Highly-linear transconductance cell realised by double mos transistor differential pairs

Highly-linear transconductance cell realised by double mos transistor differential pairs

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The Bode plots are shown in Fig. 3 and from these it is found that the phase margin is 20" approximately and the gain 30r Fig. 3 Loopfrequency response plots a Without compensator h With compensator crossover frequency is 0.68 rad/s. Suppose a minimum phase margin of 45" is required without detriment to the gain cross- over frequency. The procedure outlined above is applied as follows: (i) From Fig. 3, the frequency at which I Guw) I = - 3 dB is 0.836rad/s. This will be the new gain crossover frequency. Therefore T = 1/0.836 = 1.2s (ii) At 0.836rad/s, ~ww) is found from Fig. 3 to be - 170". The amount of phase lead required is therefore 35". (iii) a is determined using eqn. 11. a = tan (45" - 35") = tan IOc = 0.176 Thus the compensator transfer function is 1 + 1.2s G,(s) = - 1 + 0.21s The compensated loop frequency response is shown in Fig. 3 where it is seen that the phase margin is now 46" and the gain crossover frequency is 0.826 rad/s. Conclusion: A method has been proposed for phase lead com- pensator design for loops with varying gain and phase fre- quency response characteristics. It does not require an iterative process and has been seen to work effectively in a chosen example. It has also been tested successfully on a variety of other systems having similar varying gain and varying phase frequency response characteristics, in many cases yielding near-optimal design values for T and U. Even in the case of the constant phase characteristic, a working design will be obtained but it will not be optimal. The method always yields a predictable gain crossover frequency. An obvious limitation of the method is the maximum amount of phase lead angle available. Theoretically this is 45" for a = 0. In practice, it is probably about 40" corresponding to a minimum value for U of 0.09. Where the amount of phase lead required is greater than 40". Two identical lead networks can then be used in cascade and the method can readily be extended to the design of these. In cases where the phase varies rapidly with frequency, as with non-minimum phase systems, e.g., those containing time delay elements, lead compensation itself is not effective and the proposed method will obviously not apply. E. P. McCARTHY Department of Electronic and Electrical Engineering University of Salford Salford M5 4WT, United Kingdom 6th September 1990 References 1 2 3 KUO, B. r.: 'Automatic control systems' (Prentice-Hall Inc., 1987) ~ORF. R. r.: 'Modern control systems' (Addison Wesley, 1974) n'uzo. J. J., HOUPIS, c. H.: 'Linear control system analysis and design' (McGraw-Hill. 1988) HIGHLY-LINEAR TRANSCONDUCTOR CELL REALISED BY DOUBLE MOS TRANSISTOR DIFFERENTIAL PAIRS Indexing terms ' Transconductors, Circuit theory and design. MOSFET-C filters. Tunina A novel scheme for tunable transconductance cells with high linearity is described. The proposed configuration is realised by double MOS transistor ditlerential pairs with two inde- pendent linear outputs, which can be employed separately as well as in a parallel or cross-coupled connection.
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Highly-linear transconductance cell realised by double mos transistor differential pairs

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