also determine the gain and phase margins of this amplifier. Dr. Other systems may be very sensitive to overshoot and ringing so the power supply must have a phase We need to find out how stable the system is. Six Sigma DMAIC at Work A Case Study DMAIC duh may ick is an abbreviation for a method used in Six Sigma. Phase margin is determined at the gain crossover frequency. The gain margins are now 40dB and 7dB and the phase margin is a nice comfortable 61 o. Follow 12 views last 30 days SHAMANTH GOWDA on 7 Nov 2017. You will see that our phase is about 120o. Like the gain margin the phase margin tells us how much additional phase shift can occur before the 0 dB 180 degree condition is reached and the system becomes unstable. Find how far it is from 180 degrees e. I will also point feedback occurs at 180 phase. Figure 7. They are a measure of closeness of the polar plot to the amp pm 1 j 0 point. Stability and Phase Margin Phase margin determines stability as in other feedback loops 180 phase of open loop transfer function at crossover frequency f m degrees 180 atan c RC 1 atan c RC 2 c T dly c crossover frequency frequency where open loop gain G s 0dB For stability 1 RC 1 zero In the last lecture we found that the phase margin test is a way to determine the stability of the closed loop transfer functions based on the loop gain T and its phase at the crossover frequency. This guarded capacitor when combined with the op amp feedback resistor creates an open loop pole in the feedback network thereby degrading the phase margin of the op amp. This measurement is defined as the phase margin. 3. Table 1 shows reasonable values of phase and gain margins. Preliminary Setup A. Peet Lecture 21 Control Systems 9 31 See full list on mathworks. 10 90 risetime step response. For second order system the phase margin is directly related to the damping ratio of the closed loop system. The loop gain of a system can be derived from a mathematical model of the system. 02 dB and phase margin 21. Phase shift and phase margin can be calculated using the poles and zeros The gain margin is 35 dB measured from 0 dB to the point where the phase crosses 360 . Variation margin was implemented over 2 phases from 2016 2017. This suggests that the phase margin frequency and gain margin frequency are also not defined. If A 0 has 180 degrees of phase shift when it has a magnitude of unity the circuit has zero degrees of phase margin and will oscillate. In linear dynamical systems into two classes minimum phase systems that are easy to control and non minimum phase systems that are di cult to control. This measurement is only good for getting a compensation to output plot nbsp Phase margin and its important companion concept gain margin are measures of stability in closed loop dynamic control systems. Learn how to check power supply control loop stability using Bode plots on an oscilloscope. e. Footnotes The phase margin is the amount of open loop phase shift at unity gain needed to make the closed loop system unstable. Phase margin is the amount of phase shift when the VFB amplifier 39 s gain passes through 0dB. Phase margin is the difference between 180 and the phase angle of A OL at the frequency where its magnitude decreases to 0 dB. Phase margin is a measure of how close the loop gain is to having 180 degrees of phase shift when the loop gain is unity. This is a different way to measure how well stability conditions are met in a given system. Phase and gain margin are applicable to open and closed loop systems both. I am trying to meas the exact phase margin using a . Phase Margin. Noise Margin egat Vlw Lootup In V IL Vin such that Vin lt V IL logic 0 point a on the plot ep wo serleh Input High Voltage V IH Vin such that Vin gt V IH logic 1 point b on the plot 1ep w o selreh Voltage Noise Margins measure of how stable inputs are with respect to signal interference VNM H The above plots show how to measure the phase margin of T s for this case. 13 Mar 2018 In the process of doing so we shall introduce gain margin and phase margin. Margins in Bode Plot Gain Phase f f 180 Phase Margin Gain Margin f1 f2 Black Nichols plot is the easiest way to measure phase and gain margins. The gain margin is simply the reciprocal of the gain where the open loop frequency response function s phase is at 180 . need help regarding phase margin calculation. LMH6644 Phase Margin Measurement. Unstable. We must also be concerned with the phase margin to the left of the crossover. Measuring Gain And Phase Margins. The parameter which is constant along the constant N circle Schedule Risk Analysis SRA is a simple yet effective technique to connect the risk information of project activities to the baseline schedule in order to provide sensitivity information of individual project activities to assess the potential impact of uncertainty on the final project duration and cost. in This video clearly explains how to find out the phase cross over frequency and gain margin of a transfer function without plotting a bode plot. g. On the other hand it seems like keeping the VCO in lock is the only practical way to do this. Stability Margins Stability margins measure how close a closed loop system is to instability that is how large or small a change in the system is required to make it become unstable. More phase margin means more stability because higher phase margin indicates that the frequency at which the loop gain magnitude reaches unity is farther away from the The phase margin is a measure of how close the phase of the loop gain is to 180 degrees when the magnitude of the loop gain is one. 22. Gain and phase margins measure how much gain or phase variation at the gain crossover frequency will cause a loss of stability. A few simple rules can help in setting up a test system that can accurately measure two tone IMD for RF power transistors. important thing is to measure the bandwidth and margins rather than guess at them or ignore them. 8. As well as expressing the amount of jitter in time units such as ps and ns jitter can also be expressed as the Phase Margin Let q arg G iw gc then the phase margin is given by PM 180 o q. 1 Impedance Measurement for Front End Oscillation Common issues with Bode plots are that the injection signal is too large resulting in significant distortion of the bode plot and not measuring to a sufficiently high frequency. A Bode plot of a 3. Traditionally sampling oscilloscope is the tool of choice for viewing and measuring optical signals. the real phase margins for both loops are 92 phi_1 39 and 92 phi_2 39 instead Direct Nyquist Array DNA can be used to analyze the interaction of different loops over a system. So a two pole estimate of phase margin is not a bad approximation and accounts for the success of the two pole Butterworth design. Andrian. The US non cleared margin regulations require an earlier calculation period than other jurisdictions to determine whether a party is in scope for initial margin. Phase margin quantifies the safety margin the circuit has to such variations. Measuring Unity Gain Frequency and Phase Margin To measure the frequency at 0 dB gain 1. Figure 12 Cursor measurement on the Bode plot Infinite Phase Margin. Gain Margin GM 180 L j 180 lt lt 1 0dB . Phase margin is a measure of the relative stability of our power supply. 0 Vote. com See full list on signalintegrityjournal. Note Depending on the chosen feedback behaviour at the measurement point the phase margin is either referenced towards 180 or 0 . If then the Nyquist path is as shown . May 28 2016 Using Bode plots to measure system stability In this example the gain margin determined from the phase response crossover frequency is 32. though often times only phase margin is used rather than both. It is possible for a measurement to return a negative value. Figure 9 loop gain measurement Input and load By using the cursors we can read the Gain Margin and Phase Margin of the system. 2 Sinusoidal Jitter for more details . They are Gain and phase margin can be determined easily and also graphically. The phase margin refers to the amount of phase which can be increased or decreased without making the system unstable. From this measurement a safety margin can be calculated and determined if it is acceptable for the system under test. 5 and 5h3 carrier pow FIGURE 4. Therefore the phase margin is measured by determining the phase difference to 180 . There are two common measures of stability in a servo system. The smaller the stability margins the more fragile stability is. Although this initial reading may be accurate for the most precise measurement leave the probes on the circuit for at least 60 seconds to ensure the current is steady. The two commonly used measures of stability are the gain margin and the phase margin. Dec 20 2016 Phase Margin Another quantity related to determining stability margin is the phase margin PM . Phase margin is determined by how much the phase of exceeds. The phase margin of an op amp circuit is the amount of additional phase shift at the closed loop bandwidth required to make the circuit unstable i. We then terminate the zero by placing the pole created by R1 at least 5 times higher than the crossover frequency or 10Hz. Phase margin test for stability Under a some conditions Closed loop stability of a system is guaranteed when Phase margin is positive PM gt 0 i. Jun 09 2011 Phase Margin. as the gain margin. As shown the jitter component reduces the phase margin of digital signals causing errors. This report describes simple techniques for measuring the PLL open loop transfer function amplitude and Nov 14 2013 When designing opamps in analog IC design it is frequently required to plot the open loop gain phase. Interlated with something called phase margin. 3V POL using the J2101A injection transformer reveals a stable control loop with a bandwidth of 63kHz and a phase margin of 74 Degrees. Phases are always phase differences. Calculate gain and phase margin on simulink. In this video I will run through a step by step tutorial showing you how you can find the gain and phase margins using a simple bode plot. At a phase margin of zero an opamp circuit becomes unstable. The amount of phase difference at the 0 dB crossover frequency is the phase margin of the control loop. In PI control design algorithm to satisfy gain and phase margin based on a converging algorithm. Lower phase margin equals more overshoot. Another quantity related to determining stability margin is the phase margin PM . Under this definition the phase margin of the loop in Figure 5 will be roughly 5 degrees. GM must be positive GM gt 6dB 0dB 0 GM 180 . For a minimum phase system to be stable both the margin must be positive. Our phase margin is defined as how much the phase lag is above 180o at the cross over nbsp 12 Jun 2019 Phase margin is measured from the 0 degrees of phase and determined by inspection unlike a standard plot where the phase is subtracted from nbsp 2016 1 5 Supports measurement of power devices and high voltage circuits Automatically calculates the phase margin and the gain margin that are nbsp and simple technique to determine the phase margin of voltage references Stability Test Improves Non Invasive Phase Margin Measurement Accuracy. When companies mature the conversation around success changes again. Inductor L1 creates closed loop feedback at DC while allowing for open loop AC analysis while R1 provides a small amount of series resistance in the feedback loop to make the circuit more real and prevent mathematical errors in the analysis. magnitude nbsp non invasive comes from the fact that this type of measurement can be made in system quantitatively measure the phase margin how do they obtain the nbsp To achieve the desired phase margin controllers are usually designed using Bode Measure settling time Ts_tmp of system with designed temporary controller nbsp Phase margin. 1 Gain margin and phase margin To obtain any phase margin it is necessary to move intersection point with unit circle form point 1 0j to point situated in lower left quadrant on the same circle. Find the GAIN G in dB at this SAME FREQUENCY from the upper plot Then we define the GAIN MARGIN as Gain Margin 0 G dB Gain nbsp The proposed method can be accurate because the open loop gain around the frequency where phase and gain margins are evaluated would be not very high. A point comes where the phase shift is so great that negative feedback becomes positive feedback and the It is extremely useful for analyzing and testing filters and the stability of feedback control systems through the measurement of corner cutoff frequencies and gain and phase margins. should be running out of phase margin. Bonus Try to find some other path to introduce the common mode feedback explain the method and give the simulation results. The most common reason for this is that a large capacitance is being guarded on the measurement node. measure low frequency gain gain bandwidth product phase margin and gain margin. TS507 open loop gain Loop Gain 200 160 120 80 40 0 40 Stability margins c 180 G j Gc j Phase Margin We define phase margin as the phase angle that the frequency response would have to change to move to the 1 point. But unfortunately gain and phase margins are not suitable for multiloop processes. References. What 39 s more the unity gain frequency which gives a rough measure of the system response speed hasn 39 t changed all that much indicating that we 39 ve increased the stability of the system without losing too much performance. Similarly the If the frequency of the sinewave phase shift relative to 180 at the Dec 01 2001 The gain margin is 35 dB measured from 0 dB to the point where the phase crosses 360 degrees . I will also point Hello folks I 39 m trying to perform some stability analysis in LTspice of an op amp. Figure 4 Open loop gain phase test circuit . By adjusting Rp and Cff crossover frequency is set at one sixth the switching frequency with a phase margin of 66 degrees. As NJM2387 adjustable voltage regulator can measure a phase margin on your application. The gain margin GM is the gain at a phase lag of 180 o 20 dB in this case . To obtain desired phase margin 2 have to be modified as follows As noted in this introductory article New Technique for Non Invasive Testing of Regulator Stability phase margin can be determined from an output impedance measurement on a VNA which is then converted to group delay. national. The operational amplifier is an important circuit that plays a crucial nbsp 11 Oct 2020 A Bode plot is a graph used in control system engineering to determine the stability of a control system. Suchomoski 6 developed a tuning method for PI and PID con trollers that can shape the nominal stability transient performance and control signal to meet gain and phase margins. Looking at our Bode plot our cross over frequency was 11kHz. Together these two quantities give an estimate of the safety margin for closed loop stability. To measure the phase margin we need to inject a test signal into the control loop. These are the Gain crossover point where the Phase Margin is measured and the Phase crossover Jul 28 2011 Regarding the . A stable loop typically needs at least 20 of phase margin. PSM units are ideally suited to measuring the gain phase response of a control loop by injecting a small disturbance and analysing the results. In such a case calculating the GFT transfer functions can help you better understand the circuit and also show you possible ways for improving it. The sweep introduces a perturbation into your reference signal and observers the change in gain and phase margin. 5dB. The phase difference is then T 360 td 2 1 Fit one period of your waveform to 4 6 or 9 divisions. If you are measuring a 45V output power supply you will either need to set the probes to 10x for sub 10 Hz response or use AC coupling. Can anyone give me some assistance in measuring closed loop gain phase of a closed loop system I would like to use the Bode plotter and I don 39 t want to open the loop. PM must be positive PM gt 30o 60o. Add an AC injection source from the output voltage to the top resistor. Smaller phase margins like 45 degrees yield faster circuits but the output will overshoot with a step input. Phase Margin PM is routinely used in feedback systems and thus also in PLLs to measure stability. Thus a combination of these two elements can serve as a criterion for system performance assessment. Real time oscilloscopes are preferred for ample debug troubleshooting and to capture intermittent single shot These margins being a measure of the closeness of the plot to 1 0 indicate the effective damping ratio of the system. the oscillation in real board looks worse but when i change the Co from 1u to bigger or remove the oscillation peak level decreased and is gone. This is identical to the function performed by a vector network analyzer but the network analyzer is typically used at much higher frequencies. 0. Phase Margin Imaginary Axis Real Axis Figure 4. Building on our fictitious 10 million per year company if you were able to go from a 25 percent to a The phase reading can then be directly interpreted as quot phase margin quot at the frequency where the loop gain magnitude is equal to one 0 dB . As shown the measured phase margin was 46 degrees. For unstable systems the J2111A in a non invasive phase margin measurement the phase margin is measured at a load current of25mA. You may Aug 03 2015 Because of the inherent delays in the circuit as the frequency increases the phase of the output shifts progressively relative to the input. ee also BIBO stability Nyquist stability criterion Routh Hurwitz stability criterion Root locus method Bode plots amp phase margin Step response With 90 of phase margin Figure 9 the response at the output is that of an exponential single pole. The first appli cation section B describes phase margin measurements whereas the second application section C explains how to measure bath tub The phase margin measurement of an opamp circuit is one method of determining the stability of the circuit. Since an AC analysis produces complex results the values of real or imaginary parts of complex voltages of AC analysis and their magnitude phase decibel and group delay values are calculated using either the SPICE or Star Hspice measurement is plotted in the form of a Bode diagram. Introduction. The period jitter measurement is used to determine low frequency jitter in applications as it measures the jitter by measuring the clock period deviations over 10 000 clock cycles. Question Can we use the Bode plot to determine how far from nbsp Consider what happens when we connect a process measurement to a controller Determining system gain and phase margin is simply a matter of combining nbsp Someone can bring a full method to measure the stability of pll Thanks in advance . Values for the phase margin and gain margin insure the stable operation of the power supply over the specified conditions. Depending on details of component choices in the forward converter the T s indicates the possibility of oscillation occurring when we close the loop. Measurement methods pitfalls and tidbits of information have been gathered over the years by myriad sources here and elsewhere. Sep 15 2015 The phase margin PM equals 180 o minus the phase lag at f c approximately 60 o for this example . Bode Plot Measurements on an Oscilloscope Duration. A brief description of the gain margin and the phase margin is presented below. The implementation of initial margin has been staggered across five phases based on a firms average notional amount of uncleared derivatives over specified three month periods as set forth in the rules. Measuring the ratio of the DUT signal input and output at each test frequency the oscilloscope plots gain logarithmically and phase linearly. A phase margin of 60 degrees is generally sufficient for stability margin. 7. The gain margin represents the amount of gain required to render the system marginally stable. Let 39 s calculate the value of the missing capacitor in Figure 1. Gain margin is determined at the phase crossover frequency. Combined with the Gain Margin and Phase Margin a Bode plot maps the frequency response of It should be about 60 degrees the same as the second Bode plot. PhMrgnEnv calculates the smallest angle disregarding sign at which the Loop Gain nbsp and phase margin in digitally controlled switched mode power supplies SMPS . Let s take a look. 2. The dashed vertical lines indicate the locations of Wcg the frequency where the gain margin is measured and Wcp the frequency where the phase margin is measured. Unclear how to interpret the stability A related measure is gain margin. For minimum phase systems to have satisfactory performance the phase margin should be between 92 30 92 circ 92 and 92 70 92 circ 92 and gain margin should be greater than 92 6dB 92 . 4 Phase Margin and Gain Margin According to Nyquist the stability of a feedback system can be verified by checking two critical points. phase margin. We can measure the relative stability of a system by examining the gain margin and the phase margin obtained from the Bode plot of the frequency response. Restarting the measurement now leads to the following result. They are described in detial below. Measure td the smallest time difference between occurences of the feature on the two waveforms. In Figure 1 the phase margin is 180 114. The circuit requirements dictate the phase margin required. The reactance is one reason the post showing how to directly measure the loop gain and phase is so convienent. In the unstable case we have negative gain and phase margins. That is because the measurement test setup includes an extra inversion that was not part of Bode s original theory for loop Gain and phase margins measure how much gain or phase variation at the gain crossover frequency will cause a loss of stability. measure statements you used I 39 m a little confused by your use of quot avg quot to compute the voltage gain. The R amp S RTx K36 frequency response analysis Bode plot option allows you to quickly determine the gain and phase margin of switched mode power supplies or linear regulators. Yes you can used the CS328A FRA to measure the gain phase of an off line power supply. Summary. e. In most cases to make a loop gain measurement the feedback loop must be left closed due to high DC gain or bias conditions. C 1 2 Pi f R 1 2 Pi 150 kHz 3300 ohms 322 picofarads. They are illustrated in Fig. the frequency where the module of the open loop transfer function is unitary . In order to meet the 10 dB gain margin specification a phase margin closer to 60 is required. Here the closed loop gain H shows significant peaking although the loop gain T has a very large phase margin of 87 degrees and so cannot cause this behavior. 5 dB. 3 Injection 0Level Nov 25 2009 Measurement of phase timing and gain offset between 2 signals using multiple spectrum analyzers This application note describes how to measure the coherence phase timing and gain differences between two RFSignals using Rohde amp Schwarz spectrum analyzers a Rohde amp Schwarz signal generator and the R amp S FS Z10 Coherence Unit. If you recall adding gain only shifts the magnitude plot up. Nov 30 2005 PLL loop filter phase margin problems Reply to Thread. In the last lecture we found that the phase margin test is a way to determine the stability of the closed loop transfer functions based on the loop gain T and its phase at the crossover frequency. 69. A DC C regulator has a feedback voltage divier circuit which used to compare with a reference voltage. If you want t See full list on siglenteu. Explanation Phase and gain margin are applicable only to open Haven 39 t been able to find a simple way to measure phase and amplitude of waveforms in transient analysis. M j180 92 G i gc gcis also known as the phase margin frequency M M. P O Gutman. This is the measurement of your current or amperage. Step by step answers are written by subject experts who are available 24 7. TSC. However the two pole estimate of gain margin is terrible as explained next. There the LG nbsp 30 Dec 2010 An example is given in which the phase margin is measured to be. This stage is tuned with approximately a 100Hz bandwidth. Noise margins Logic circuits must be regenerative Able to restore clean logic values even if input is noisy. If we have any loop gain remaining here we will have a very unstable circuit. Based the. Please help me out to measure phase margin of LMH6644. Figure 3. Note that G is in dB here For example if the open loop phase does not cross 180 degrees then the phase margin is not defined. The phase margin is equal to 180 minus the phase of the open loop frequency response at the point where the gain is 0 dB. The amount of phase difference of the two signals is the phase margin at the 0dB crossover frequency. phase margin in cadence calculator Run AC analysis View waveform of gain and phase then measure phase at 0dB gain this will give you the phase margin. frequency plot and a phase vs. Since the phase margins of the little loops are different than the phase margins for the big loop I have come up with example situations where an inner loop is close 1 degree to instability but the main loop has plenty of gain and phase margin. meas ac res4 FIND ph V out V in out when mag V out V in out 1 This tells LTspice to create a variable called 39 res4 39 whose result is the phase of the open loop gain when the magnitude of the open loop gain is 0dB. Jun 16 2016 This is known as the phase margin. com Measuring Phase Margin Measure The Phase Margin Of Power Supply Control Loops Phase margin is a critical figure of merit which serves to indicate the stability of a closed loop control system. Is the gain crossover frequency Phase margin is the most widely used measure of relative stability when working in the frequency domain. because pure phase shift controllers do not exist this is not quite such a useful concept as the gain margin but it provides a measure of the amount of additional phase shift which a process can withstand before becoming unstable May 16 2012 The cursor is set to the peak of the group delay so the software can measure the resulting bandwidth Q and phase margin of 19 kHz 2. This Application Note provides tips for estimating stability through a simple test that uses the step response method. Angle of positive real axis determines the phase and distance from origin of complex plane determines the gain. I thought that once you obtained the input and output P P voltage measurements your tmp1 amp tmp2 that these quantities were then both scalars that could simply be divided to obtain the ratio but it looks like you 39 re taking the gain phase margin is a good robustness measure. The open loop frequency response is defined as B E i . Figure 6 Measurement setup with power supply resistive load Ampere meter and Bode 100 2. MEAS directives sees me wading through the help file time and time again In desperation I resorted to AC analysis as it gives you phase and magnitude but as I wanted values at only Three potential measurement techniques of the stability test system for DC DC converters impedance measurement gain phase margin measurement and oscillation detection technique were experimentally studied using data processing and signal analysis methods. So the phase margin can be selected to meet the needs of the system. It provides many benefits in measuring optical signals with low noise jitter and various measurement features optimized to characterize the optical signals. 6. Otherwise make the measurement as buzzp described in increments over the band of frequencies you will be using the amplifier over. Which of the above poor phase margin Phase noise ears if phase margin is poor Frequency response of modulation demodulation Despite the significance of the PLL loop gain on loop performance there seem to be few well known measurement techniques. Find that frequency on the phase plot and find the phase e. 1. Similarly the If the frequency of the sinewave phase shift relative to 180 at the Phase margin could also be measured but some angles are difficult to measure with an oscilloscope especially near 90 degrees. Stable The gain and phase margin is shown for the stable K 120 case but may also be de ned for the unstable case as well. The phase margin will be infinite if the magnitude of gain of L s is never greater than one. Discussion in 39 Electronic Design 39 started by steve Nov 29 PLL Phase Margin Measurement Technique. The Phase Margin M is the phase relative to 180 when jGj 1. 2958cos 1 4 4 1 2 2 Overshoot 100 exp 1 2 For example a 5 overshoot corresponds to a phase margin of approximately 64 . Aug 09 2018 We can find out the gain and phase for a given frequency. Besides the 0dB crossover point other measurement points at lower frequencies may be taken. In this case we cannot measure the actual phase margin for comparison using traditional Bode methods so a small signal transient step load measurement was used for correlation. Our phase margin is defined as how much the phase lag is above 180o at the cross over frequency. Dec 17 2017 Negative feedback increases control over a system. We can usually read the phase margin directly from the Bode plot as shown in the diagram above . Gain and phase nbsp 8 Sep 2016 We can calculate the phase margin from the raw data by first confirming that the gain magnitude at 5464Hz is 1. This is a measure of how much the gain would need to be reduced due to parameter variations before the system would become unstable. Figure 4. com 2 AN 1889 Aug 14 2019 on stability measurement as opposed to using Resistive load when measuring phase margin gain margin of a PMIC It is convenient to use electronic load to sweep current and see phase margin at various loads than soldering different resistors on the board there might be tunable high power resistor available but I don 39 t have it currently Praveen Phase Margin for NLLoopGainEnv 2 port only NLPhMrgnEnv Summary NLPhMrgnEnv calculates the smallest angle disregarding sign at which the nonlinear Loop Gain Envelope magnitude equals 1. Using the real and imaginary nbsp The proposed method can be accurate because the open loop gain around the frequency where phase and gain margins are evaluated would be not very high. For the voltage injection form of the loop gain measurement method nbsp Gain and phase margins are measures of stability for a feedback system . Everything I read on the web concerning this question says that in order to measure or set the phase margin of an amplifier the loop must be opened and the phase lag around the loop measured when the gain around the loop equals 1 unity loop gain . Dec 06 2010 Phase Margin The amount of phase you have before hitting 180 degrees phase at unity gain gain 1 0 dB . Assuming the gain plot crosses unity 0 dB only once which for voltage regulators with a low pass filter at the output stage is virtually always the case the Phase Margin De nition 3. Sensitivity nbsp . The primary stability parameters of phase margin and gain margin are easily determined from the Bode diagram. The response with 11 of phase margin shows damped oscillations. The amount of phase shift which is required to cause this situation is called the Phase Margin of the process. In current mode control designs the phase margin at very low frequencies is usually enough to yield a stable design. Capacitive load circuit with components to measure the loop The Bode 100 can easily be used to measure gain margin and phase margin of electronic control loops in a frequency range from 1 Hz to 50 MHz. Gain and phase margin speci cations may fail to guar 92 begingroup phase delay 92 tau_ 92 phi 92 frac 92 phi 92 omega group delay 92 tau_ 92 text g 92 frac d 92 phi d 92 omega gotta know what 92 omega is. 6 0. This webinar starts with the basics of the correlation between output impedance and phase margin shows various Output Impedance measurement methods as well as an example on how to improve line disturbance rejection of an ADC by optimizing the decoupling of the voltage supply. Q Calculate the sideband power in an SSBSC signal when the modulation index is 0. a Phase margin b Gain margin c Phase and Gain margin d Stable. Avoidance of signal errors requires accurate measurement of jitter caused by devices. 22 F and Cp 22nF. In this lecture we 39 re going to ask how much phase margin is enough. A closed loop step is measured and the FFT is calculated by the nPoint software. Notice that when you measure the loop with the circuit of Figure 1 the measurement will give the phase margin directly without having to measure it from 180 degrees. As circuits age their components will vary possibly pushing a marginal circuit into instability. Phase margin is determined by how much the phase of tex G jomega tex exceeds tex 180 circ tex when tex left KG jomega right 1 tex . You can measure the phase margin if you compare each phase difference of signals between the applied reference signal and the output signal. The resulting crossover frequency is about 61kHz and the phase margin nbsp 10 Oct 2019 While Gain and Phase margin data are not available. In assessing stability margins I presumably have to consider both voltage and current gain. Stability can be explored by investigating if the signal Phase Margin PM is routinely used in feedback systems and thus also in PLLs to measure stability. Answer b. meas commands it is misinterpreted as 39 ugain 39 39 freq 39 . 5 Phase Margin Phase margin is defined as the difference in degrees between the total phase shift of the feedback signal and 180 at the frequency where the loop gain is equal to 0 dB unity gain . sufficient margin. While phase margin comes from the phase where the loop gain equals one the gain margin is based upon the gain where the phase equals 180 degrees. One could open the loop by removing the summing junction at R B E and just input a sine wave at E and measure the response at B. 5. If the loop gain has a phase shift of 160 degrees the circuit has a phase margin of Jul 17 2019 Figure 4 Gain and Phase Margins. With the loop gain we can apply the Nyquist stability criterion to measure the gain and phase margin and determine the overall stability of the closed loop system. Figure 2 shows Example of Clock Period Jitter Measurement of ON Semiconductor s Programmable Clock With inputs R and A of the network analyzer connected to the input and output of the loop respectively the phase margin is determined by measuring A R. The measurement indicates a Phase Margin of 83 and a Gain Margin of 9. The gain margin is the negative gain at this frequency i. Phase margin and gain margin are a measure of how stable a system is how far it is away from oscillation. 6. A phase margin of 60 corresponds to a damping ratio of 0. Vote. Schematic. The phase margin is a measure of how close the phase of the loop gain is to 180 degrees when the magnitude of the loop gain is one. The results of the step load test are shown in Figure 4 while the output impedance Table 1 Phase Margin Table. Implementation of the Uncleared Margin Requirements began in September 2016. the phase margin and gain margin are zero. 418 and 23 respectively. Maintaining ample phase and gain margin in the control loop ensures that a power supply will not operate too close to instability. Loop response with an open loop crossover frequency of 42kHz and an unacceptable 2 of phase margin. We could get either stable or unstable behavior depending upon the sign and the magnitude of the phase margin. Besides measuring the injected and output sine waves at the 0 dB crossover point you should also measure the sine wave riding on V OUT at lower frequencies. The open loop transfer function Phase Margin PM Let 0 be the frequency at which the Open Loop Gain is 0dB unity gain . To generate a Bode plot you must sweep the signal generator s frequency across the frequency range of interest and measure the gain and the phase shift between the input signal probe B in Figure 1 and the output signal probe A . Because we desire good phase margin we insert the zero at the desired crossover frequency divided by at least 5 or 0. From the above Bode plot this phase margin is achieved for a crossover frequency of approximately 10 rad sec. The CS701 allows injecting signal into the feedback path with up to 300V Class II isolation. At the frequency where the phase of the control loop reaches 180 the gain margin can be measured. This is because the phase margin is related to the Q factor and through the group delay information a conversion can be Measurement results After the sweep has completed press Run again to stop the sweep. Note that the BLUE TF was the one shown on the previous page which we found to be unstable when we 39 closed the loop 39 . As NJM2387 adjustable voltage regulator can measure a phase margin on your application. Phase margin indicates relative stability the tendency to oscillate during its damped response to an input nbsp 19 Apr 2020 In this video I will run through a step by step tutorial showing you how you can find the gain and phase margins using a simple bode plot. Closer the response to 1 0 lesser is the effective damping ratio. Common Method for Measuring Phase Margin For LDO phase margin measurement a signal source is Phase margin rule Keep the phase margin greater than 45 degrees. A suitable location is the top of the feedback voltage divider nbsp 9 Aug 2018 This stimulus and measurement is exactly the Loop Gain needed for a phase margin assessment as shown in Figure 3. 1 Introduction The basic idea of loop analysis is to trace how a sinusoidal signal propagates in the feedback loop. Apr 17 2013 The traditional method of ensuring stability in a closed feedback circuit is to measure and plot the gain and phase for the complete path around the loop. the phase margin Pm and the associated frequencies Wcg and Wcp for the SISO open loop model SYS continuous or discrete . The Bode plot further shows a gain of 10dB at the point where a phase shift of 180 is reached the gain margin is therefore 10dB 0dB 10dB . You might try plotting the open loop gain and open loop phase from your analysis and visually inspect the two to verify the existence of a phase Also a recent method for deriving directly the phase margin of a circuit is extended to estimating the gain margin too. 6 65. Therefore a voltage follower configuration is the worst case for stability. pptx LMH6644 PM Measurement. The gain margin Gm is defined as 1 G where G is the gain at the 180 phase crossing. Propagation delay time for logic gate to perform its function. Apr 09 2019 Variation margin refers the amount of funds needed to ensure margin levels for trading. The amplitude difference between channel A and Phase and gain margins are related and 30 of phase margin typically yields about 5 dB of gain margin. Explanation As the angle is with the negative real axis hence the Phase margin will be 45 . Comparing these gain and phase margins to the target values of 20 dB gain margin and 60 degrees phase margin confirms that the transient response and regulation of the power supply tested would be overdamped and unacceptable. The bigger the phase margin the further it is away from instability. The gain margin 6. Find the GAIN G in dB at this SAME FREQUENCY from the upper plot Then we define the GAIN MARGIN as Gain Margin 0 G dB Gain Margin 1 M if you are measuring Magnitude M as a ratio not is dB . For this discussion f 1 and f 2 will denote the two signals input into the device and With the loop gain we can apply the Nyquist stability criterion to measure the gain and phase margin and determine the overall stability of the closed loop system. Conclusions on the accuracy and suitability of the analyzed methods for May 05 2015 Figure 4 shows the Bode plot measurement results using the test setup shown in Figure 3. Phase and gain margin will be expanded upon below. Example 1 Given the following Bode plots The phase crossover frequency is at 1. Gain Margin. The range of frequencies in the phase diagram with a value lt 180 In other words a negative phase margin are those frequencies where the values of the magnitude diagram are The multi sine AC sweep was introduced in PSIM v10 and can be used to determine the transfer function of simple converters like a buck or more complex ones like a 3 phase voltage source inverter. One way of doing that is to use a high feedback resistor and very high capacitance so the feedback network has an extremely low corner frequency linear dynamical systems into two classes minimum phase systems that are easy to control and non minimum phase systems that are di cult to control. When using Bode plots you generally want to measure the phase margin which is the phase at 0 dB gain. Simply trying to line up cursors seems a complete waste of time as I get massive errors and resorting to . Conditionally Stable Systems. When it crosses the 0 degree with magnitude gt 0 dB the feedback circuit is unstable according to phase assuming there are no differ of servo components can result in at the frequency for which the entiators or integrators in the loop . The PSPICE circuit for this amplifier is shown in Figure 1. Control loop analysis system To simplify system configuration Tektronix offers a Control Loop Analysis Kit combining the key pieces of equipment and software needed to measure the stability of your power supply design. I am now using Middlebrook 39 s Method to measure phase margin. Servo designers frequently choose 45 as a design guideline for phase margin. C. 4 deg displayed in the title are marked with solid vertical lines. Besides the 0dB crossover point other measurement points at lower fre www. 4 Deg. Phase starts to change on the Phase margin and gain margin are the measures of closed loop control systems stability. Figure 5. Figure 5 shows our parameterized op amp in the same circuit as Figure 1 but with some new components added specifically Vt Ct and Lt. Figure 9. Use dB Magnitude Probe to measure the Gain between the two nodes of the AC injection source. The phase margin is the additional phase required to bring the phase of the loop gain to 180 degrees. The measurement algorithm is split in a common section and two appli cation sections. Figure 8. Optical signal analysis. 9. specify relative stability are gain margin and phase margin. Growth is important but the focus moves to year over year we can calculate a phase margin of 63 180 117 . 3. It is the difference in phase between 180 degrees phase shift and the measured phase at the unity gain crossover. If the amplifier in question is an op amp just look at a datasheet to get the information. This figure presents these two margins with the Bode diagram. 1. If there is a phase shift phase difference or phase delay of the phase angle Greek letter Phi in degrees it has to be specified between which pure signals You can measure the phase margin if you compare each phase difference of signals between the applied reference signal and the output signal. Phase margin for the amplifier is how many degrees of phase shift could be added too the loop gain by the feedback block K s before oscillation would start Open loop gain is defined as Usually phase is a monotonic function so the phase margin is 180 Phase A s at frequency for which Nov 23 2015 The more commonly used metric is phase margin perhaps because it comes with a handy rule of thumb an amplifier should be designed to have a phase margin of at least 45 . in the cross over frequency region arg L j c 150 Qsyn the toolbox for robust control systems design. All the literature i have seen refers to the Open loop bode response typically G s H s in terms of calculating the phase margin. The loop gain has a dominant pole at . An amplifier with lower phase margin will ring for longer and an amplifier with more phase margin will take a longer time to rise to the voltage step 39 s final level. Digital scopes often measure f 1 T automatically. Figure 3 shows the DC DC converter phase margin measurement setup with FRA. an inconvenien quot ring phase shif quot t tendency to t becomes 180 is known at a certain upper frequency. Cpass 0. slew rate and small signal e. 60 phase margin upto about 180 is considered stable. Illustration of phase and gain margins Figure 4. Therefore when a lower order PLL is designed with a prescribed Phase Margin and there is a need to improve or modify other PLL parameters it is important to keep Phase Pargin constant. The gain margin in dB is derived by Gm_dB 20 log10 Gm The phase margin Pm is in degrees. This is valid since B E i G 1G 2H i . with phase margin 65. Learn how to evaluate the frequency domain characteristics of DC DC converters and associated passive PDN components by using the LF RF network analyzer. pptx 6 Procedure 1 Draw vertical lines through 0 dB on gain and 180 on phase plots. how to measure phase margin

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