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Oversampling Data Converters
Published in Bang-Sup Song, Micro CMOS Design, 2017
Figure 6.59 shows the simulated fast Fourier transform (FFT) spectrum of a third-order modulator with a NTF zero at DC and two on the imaginary axis. With no time constant error, the injected tone disappears as shown in the middle, but a residual tone remains in the other two cases. If the time constant is −20% shorter or 20% longer than that desired, the non-DC zero of the NTF is placed at a higher or lower frequency, respectively. In the former case, the system may have a poor phase margin and become unstable. In the latter case, the in-band quantization noise is elevated at the edge of the signal band, and the dynamic range is reduced. It peaks within a narrow range of time-constant values, and the modulator easily becomes unstable with large time-constant errors. Therefore, unless auto-tuned, CT filters should be designed for somewhat compromised performance to make sure that the system stays stable without regard to the time-constant variation. Selecting the right filter coefficients is a trade-off between the dynamic range and stability requirements, and it is difficult to meet both simultaneously unless they are very well controlled.
Linearization of the Synchronous Machine Equations
Published in T.A. Lipo, Analysis of Synchronous Machines, 2017
The gain value of 1.2 has been chosen to produce a phase margin of 45 degrees. The phase margin is the difference between the 180 degrees and the phase angle of the transfer function when its magnitude reaches unity. When the phase margin is zero at the point where unit gain is reached, the system becomes unstable. This point is also termed the crossover frequency. A value of phase margin between 30 and 45 degrees is commonly considered as good design practice, in which case an integrator gain of 1.2 is roughly the most that can be tolerated for acceptable design. This value implies that the gain introduced only amounts to 1.2 when the input frequency is 1 radian per second or 0.159 Hz so that the tracking of error even with a low frequency content will be poor.
Timing and Clocking
Published in Vojin G. Oklobdzija, Digital Design and Fabrication, 2017
John George Maneatis, Fabian Klass, Cyrus (Morteza) Afghahi
The value of this factor will set the frequency at which the loop gain is unity. This frequency is significant because it determines the phase margin, which is a measure of the stability and the amount of damping for the PLL system. The phase margin is measured as 180° or π radians plus the loop gain phase at the unity gain frequency or, equivalently, the frequency where the loop gain magnitude is unity. The unity gain level on the plot is the inverse of the gain normalization factor. No phase margin exists at unity gain frequencies below 0.1/(R · C) because the loop gain phase is about −180°. The phase margin gradually increases with increasing unity gain frequency as a result of the zero at frequency 1 /(R · C).
A low-profile, high-performance, GaN converter design for a portable SPV charger
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
Chandrasekar Venkatesan, Chilakapati Nagamani, Ganesan Saravana Ilango
The aim of the proposed compensation network is to get an effective loop bandwidth and loop stability margin. The loop bandwidth is quantified by the operating crossover frequency, where the loop gain of the T(s) is unity, while the loop stability is achieved by phase/gain margin. A 40- degree to 60-degree minimum phase margin criteria is to be ensured with the optimum design. A step-by-step procedure for achieving the design is detailed with the assumptions that achieve the optimum bandwidth and the loop stability margin. The design calculations of the compensator values are evaluated using MATLAB.
Tuning PI and fractional order PI controllers with an additional fractional order Pole
Published in Chemical Engineering Communications, 2018
Kianoush Ranjbaran, Mohammad Tabatabaei
Consider that is the desired gain crossover frequency of the open-loop gain transfer function. This could be selected according to the desired transient response speed or it could be selected around the frequency obtained from the relay-feedback test. is considered as the desired phase margin (in control engineering, the phase margin between 40° and 80° is appropriate).